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Despite the tremendous success of Deep Neural Networks (DNNs) for image recognition, DNNs have been shown to be vulnerable to attacks {{cite:bdf35356ea8eb43314f12948eeec87a595151ace}}, {{cite:8a805deee4b564b0fb51eeb6d141df2ebc1e45a8}}, {{cite:dba5004391437e1def82329934629542049700cf}}, {{cite:0f64380a951497a174d7824a111ec137abb9b157}}, {{cite:a27d597820da7e592e8cf85a9629e9fe6ccb456f}}, {{cite:e946408c24e03ca5e277e4d146968cb171bee1c9}}, {{cite:b92d313815d17c290de3a4e7d1e9353f588d0207}}, {{cite:fa2707612a4f8714a5b7a235d24a9265b8f68394}}, {{cite:dbdb8ec1f93a3f3579b83c5079667a93997bc4c6}}, {{cite:9dbe70e5755c051b61d5cf89734ce795c7f78e1d}}. Adversarial attacks are imperceptible image perturbations that result in incorrect prediction with high confidence. They have highlighted the lack of robustness of DNNs and have become a major security and safety concern {{cite:689fc64143d14c1b4624229080e7535c0eb41697}}, {{cite:02fedc3246e9281f8f563fa5a9e6464693b53fdb}}, {{cite:192ee1391282809a8d5b6bf520f1757c32435b30}}, {{cite:4e7a8c78a1fd1a88c167d8b3b19d6392104b28f9}}. This has motivated a large body of research on generating small imperceptible perturbations , and subsequently using the attacks to design robust defense mechanisms, e.g., by detecting attacks or retraining the model using perturbed images. The majority of existing works, however, have focused on multi-class recognition, which assumes that only one class is present in an image {{cite:2dd3c36f50f4ddfb850ae13c7bf09c7eb777ab5b}}, {{cite:c8bf24cf1724df5e6219416858ee1061c6fa261e}}, {{cite:deb2fa621b97b48914df89637ddd097cf9a7f1d2}}, {{cite:0b91e8d18ab12dd999363ae251cd71f1c945098d}}, {{cite:6148f5eedb568d3aef66d5e9bdb2b88bd51175e3}}, {{cite:cbb667d618eff65132f16bc3737f96d818560488}}, {{cite:86f4bdbd3a79d7c3b616da7239f6a57fb10fb2dc}}, {{cite:93361cfb7513464821a7db96a94c516295ca33ed}}.
{{figure:d2604206-4e5a-4762-b07b-7ccd64a6e6b8}} | i | 6732d189886cafbdc9ce4a8d932df877 |
{{formula:9f919751-9ec7-44f1-b5cd-c813f574ae19}} -Nearest Neighbors ({{formula:6c34af98-f8f8-4bb5-83da-b1ccc339f442}} -NN): the {{formula:eb7fad2f-8abf-4ba8-9ff3-90966953b383}} -NN is a non-parametric supervised learning method that outputs a class membership by assigning the most common class label among its {{formula:07d7479f-5804-4460-a045-98abc4ee717b}} nearest neighbors. Specifically, we set {{formula:93c491c8-98c4-4185-a69d-d760063be2e5}} to 3 and leverage euclidean distance to select the nearest samples.
Support Vector Machine (SVM): The goal of SVM is to find the hyperplane that separates the group of data points {{formula:32d05f90-f2e6-44a0-aab0-9b9b0799bbee}} with maximum-margin:
{{formula:f1d7b266-3fa7-48c8-b100-a6b2eb5abd21}}
where {{formula:cff5e2a8-3365-4e35-9c2d-5d71f7358934}} is the normal vector to the hyperplane.
We trained SVM with the linear kernel (linear) and used squared hinge loss.
Logistic Regression (LR): LR is a statistical model that models the probability of each class by having the combination of log odds from independent features:
{{formula:f06ad8cd-9477-46be-89d8-2744c7adbbb5}}
where {{formula:3195e42f-a41b-468b-b93c-7a32aae9c0ce}} is the sigmoid activation, {{formula:8e79ffe0-aa60-442a-9e41-318b9fb37b6d}} and {{formula:4edecb92-7d52-4175-b8d5-d556097687e5}} refers to weights and bias.
Then the probability of input {{formula:13d3626a-06a7-490f-a482-01a3f99d0483}} belonging to class {{formula:e2221d39-dc19-4cfc-9c53-e0bcd26f1da4}} can be written as follows:
{{formula:e564c536-e650-4078-a1c4-786f4794ace2}}
where {{formula:7b3b5448-fa21-4edc-a18a-fc3be137b2fb}} is bernoulli distribution, {{formula:006595fa-8eb0-49e1-9ac0-fca49eca49b8}} usually termed as logit which is combination of log odds from variables.
Single layer perceptron (SLP): SLP is a single-layer version of the neural network, which we commonly use in machine learning literature:
{{formula:f185bf63-a81e-435a-8950-da1cdac8ad7f}}
where {{formula:06aebbb6-7473-4d7a-902e-7d9263afdfa7}} refers to an activation function.
To train SLP, we used ReLU activation, cross-entropy loss, and Adam optimizer with a learning rate of 15e-5. For the training batch size, we set it to 2 for the few-shot setting and 16 for the full-training dataset.
Gaussian discriminative analysis (GDA) :
GDA is a generative classification method, unlike other probing methods mentioned above.
Generative classifiers classify the given input via the Bayes rule, while discriminative classifier directly models the class posterior:
{{formula:da58970d-9106-4dce-b9e7-3477663731fc}}
Formally, they estimate posterior from the class likelihood {{formula:eecfe773-5142-4cb3-8b2f-27c2aaba993d}} and prior distribution {{formula:7beed850-feae-4c1b-b185-e23a1379381b}} .
Then GDA computes the most probable class label as follows :
{{formula:756bb611-925c-4f52-acf6-b27982e288ab}}
Meaning GDA classifies new input with the label {{formula:fe27209b-9c8e-4754-ace9-5170c92a2d56}} which has closest Mahalanobis distance (i.e., {{formula:ca08a240-f35a-404d-92df-6719674371e4}} ).
We estimate tied (shared) covariance {{formula:847951eb-5cd0-4ea8-bc68-faedbb193609}} of GDA with the Ledoit-wolf shrinkage method {{cite:0ab4b8c8d99ec88eefccee9f0b02fe6b190aa5e6}}.
In-Context Learning (ICL): In-context learning (ICL) is a training-free paradigm that attempts to generate the desired output by guiding the model with a few examples of the target task (i.e., demonstrations) plus a set of templates tailored for the task.
Formal descriptions are in the main paper.
The template and verbalizer for each task are in Table REF .
Specifically, if only input comes as an input {{formula:6be19a3b-f371-4390-baba-eb2353954761}} the label is left blank, and when a label also comes as a pair {{formula:227c4e4e-4929-446c-83e6-e77dc009ce48}} , a verbalizer transforms label into a natural language label.
Verbalizer for some tasks (i.e., CLINC, BANKING, BoolQ, CB) is not defined as not viable through ICL since they are too long (BoolQ, CB) or has too many classes (CLINC, BANKING).
These tasks are used in the PALP-T method that applies only templates without attaching demonstrations.
Fine-tuning & Adapter:
Fine-tuning and Adapter are representative white-box tuning methodologies.
The training process is analogous to SLP, which utilizes cross-entropy loss with gradient descent.
For fine-tuning, we used AdamW {{cite:832d4914a14f7669432df3d4349f683d0b0fce47}} optimizer with epsilon 1e-5, weight decay 0.1 and set the batch size to 8.
Additionally, we used deepspeed {{cite:0ef6b14149803e5fe6f46f6cf2f00aa156927608}} to train models.
Specifically, we used ZeRO2 with CPU offload on a 240GB RAM CPU.
In this setting, fine-tuning GPT-J on CLINC150 full dataset takes about 7.1 GPU hours per epoch.
For the adapter, we utilize the baseline adapter proposed in {{cite:284722a92d2c39cb50859789033c681184fc7403}} with additional 1% of the backbone PLM.
We used AdamW {{cite:832d4914a14f7669432df3d4349f683d0b0fce47}} optimizer with epsilon 1e-5, weight decay 0.1 and set the batch size to 8.
| m | b7b327ee32d2c86cedf636b0f5d29497 |
Let me continue on the spatially compactified setup.
We have discussed that the system is non-perturbative and confining at small sizes of compact dimension
beyond the {{formula:cd6f3824-bf84-4ba1-9415-8e6f737a57a2}} critical point.
Presence of (fundamental) fermions makes it difficult to define confinement {{cite:3f8eeab9ba9cef2124e11829bfdd265eb42b6d33}}
but the behavior of fermions in otherwise confining vacuum can be studied.
To this end, it would be very interesting to see whether {{formula:c01ec433-de4f-4f94-aca3-6fe281af620b}} SB also persists
across the spatial {{formula:88a8822a-cbf9-4065-a3cd-a95ef66724d0}} transition.
(The {{formula:b4a45fcd-3c28-4ba5-a545-d0ff9e4a4ccf}} transition would no longer be non-analytic but the spatial Polyakov loop should still
show signs of a smooth crossover transition, such as a peak in the susceptibility.)
Because {{formula:cd579e7e-c425-4068-9ba2-dc20b194c3c0}} SB may not be directly related to gluodynamics (think of NJL),
the chiral condensate may have different behavior across the phase transition.
Thus, the spatially compactified system here is not just an academic curiosity
but it could shed some lights on the relation between confinement and {{formula:01afb48a-7fc7-4999-90f2-9290db8abd70}} SB, or lack of it.
| d | 78d4fdd140f5b62c2d4f7ee058176f8f |
Non-minimal CHMs are very predictive in comparison to their renormalizable counterparts built in a bottom-up approach.
In CHMs the light scalars are indeed the pseudo-Nambu-Goldstone Bosons (pNGBs) of a spontaneously-broken global symmetry of a new strongly-coupled sector. The derivative and gauge interactions are hence fixed by the coset structure. The leading-order one-loop potential is instead computed as an expansion on spurion insertions parameterizing the explicit breaking of the global symmetry {{cite:575770abec70cac70ab363a341c57b0d730340b0}}. The crucial point in this regard is that the number of independent spurion invariants is generally smaller than the number of independent interactions compatible with the remnant symmetry, which in addition may be larger than the SM gauge group. A caveat is still in order for that matter, namely small spurion multiplets are typically disfavored. In fact, they use to generate no quartic term for the Higgs boson at leading order; the proper size of such a term arising only by assuming large next-to-leading order corrections, which tend to make the usual perturbative ordering unreliable {{cite:575770abec70cac70ab363a341c57b0d730340b0}}.
| i | d95561fa0e6a4d9407fa1bd2f50ed74a |
From last decade, rare decays induced by flavor changing neutral
currents (FCNCs) {{formula:71730585-8c73-47da-a353-43a1d60e04c6}} have become the main focus
of the studies due to the CLEO measurement of the radiative decay {{formula:d96fba39-cb8f-45ca-a4ba-1eee1cd721b9}} {{cite:f41743e1a3f596b8e9d99dc2b1e0fbb261909bb0}}. In the standard model (SM) these decays
are forbidden at tree level and can only be induced by
Glashow-Iliopoulos-Maiani mechanism {{cite:fa05e676fa7611b51e6b7e4820ae528efe676dee}} via loop
diagrams. Hence, such decays will provide helpful information about
the parameters of Cabbibo-Kobayashi-Maskawa (CKM) matrix , {{cite:a225ccacb1260b61f356d620e0fd25d09e9ecc42}} elements as well as various hadronic form factors. In the
literature there have been intensive studies on the exclusive decays
{{formula:993daa29-9082-4505-8210-3fc44964ab55}} {{cite:71b9f4405b41c6dd76eb6f0b500109c34652b118}}, , {{cite:c53eec1c6fdbd3d863bbb5bc1e5f93185ceb66b4}}, {{cite:555a3a390726a8fc62ba9436d64fb3e8e12289c6}}, , {{cite:c32c7d656924b2414740e913b2bb8a7e1e2a7e99}}, {{cite:3b109f69ad62ebe1143bb7b83e1d32b68bbb1a31}} both in the SM and beyond, where the
notions {{formula:4a443148-5279-48b0-a6d2-59abe41181a0}} and {{formula:b26872e7-1ed8-44b3-8190-cc0c78d0052c}} denote the pseudoscalar, vector and axial
vector mesons respectively.
| i | 97d3eeab36f7c811134079bc230508c1 |
We performed a simple exponential analysis on QoIs {{cite:1d56cf66b07965d1d0d1377f80cdf20c4bda8907}} to see the scaling exponent dependence on input parameters.
For example, Fig. REF provides the relationship between scaling exponent and input parameters for degree of mixing for species {{formula:ffddcbc3-7702-4850-8b33-e42871c2c799}} , {{formula:2114b768-f356-4ffc-bf7d-6b53db2270f1}} , and {{formula:ec5de63e-6182-46b7-878e-92bd90200185}} .
The exponential coefficients are obtained through a naive fit by an exponential function.
Lower value for scaling exponent means the system has mixed well while higher value implies the system is segregated or mixed incompletely.
Then, {{formula:4758be22-90b3-49f5-80fb-799fdece215c}} -means clustering is performed on these scaling exponents to identify the features that demarcate high and low mixing states.
{{formula:8e1b4592-e7f4-4aed-862f-7e676c0838bb}} -means clustering aims to partition a set of observations into {{formula:1de4983e-022d-40b7-b399-f9579836b5d4}} clusters in which each observation belongs to the cluster with the nearest mean.
This helps the user to understand the natural grouping or structure in a dataset.
Elbow method {{cite:f77d2128e36dd1440afdff7a9598ac83bede6b52}} is used to identify the appropriate number of clusters (which is the {{formula:9cfc0199-3812-4f76-adc6-65e197c6c633}} in {{formula:a264cff3-28f1-439d-85fb-b13d309d6d37}} -means clustering).
This method looks at the percentage of variance explained as a function of the number of clusters.
Percentage of variance explained is the ratio of the variance between the cluster groups to the total variance.
For our case, we found {{formula:9b9c7fc0-316e-4338-a928-80a1538ed3e7}} to be optimal as it satisfies the elbow criterion {{cite:f77d2128e36dd1440afdff7a9598ac83bede6b52}}.
Meaning that, beyond {{formula:ae623e39-42b1-4511-a99f-376cf3f97a74}} the marginal gain in the percentage of variance is low.
Fig. REF provides the clustering details for this value of {{formula:5c0755d0-f7a2-4883-98ff-eef814ddbdc1}} .
Each color represents a cluster.
Among the various sub-figures in Fig. REF , scaling exponent vs. {{formula:52399970-0540-4797-a9d3-b99a3591493f}} (see Fig. REF (d,e,f)) for species {{formula:f9478430-5ee2-4150-a94d-943d82816560}} , {{formula:904d937f-fe7b-4ac6-9a91-5bdbf6b53030}} , and {{formula:a7a04ca0-1931-437d-bdf9-5cc92be192b2}} provide the most useful and interesting insight.
Other sub-figures do not provide much insight into the relationship between scaling exponent vs. remaining input parameters (which are {{formula:5298da53-8270-4458-870e-33e88c6f7c50}} , {{formula:b77f8d55-cdcd-4c4e-b906-0544d54a318f}} , {{formula:7f66d58d-452b-422a-be8a-fc03214b9c24}} , and {{formula:55bbb765-d831-44a3-985f-48b2c32c3a9f}} ).
A main inference from Fig. REF (d,e,f) is that for lower values of {{formula:b6d5c577-b984-4021-b85a-967cac14e064}} , the scaling exponent is low ({{formula:6b725a8e-54e2-4659-ba43-6cc12b0292bc}} ).
Meaning that, enhanced mixing occurs when {{formula:d38059d7-785d-48fc-b356-39aa8fba220b}} , which is in accordance with the physics of reactive-mixing {{cite:d8cc7063ec0e4068e68153715018ab0adc00e2e7}}, {{cite:4dc5a951fe6afffb79324bca3535e99aa70f8815}}.
Reaction-diffusion system tends to be more diffusive along streamlines if anisotropy is low.
As the ratio of {{formula:83bab783-11bb-4606-a367-e9ca33ad2050}} increases, we see incomplete/preferential mixing due to high anisotropy.
| r | 548f27d3490a2fc69250d3f8df4f73e3 |
In this paper, we studied and proposed various approaches that can help to avoid catastrophic forgetting in the output layer. We have seen that layers that do not rely on a bias or a norm to make a prediction can better avoid interference, such as the Coslayer or the proposed variation of WeigthNorm; On the other hand, masking avoids forgetting by preventing the modification weights of certain classes. Finally, the last cause of catastrophic forgetting is projection drift. Unfortunately, it can take many forms both in incremental and lifelong settings, and there is no general way to address it. Some approaches from other papers aim at reducing it {{cite:9650af76345bd21cecbfbdb1da6e588dd3dd5d83}} or compensating it as in {{cite:0e1cd3c99275b1fcb6c61b5a09479ea3cb12a80b}}. In this paper, we used a frozen pre-trained model to avoid any projection drift. However, even if it was convenient for evaluation purposes in this paper to ignore projection drift, it stays fundamental to be able to train a feature extractor continually and to continue research in this direction.
| d | dae83c876168f84aedf58a38414fb6fa |
Here, we consider the case where the transition probability of the Markov chain {{formula:f5482f55-e4c1-49aa-a9cd-cc005d730378}} depends on an unknown parameter {{formula:6b4ff2c3-e08d-47a6-bd01-b152c29d3e45}} . In general, the standard approach in Bayesian control problems is to reformulate the problem into a partially observable optimal control problem {{cite:868a3f49c2d4e0602945f6d2cc143450517176db}}, and then proceed to the separation of estimation and control as before. We apply the same principles to the observation control problem and derive a dynamic programming equation involving the `prior' and `posterior' distributions of {{formula:79d76148-bdae-4035-98ab-5f748b101253}} . In particular, the reward functional is now augmented to be dependent on the tuple {{formula:e7bc05ce-862e-47fb-8259-bbc897f5623f}} , where {{formula:5be2438b-d506-4435-a518-0968f26aec63}} is a measure over the parameter space. Whilst the resulting equations are often infinite dimensional in nature, this can be reduced back to the finite dimensional case if one considers conjugate distributions for {{formula:4db1fed3-58d4-4cbd-97a1-871bb95d9cf1}} . We demonstrate the solution of a model problem on a random walk involving beta conjugate priors in section:numerical example and investigate its corresponding numerical properties.
| i | a5b0928d4078d2642a5a5121ac64ae68 |
Language expressions are quite sensitive to individual words or clauses, where noises against those would likely generate incorrect or biased training data with wrong labels {{cite:cc2fea61907e414fc22c237f6f1464a440491843}}.
Following prior success in applying adversarial training to NLP models {{cite:b9752029be05906604329cf0caf50ed378589321}}, {{cite:0425a2b85d7eb59a2129b457af2ae044c1cca015}}, we apply noises to the continuous word embeddings instead of directly to discrete words or tokens. The term {{formula:7ac93deb-3d83-45f6-bab6-257a534e2976}} captures the prediction deviation from the noise. In a given round of the game, with respect to the first player's proposal, let
{{formula:086c218c-78d1-4135-8340-bbbfa234cf78}}
denote the transformer network under consideration and {{formula:29265fcc-2412-4f73-b986-6fc2069abec4}} be a large batch of data sampled from {{formula:7000f43d-1911-4126-9bf9-619594e1356b}} . We construct a label for the second player as {{formula:510bfad3-006d-4312-80fb-24292ab7b840}} . Next, for classification tasks, we choose {{formula:529f4b5a-39c9-406d-9e2d-4a650cb8e892}} to be the symmetric KL divergence {{cite:6bff16f5bff4264327c6d548f2bd2650eaa2b38d}}, i.e., {{formula:ac25d1a6-e1c3-42be-bc25-1865a1f68599}} . We use symmetric KL divergence to measure the distributional divergence to generate adversarial noise.
For regression tasks, we choose {{formula:ceb02b62-a0f6-44dd-9a13-acab15d58214}} to be the squared loss, i.e., {{formula:5a08c6be-6e5c-4c16-8aa6-efee58d36235}} . In practice, we add an {{formula:528f2d29-a61f-443d-a546-386414d624d5}} constraint on {{formula:0c083596-b31a-491d-a1a3-1574fee866dd}} , which is achieved by simple clipping with a radius of {{formula:ba0c1409-53f6-4382-bad6-848610c3c191}} (projection). Intuitively, a large {{formula:f1149634-f494-4fe3-bacd-deb461ed59ab}} corresponds to a situation wherein the transformer is highly sensitive to a given noise in the input, suggesting that the model parameters are close to a sharp minimum. Augmenting the original training objective with {{formula:eedc2040-320e-4457-ab9e-632c01061651}} makes the first player incur an additional penalty if the outer minimization solution veers closer to sharp minima, thereby encouraging flatter solutions and better generalizability.
{{figure:18dc9eb2-e9a5-4195-a88a-6eddb5ccedae}} | m | 2c409f4516c91366688649690579c3ff |
In this paper, we are going to study the distribution problem of closed geodesics on closed Finsler and Riemannian surfaces. This problem can be traced back to the work of Hadamard {{cite:7dfbb5bf2b8fc676a9dd43c949ca3e672de0eb41}} at the end of the 19th century. Combining the Poincaré recurrence theorem, he showed that the closed geodesics are densely distributed in any negatively curved closed Riemannian manifolds. This can also be proved by Anosov Closing Lemma with the fact that the geodesic flow on negatively curved closed Riemannian manifold is an “Anosov" flow, (see {{cite:98e5da806dd01cef3395f1cbbff1a16cce04eb16}} or Theorem 6.4.15 and 17.6.2 in {{cite:1a38c18ceba44a795f80311b2e4b6c6690dfb336}}). For more general denseness or equidistribution results of closed geodesics, we refer to {{cite:c10dc6c8c04a5b1753f03ad6e9c8b380f2c1fb73}}, {{cite:0989d15540048b49e82aebf0c7d1af3f9ef69373}}, {{cite:994b1b543be77af841156c4a1c639e6acc940554}}, {{cite:cc730190cd3276614ec13464ca9a3b8b5b38055f}}.
| r | 28ed2d1b2fda029ee3983fcef26bf2ed |
The formal statement of the theorem and its proof follow closely the classical work of Hájek and Le Cam {{cite:63a7be5240e450dfea7bf64c0d0679a704b6c055}}, {{cite:0fbdb8847ee2f91993ba1c59a416f5fef9f40718}} on statistical lower bounds and the more recent work of Duchi and Ruan {{cite:067d9db0b5182538e82665e12f1ec20d2a498de0}} on asymptotic optimality of the stochastic gradient method. In particular, the fundamental role of tilt-stability and the inverse function theorem highlighted in {{cite:067d9db0b5182538e82665e12f1ec20d2a498de0}} is replaced by the implicit function theorem paradigm.
| r | fff31b99de30b5a1cc5c376dc4ea8f6f |
In top-{{formula:345df008-872e-41dd-8b65-f1f1c56f1960}} variation of our method, {{formula:69c9ff4a-7077-4acb-8679-2bd9bb0bab36}} is equal to the total size of {{formula:68580e20-9c26-418f-aa16-342538357dd6}} . Note that since {{formula:d533f593-95e0-4237-8b27-dad6b14c5b3d}} itself is included in the nearest neighbor search, by limiting the size of the constrained set {{formula:79ec516f-7290-488b-9434-c929a8432466}} to one (top-1), the method will be identical to BYOL {{cite:8c2c6571b9c932db0916e4bd52307185cd2f8141}} and by setting {{formula:5a5b7a3b-216b-45b8-bf71-13d0f5ca82cc}} , it will be identical to self-supervised mean-shift {{cite:6d4a008c1be5e2dc8f18e5d941a013fd019258bc}}. Hence, our method covers a larger spectrum by defining the constrained set.
{{figure:ebabf2d4-c0c3-4da8-8cc2-56985e1d8e83}} | m | f4fdba6082146e4d1c740525ccaf2f6a |
We compare the proposed MODE-based method with two gridless alternatives, i.e., root-MUSIC {{cite:99f062f985feaf5fe2e6fc7cef338e5169f20dd2}} and root-ESPRIT {{cite:7ef650bffd091e2a1c5a11ef86ed30fed1505644}}.
To quantify the estimation accuracy, we evaluate the normalized mean squared error (NMSE), i.e.,
{{formula:81c5d2cb-c2cb-46f3-839b-3b504cbe3263}}
| r | 38606ac182d6b5a08bf5f9fb0a1d09a2 |
The uplink CSI and downlink CSI are generated by QuaDRiGa {{cite:b011bb7077a42083baf56d0131ed537a7efbf431}} according to the 3rd Generation Partnership Project (3GPP) TR 38.901 {{cite:4e67be92630025f213daf1c28aee6dbd0c6fc8d8}}. We create an open indoor scenario in which the downlink center frequency is 5.2 GHz and the uplink center frequency is 5.4 GHz. The BS is positioned at the center of a square area with the size of {{formula:173aa086-01a1-4ff6-8f29-eb42124b76b6}} . A uniform linear array (ULA) with half-wavelength antenna space is deployed at the BS. The number of the antennas at the BS is {{formula:e1e48c74-66b8-4d3a-985d-2d21f078c77f}} and the number of the antennas at the UE is {{formula:276396a9-bfce-4b2a-9c8f-31d07ddf89c4}} . Both the antennas in the BS and in the UE are omnidirectional. The heights of the BS and the UE are {{formula:b122e3f4-e54b-4ce3-8616-fca3df7bc609}} and {{formula:1c5553aa-0243-4b7a-914d-c83b373bb64c}} , respectively. The uplink and the downlink both have {{formula:40291b90-7c97-4c85-8978-ab9ebde1915d}} subcarriers. The training, validation, and testing sets contain 100,000, 30,000, and 20,000 sample pairs, respectively. A sample pair contains a downlink CSI sample and an uplink CSI sample. Following the setting in the existing SC-CSI methods {{cite:a94198474ad31eea1fb7e0769d819d03e831a053}}, {{cite:827ca38d06dd3a08b094d29b2762a2dab74e518e}}, {{cite:cef551eb071283a5b461b6f21ae79014b1b5823f}}, {{cite:a56fd3ee89f25a477e12c8bc923a73a59c64fd15}}, {{cite:40a763b50b525c9e883e967a4d21c35ff0715005}}, {{cite:6b0b07678ece5180fd6672127f65a8d71b6484c7}}, {{cite:a8df7bbe23e8844ea0e37efe6e64bda93ff9f18a}}, {{cite:5dfc54a23077c9a9aa24548949207b33c3abf824}}, {{cite:95ee8e7c1ec0a9a03a29ec4411799fcb6becf251}}, {{cite:83e488a7eedd9e0c687ff7fad965d667b90d758c}}, {{cite:ff1b964879d537c82baeffca3b0f623432ad5e10}}, {{cite:c1500d71355ce8c9e4177838b6983c2edbd907c6}}, {{cite:33b77fd20942e41de1bacd1d4e12f9ac07d888c1}}, {{formula:e0d63b53-c589-4328-9d25-ef05fb7d4a4f}} is set to 32.
{{figure:d8dc4ced-c31e-4dce-bd1d-3eaf667a4ad7}} | r | d90f221130b69a7184e36abac7306d43 |
Similar to many of the prior work in local computation algorithms, and following a connection first used by Paras and Ron{{cite:79a507bc4f2f974d090e9b1995d4364dec0bf342}} (see also Lovasz {{cite:73ed4c8c617c42b063241b557e5a026dd62c74e8}}), the core ingredient of our LCA is to simulate a local distributed algorithm for (nearly) maximal independent set. Let us first explain this connection. In a distributed algorithm, initially, nodes do not know the topology of the graph, and per round each node of the graph talks to all of its neighbors. Because of this, it can be shown that a node's behavior after {{formula:6049d110-13ac-44ec-bfb7-20097871dd2b}} rounds is a function of only the information initially available to the nodes within its distance {{formula:e0b433c2-cef6-4a48-a384-0fc3a16d77d1}} . Since the number of the latter nodes is at most {{formula:16b2f96c-5b17-429f-8ae4-94539b946218}} , this indicates that any {{formula:632bd29b-7647-4a2c-bd7d-44216829c546}} -round local distributed algorithm can be turned into an LCA with query complexity {{formula:e26e28fa-7a36-4503-b9b5-b33845fc7dce}} .
| m | f669386c9069cad758f954122f1a2538 |
In the case of PDFs, much progress has been achieved in past few decades.
However, there are still some different issues which must be studied
to make more precise predictions for hadronic collisions, specifically, at the CERN Large Hadron Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC). One of the important issues is
the accurate determination of the sea quark distributions which we intend to study in this work. This would be possible using the xFitter program {{cite:c33fb18ca590d4f66e4d20a9797e596f06bff164}} and its facilities. It is now possible to study the PDFs in a faster way in some global analyses including a wide range of experimental data
at an arbitrary perturbative approximation up to next-to-next-to-leading order (NNLO) (see for example Refs {{cite:b78b75326d2531a798bf24df8e5d2c79d951635f}}, {{cite:ee4f33a0e00f847618bcf608e4a186195aa9ad47}}).
| i | 61a6d04536ca26865643270603b1fbed |
Computational complexity is the study of the innate amount of resources required to complete some task.
We assign complexity classes to sets of tasks that require similar amounts of resources; from here, the goal is to understand the relationship between complexity classes.
There has been some success proving that two complexity classes are equal, for example {{formula:a4e82c14-d96b-40d7-a3fa-385ab4ea5652}} {{cite:916a1d48f96b1f8668a6ea5eb1b9f0c44ea76802}}, the PCP theorem {{cite:1baf1100ab9e463aa4913175b83b1ee910742877}}, and {{formula:059b03bf-a217-4d20-8b77-0a27f700280b}} {{cite:7bd1bd28232313014205540512507130b9208268}}; however, proving that two complexity classes are unequal has been much more elusive. For example, we cannot prove {{formula:59b9d879-ad7c-4894-bab0-03bdd93c1e8c}} , let alone {{formula:de8774e5-c979-401b-af2b-cfc7b8d35ab5}} .
| i | 306ce44f853650f7737a8c2dc0ea1caf |
The key similartiy between {{cite:1a64d8d150e8b25a1dd9316b6cce30ad9c63f41e}} and {{cite:6e250e8849be141542b07daf1593ef4ee98b8123}} is the set of controls making the set invariant,
{{formula:b8c8338b-2f9c-4532-b092-926853ee805b}} in Equation (REF ) and {{formula:20ce37d3-554d-4fd4-ad2c-eabaa0866c53}} in Equation (REF ).
| r | 50a3673043536e47d8539934719188d4 |
For any {{formula:9bb73721-f0c0-4bec-b648-15f6489a4115}} , denote {{formula:9026623c-b2f4-4b4c-ac96-421716da8844}} , {{formula:9c11f730-5578-4041-bca3-56fe472d0ebd}} , {{formula:e07299e0-1bbd-4b36-830e-02e957a13819}} , and {{formula:cc8ecbc6-f16f-49a9-858c-4b303f9fc910}} the open line segment connecting the two intersection points of {{formula:88889b2a-f39b-476e-a6ba-62db3761f149}} and {{formula:080b5af3-23eb-4236-8669-0b63358858fa}} . {{formula:fb9f186a-e8fd-4485-96da-692d7fa9b14e}} divides the element {{formula:5ba2f35e-101e-41cb-a87b-02f083e32eb1}} into two polygons {{formula:0e3289ad-8323-4e07-8856-07b758f8007e}} and {{formula:05079f50-b3b4-4681-8f8c-b2f521c6a8a0}} which are the polygonal approximation of {{formula:39f42006-c579-46bc-a8cf-d56f1a2fe65a}} and {{formula:2f841096-1ed3-415a-8fc9-c298d4ba2d95}} , respectively. An important property of {{formula:ce1a39fa-060b-41b6-8493-c88344c41595}} being a large element is that {{formula:7d9dba20-7963-49cc-bfb8-d4cb7a088c21}} , {{formula:78918ff3-2a4e-40eb-ae20-8309807394fd}} , is a strongly shape regular polygon in the sense that it is the union of shape regular triangles in the sense of Ciarlet {{cite:05137cfff4f5d4e18bf94cd89ccb807d949e40cf}}. We remark that there are different definitions of shape regular polygons in the literature, see, e.g., Ming and Shi {{cite:7da0353879b914d862550b9fb1e8abbc94156d5b}} and Brenner and Sung {{cite:c1cb4c9518b2a95cae6db68107a3df2fdcd2af2d}}.
| m | f99ff91a8925c4c88ab4b267b87ed6c6 |
Stochastic analysis on interacting particle systems is important to provide useful models describing equilibrium and non-equilibrium phenomena studied in statistical physics {{cite:97b29e267dee0dfe76a03a399bfa047d0a056f38}}. Determinantal process is a stochastic system of interacting particles which is integrable in the sense that all spatio-temporal correlation functions are given by determinants controlled by a single function called the spatio-temporal correlation kernel {{cite:b361894d1c4c84671c9a9783cef575b30e95c085}}, {{cite:0979cd798a8ed96431868b4e571cdaaac7cce6bd}}. Since the generating functions of correlation functions are generally given by the Laplace transforms of probability densities, the stochastic integrability of determinantal processes is proved by showing that the Laplace transform of any multi-time joint probability density is expressed by the spatio-temporal Fredholm determinant associated with the correlation kernel. The purpose of this paper is to present new kinds of determinantal processes in which the interactions between particles are described by the logarithmic derivatives of Jacobi's theta functions. A classical example of determinantal processes is Dyson's Brownian motion model with parameter {{formula:7630649d-121d-47ce-ada8-9a830c09f238}} , which is a dynamical version of the eigenvalue statistics of random matrices in the Gaussian unitary ensemble (GUE), and we call it simply the Dyson model {{cite:cb0f23ea197c32c8d697f97ab20271088226a84a}}, {{cite:97b29e267dee0dfe76a03a399bfa047d0a056f38}}, {{cite:5e7d04640525287393503b90efe80d5a1d60ef4d}}. We will extend the Dyson model to the elliptic-function-level in this paper. We use the notion of martingales in probability theory {{cite:29c636044a75307ff54efd2e600be8348cda7b11}}, {{cite:97b29e267dee0dfe76a03a399bfa047d0a056f38}} and the elliptic determinantal evaluations of the Macdonald denominators of seven families of irreducible reduced affine root systems given by Rosengren and Schlosser {{cite:869a087003eefcc00a5e095d404d1c313ab7ba97}} (see also {{cite:4446f4f7c3d62d0f8f261411f4f3828110eb86fe}}, {{cite:00a01794ab61ff8b4baa271027964a205f9aadd0}}).
| i | 4343193a3d12a6ff1c463c509f90f550 |
These properties are of crucial importance for the geometric aspects of the theta correspondence and singular theta lifts for arbitrary signature, see {{cite:d3f8637f7ddaf13435cbad25e0be2699596b904d}} and {{cite:3059b440a665bc496de91bd42b99c05e4df1b449}} (in our case of {{formula:af78a7cd-dcb3-4833-bf16-2df4a6bd1863}} it is the case {{formula:d2364fa6-15d3-4bba-a245-cde7944828c2}} ). For {{formula:95a5b4cf-8b6b-4c2b-907b-5f57df9f421f}} , it can be also found in the setting of differential forms with values in local systems in {{cite:95facf24424b67677b041757b3968e47ab7b828c}}.
| r | 8cb183a6f993d5ca014495a89e5f9199 |
Fully genuinely multipartite entanglement. A general isolated {{formula:86ae7af8-1a29-4495-9fcb-6c766a5dca47}} -dimensional quantum system is represented by a normalized vector {{formula:45625412-9cd8-44b3-9504-e2c1d0e65012}} in Hilbert space {{formula:91091298-6ad7-4c2f-b756-0ac48b3c5fa2}} . Instead, an open system is described by probabilistically mixing an ensemble of pure states {{formula:e27ce15b-12df-4663-a939-4a248d53445f}} , that is, {{formula:56627df0-49cd-4500-a78a-af3b6d3bd205}} , where {{formula:958f5d7b-c8ca-4b42-b590-7a0554fe5fc6}} is a probability distribution. An {{formula:9f34fe32-e5db-48dc-8bb8-406038b2103f}} -particle pure state {{formula:f157690c-e59e-41af-b3ba-5640ac7ba6db}} on Hilbert space {{formula:826f7ddd-5744-4574-b219-e1ed959820e8}} is biseparable {{cite:59b439d9a622d82a7a4d6db83aadac6cdd8e93f2}} if {{formula:397bd9f9-7966-41ae-bf36-8889fe5bac49}} with pure states {{formula:d8c648f4-327c-48e3-aee0-ce6987811d17}} and {{formula:9f2a34c7-15c4-4595-a601-8ca7cf892d0a}} , where {{formula:8d8ce418-feb0-45be-9021-17bde7dd2924}} and {{formula:2fae6d82-83e1-4e77-ba88-de39896aeb4b}} are bipartition of {{formula:88024d8c-f7af-40bc-9cd9-cbe3d0bfd6d4}} . Here, {{formula:11bff770-26f6-4ba1-899c-15dd96bf0e96}} can be generated from a fully separable state {{formula:47d4f171-4fa6-45bb-ac99-85a19a181505}} passing through a biseparable quantum channel {{formula:cbcc46ac-c1d4-4843-9fab-44a3e5a35fbd}} , that is, {{formula:9f06a613-a80f-4deb-b805-f3e188093c71}} , where {{formula:62599442-8040-493c-98f5-2e6d5fa453f6}} and {{formula:3602d4ba-9d8b-4f89-a0b9-e523b5345340}} . This intrigues a multipartite entanglement model. Define a biseparable complete positive trace-preserving (BCPTP) channel {{cite:125f2d6575d943f8b7c26a90fa8e261614e0a788}}, {{cite:59b439d9a622d82a7a4d6db83aadac6cdd8e93f2}} on Hilbert space {{formula:7b2fc483-505b-4fcf-84ba-3ac24af751c8}} as
{{formula:7679e2da-aaae-49b1-b761-e16b1e745a25}}
| r | 1cfa4adf6d7614eb00ad491d7e42d29f |
We presented a collection of state-of-the art metaphor detection models achieving accuracy higher than 90% for the Greek language. This extends the work of {{cite:5705626e35ca7921fa2a110058e7761baf330a0a}} and, to the best of our knowledge, sets a new state-of-the-art for metaphor detection in Greek, dealing simultaneously with the lack of linguistic resources for Greek. We aim at continuing our work by exploring the performance of contextual embeddings such as ELMO {{cite:d0998ea059434612809478b8d10bf0415729d1a3}} and BERT {{cite:f02a9934eefc925fede0bd96f5af17847ad08a88}}. Another recent promising direction, especially for small datasets is Graph Neural Networks (GNNs) {{cite:20f9f4c1dec51e20d323e280b555809d85988221}}, {{cite:4110e96ee921bd66393bcd7de3d18b7bbc2bca81}}. In this specific variation of graph neural networks, the entire training set is represented as graph {{formula:95547c3c-57df-4144-addd-46fdeb916039}} and the task of the model is node representation and classification, even with potentially few training examples. This is achieved by exploiting the graph structure and the representation of adjacent nodes in the graph.
| d | 90c548b814658875382c5c0aea37f1bd |
Fine-tuning vs. linear probing.
Fine-tuning (FT) and linear probing (LP) are popular transfer learning algorithms.
There is substantial evidence of FT outperforming LP in-distribution (ID) including recent large-scale investigations {{cite:78367ca96ab076cc994bfcc0e8cb04c769ffe675}}, {{cite:d20d52313de27d37f2aa8bfe9225fa44e9789942}}, {{cite:bb64b58bc4f9fbc36fbfc82a1da72d1b18259ad8}}, {{cite:46ba041ac8c5ffb717704bf07b1494d4810e4fe9}} (the only notable exception is in {{cite:a96f6bf8288594d19a5720f2bf25bc7cf5e3a2fc}} where LP performs better than FT when using ELMo representations, but worse using BERT).
This is not intended to be a comprehensive list. There is a large body of past work across different domains that have reported a similar observation.
FT is therefore the method of choice for improving accuracy, while LP is used to analyze properties of representations {{cite:9b0d1bae26cb3adddc8a8089d8c15f4ab1ffb53e}}, {{cite:30c999a3cf11407e9f6000c384befb8c756a272f}}, {{cite:332211e9f708c3a71561cb357baddda918c28532}}.
In our work, we find that FT can underperform LP especially when using high quality pretrained features in the presence of a large distribution shift.
There are a variety of other fine-tuning heuristics {{cite:da0b62296de611a7a120d534f7fd54f1dda816bc}}, {{cite:d5d9abdac5d58b5cbbce8ad1715cf552152ef797}}, {{cite:f17d7b5bee9bc6ef6f163215debc87cd7d5bae91}}, {{cite:acb246c45773db5f645bf640bab1467b1f83a7b6}}, {{cite:410041f7f9186416404329be48ccf9665f396478}}, {{cite:1cf8b80200746823a8cddba7edf6d2551dd68f6d}}—combining our insights with these ideas might lead to better methods.
| d | d2b7ac720a1a79163fdfdb8ed8b0cbaf |
A simple but powerful method to ensure the existence of (ultra)distributional boundary values of holomorphic functions consists in combining Stokes' theorem (more precisely, the formula {{cite:08113d35b4f3b546847a1630df022ba703422e0f}}) with almost analytic extensions. This technique was used for the first time by Hörmander {{cite:08113d35b4f3b546847a1630df022ba703422e0f}} for distributions and was later extended to the ultradistributional setting by Petzsche and Vogt {{cite:6155cffd71fd30f5244b7114cc84fa8c2b06afae}} (see also {{cite:909aae13aebf231c4aae96997dc73616fa3c7a56}}). We mention that the characterization of Denjoy-Carleman classes by almost analytic extensions goes back to Dyn'kin {{cite:067e89626306f9985f6f325a7db69171750f7780}}, {{cite:84de25b9a33b5253433c1a7366a870b3137b3b62}}. We refer to the recent article {{cite:99a3d92819ea046eedfa62ec497f19caecd668fa}} for the newest generalizations of such results and an overview on the topic of almost analytic extensions. We develop here a similar method to establish the existence of ultradistributional boundary values of harmonic functions. Our method combines Green's theorem with a novel description of ultradifferentiable functions by so-called almost harmonic functions. Therefore, the first part of this article is devoted to an almost harmonic function characterization of ultradifferentiable classes.
| i | 9535a16e452304927753cf2103299825 |
Ours (RAFT) achieves significantly higher PSNR and SSIM than Baseline. Although the disparity maps between input SAIs are also provided to Baseline, its performance is still limited by the fixed and content-independent weights employed in the commonly-used warping operation, which demonstrates the advantage of learned dynamic weights in our method;
Ours (PWCNet) is worse than Ours (RAFT) but still much better than all the compared methods. Although the estimated disparity maps with different levels of quality are involved, our method may adaptively aggregate content features to provide gains for learning dynamic weights, which can demonstrate the advantages of learning dynamic weights over commonly-used ones. Besides, it is highly expected that our framework will be further improved with more powerful and advanced optical flow estimation proposed in future;
our method achieves higher performance than Wu et al. {{cite:c404c25284cf89f29974bbb75d0bb5beae34d60b}}. The reason maybe that Wu et al. {{cite:c404c25284cf89f29974bbb75d0bb5beae34d60b}} reconstructed LFs in the perspective of reconstructing 2-D EPIs, and neglected modeling the correlations between two spatial dimensions, which limits the performance. On the contrary, our method employs a geometry-based refinement module to refine the correlations among pixels of novel SAIs, and further improves the reconstruction quality; and
both Kalantari et al. {{cite:78d2a656ee53a88192b430cea40d0d92bea200ce}} and Jin et al. {{cite:fc3c5d411f1442c3859eba86854772c1b2cdedbb}} achieve worse performances than our method. In addition to that they cannot estimate disparities well from extremely sparse LFs with a limited receptive field of CNNs, they also cannot handle severe artifacts brought by the warping operation. By contrast, our method can effectively mitigate the warping errors in reconstructing extremely sparse LFs by dynamically learning content-adaptive weights for each pixel of the novel SAI. Besides, the geometry-based refinement module can further refine novel SAIs to improve the quality.
{{figure:9b889fdc-6216-49c1-9d2b-cac22e402507}} | m | b3053e354c778fe889caf8cc6604e29b |
It is to be noted that, to the best of our knowledge only S. Manna et al. {{cite:73a56c97236207f8e3741ca251c011b6b1038885}} and SSLM {{cite:3672af4453a5f6dfc346935a101670a63fdfc543}} has used MRNet for their experiments. Thus, it has not been possible to compare with other self-supervised methods. Although the work {{cite:1f409b594e8886b00a51fb92873bc40276e3f0f8}} also presents a 3D adapted version of the self-supervised algorithm SimCLR {{cite:cf05baca2cd56ce38c0cc73460ef8796aa10d5dc}}, it is not possible to implement gradient accumulation on that algorithm as it requires negative pairs to be accommodated in a batch along with a positive pair. Furthermore, SimCLR requires a large batch size to give satisfactory performance. Hence, it will not be possible to compare with the work {{cite:1f409b594e8886b00a51fb92873bc40276e3f0f8}} here under identical circumstances.
| m | 963fe72d2d0c338b97cf8572b15bba40 |
In this paper, we first defined a completely new end to end non-intrusive time-domain reduced order nonlinear model construction method. This latter, being a mixed interpolatory - operator inference approach, stands as the principal methodological contribution of the paper. The global rationale consists in a constructive approach. First by approximating the data with a linear dynamical model, and in a second step, to adjust this latter through the addition of nonlinear terms. As it gathers the ingredients and benefits from model approximation {{cite:35fe834c7fcf636e50fc95a2d6d3152de991fdac}} and operator inference {{cite:5af584b9c76b487e598d228fdda512572fc4e77f}} methods, it is shown to be applicable in a very large-scale and complex context with a reasonably low computational cost (all computations are done on a standard laptop). All steps make the process easily scalable and fairly applicable to any complex simulator in a non-intrusive manner. It makes possible the construction of surrogate linear or nonlinear reduced order model from a set of input-output time-domain simulation with low human and numerical effort.
| d | f49f2934012f22a6e66c002ea82f6c88 |
We start proving the generalized Spitzer-Baxter identities stated in Thm. REF . The proof follows the line of that for the classical Spitzer-Baxter identity as in {{cite:9e4c2cc08f4d418eb1ec8f5e4b09d2e627a2ee9d}}, Paragraph 8.4.
| r | 4fa53b15d1f947c4331ef87ccc24cee3 |
To verify the significance of differences between pairs of algorithms (RFE{{formula:30c0a447-34ea-4019-b1cb-8f628a09da9f}} vs. 3-SRFE, RFE{{formula:bf26298a-ee64-4a66-84ce-4ac2e52d718d}} vs. 5-SRFE, etc.) we performed the non-parametric Wilcoxon signed ranks test {{cite:7568341a82d03f9d3b9d4110ef498989a602d26c}} for each pair. Table REF reports the results of these statistical tests.
{{table:ee225c47-eb13-4267-a83f-ea9f19789383}} | r | 8b2e79bb40e7b4f692c9c83e73aa282f |
From the burst lightcurves of LE and ME, the burst rises tend to have a convex shape, suggesting ignition near the equator {{cite:ead50cad8411873d18ccb4d35f7849a45808d315}}.
This scenario is somewhat incompatible with the hot spot near the poles.
The inconsistency above may indicate another channel of accretion onto a magnetized NS, e.g., via Schwarzschild-Kruskal instability (the magnetic version of the Rayleigh-Taylor instability) {{cite:5ab5f6e6e87a199a2621c8dd8f259e0b355bf980}}, {{cite:300f0080ce63d89654a174d21d56234cd65354e1}} in the disk equatorial plane.
This model proposes that several “tongues” of plasma penetrate the magnetosphere and impact the NS surface at random positions.
This model has also been used to explain why bright LMXBs do not pulsate {{cite:cfe00cc3e3f09e49705ae4d434aa9d8ce33c59c0}}.
| d | 92d665e95b529fabd46d6f9ff2daa39a |
Table REF shows the results. It is seen that our method shows significant improvement over the previous methods {{cite:a6d47df7a42c2215da8dd15c7a5664cc85f9f4ba}}, {{cite:90dadc4236c8be2ea76d496c9289f88d07539f23}}, {{cite:e1833b4014ec71aedc9aa0d631f6f88b3602d51e}}, {{cite:663d128e17a879a42e6fd2e36ce32beabaf2cdfc}} on all metrics. Our method also achieves better PLW (path length weighted) scores in all the metrics (indicated in the parentheses), showing its efficiency. Notably, our method attains 8.37% success rate on the unseen test split, improving approximately 20 times compared with the published result in {{cite:a6d47df7a42c2215da8dd15c7a5664cc85f9f4ba}}. The higher success rate in the unseen scenes indicates its ability to generalize in novel environments. Detailed results for each of the seven task types are shown in the appendix.
| r | 626eb75c0a8e1a6f1890676990889684 |
Singular value decomposition (SVD) and spectral methods have been widely used in statistics, probability, machine learning, and applied mathematics as well as many applications. Examples include low-rank matrix denoising {{cite:e6bee291df084c93fa18c1f8b36e3762c318a374}}, {{cite:4ebae9f3c89f008a56b803e54c4f262bc98bcef5}}, {{cite:91c6cf678a7f90e0c0649c127f34c4ef0358554a}}, matrix completion {{cite:99c8a24d3292af38fd2020ed1a1edee222e5d720}}, {{cite:0385c207145ce0b93810506e785572a04a343654}}, {{cite:fada36ec08b3c215931d0cf0e43cfbb9ee5553c5}}, {{cite:36766ee34ec09607a6e81a4bc9eb408aed09dfd0}}, {{cite:0391f54ca7a327278d20761834ab85800abf448b}}, principle component analysis {{cite:40b00d53ac7bb7c42a408b0208a54dca65f49ad7}}, {{cite:584d020633bcfe2ace347926f9504dad662adb99}}, {{cite:c5882381b6bc40ce1846475df086b19979707f3b}}, {{cite:df2176c4ec9bc00882655e0fca91923d676ed667}}, canonical correlation analysis {{cite:fca6c20d8223b9beb47418f58c741ab20c743079}}, {{cite:9c175bd637dd47a015bb261dce26241847c266a4}}, {{cite:f16b6996b863283314b4019508994c88b9d80223}}, {{cite:2d8c00bacd65902d6967e271a5caea040f95c862}}, community detection {{cite:922131f2ba44ed761a0c20637010cf3c12837d95}}, {{cite:9c0441d4697793b459e483aaa47f51902ab97651}}, {{cite:0d87b0eb15c7930eb1e8667aeed8fd7f3ecbdc05}}, {{cite:6df6196d772b01ff0b39b7aeaca5e705425f97d1}}. Specific applications include collaborative filtering (the Netflix problem) {{cite:2c40fa0873612689952093a8188422be3640b6fb}}, multi-task learning {{cite:badd9eb383db5ff548f256958707ee6fdc68a52c}}, system identification {{cite:4bf574e4270a2285655a0dd767dc2e69300fbc3b}}, and sensor localization {{cite:12705322886454ec3b6fe5c202cdce5ca9506ac8}}, {{cite:6c4dfba68e6c517a62cc88194484d81d772880e0}}, among many others.
In addition, the SVD is often used to find a “warm start" for more delicate iterative algorithms, see, e.g., {{cite:838f7921f73f1017c0cf68597f7be59873f387b8}}, {{cite:41b0cfa96bfe9b9789ee3813897e75ea3cdb1760}}.
| i | d6a16dbd5c9fc5061a63aebea7997722 |
Invariant Risk Minimization (IRM): The goal of IRM is to extract representations that are invariant across environments: {{formula:511c5250-fefb-4e2f-a571-7861261c965b}} , each encoding different spurious correlations {{cite:1cad39484b237379ea3b8fe0f498ea46a961e59e}}, {{cite:ce305c20c9828ee35893cca193d3149ff8d4e13b}}, {{cite:46476a505ef7574897ea0aa2b483829280bc29ef}}. Such representations enable the same classifier to be simultaneously optimal over all {{formula:4be7a979-f786-4bbc-969a-7776955da183}} . For this, {{cite:1cad39484b237379ea3b8fe0f498ea46a961e59e}} propose to regularize the gradient norm of a fixed linear classifier. More recent variants include regularization of variance of risks {{cite:de423d1965b4b70e42255decf98875b3b2934b81}}, {{cite:c12688160b7d4d3cbd7a52ca48bd6ec96d43b02f}}. However, {{cite:02f7b98fd50dd0db6cbf0cc544f022f7ecd817f9}} have shown that such objectives can fail to recover the invariant features in practice. Despite this negative result, we still compare against IRM since it is a promising research direction.
| m | 2ea02ecd51b621b68a9f11ff6eed242c |
Vessel enhancement approaches consist of filters that improve the contrast between vessels and background. We chose four well-known handcrafted filters for blood vessel segmentation, based on implementation availability and previous applications to the enhancement of tubular-like structures in retinal images: Frangi {{cite:1b9ec33c36529124855cdbcf475c75e3bb4bd1ff}}, Gabor {{cite:1f63c46b0fcfb590ea08211c19ffb7276c555457}},
SCIRD-TS {{cite:b9cd9f46dd86c4d57db80d5fb2dc7be8f7fad94d}}, and OOF {{cite:5ac9b8feed44b8311652650fad98ffce97161345}}. All these filters require parameter tuning. In our case, from a range of possible configurations we selected the optimal set of parameters that gave the best performance when compared to the manual segmentation (see Table REF ).
| m | 623a464bc29f95871e0af248509a11e0 |
(3) Which scale to process and represent data.
Local-scale methods {{cite:da8c140463ad64d1fd9a339a2fd7881db03c5e5b}}, {{cite:ee108fab0954497aef1bd36c1862f76e55a987e3}} use the idea that complex structures can be reduced to a collection of simpler geometric primitives. These methods learn local models which are used to reconstruct a surface in patches. While this approach can generalize better, patch-size plays a critical role and must be carefully tuned per object (Fig. REF , bottom). Furthermore, without any notion of global context, these methods are unable to complete larger missing regions, leaving a fundamental gap in their generalization performance.
| i | 631256cabcc407c5762292df0a5998b9 |
Skill Discovery.
The key difference from prior skill discovery work is the lack of episodes.
The most relevant work to ours is DADS {{cite:3b8d1d0ecb661adb19abca1e954490a138b2b447}}.
Unlike DADS, we plan over the model with action predictions, which allows for accurate planning even if the discriminator is not accurate.
Most other works {{cite:a82d8fef8c537ab144d861245d568d7bc2669a55}}, {{cite:51a1b8d7401a0f6b9b845d0bd350c301bc8ee9d9}}, {{cite:9e79e12fc65bc8a755cd6708b82562f27235dbfe}}, {{cite:179e0ad12d2f501554bb8fc7626922c50930edf0}} are complementary methods that can help learn a set of skills.
Some seek to use skills as pretraining for episodic learning, as opposed to our focus on safe reset-free acting.
| d | 591c9f78714cbe393af75c3e3b3475cd |
Let {{formula:ef3c8380-c515-4fb0-beea-031c3d5375b8}} denote a batch of images sampled from the dataset, {{formula:7bdd6e09-625e-45ee-910b-66feee469787}} denote the distribution of image augmentation for the {{formula:a98537e1-4cd1-4848-ac2d-3905a600dff3}} 'th task (e.g., cropping), and {{formula:27950d0c-32a0-48b1-b88c-c552e64a0ad6}} denote the deep SSL model consisting of a backbone and a projection head. At task {{formula:02ec7c20-f2c5-4dce-9f1c-f5bbcd76a0b7}} , two distorted views of the input batch are generated as {{formula:02da64d5-2248-4e49-aec4-983db934a03f}} and {{formula:2a10990e-e95f-406f-8c77-4cc16806bd6f}} , where {{formula:de189682-3b38-4e39-9d60-33f986f7e454}} for {{formula:b634556c-42fa-470a-9812-82a2ff9db84b}} . The distorted batches are then fed to the function {{formula:5879e42e-00b1-434a-bf7f-2ae4e4edaef7}} to produce batches of d-dimensional embeddings {{formula:443806eb-e192-487d-b15d-c94ee1c9d867}} (we use {{formula:c72a3443-a600-4a88-8932-3c4d0a378ad6}} , and {{formula:e00a04b0-c60c-463d-ba39-380401f6781b}} ). We adopt the Barlow Twins framework {{cite:22823992e2f34e051b065f2c32899e08b712e704}} and enforce the cross correlation between {{formula:1bea5f70-f3ac-4c44-a098-8677ccc4dff8}} and {{formula:7f5d5207-7b5d-488f-858a-8ac516dafb62}} to be close to the identity matrix by minimizing the following loss,
{{formula:35cf9b40-762c-4373-8fba-d97e8a583e07}}
| m | 09098dacd56c042fcd9ef512a991c0be |
Learning to discover novel classes. L2DNC was proposed in recent years, aiming to cluster unlabeled novel-class data according to their underlying categories. Compared with unsupervised learning {{cite:44e1e02b6dab13df6122922cb3ddfb651e1aca2d}}, L2DNC also requires labeled known-class data to help cluster novel-class data. The pioneering methods include the KL-Divergence-based contrastive loss (KCL) {{cite:1d946cd856df7e717e03e22b73dd98dde48f05ca}}, the meta classification likelihood (MCL) {{cite:10bdc9764a5a45c6362269f89f4e9e6bdb782516}}, deep transfer clustering (DTC) {{cite:754f9927786c2213ea043448b3d7841b3f6bf10e}}, and the rank statistics (RS) {{cite:fc9767447501ec21a69c0185b0ddd960f701f059}}. Detailed introduction of these four methods is in Appendix . Comparing existing works {{cite:1d946cd856df7e717e03e22b73dd98dde48f05ca}}, {{cite:436d0d065a3e687ca1d2d40d3bb5fa87e8e3561a}}, {{cite:6a7624705c6fec11de042d5ccbf482dc5e73bdf4}} with ours, we aim to cluster unlabeled data when their quantity is few.
| d | ad363c2014303a09a1a29f4ebee6449c |
{{formula:c0286e31-9453-404c-97fc-32f676521590}} , MIS in {{formula:1f20f787-ced2-49df-89cf-fb521e9080f8}} -free graphs has a polynomial Turing kernel.
The problem is polynomial for {{formula:6ab2a232-2a25-46ae-8240-498a3c66c9ee}} and {{formula:b1ed86f8-7328-444f-8466-8a766a1420fa}} , hence we suppose {{formula:a6339eb3-37c0-411d-b5ee-e65babd516e0}} .
Suppose we have an algorithm {{formula:c6677659-fcf5-4b74-bc5c-ffa7c7d6aee8}} which, given a graph {{formula:bfc4bce2-7b92-452e-bd5e-f1735754db05}} and an integer {{formula:c098ffeb-5e19-4f81-bf1d-f7d85aef85f4}} such that {{formula:eceed288-923c-4607-90d8-ed68f64048ca}} , decides whether {{formula:c8c48ef3-9b39-46dd-af0a-8536294dd39c}} has an independent set of size {{formula:60bcdb60-10bf-4938-a66f-8f33aa9d4a89}} in constant time.
Having a polynomial algorithm for MIS assuming the existence of {{formula:3d6401bb-b778-4645-9327-9fd1d3a5db9a}} implies a polynomial Turing kernel for the problem {{cite:9199b9804af6df57e5727ca03d8ebd5d696834aa}}.
To do so, we will present an algorithm {{formula:0cacc3e7-fbf4-4dca-8a99-20376a09fb6d}} which, given a connected graph {{formula:50be15b7-293e-4672-a9c2-fab93a8011ac}} and an integer {{formula:b3a06e7a-8119-4cba-8d13-50d3c0b9d014}} , outputs a polynomial (in {{formula:a03645c4-57e0-426d-8d1b-5b18170f81a1}} ) number of instances of size {{formula:98b21c32-08dc-4e17-80ff-7b9302f0bc5a}} , such that one of them is positive iff the former one is.
With this algorithm in hand, we obtain the polynomial Turing kernel as follows: let {{formula:db7fcd10-c96a-431f-aa86-d1bad8b9b1ad}} and {{formula:98f13d69-b607-45fa-aa48-d4d3398cff5e}} be an instance of MIS. Let {{formula:0da364d4-10ec-40a8-9323-85315a721b99}} , {{formula:56dc5b19-06be-4f88-827c-bdd3fe2c4f63}} , {{formula:d4d8de10-1e05-4832-a42c-ff15d0dcf313}} be the connected components of {{formula:f190c426-850e-4b82-a54f-8bdf6950b69b}} . For every {{formula:d6179793-6bce-44e2-bb94-47a9265b49a0}} , we determine the size of a maximum independent set {{formula:0f6db3b1-45dd-4e46-bbf1-b7b7c9b7397e}} of {{formula:d97d39b4-1edc-44e8-af36-25125b66448b}} by first invoking, for successive values {{formula:5567c5b5-c29d-4818-b996-aacd485a5fd3}} , the algorithm {{formula:fec74223-ab2a-403b-abec-d663e409aa3b}} on input {{formula:bc661f2a-19b4-40d8-aae0-3b149fb3df06}} , and then {{formula:3308adc6-186b-40de-b66a-f8edbdf93df1}} on each reduced instance. At the end of the algorithm, we answer {{formula:961a163c-13fa-4687-b045-a820f452ce70}} iff {{formula:a6ab69f5-3e15-4fff-85ec-a1757eae1ab0}} .
| r | 57bed4b96d282c82151e3cbfb43c0128 |
However, dimensionality reduction algorithms such as GMRA have historically been limited by the von-Neumann architectures they execute on: primarily constrained by small system memory (DRAM) capacity. In contrast, modern research has become dominated by “big data”, with datasets such as ImageNet {{cite:54d7da478960802b0eee2d7291a335e807733ce5}}, Cifar100 {{cite:d93e76213b671ed766170437746323c5173f696e}}, MusicNet {{cite:99c0723364dae8d4c19942c1fb61832e6ee08bd3}}, {{cite:299f744f22b50b6b6c8ac61a1a4f575eb024ce49}}, WMT14 {{cite:c1b0fb94bc02364efcc421308a703eb77ff06ac1}} being exponentially larger than any in history.
| i | 735e9b1d44d15f9ecc4536671b67d65b |
Adaptation of deep learning (DL) to graphs and other non-Euclidean objects has recently witnessed an ever increasing interest, leading to the new subfield of geometric deep learning (GDL). In particular, geometric deep learning is an emerging direction in machine learning which generalizes concepts of deep learning for data in non-Euclidean spaces, e.g., graphs and manifolds, by bridging the gap between graph theory and deep neural networks {{cite:ffb024d9113c8b3fce4789d4724d5248fd9f6025}}, {{cite:7f428cf2161877f7c4abe82d1c9888ffe01a77a4}}, {{cite:b2afbaab4d22c3fd39c6c1cec37a8b375b2e18c3}}.
| i | eb9ba41064399304cba416a46e4f08a3 |
NMS eliminates the redundant bounding boxes completely, which may lead to false negatives when there are overlaps between the ground truth bounding boxes. Soft-NMS {{cite:52015a0e8a70ac94a7bcf9be2b694ccaf363ab54}} alleviates the problem by keeping all the bounding boxes and only mapping the confidence scores of the to-be-suppressed bounding boxes to a lower value.
| m | 39da54a05cdfd9e3c3c291614f67c0ff |
The severe limitations of the direct solution necessitate the development of techniques that would enable one to split the system and solve the smaller Stokes and Darcy problems separately while exchanging information through the boundary conditions only. We develop a numerical scheme based on the sequential Dirichlet-Neumann (D-N) iterative method {{cite:03f31aaa3c7ae08142735f8ef6177584033898fa}}, {{cite:727d5249abf503b25d365f06c5a746af9986c81e}}. The outline of the algorithm is as follows. First, we define {{formula:6e81cd0a-7994-448f-8c17-8526bcb7bfc3}} as the iteration variable on the interface {{formula:6eaaa3b1-b061-4eb0-ba76-3c6b6d1be743}} , and choose an initial guess {{formula:5c106243-895b-42ff-974b-0cdf578aedc4}} . Then, for {{formula:b2e935b5-7179-4e51-b9a7-c74ca1ce0a6b}} until convergence, perform the following steps:
| m | 3d72c1805ba563a198b9bf106e1628ed |
Topology in condensed matter systems has been a major theme of research in the past decades {{cite:e931f47c272e01d6b93be842f0bda04bc465e8e3}}, {{cite:576d738ad74a75117db2c8d2048165fb38504e6e}}, {{cite:a21d931aa21d61d7e825a4c5dd93456c2cc2d7a8}}, {{cite:c886c3c43713602aebd9d766549d37fba2c64ba3}}. Starting with the discovery of the integer {{cite:82c0e1e02edae9d3df6f45f90c2d1d72c3ef82df}} and fractional {{cite:06fd6cefb3fc815ebf16af23bd3ec30ef4ae1088}} quantum Hall effects, which were explained later on using topological arguments {{cite:c179ac22b829d1e93d8ad9d60908e17d96e927af}}, {{cite:eae5aa3ae8f9f9b8c61dc2f2b8cdeb8689113c48}}, {{cite:d2473e20d297c459d78be4153cc74921882c17de}}, the field has seen a massive growth in both theory and experiment. Noteworthy theoretical milestones are the discoveries of Chern insulator {{cite:e0a604265eae95c2a9f058ac0556faa4e36f9b1a}}, which are analogs of the quantum Hall effect with zero net magnetic flux, and topological insulators {{cite:b08ebd92e851b75cbcbd9f517786c3cfd9281298}}, {{cite:4126b9acd35fea250e77a1cd4cd4955fe3454098}}, which can be thought of as two copies of a Chern insulator such that time-reversal symmetry is preserved.
| i | 3febf84cddb0d86d6314722c8d60fc24 |
We illustrate the methods just described by checking that the distributions studied
here behave in line with the large deviation principle {{cite:6d5a08af38b9ec6a7bdcb35c940b7b45f69c616d}}, {{cite:98e76468bef6367e02815515c23c7eb808708cbf}}, {{cite:8c1a416ba29bb06cfb8efae1fd1a99b27aac397a}}.
We do this by evaluating the size-dependent rate function {{cite:bb3e45f3bc0f288cb0b73ee8f0ad42b0e1fdebe2}}, {{cite:27bece85f582e865be5df6ee7a7e523ca65054bf}}.
It can be seen that the size-like parameter in our problem is the final time
{{formula:0f05e435-95fa-4346-8911-eb32343aea46}} {{cite:8f528bb7fc0eb228a07265113d36d729f4795a94}}. It follows from Eq. (REF ) that the maximum
number of particles at time {{formula:c174d391-345f-49f7-8872-a6b5e42cab98}} equals {{formula:54c60557-f261-409f-8fe2-38e3ad5d9baf}} . So we take
the density-like quantity {{formula:6e4b8eb7-c1ff-4dab-bf10-4acd507ba00c}}
as the scaled variable to be used when comparing the {{formula:9f26601a-cb09-407f-8437-bb6e2616ba57}}
for different final times {{formula:1b8b1307-ff06-4ed7-b2f6-5298572771e0}} .
Accordingly, we define the rate function {{formula:35491a9b-6a43-4ce9-ae64-b2036a271436}} as:
{{formula:fadee5e0-52c0-49e7-85d0-e54cfd44e4b7}}
| m | 10ce8b564a7459c0dadccf9cf70a32c2 |
Figure REF demonstrates the workflow of the proposed methodology. For a video sequence like {{formula:b425db7b-a14b-4ff1-9598-a7e5003ef8a5}} with {{formula:2395d845-1b80-47d4-849c-8800f70169ca}} frames, the input into the proposed gait recognition system are the intensity {{formula:8d73f30c-3e66-4179-9038-932d63db1106}} and range data {{formula:48a18df4-44ef-4fa8-addc-4a5c7d39fe4f}} , recorded by a single flash lidar camera, where images are preprocessed to reduce the noise. Figure REF shows sample intensity and range data in the first and second row. OpenPose, a state-of-the-art real-time pose detector {{cite:1d6bf60c166a83a82fd5b4a8adc5c484e1c27a7a}}, is leveraged to extract a skeleton model from the intensity information of lidar. The employed skeleton model is illustrated in the left side of Figure REF . For each frame, we present the 2-dimensional coordinates of skeleton joints in the vectorized form
| m | fb2d2e8b97438e7f5746bb457dc1c888 |
This research made use of the Common Astronomy Software Applications package (CASA), {{cite:ef3b53ead07cca558b309e533366d1097f047e9e}}.
This research made use of Astropy (http://www.astropy.org) a community-developed core Python package for Astronomy {{cite:6e3aa189184d35fdca70fa7223b6f03aaeda5b83}}.
| d | b4f4b95ff83c00658079c487bc80e6de |
(a)
The polynomial {{formula:5aed834f-bf8b-42c8-83b4-7751e4d9879e}} is commutatively nonzero. That
is, it is nonzero on {{formula:5542e146-1785-44b7-8d72-b9126f326337}} (or on {{formula:e117875b-dfe9-4a2a-b82e-4031e9f1f3a4}} for a small extension
field {{formula:7d4570dd-c849-4d06-866a-fc7c412e2a88}} ). In this case, by the DeMillo-Lipton-Schwartz-Zippel
Lemma {{cite:0b009ef6c73688c2050f83e43f92a2df2a7e0a02}}, {{cite:b17f0c070b8b6b7bba9668f17f9e6b1789366079}}, {{cite:93db81dcaae5dcd7bc6a6141734879af9886f7ba}}, we can do a linear shift of the
variables {{formula:7c63f2cc-59ae-49d1-a7ea-07834f2d720e}} in the polynomial {{formula:c3ce36b8-b7d1-43f9-a81e-96f3216ae559}} , for
{{formula:79928fb0-db14-489a-94f1-9fb5c4cf302e}} randomly picked from {{formula:82d524d7-a587-483c-a60f-ac5bf05c69f7}} (or {{formula:e01b2e88-02c0-410d-9fee-95edcff0630b}} ). Let the resulting
polynomial be {{formula:4fea295e-39d5-4a9b-9388-b4807d798079}} and let its Higman linearization be {{formula:a5c5a8b5-90b2-4b10-a3ac-84443a257f60}} . In
{{formula:ef69decd-02b0-4460-9606-437cd04e2efa}} the constant matrix term {{formula:f7bbc11f-0056-4e69-84f2-f49945a4ec88}} will be invertible with
high probabilty, and the reduction steps outlined above will work
for {{formula:02627643-5d66-4d13-be31-9bee1edaa992}} . Furthermore, from the factorization of {{formula:960e60e8-7a7a-4157-8bd4-569ee1d60680}} we can
efficiently recover the factorization of {{formula:07f8c64f-dae4-4642-90f3-dccb094d1445}} . Section
deals with Case (a), with Theorem REF summarizing the
algorithm for factorizing {{formula:d719d366-f52a-4e09-8571-bb31bda87e94}} . Theorem REF describes the
algorithm for factorization of the linear matrix {{formula:8b919f05-534d-468e-bec8-d504d1eb8e86}} , and the
factor extraction lemma (Lemma REF ) allows us to
efficiently recover the factorization of {{formula:58733ed3-b716-4fa8-8ece-291a68552fa9}} from the factorization
of {{formula:dc82f2b3-76a8-4a65-ba28-bf61c3f4a789}} .
(b)
In the second case, suppose {{formula:1d4e2a03-dda1-47c4-aa6d-76712282a07a}} is zero on all scalars. Then, for example by
Amitsur's theorem {{cite:90cae5642231cbe40a6707c1a262dff59411f338}}, for a random matrix substitution
{{formula:4bd0359b-5487-4164-8a1c-151ae463bc4f}} the matrix
{{formula:d73e3868-413b-4566-833a-117f8fb45d85}} is invertible with high probability,
where {{formula:ee537d40-a3a1-402c-ac3c-b558e7bf393a}} is the formula size of {{formula:536e6929-ee1e-4c22-81ca-8f421185d8fb}} .Amitsur's theorem
strengthens the Amitsur-Levitski theorem {{cite:404294d1f46425463d52eabb3dbd91d5d021e421}} often used in
noncommutative PIT algorithms {{cite:94ba517d30efd66074b51c2f2fe5017ece6d8dc5}}. In the actual algorithm we pick the matrices {{formula:7b067d05-26f3-4a87-99f8-ab790c989bcf}} using a result from {{cite:45b7ddc7a42e32319df0b48dd0f305cba6fda49d}} Accordingly, we can
consider the factorization problem for shifted and dilated linear
matrix {{formula:9c100f34-cdf6-4db6-a1ad-8836c81be32d}} which
will have the constant matrix term invertible, where each {{formula:5c64335e-d401-43f3-b7ad-ebf4728d06e6}} is
an {{formula:1416d6c7-b52a-4fa9-bae0-3c2bb44a8dfb}} matrix of distinct noncommuting variables, where {{formula:6c95a781-a700-48d7-a8b7-ecd51394ea61}} . Recovering
the factorization of {{formula:bbff75ff-c12b-49b0-b1b5-398eb25868ab}} from the factorization of {{formula:428e85f5-a66b-4873-96ac-7b7006b94be0}} requires
some additional algorithmic work based on linear algebra. A lemma
from {{cite:f70ca4aebc5c74e08e7431779ec23af3cca99b3d}} (refer Section and the Appendix for the details) turns
out to be crucial here. The algorithm handling Case (b) is described
in Section . Indeed, the new aspect of the algorithm is
factorization of the dilated matrix {{formula:a755817a-ff74-4c92-8758-77657472f724}} from which we recover the
factorization of the Higman linearization {{formula:0f021a4d-cbc2-4e13-b413-0f5ecdc132ff}} of {{formula:88b99339-7ef3-4367-9751-54c332bf706a}} . The
remaining algorithm steps are exactly as in Section .
| r | 7401be516d70f273769cb736eee48afd |
In this section, we present five numerical examples to show the application of the new DEM model in elastoplasticity problems. In the first four examples, the geometry of interest is a cantilever beam of dimensions 4{{formula:8b98aaae-34fa-41dc-ad9a-394d121701f5}} 1{{formula:14c64a6e-dbe0-4606-806d-86026f01152e}} 1 m{{formula:0d0dc831-797f-4041-bfbc-202c5575661d}} , fixed on its left face. The beam is discretized by 13500 structured hexahedral elements, forming a 60{{formula:5cc7362d-4f6f-4c95-94e6-f5e92dbdfd90}} 15{{formula:ee7982fa-db3f-4a3d-9e02-b4a242aa80a1}} 15 mesh. The elastic properties of the beam are: {{formula:eb07f3dd-54db-4279-9e78-1fa4fd7cb373}} MPa and {{formula:dcb4ffc3-378e-4955-bb81-e8a18a78e7bb}} MPa. The initial yield stress of the material is 50 MPa. The DEM model was implemented in PyTorch (version 1.11.0) {{cite:c171069244db977690c43a7c7fb4359b683b5394}}, which has 6 layers, including input and output. The number of neurons in each layer is 3, 100, 200, 400, 200, 100, and 3, respectively, resulting in a total of 3009 trainable parameters. The hyperbolic tangent function was used as the activation function for all layers except the output, which has linear activation. The L-BFGS optimizer {{cite:827f43bff761fd5219d8756571ade07d9478bda3}} with a fixed learning rate of 0.5 was used to train the models. The training process was stopped when the relative change in loss function value was less than a user tolerance {{formula:2d901650-9178-4c18-ac7e-150273129d69}} . In all examples, we used Abaqus/Standard {{cite:550d4e20de1a0e75687ed2bf8ac808c15943ad31}} to solve the same problem using FEM with an identical mesh. To quantify the model accuracy, we compared the DEM solutions to FEM solutions generated using identical node layouts. The FEM solutions were generated using the same number of load steps as in the DEM solution we compare against. The training of the DEM models and FEM simulations were done on an Intel i7-11800H processor. The absolute difference for a field variable {{formula:0446dbf4-e68e-46a3-94c2-8e7dd20ad1db}} is computed as:
{{formula:d0cbcdd3-2645-4feb-83c0-77b1181bb91d}}
| r | 8c8e98e5cc0289bd5bd606517acfacd2 |
3D Convolutional LSTM.
To further compare with RNN-based fusion, we remove the multi-scale context-aware fusion from Pix2Vox++/A and add a 3D convolutional LSTM {{cite:fa7d448cafd986b9779eb48280becf19dc5ff645}} after the encoder.
To fit the 3D convolutional LSTM input, we add an additional fully connected layer with a dimension of 1024 before it.
The resulting method is named Pix2Vox++/A-R2N2.
As shown in Table REF , both Pix2Vox++/A and Pix2Vox++/A{{formula:c1e95fbf-6596-4d7e-b238-b505af103709}} consistently outperform Pix2Vox++/A-R2N2 in all numbers of views.
| m | 4eb6344fb88d54deedfa6a8138a9429c |
Drop-column FI only gives a general view of the trained GB model, but the underlying functioning of the algorithm remain unresolved.
In order to get a glimpse into the GB itself, Shapley values can open a view into its depth.
{{cite:730d14b9999e1b71ce1829d9fe4285332a604e28}} proposed a measure to identify the bonus due to cooperation within a cooperative game.
The surplus that each player contributes to the outcome of the game is called the Shapley value.
The principle of a cooperative game can also be applied to the GB regression of this study.
Here, the ML features resemble Shapley's cooperative players.
The python package SHAP provides functionalities to derive Shapley values from trained ML algorithms {{cite:e8697bc7b45a1fb03f2b86b6a8b5e7d11d6050b1}} and was also used for the random forest analysis in this study.
| r | 1650c3cfb85435bd728ec7bc467e7072 |
We shall give particular attention to Chern-Simons (CS) modified gravity {{cite:4cad9f82c5788f549047509ed49d08a821738092}}, {{cite:9cb55bc933dc50facc8d4e7dbdd3f2151939c4f7}} in this work. This modification in this theory consists of adding to the Einstein-Hilbert action a Pontryagin term coupled to a pseudoscalar field (which, in general, may be either dynamical or non-dynamical). The Pontryagin term commonly appears in a variety of distinct contexts of high-energy physics—in field theory, where it is proportional to the gravitational anomaly {{cite:2fcda5a37ac15f2250ddae0f0e53862b5657ffe7}}; in loop quantum gravity {{cite:3286bbc15a8bd08852335266b6ee7c9859da48a5}}; in string theory, in which it emerges via the Green-Schwarz mechanism responsible for the anomaly cancellation in {{formula:11b234a3-3b2c-45b4-8260-84c4f2dfdfac}} and {{formula:ed278e29-d2b0-4ce3-bdea-d1e101a0dfe1}} heterotic string theories {{cite:63c770aeceae168fbce05c480b3e5e7f2c4d5062}}; within studies of local Lorentz symmetry breaking {{cite:4cabb9d265fa52b157cf3630f06ca0d7a0afea78}}, {{cite:b4f4357f9fc47e5e508ff89f4b7541086eeb78e6}}; and in other contexts (see, for example, {{cite:dbadd634fb702fceae8dca119eb1dfd631588680}} and references therein). Such multifarious occurrences demonstrate agreement on the highly relevant role of the Pontryagin density in high-energy physics; and it follows that CS-modified gravity is not just one of many arbitrary modifications of GR, but is actually closely tied to concepts that have many nontrivial applications.
| i | 5d8db75466ae1a5396ea4feb3dabb303 |
Suppose that {{formula:befb338c-2376-4884-814a-5627597e9005}} can be extended to an open neighborhood of the manifold {{formula:417eb934-2c1e-4261-a3b9-38b0662a3e76}} in {{formula:10058a7e-ee1e-4a77-8c99-0f3e04d05d93}} .
If we were to naively apply the standard UKF devised in Euclidean space, we would discretize the system () using the ordinary Euler discretization without considering the manifold {{formula:8a981ab9-0762-4e1a-8c52-60b60aa9f626}} , and apply the standard UKF.
In Appendix , we give a brief explanation of the standard UKF described in the paper by Wan and Van der Merwe {{cite:3ea8c5b8d1bd22d2847875c27171bbe905e1d78b}} and the typical values of parameters used in the standard UKF.
Since the manifold {{formula:20a13217-6763-4287-a63b-5624eeab945b}} is not closed on Euclidean addition and subtraction, there arises the problem that {{formula:0b25c951-8fd3-4165-a386-68e9f9e168c9}} may not be stable for the discretized system, i.e, discrete-time trajectories of the discretized system may diverge off the manifold {{formula:9e825c82-7a42-4380-8d64-e34da4a115ab}} .
Some researchers use the forced projection method to compensate for the state estimates deviating from the manifold.
This method projects the state estimates {{formula:8c323506-74e2-4efc-817d-8cb9a6b5f767}} at the end of each UKF update to the manifold {{formula:9870d6d0-6eb3-442b-8058-b420c5d85ee8}} by solving the following optimization problem {{formula:36ce8688-8c65-4d41-90fd-e9b8c54b4e26}} .
This least-squares optimization problem can be solved by using an appropriate gradient descent algorithm regarding the manifold, but it can be computationally expensive.
Detailed explanation of various optimization algorithms can be found in the book by Chong and Zak.{{cite:42ce15321081a201fe127d317328795a8ed6c403}}
| m | 16445da2e527e83520dde7c7217bcdeb |
The proposed model is implemented with Pytorch and evaluated for object detection in the autonomous driving application using the IVS 3cls {{cite:1f28a701acf612fd87f672a90aa2097087ca6165}} dataset. IVS 3cls is a cityscape object detection dataset with about 11,000 samples, including 10,000 training images and 1,000 test images. This dataset contains three types of objects: vehicles, bikes, and pedestrians. Its images have the resolution of 1920{{formula:9c377ba1-2421-436d-bdb8-6c962935837f}} 1080. We resize the images to 1024{{formula:ad1b2b6e-9f1d-4a5b-b928-e409be302871}} 576 as our input in our experiment. For model training, we use the AdamW {{cite:8f77c897b377075cd45d3bdffac5b067d9bc8a56}} optimizer with 10{{formula:9f4167c1-5696-4684-bb45-91f014042e8c}} weight decay. The learning rate is warmed up from 10{{formula:adc829b2-7e94-47f5-a3d7-bd1656c8f84c}} to 10{{formula:d9ef6357-414c-4d1d-b64b-9dea382385b6}} at the first five epochs, and finally reduced to 10{{formula:aedd94f5-ad85-4dec-88d3-1eea72eb2cf5}} . The batch size is set to 32. We train our baseline SNN model for 160 epochs with two NVIDIA Tesla V100.
| r | 37cf25ed036e12b4f46e88d768f71594 |
In this work, our ultimate goal is a universal re-ID representation that generalizes well across different test domains. We gain insights from the success of the face recognition community {{cite:66219e784181abd8434a9addfc2f21f1b3f28a3e}}, {{cite:a6dd0f4af2397f0e7b1ff83777f1896bcc80e939}}, {{cite:6a1fb20ba028912c9d51c4981d1c7a58d5082992}}, {{cite:baf7565d2bc675044fea0694c004bece21d94a46}}, and factorize the key elements to achieving the above goal into two fold: 1) Large-scale training data collected from a diverse distribution, and 2) a scalable algorithm that can make full use of the massive data. We carefully design the two elements with a consideration of their close connection.
| i | 38d582e267e98cd164930a7bbb282903 |
The existence of a relativistic enstrophy current suggests, via the gauge-gravity duality {{cite:636639fa04c43c635bd2729da7ae78b85855762e}}, that AdS{{formula:a68a1073-0751-4886-b5c3-94a5de2dda36}} black branes possess an approximate symmetry associated with approximate enstrophy conservation.
Since the enstrophy current exists only in the hydrodynamic limit, one might expect that an associated approximate black hole symmetry will exist on the event horizon.
| i | 4b23ffee39f13765f20623afd37b7a83 |
Attentive readers might notice that the first and second attacks are
specifically designed for Krum and TrimmedMean.
Careful readers may wonder about the feasibility of designing an attack particularly
for FilterL2.
We argue that it is non-trivial to design such an attack using the same idea
from {{cite:80b2e532ca8500f72aec39f4ee4ef706080723b7}} since the optimization problem becomes intractable
when FilterL2 is plugged in.
Due to the theoretically stronger robustness, we assume that it is very
challenging to design targeted attacks for FilterL2 like Krum or Trimmed Mean; we
leave it as one important future direction to design such an attack or
rigorously prove the impossibility.
| m | 62ec2f54bac834ad696db34d2bb3d94c |
We confirm the observations made by Niklaus and Blau {{cite:7cce2e61d364c79864323a7119e4d02c427e74cd}}, that pixel-perfect and perceptual metrics may be at odds with one another. Despite our slightly lower PSNR/SSIM scores, users still consistently prefered our outputs to those of AnimeInterp. We see a possible explanation of this in fig:dtmex, where the predictions do not align exactly with the ground truth. Since animations have large displacements, the middle ground truth frames may be quite displaced from the ideal halfway interpolation. SSIM, as noted by previous work {{cite:34fcb03f065fe4212a771e2304819cc70adcc70c}}, {{cite:d4143a8dc376c2f12eb7fb8e4859a562b8035e1f}}, was not designed to assess these geometric distortions. Color metrics like PSNR and {{formula:148ecb72-3516-46f1-9e85-bb163be3efb1}} may penalize heavily for this perceptually minor difference, encouraging the model to reduce risk by blurring. LPIPS on the other hand has a larger perceptive field due to convolutions, and may be more forgiving of these instances. This study provides another example of the perception-distortion tradeoff {{cite:7cce2e61d364c79864323a7119e4d02c427e74cd}}, and establishes its transferability to the artistic domain of 2D animation.
| d | 14334233f7c537480c33162a15df9930 |
A similar but different approach was also used in the Google team's supremacy experiment {{cite:a6ce24c063612d937b73bceeb71f691491281d3a}}.
To characterize their 53-qubit chip, they divided qubis on it into two small sets, which are called patches, by actually removing all interactions between them.
Their verification method was experimentally validated under their noise model.
However, their method would not work in the general case.
On the other hand, since our method “virtually" removes some two-qubit gates (see Eq. (REF )), it works in any case.
| d | 0773a606760db4c9591637d2379d8fff |
Conventional statistical methods for NSCLC survival analysis only use the textual modality and involve modelling time to an event. They can be divided into three types: non-parametric, semi-parametric and parametric methods. Kaplan-Meier analysis (KM) {{cite:fc6a5eea05a6937c990e1b0565215ca796f5eec9}} is a typical non-parametric approach to survival outcomes. KM Analysis is suitable for small data sets with a more accurate analysis cannot include multiple variables. Life table {{cite:64981a6c9306230649eabe7a6d494db640ad3239}} is a simple statistical method that appropriate for large data sets and has been successfully applied to European lung cancer patients {{cite:ed36acb85f9d649eeaeac8180341ccaff6b596c3}}. The Nelson-Aalen estimator (NA) {{cite:4a7b35dc531863b577d3f1b33c98180a80f8b067}} is a non-parametric estimator of the cumulative hazard function (CHF) for censored data. NA estimator directly estimates the hazard probability. As for semi-parametric method, the distribution of survival is not required. For example, the Cox regression model is used in {{cite:ce7b7393bca83f4a37a6c5883d30c6e43c319492}}, which discovered the critical factor that has a greater impact on survival analysis in lung cancer. The Cox proportional hazards model {{cite:64981a6c9306230649eabe7a6d494db640ad3239}} is the most commonly used model in survival analysis and the baseline hazard function is not specified. Coxboost can be applied to high-dimensional data to fit the sparse survival models. Better than the regular gradient boosting approach (RGBA), coxboost can update each step with a flexible set of candidate variables {{cite:7e8cfb9982bd909fdd54762b8879d5f00dd7283e}}. The parametric method is easy to interpret and can provide a more efficient and accurate result when the distribution of survival time follows a certain distribution. But it leads to inconsistencies and can provide sub-optimal results if the distribution is violated. The Tobit model {{cite:ba35ffd6c417aaaadb593fe372ec40cac7a149df}}, for example, is one of the earliest attempts to extend linear regression with the Gaussian distribution for data analysis with censored observations. Buckley-James (BJ) regression {{cite:a22ba241cee020ff319763ba16595a28df51d941}}, {{cite:f19f4092cdf97ea872c8b145af3e1547ceb750fe}} uses least squares as an empirical loss function and can be applied to high-dimensional survival data. BJ regression is an accelerated failure time model. Bayesian survival analysis {{cite:ec07b735583d1acbf06dc15615fa0788ac7b5242}}, {{cite:f87d9040807f5d4742022614cecdb2fcfead1e73}}, {{cite:5c841b57b25cb2da03addebe08f19bfa2fb98e02}} encodes the assumption via prior distribution.
| m | 3e45a94115054f2ae59679be28455da6 |
We trained Word2Vec {{cite:b0a67cfc2221bbac4da8a220af1a08900fbddec4}} and GloVe {{cite:93c901246cfdd0c86106106d4ac3730d18b1f7ba}} embeddings from LOINC codes grouped by visit and order. Codes within the same order were shuffled. The shuffling is suggested in {{cite:6c6a9130978b5a48bde0c24d56f6bab83f4bf234}} and motivated by the fact that the ordering of LOINC codes within a given lab test order is irrelevant, unlike the case of words within a sentence. For Word2Vec embeddings we consider skip-gram and continuous bag of words (CBOW) approaches. We produced set of embeddings with dimensions from 50 to 300.
| m | 21a706b2b6a112fcbfedee66223d8803 |
Fig. REF , where threadlike structures can be seen,
illustrates this well. These patterns are made of embeddings from close
overlapping patches within the same input image. This prior spatial organization
may be the cause of the low performance of our method. This is especially true
as the classifier on the representation space is equivalent to a linear
classifier (see {{cite:6a9e29752ba102f53560b67c585393b7b1ebcdb2}} for details). For few-shot
classification, there is no such prior organizing the representation space as
two different images cannot belong to the same larger image. Hence, the
structures and colors are not as similar as those of two close patches for
object detection. Fig. REF shows that training is able to
overcome this and organizes the space into semantic clusters. Yet this only
happens for training classes, for which strong supervision is available during
training. For test classes, the weak supervision available is not enough to
build a semantically-aware structure: the test classes representations are mixed
together and with negative examples representations (in black in Fig.
REF ).
| d | f482d078080d6d43160bfa383f44e69a |
By Theorem REF , we see that {{formula:b80e8765-91b4-4f14-88fc-2ad93d2c6bdc}} has
a distribution with standard regularly varying tails so that
{{formula:72953382-d3e4-4c3c-a198-ff3843679f25}} has the same tail index {{formula:9c4b68e5-b4c4-43c8-a276-efcfb498ba66}} as given in
(REF ).
Given in- and out-degree sequences {{formula:8c5c8ee6-ed35-420d-9a67-05c322881696}}
from a reciprocal PA model with {{formula:c16abbb3-1fbe-4ced-868a-22f25e0443ec}}
steps of evolution, we apply
the minimum distance method (cf. {{cite:476d67f726fa9a1cd8a3d78ec989d3800c3dac9f}})
to
{{formula:ea150ac6-5caf-4a7e-8f93-c32298bbe859}} to obtain the tail index estimate {{formula:9f64e2f0-ed72-4a2d-a1ff-90fa13ac5d78}} .
Further, recall from (REF ) that
the limit measure of the regularly varying measure {{formula:351c2d1f-622c-427b-a8d0-fb1209cffb72}} concentrates on.
{{formula:bb4d9566-11f2-4b67-b5b2-324f0c608a30}}
| m | 5b1c75adf6ee493f036dba5cbb9d4ae4 |
To further understand what the models learn during the different training methods, the generated embeddings are inspected visually. This is performed by training a UMAP model {{cite:8f6f9cae0122f3b2f7fa65d6235e3212dfb92530}} to project the embeddings down to two dimensions. UMAP is a manifold learning technique used for dimensionality reduction tasks. The model will look at the 15 closest neighbours when calculating the projections, with a minimum separation distance set at {{formula:11d66c40-04b8-406f-ae33-4c483685891a}} , using the Cosine distance. The other hyperparameters are the default values set by the software package {{cite:54c8e6600cff241a23543b8dd7d22d774b0f2f37}}. The values were chosen in an iterative way until the clusters formed were interpretable. The UMAP model is trained using the NHCLT train set embeddings.
| r | 7ba15180c527fd0b86a33079f86242e5 |
As the assignment of word forms to clusters is context-independent, the approach also cannot deal with homonymy.
We believe this could be solved by switching from context-independent word embeddings to contextual word embeddings, such as
BERT {{cite:42d245b26ebbba59d67fc79a7bc5502e7d7b87c5}}.
{{table:3cbfc962-f9f8-461a-9b0f-e90f9147a922}} | d | e7340d15735caa777d966bd459fa94b6 |
The process of computing cross-correlation for all the neural patch pairs between the hole and the remaining region (e.g., boundary) is computationally prohibitive. To alleviate this, the strategy in {{cite:0f5a8d23a280dd17c299be411754ee78e3c9b41f}}, {{cite:675c8ae264c5e0da9bfeab781c8968031fa84cb7}} was used to speed up computation via paralleled convolution. In practice, processing one feature map only took about 0.1 seconds.
| r | c2c8177f0bd14e58cb632cee65276513 |
Lately, AttentionXML {{cite:8c823371a73febb7782a0ff510f2f1e0b9914b54}} incorporates Glove embedding {{cite:5c67c1e40d94e1c7094f938e811baa753bdd9654}} and the attention mechanism {{cite:2a45063b08aa5765136c368ce80736408db9119a}} into XML to learn semantic information from raw text data using LSTM {{cite:6641908a52fd360b8300bc2a445bb44ceafd8e13}}. To speedup the training, it builds multiple probabilistic label trees. For each tree, it trains a single conventional multi-label classifier at each level of the tree using BiLSTM {{cite:fca19f9c375d8345bb18b7d1df0a8421d0a04d89}}. With respect to the depth of trees, Bonsai {{cite:91eb6c933e3de5b44c1bde6cb04050d28fbffa08}} claims that shallow trees are superior to deeper trees.
| m | 084631082c4281b4dd50f17aca8c7f8a |
In this work, we introduced an orthogonal polynomial-based DPP paradigm for sampling minibatches in SGD that entails variance reduction in the resulting gradient estimator. We substantiated our proposal by detailed theoretical analysis and numerical experiments. Our work raises natural questions and leaves avenues for improvement in several directions. These include the smoothed estimator {{formula:43fa5efe-b3bd-4b16-af25-da40ab73580f}} , which calls for further investigation in order to be deployed as a computationally attractive procedure; improvement in the dimension dependence of the fluctuation exponent when the gradients are smooth enough, like {{cite:17cb8c1699953bb858a7bea613c09be6721ed770}}, {{cite:46dc7881be3b32c9f5550f768a1e9f9e743834e6}} did for {{cite:c03f8c52f442cf74147e6d999354baf87fe293a8}}; sharpening of the regularity hypotheses for our theoretical investigations to obtain a more streamlined analysis. While our estimators were motivated by a continuous underlying data distribution, our experiments suggest notably good performance in situations like logistic regression, where the data is at least partially discrete. Extensions to account for discrete settings in a principled manner, via discrete OPEs or otherwise, would be a natural topic for future research.
Another natural problem is to compare our approach with other, non-i.i.d., approaches for minibatch sampling. A case in point is the method of importance sampling, where the independence across data points suggests that the variance should still be {{formula:089e0565-c435-4c55-b24f-95df2fbda164}} as in uniform sampling. More generally, incorporating ingredients from other sampling paradigms to further enhance the variance reducing capacity of our approach would be of considerable interest.
Finally, while our results already partly apply to more sophisticated gradient estimators like Polyak-Rupert averaged gradients {{cite:f5418f14588e699f378892055783979e840a669d}}, it would be interesting to introduce repulsiveness across consecutive SGD iterations to further minimize the variance of averaged estimators.
In summary, we believe that the ideas put forward in the present work will motivate a new perspective on improved minibatch sampling for SGD, more generally on estimators based on linear statistics (e.g. in coreset sampling), and beyond.
| d | b58d00402959116cfb2c1a500f06f006 |
Here {{formula:e4f80b93-7c1b-4198-88d0-056c0ae6fd55}} is the covariant derivative of {{formula:da847e07-059b-4f59-b921-4960c573e956}} in the direction of {{formula:d9481c3b-72ef-434d-9c31-459ebc667116}} (see {{cite:adf3e2fd7f94c86ef83a21453d330bb2fb8faa92}}) and since {{formula:a0de09d6-fd28-40b5-a104-4853b97bba1e}} is the Riemannian connection it holds {{formula:6dce1767-683f-4067-aa8e-6a67e3473bea}} for every {{formula:600e0cbf-67f3-4226-84a7-798b245dc00a}} . We denote the {{formula:e30183d9-e125-4304-9e46-cab322062d37}} :th order covariant derivative of a function {{formula:795d321e-243b-411d-ab95-662e6b6fdc62}} on {{formula:7754a788-edf0-462d-b32d-5cac00d86ad9}} by {{formula:7768e661-48a1-4e35-bc57-cf1937c07aa1}} . The notation {{formula:cc0eb141-7ef0-45dc-ac15-c4d0ec11aa10}} means a coefficient of {{formula:5f9f681d-4f11-41b8-b999-ace0cefad138}} in local coordinates. We may raise the index of {{formula:c8671f39-0faa-4f3f-a985-5cd8fd548958}} by using the inverse of the metric tensor {{formula:01ebe9e0-33a6-4d7b-ba92-ff9888025251}} as {{formula:fa9cd34c-7a74-4234-aaf6-5e886ac984f8}} . We denote the divergence of a vector field {{formula:57023094-8500-469a-a203-741652f9321a}} by {{formula:a26c175b-07b5-464e-b867-7369ca0f1cb8}} and the Laplace-Beltrami operator for a function {{formula:046e4e72-2b4b-4661-9386-51f418a419cc}} by {{formula:3902be9f-a146-48db-855b-10e26512a04e}} . We recall that by the divergence theorem
{{formula:5d76ed79-baf8-43f7-a601-cef7f00b896b}}
| r | 06c8ed989392354ca5c30b015ae06610 |
Specifically, applying proximal methods to the objective function {{formula:fd5aa8cb-6509-4e24-8bf6-64154c7653c2}} of eq:sparseobj, the smooth term {{formula:3661173c-df5f-443d-a4fb-a45ea437a4c3}} is approximated by a quadratic function while the term {{formula:a4a30bc5-2b05-4023-8101-0eae6dda3fdd}} remains unchanged. This approximation yields a linear LASSO {{cite:f712b8aa244d6fd7632cd98f7669fdbd8e8d345b}} problem ({{formula:c6703179-5ef2-4ea5-b9aa-c3f18de1a5a9}} -regularized quadratic objective). Once defined, we minimize it approximately using a LASSO solver. Denoting the descent direction at the {{formula:b5556883-48a5-44e2-a3ba-aa4c1f0401a7}} -th iteration by {{formula:01db9757-2350-4932-95a8-fd6b6b19b7ab}} , then at each iteration we solve:
{{formula:6dd646ed-8b4f-4218-8828-0c93d9168b04}}
| m | c8d36bf51e8d64cc46476e8c9469f20a |
Under these circumstances, it seems wise to take a less ambitious approach. In the search of some dark matter signal, both effective field theories (EFT) (see e.g. {{cite:12b1e07bb051d2d25fd226b5345af688b461398b}}, {{cite:e7317a57e77965400a9f940a9837fbdc0ed80df9}}, {{cite:004df600be9c46741c64cf5d14604f830fb3f201}}, {{cite:19d34c0b22c3b690f387697ef62221220081269c}}, {{cite:2ed2f4f48809c5f71bf4b6a33de350bbe92af3ec}}, {{cite:8bdd58a09e14f7ec557590004322934741e283ba}}, {{cite:db36f83b66cb801107687d88312dd9090a73fdf4}}, {{cite:b609630876d4ec41501f3c8ad6948b128e00416b}}) and simplified models frameworks (see e.g. {{cite:7d1f35cd29b558aa63c4d2fcd515ca5c01003721}}, {{cite:ff330a53cffb9a862a0766981bdd7d3d99ca0603}}, {{cite:bfc04a25937344dd2db9c86e51b7472bc2dd64a5}}, {{cite:7efda4503cb496f678e90559672a627ab901839d}}, {{cite:0de54c78cdf1b64bcaacfea877a83267a332b0c1}}) have been used as a guide of search. In the latter framework, both scalar and fermion dark matter has been the most explored line by their simplicity (for a classification under SM quantum numbers see {{cite:e8b801bb5db3e24bf67feed7dff4496bcacf40c0}}). However, it has been shown that vector bosons may perfectly play the role of dark matter, most of them motivated from hidden gauge sectors {{cite:22c8f6be0c06e4994adf39da72162de5ab82589a}}, {{cite:0fbf6331943d1142bc7ba20ec10c13b51edc91cf}}, {{cite:e94e349d67979bac7eda8769656e2ad598558e6d}}, {{cite:6fc1c3436658c2a7d4ef58ccd49f51b14b0008a6}}, {{cite:91746851013bfe979a4880e7480194509fefe656}}, {{cite:cd6652e17313d0a124ca168a0540f057ed06d5e6}}, {{cite:b73d39a70305e7c93378fa6da5187316e43621d2}}, {{cite:8368f46b7c25547a68d013b02c428f889ae403bb}}, {{cite:6bffd64ddeb2aff50209901bf046054a64559fd2}}, {{cite:59ed4956e00aa6163da10cc281d8dad87b0cb76c}}, extra large dimensions {{cite:d06944782d651f9cfba4d988a57b26b4d9e8f69f}}, little Higgs model {{cite:358c4a1e97df8020d32e597b6ed9538107f2b162}} and from a linear sigma model {{cite:3e9388aa5fc30580bf3859ef86ffdca0cbe940b3}}. Recently, the neutral component of an electroweak vector multiplet has been shown to be a good dark matter candidate, such as multiplets transforming in the adjoint representation {{cite:0a1f232c7b5a95231cdc82eb8fa6a3e2e7958099}}, and in the fundamental one in the context of 331 models {{cite:6f88eb67dd7d89792619ed41d5239761a3d0dc54}}, {{cite:38583390f2ec97e15dbe5f17facf065a05d70f10}} and in Gauge-Higgs unification framework {{cite:59c5edb28256bcfd0281628615db1ef3b23f8fa2}}.
| i | b23bcd96c12d07f3bf963bd27d3117ca |
We have found that a combination of invariants, the 2D invariant {{formula:ca372547-b10e-4258-b23f-e55657e069d0}} proposed by Simsek and Mintert {{cite:dbc7486ee4939a29c52cb7acf288494723d5b5dd}},
and the 2D linear invariants used in Tobalina et al. {{cite:d2c9ed558e5c6257e57f5d17961ae0c7ff48c50c}}, allow for fast inverse engineering state transfers,
more specifically vibrational quantum number swapping for any (not necessarily known)
quantum numbers, in coupled oscillators. The linear invariants and their powers
serve to solve the “degeneracy problem” of {{formula:880b2333-5726-4e45-84b4-b7698d2e5dc4}} , by which its commutation with the Hamiltonian at boundary times does not guarantee perfect transfer
except for the ground state. They also provide explicit expression for the Lewis-Riesenfeld final phase for each state, see Eq. (REF ).
Different systems may be described as coupled oscillators, and we have paid special attention to a particle in a trap whose final
form is rotated by {{formula:c7d30085-5e01-4e09-b897-82d021d8a6a8}} with respect to the initial one. In this case the method allows for rotations that produce final eigenstates
of the Hamiltonian rotated with respect to the initial eigenstates.
The method can be extended easily to arbitrary rotation angles, see Appendix ,
as well as to more complex operations such as a trap translation combined with its rotation, i.e. to the process
considered in {{cite:dbc7486ee4939a29c52cb7acf288494723d5b5dd}}. The methodology presented here may be extended into problems in higher dimensions such as ion separations {{cite:278997af662c496bd00a3837b379b07553c18567}}. A further extension concerns the boundary conditions for the potential.
Suppose that a quantum number exchange is desired, namely {{formula:b3a14eee-0d31-4776-b226-d3caee06234d}} up to phase factors, with {{formula:cd975c0a-3567-437c-a5fc-fecdfffd9b9e}} ,
as in the main text, but such that the initial and final oscillators
are equal, i. e., such that {{formula:5655205b-e532-4cfb-a00d-3f3d7e65ea0f}} , {{formula:2dddadbc-85c4-4e6c-a1b4-0bcb86fb0e07}} . The process may be designed in two STA steps,
the first one as in the main text, and
the second one as an STA expansion or compression of the oscillators {{cite:ec3a2c32287ec02dd9c7820db4bf0b706e6aa98e}} keeping the coupling {{formula:313344ca-895f-4faf-8e50-e58255363bd2}} zero.
Quite different boundary conditions and Hamiltonian parameter controllability have been set in ref. {{cite:bd789528b962c40a74117b5e1d9c8981c1e19be0}}, where an STA
approach based on counter-diabatic driving and unitary transformations to get rid of terms difficult to implement {{cite:b2147cebfa84f63bb23873cb87719fe76081086b}} was applied, see also ref. {{cite:68434ba0fb323a409df9688f425cab4cc5f2f77a}}.
A detailed comparison will be carried out elsewhere.
| d | 834423f2a260dbf7c7e64af367e91be8 |
We demonstrate the performance of DURA on several semantic matching KGE models, including CP {{cite:08ceab19731630e21f429c510b77059412802aed}}, RESCAL {{cite:b33daa39f3478ea0bf2609cda4cbfda76387a626}}, and ComplEx {{cite:9e60197a907c4afcaed3f318fc729dec1042e908}}.
Note that we reimplement CP, ComplEx, and RESCAL under the “reciprocal” setting {{cite:24ef2f3394706ac06be7cbaa783f4b13ae86fe39}}, {{cite:aa3b79df0f5ff290bdbd7eaf7e87152423352cbc}}, and obtain better results than the reported performance in the original papers. Sun et al. {{cite:563290ce1ab01e70af6659f12ba0020d76d2bbe5}} demonstrate that many existing learning-based models use inappropriate evaluation protocols and suffer from inflating performance. Therefore, for ConvE, ConvKB, and KB-GAT, we take their results from {{cite:563290ce1ab01e70af6659f12ba0020d76d2bbe5}} for a fair comparison.
| r | 706eb6fd238b763a34c346e4446995ef |
Recent chit-chat with the neural model, like Meena and Blender, shows impressive conversational performance {{cite:94eabeb347724d576faa9c1c9d7cd34c5ca2c83b}}, {{cite:16cf350fff9fcdefd9ecb24c0a8d931ea26130a8}}, {{cite:ac4b4262cbf9ecd0a73cb571874d40b383e3844d}}. However, such a conversation system uses a lot of data, and it cannot make a new style of conversational system in an instant. There are also plenty of researches on style transfer. However, these methods do not control the detailed style of the conversational system {{cite:e025ee88cceefa8ce3f0166490364bb5e25e7802}}.
| d | 07b6a74253a09069d10c63df56f8f8fa |
By the continuity of {{formula:b5c88a79-0873-40b0-8106-51490fffa5e6}} and {{cite:f9633c467df2fb10e78b189386cff20a1c7702b4}}, we conclude that {{formula:f91eccf9-59b6-4f55-a1f2-d02703ffa1d3}}
By {{cite:f9633c467df2fb10e78b189386cff20a1c7702b4}}, {{formula:297d2f26-0f5b-40b8-a2e7-0906732c1d65}} is closed. Therefore, since {{formula:ee29915a-8675-435b-9d0c-43b8d423f5f6}} , we conclude that
{{formula:97bf34c3-14e7-4e54-bd58-e73461b953a3}}
By {{cite:f9633c467df2fb10e78b189386cff20a1c7702b4}}, we obtain {{formula:ed84f98c-926a-4725-9a74-9c55631db400}} .
| r | 258032a5eddffc462a5093ea8161eebc |
We now turn to symmetric polynomials. A polynomial {{formula:c1c5a001-ab9d-4091-8d1a-4501942a7a05}} is called symmetric if it is invariant under permutations of the {{formula:eef79ae4-6abd-450d-8e11-f69af10e868e}} 's, i.e., {{formula:83515dcf-72dd-422d-bef9-e41a3721b31c}} . Symmetric polynomials have been intensely studied for over a century with diverse motivations and serve to interconnect many disparate fields. We refer the interested reader to Macdonald's seminal text {{cite:30f4bcbfea05420fe0cfd1794424b18ea4055aa4}}. Yet, there seems to have been relatively little work on polystability.
| r | de30e9ad79f9bb684d23e22b8f28d04c |
As baseline research, several state-of-the-art models i.e. BERT {{cite:c8492ab2de912774f3c92966e71f5d8932e6b5a1}}, USE {{cite:e8119f0c771f705034593e4bb27be1d9795c3c59}}, and ULMFit {{cite:da5a4e009608779c5790228a2e26c8265e67054d}} have been trained using the proposed Arabic dataset to make-sense of the provided couple of sentences. Trained models were evaluated based on their performance accuracy.
| r | 442ad0d8b96460b778700f21b45c9ca5 |
In general, the quadratic problem of finding a set of points {{formula:d8073276-7e5e-459d-b633-f083cb3d96e1}} satisfying the constraints in {{formula:fd97587b-3340-4955-a181-d205caa7b1ed}} is a difficult problem and there are many attempted solutions, all involving nonconvex optimization techniques, that date back to the early days of psychometrics {{cite:c11ff0eb3636f0dc280ede70a23e1ef86633f7f7}}, {{cite:87240a36dab82d9ea04bf5fbe738366ed85f2324}}. Unfortunately, none of these methods have theoretical justification, but in practice will find a set of points satisfying all the constraints. For our empirical studies, we solved the following optimization problem:
{{formula:c059c175-d59e-48d5-b18b-36bfcabea3e6}}
| r | 0dbe03b3622d0f91b8d2f3e5b77cbbb5 |
A natural tool for developing such intervention strategies is optimal control with the objective of minimizing the risk of an outbreak, which is defined as the expected accumulated impact of the event over the time horizon. Typical models for spreading processes are the Susceptible-Infected-Susceptible (SIS) model and the Susceptible-Infected-Removed (SIR) model {{cite:3bf813bf40f4cd5988f0c8899b6aed32a2e07c21}}. These models are stochastic which can further increase the complexity of optimal control problem. By using mean-field approximation {{cite:25f4019b8522cfbed2dedf56a79a290195767698}}, one can obtain approximate models in the form of nonlinear deterministic ordinary differential equations (ODEs). It is proven {{cite:3dff146ce3594ccde7690d5ce0c69d734d5e6020}} that solutions of these deterministic ODE systems are upper bounds of the expected value of solutions of the corresponding stochastic models. Thus, they are usually the object of study in control design.
| i | 615d972c5030bf613aa155a759f9a2d0 |
If the sampling has a coverage radius {{formula:96a1c2e0-158a-457d-af7b-b8c3268f64e8}} for some {{formula:f02db898-8135-4003-9c7d-3ccc5f96c831}} the conditions of (REF ) hold.
To satisfy the conditions of (REF ) as well and thereby ensure angle bounds on all triangles in a Delaunay triangulation we first sample along the boundary, enforcing a maximal distance of {{formula:aff0320b-de04-4f7b-86bc-52db3adf46b1}} between boundary nodes.
As shown in {{cite:1e0ff32db5beeceb172b50481046e80bd3844b01}} and {{cite:4467fe01d36077a8d484946244d4b604dfe7f603}}, we generate new candidates for our sampling randomly on an annulus around an already accepted node.
This is illustrated in Figure REF .
The inner radius of this annulus is determined by the minimal distance another node could have to the center node, while still preserving the empty disk property, whereas the outer radius is determined by the maximal distance a node could have to the center in a maximal sampling.
For our choice of inhibition radius, assuming the same radius as coverage radius, these distances can be made out to be {{formula:0140d3fa-0250-4ea9-b5eb-9d4674934da2}} and {{formula:cc1935d6-eb8b-47a2-95f1-7d5d060c77b2}} .
{{figure:fba17880-c824-4bf7-9c8a-2103e9d366ac}} | m | 595b420ba6aea8ced73c7f73e4ea459d |
Coreference resolution.
In table:maincorefresults, we compare the performance of our method to text-only baselines and a weakly supervised multimodal baseline (MAF) {{cite:d37fc837e222f4b85e5850e8eeba67c34838ed2d}} in CR.
For the text-only baselines, we consider a rule-based method {{cite:be17d9b6ddcd069cebdab8aeb641b552a8511b16}} and an end-to-end trained neural CR method {{cite:020a0e5605f310bf8b42d399c44d15b2eba7a8ca}} trained on large-scale supervised language coreference dataset.
We train the MAF baseline on the Flickr30k Localized Narratives training data. For our method, we report results with the transformer encoder (Tr) trained with the language prior regularization (Reg) in sec.method.
Note that, unless described otherwise, our method corresponds to the variant that use the transformer variant, trained with image, text and mouse traces with the regularizer.
| r | de5e6580e36349e77ec497d2f5d60174 |
where {{formula:14d17301-1a0a-428c-b663-0475050bb1b1}} and {{formula:58acbc3b-8703-4d76-9f87-dd4d5b0da072}} . We adopt a position angle of {{formula:808797ae-2fe1-401d-81ca-6788ece828b6}} for the major axis of M31
{{cite:7d9965292d11dc327b48d221a71db5aaeef450dd}}. We divided the GCs and GC candidates into four age groups: (i) very young ({{formula:a48a0cb9-6c9b-46bb-b36f-332dbc34542a}}
Gyr), (ii) young ({{formula:9a7afa83-5a91-456f-9258-e3fbbf23f790}} Gyr), (iii) intermediate-age ({{formula:35b49fca-a07d-49a0-a678-514012f2629a}} Gyr), and (iv) old
GCs and GC candidates ({{formula:21cd26eb-25de-4207-89aa-0236cef1a8be}} Gyr). Figure 10 shows their spatial distributions. Although our
sample of M31 GCs and GC candidates is not complete (in spatial, radial terms, given that we are
limited by the six observed fields), we note that there is a tendency for young GCs and GC
candidates to be nearly uniformly distributed around M31. The majority of old GCs appear to occupy
the central regions of the galaxy, although this restricted distribution may be caused by
selection biases. Figure 11 shows the number of GCs and GC candidates as a function of projected
radial distance from the M31 center, confirming our conclusions derived from Figure 10. Figure 12
displays the cluster ages as a function of projected radial distance. The crosses indicate that
the ages are from {{cite:5f500031340cdbf9bf19dc07bfc0c86dd419ea94}}, {{cite:7a63b9958b8c7745a718778f09c16dfca4995a71}}, {{cite:06d52c359ae5f4ab8a31e454fe157e4045390efa}}, {{cite:15046d6cc669f47562b5e06dc500e023f72d10b2}}, {{cite:326e5a80136eba92a18ef6c33f8bd2d862dccb97}}, and {{cite:9820b9c54207ae5b631fd0bc0c34ff029493c255}}, which were
obtained using the BC96 or BC03 SSP models, while the circles indicate that the ages are from
{{cite:33d2782eaafc2e516e7af507ec77b85f0777b746}} and the present paper, obtained on the basis of the galev SSP models. Figure
12 shows that young GCs and GC candidates are distributed nearly uniformly, and that most of the
old GCs (and candidates) are more concentrated.
{{figure:1db96143-54ab-497b-8a32-61d2a5dc657b}}{{figure:5e635352-05dc-4a86-91ec-5ddf5da34e58}}{{figure:3a40b691-9293-4d12-9d20-10566bb80762}} | r | 784454adf81b8e7e3a1995ce19867ba1 |
GCN-based Methods: GCN {{cite:e5ab94474987d25c195946fd54f75985fb9ad98d}} and GAT
{{cite:38708570ff42add63c62a76f2ccd838d715b187c}}.
Propagation-based Methods: LP {{cite:f670e4ae9f73ded77868d5568bc0f2745f731cfb}}, APPNP
{{cite:91b4a2c05b06a1b4ad786fb1733182d85b705c4d}}, C&S {{cite:84d1592ed2d767b2e35b6e9b0bccdf808ba6ad4f}}, and GraphHop
{{cite:68b58ae452ff20cd77643c99cab7e0cb779d509f}}.
Label-efficient GCN-based Methods: Co-training GCN
{{cite:037c796eec10f06c7a99fa2f2d01f4f9242b36e8}}, self-training GCN {{cite:037c796eec10f06c7a99fa2f2d01f4f9242b36e8}}, IGCN
{{cite:3df114228fa4f77b8b4157ad4d0af341052bbabc}}, GLP {{cite:3df114228fa4f77b8b4157ad4d0af341052bbabc}}, and CGPN
{{cite:68d39f62f4c00798e4de8d6c4b7f0ec8c5f318a5}}.
| m | d7ae6a2c1f25389c6db445f2cddad63c |
Exploration and state coverage: how well does AS explore the underlying state space in a stochastic, partially-observed world, as compared to alternative methods? Given our theoretical results in Section , we hypothesize that methods based on novelty-seeking will become distracted by noisy elements, while AS will fully explore the environment. We will use the number of rooms visited in a navigation task as a measurement of state coverage.
Control: will AS learn to take actions to control its environment, and recover from surprising situations? We measure control as the number of actions taken that cause changes to elements in the environment, such as flipping a switch to stop flashing lights.
Emergence of complexity: is AS able to produce an arms race between the Control and Explore policies that leads to the agent's acquisition of increasingly complex observable behaviors? If this is the case, we expect to observe the alternation of relatively long learning phases, where the two policies are competing without visible change in the agent's behavior, and relatively short phase transition that separate two clearly distinguishable behavior.
No-reward learning: will AS enable the agent to learn meaningful behaviors in the absence of any external reward? To assess this, we train the IM methods using only intrinsic reward, then assess the amount of task reward they obtain in the standard Atari benchmark {{cite:f5063bd1016a4f1de3215af679aacf32c093f87f}}. While there is no reason to expect AS to always correlate with the objectives in arbitrary MDPs, we expect that the twin goals of maximizing coverage while achieving high control should correlate well with objectives in many reasonable MDPs, particularly video games of the sort present in Atari. Many of these games have a notion of progress, which roughly corresponds to coverage, but at the same time have many dangerous states that could result in `death', which leads to an unexpected jump back to the starting state. Therefore, we hypothesize that AS should, without even being aware of the task reward, perform well in these environments. Comparing to prior methods in these domains is interesting, because prior work has variously argued that both novelty-seeking exploration methods {{cite:c440890b85b943c325d2c6310952f1644b9dc586}} and surprise-minimization methods {{cite:1bc53b0748d177dd24d017f5e4ef9eeea7b865bb}} should be expected to achieve high scores in these domains.
Note that when we assess all three metrics we look at the performance of the agent as a whole, which is jointly controlled by both the Explore and Control policy.
| r | 1e1bc1954db1adebf80d2b07a31d8fb0 |
Recently, this idea has received increasing attention in neuroscience. Neuroscientists have identified the fundamental role of information thermodynamics in supporting brain functions {{cite:a10f7a0b169684f8edcfd53e5db26b9ba6fbeeb0}}, {{cite:4709281616d4a2603da8e6f2294b9c10db903cd1}}, {{cite:6eac81882c82d6c414389d221f61d0b7b83ef845}}, {{cite:4312b73e6cf19416721bb3b13862015558187b6f}}, {{cite:16a9d2e10e2a4f9c2c272771e13770eaf3f93f27}}, {{cite:e8741abff359a8b9d4462cf3d2fb58f68057c9f9}}. Historically, the physics mechanisms underlying brain functions used to be elusive {{cite:9ab203c3a4a8d9104418ca35373f9bec2710f888}}. The brain is a system with complex topology {{cite:4a0929b6eeff0a312f44064b690b5285150639b8}}, geometry {{cite:7d346fc21ede6bb57aef9e7f55ca40cc8e409083}}, and dynamics {{cite:47471d0a1e4aa03d67ca2974f204b3448ecf3433}}, which creating numerous obstacles to study how the brain processes information. The application of information thermodynamics in neuroscience may help overcome these obstacles, suggesting a potential direction to understand neural information processing at a physically fundamental level {{cite:a10f7a0b169684f8edcfd53e5db26b9ba6fbeeb0}}. Based on previous studies, our research moves one more step further to explore the information thermodynamics nature of the brain. As a non-isolated system of neurons, the brain is demonstrated to act as an information thermodynamics encoder with intra-system coupling. By deriving the thermodynamics of encoding based on the nonequilibrium second law of thermodynamics, our theory helps reveal the physics foundation of how the brain encodes the information of an external source. This framework might contribute to understanding the intrinsic relations between cognition and the physical brain {{cite:a10f7a0b169684f8edcfd53e5db26b9ba6fbeeb0}}, {{cite:2e53be90d6045bf9c2749468cd957810431dcdad}}. Moreover, we combine information thermodynamics with the theory of information synergy and redundancy to implement a unified analysis. We demonstrate that the intra-system coupling within a system allows the encoded information in specific sub-systems to exceed the information thermodynamics bound on the whole system. In other words, more information of the external source can be encoded (or hidden) in certain sub-systems in comparison with the whole system. The emergence probability of this phenomenon is affected by the internal correlation strength inside the brain positively. We suggest that this finding may provide insights into the synergy and labor division among neurons and cortices during neural information processing. Classically, the decomposition of the information encoded by a system of elements is implemented utilizing information synergy and redundancy. The possible significance of synergy and redundancy in the neural system has been discussed for decades, discovering various effects of redundant or synergistic collective dynamics on neural information processing {{cite:68d0ee15257d6ca05f8cfb5376943dc48eb21ad8}}, {{cite:eb5e5868cdef52be9d9e221fac3d012984478bc8}}, {{cite:a67558daa61ce83ecd5c3377d503fa74207893d8}}, {{cite:57f0ac7e8cbc6bcc99766ec635195d6f573be3f8}}. Our research further connects these previous theoretical findings with the thermodynamics of encoding, revealing the thermodynamic foundation of information synergy and redundancy during the encoding process. This finding may offer a possible explanation for the stimulus-dependent superiority of specific neural or cortical tissues in encoding efficiency comparing with the whole brain. For instance, the superiority of the visual cortex during visual perception {{cite:cfc2606cb58d6952874510d9a9dff4529251a79b}} not only means the relative redundancy of other sensory cortices but also corresponds to the larger encoded information quantity that is not restricted by the information thermodynamics bound of the whole brain. In sum, the theory depicted here features the potential to be further applied in neuroscience and related fields, which may help deepen our understanding of the physics foundation of neural information processing.
| d | 541e52f8c1471a073d799d8984dbc3d4 |
MIT-Adobe FiveK {{cite:0a7221f3effc09104679bfecf7956ed483af545d}} dataset contains 5000 images, each of which was manually enhanced by five different experts (A/B/C/D/E). Following the previous settings {{cite:656977a8d72e747a67df48675582ece83d988c3b}}, {{cite:752e2ecd9091b48ad540723190d03cbbc763111e}}, {{cite:7d3150a17628ff75d10b69033d5777d0be56bb26}}, we only use experts C's adjusted images as ground truth images. For MIT-Adobe FiveK {{cite:0a7221f3effc09104679bfecf7956ed483af545d}} dataset training, we use a single L1 loss function to optimize IAT model. We compare our method with SOTA enhancement methods {{cite:8463b66fbf9f24b0ee26ff10f6dd8e754d12e6c1}}, {{cite:46a4209391e8ac6525caf078e8e46c747f0160af}}, {{cite:1dfce82b7a6a98f567027f254f3ae28c5f9b5bb4}}, {{cite:85669133bef8b54db29598afee8ab64853652647}}, {{cite:656977a8d72e747a67df48675582ece83d988c3b}}, {{cite:656977a8d72e747a67df48675582ece83d988c3b}}, {{cite:7d3150a17628ff75d10b69033d5777d0be56bb26}}, {{cite:752e2ecd9091b48ad540723190d03cbbc763111e}} on FiveK dataset, then report image quality results (PSNR,SSIM) and model parameters in Table. REF . Our IAT also gain satisfactory result in both quality and efficiency. Qualitative results of LOL {{cite:be2f20ba98654a1e68594ea3a736c95758637624}} and FiveK {{cite:0a7221f3effc09104679bfecf7956ed483af545d}} has been shown in Fig.REF , more results are in supplementary.
{{table:c188ef25-920f-4d27-8ace-06ba8dc26836}}{{table:5467c083-b95a-411e-8483-34494b269784}}{{table:acaa56b1-0244-45eb-bd7c-d3cfa6e72602}}{{figure:d7cdbbd5-5ad9-470c-aa71-47babfdf6c58}} | r | 578f726204f2b42666711356277a91e6 |
In principle one could also use optimization methods to explicitly minimize {{formula:55440d8c-97e1-4a0b-8a14-d50e55edf8e1}} for any of our choices of {{formula:6cf7e4a3-24e0-46f5-b2d8-d4490068ec92}} . In fact, line search and trust-region strategies for global convergence implicitly minimize this function {{cite:97f580a0dd55b1a899ffbe5866ac7b116d9374be}}. Computations of equilibrium prices benefit from leaving this implicit, as explicit minimization via Newton's method requires third-order derivatives of {{formula:66e8ac16-0256-419d-8f32-8352943bac99}} , increasing both differentiability requirements and computational burden. The Gauss-Newton method {{cite:a6fbe4b63084c7978b1de6915155ba5d35ecc1a2}} is obtained by neglecting the influence of the third-order derivatives of {{formula:b95b9f76-b481-4de4-bc6b-44519d106a9d}} . This defines the Gauss-Newton step as a solution to the (symmetric) normal equation {{formula:8f6ef923-e124-4e6b-9751-33cec29f6388}} ; note that the same problem arises should one wish to use the Conjugate Gradient method to solve the Newton system. So long as {{formula:e333e5f7-2012-43cb-8e62-ccee1ac5f045}} is nonsingular the standard Newton steps will be recovered from the Gauss-Newton method. However they are explicitly formulated as solutions to linear systems that are more poorly conditioned {{cite:739e148fb3d56a86ef4a036590b739eadd605aad}}, {{cite:768b7a6c1af994b723737eb6a0984feb5c0ab0da}} and thus we should at least expect to accumulate more error in the process of solving for the same steps. The burden of computing these steps also increases because of the requirement to multiply by the transpose of the Jacobian of {{formula:ebc3d81c-08c8-495b-95ea-df4763a18e03}} .
| m | aac6ac2a1b44fb5c68e77aead4d07924 |
Future directions: In the recent past, with the introduction of precise segmentation capabilities to visual trackers, the connection to video segmentation has become apparent.
Some top visual tracking methods perform well on video segmentation benchmarks {{cite:37891a70e3f0782b487075cd282788b261bc9e2e}}, {{cite:6dad09e954ece53e26ef340bce97bfe2bbbef415}}, despite the restriction to causal processing of the input.
| d | 3b184405e8f8f418f40d4d86a1c7f719 |
Remark. Contrary to NiftyMIC {{cite:ab0649ecd4f5442b66322e7a9a9c728ff34cc344}}, MIALSRTK {{cite:1d967993c4a273e6903073e206cca13c04ea80e3}} places its regularization parameter {{formula:1b4ba50b-1e0b-485e-8e94-e7951b00967b}} on the data term. For the sake of consistency, we will only use the formulation of Equation REF , with {{formula:6824e017-6f47-40f1-a148-bbf1c0409e58}} in the case of MIALSRTK.
| m | 1bf833138b24d3d20224ec659871f142 |
In this section, for clarity of presentation, we illustrate how a specific ROM closure model (i.e., the D2-VMS-ROM outlined in Section ) increases the ROM accuracy for the 2D flow past a circular cylinder {{cite:b6ae1f0d02791c9f2cda952bc001084e8a6ea0fc}}, which is a simple test problem commonly used in the ROM community.
(We note, however, that the D2-VMS-ROM was successfully used for challenging test problems, e.g., turbulent channel flow {{cite:c8c0c9de637ba1d40f40a56dba57a79e07cfc98c}} and the quasi-geostrophic equations {{cite:1a5d81fc0868126d284f1aa08624276195497843}}.)
In our numerical investigation, we use a Reynolds number {{formula:13ff03a8-03ff-4f7f-b28a-2c0910bca0f1}} and four ROM basis functions (i.e., {{formula:a4a26811-8507-4a6c-a1c5-7dfc67a24725}} ).
Details of the computational setting can be found in {{cite:b6ae1f0d02791c9f2cda952bc001084e8a6ea0fc}}.
| r | 849e32c3afedbeb1bf2840ba7b9b7302 |
In addition to improving the detection accuracy, reducing the computational cost to achieve real-time on-board processing is also very important for UAV-based object detection approaches. One way to improve latency is to skip unnecessary computation. For instance, {{cite:f5683516360ac602ae83bc27cbd5341c3d8967a0}} proposes to extract candidate regions of target objects first via over-segmentation. After that, only windows around the candidate regions are sent to the pre-trained CNN and linear SVM for feature extraction and classification. Another way of reducing computational overhead is to use more efficient one-stage object detectors, such as YOLO {{cite:af6d7ebbbe7f87a10b15410171763a57af3e711a}}, {{cite:fd285af2dbb7f1f8d26f40f90eb41d6ef485feb9}}, RetinaNet {{cite:6cf3b39d41f864cf7fd506425901d9ac28ca925f}}, CenterNet {{cite:d85d98425308f9957432b12aaac2fff04c64335d}}, and EfficientDet {{cite:4dcd38d02fac4c857544223a593c139ac2ac9db8}}. These one-stage object detectors directly classify and locate objects without generating region proposals, resulting in improved latency. As an example, {{cite:6d818ee1508ab8357e0fb65f39434dae8c7279f7}} adapts the original network architecture of YOLO by making it more suitable for UAV-based object detection. In this paper, we also utilize YOLOv5 {{cite:fd285af2dbb7f1f8d26f40f90eb41d6ef485feb9}} for all the experiments due to the advantage of its low complexity (Tab. REF ).
{{table:8ca85d88-5278-455c-81f9-dacc400127b2}} | m | b6112238c11623d778efbdac2cfc02ad |
The comparison with EBHIS data at {{formula:63e90f54-d7d3-4afa-90d4-087a2f731493}} shown in figure REF shows the A/F star data line up with the main {{formula:cc8060c3-0312-4a42-9b11-2a35328bffe3}} km s{{formula:dd9680eb-4023-4add-b25e-1b006790952a}} H i emission peak, while the peak at {{formula:68ce189c-81e6-4164-a7c4-56e424405b74}} km s{{formula:534f6be3-47ed-42e3-8001-5971bd5edc66}} (from the Local Arm, seen in H i) is clearly absent. This is to be expected given that none of the A/F stars selected and measured will be in or near the Local Arm. The H i data also present a peak at {{formula:754aec6e-8f1b-4554-9e74-9fe5f586e3c9}} km s{{formula:242b9768-e639-485f-b3da-97f9bd0e2b6a}} that is largely absent from the stellar data. This is unsurprising since our central result from the {{formula:8674cb0a-779a-4ebd-b969-0aef6147e08d}} sightline is the RV flattening that implies a relative absence of stars in this more negative velocity range (at distances where a flat or gently rising rotation law would predict they exist). A reasonable inference from this is that the H i gas at the most negative radial velocities lies mainly outside the range sampled by the A/F stars. We note that the CO data from the COMPLETE {{cite:922f9a499df525e571b90ea8b31d06b88d7a9c38}} survey exhibit the same RV peaks as the H i data. This difference either indicates that the H i and CO gas lies beyond {{formula:fe3492f1-4a8d-4794-b5bd-42b6b73ef95d}} kpc, or that the distance range occupied by our sample of stars does not extend to the distances where existing rotation laws would predict RV{{formula:56f528ff-a75a-4bd7-b138-060be2191263}} km s{{formula:cfe414ff-1e20-413b-babb-0a2af7a01e8c}} . From figure REF , it can be seen that these laws associate a distance of {{formula:7eeb2075-61d8-4299-9b01-c3d69923d476}} kpc with this RV. We argue below the stars in our sample placed at {{formula:4815ef24-878e-4568-af71-190a4bc6e843}} kpc are not there simple because of distance error.
{{figure:f4dc55c4-0ad4-4374-bdcb-876d2c7aa8ab}} | r | 040da41be9239575c88222fe005f071a |
In this method, one of the objective functions is chosen to be optimized and all the other objective functions are converted into constraints by setting an upper bound for each one of them {{cite:a0128fa379042a49890fc572095cdfcb9b0e5123}}. BOPGVEC can be formulated as follows:
{{formula:e3db0297-1375-43e0-9039-36057473c67a}}
| m | ca618bbfddfc8860460c89842e23c0d0 |
In all the cases above mentioned, Derrick's theorem is violated by imposing that the static scalar field is situated on a background geometry with axial symmetry and no backreaction. Furthermore, the models mentioned so far also have in common the fact that they use real scalar fields in asymptotically flat background geometries presenting isotropic scaling in coordinates. In the present work we study the formation of static and spatially localized scalar field solutions on Lifshitz spacetimes, which arise in the context of the Gauge/Gravity duality {{cite:d49aa05b956b5eb0dda3e67f2d0ae861be66588c}}, {{cite:72fbaac1b56c167ea74a333579d6b8702f22e7bb}}
as a class of spacetimes such that their dual field theories are non-relativistic and present anisotropic scaling of the Lifshitz type {{cite:961909afd73d06d0e4afded0f749b92f142fb531}}, {{cite:fb1fc6cd168a85d217064a41d453050130af561d}}. In this case, the gravity side of the Duality presents a non-asymptotically flat geometry derived from Einstein equations in the presence of massive vector fields which has anisotropic scaling symmetry. Hence, it is not covered by Derrick's theorems and extensions formulated to date. Due to its scaling properties, Lifshitz spacetimes have been explored in different contexts, constituting a great source of applicability (see, for instance {{cite:3e804cd19c165e48f2f5514e7d095d8e1a45a27b}}, {{cite:80c6695315d6ae069d9b159313869177ea54ade4}}, {{cite:3122fec4b05972c9f6d3400d973ba21d6f21b12a}}, {{cite:d38ca68430885a96fb980ec9ca5db49025e019ec}}, {{cite:f5d3d0096acb29ef255e16fadad3f88065aa42e5}}, {{cite:8d83aa2baf55efc4df9c2fc146d3255a8f880675}}, {{cite:4b26953b46e07b8d95caf4195e6657138c94e546}}, {{cite:89b3aa955650efb5af5afc61bd6e2fe2616d6fbb}}, {{cite:1b84b46dfaa93a244673e466a637b338ee9a4d36}} and related references). In Gauge/Gravity duality, the mass of the scalar field in bulk is associated to the scaling dimension of the scalar operators in the boundary and by dealing with non-relativistic setups we can provide ways to approach non-relativistic field theories with applications in Condensed Matter systems {{cite:39e4d7077a0288e38ba15472ad66f46be0d5c4eb}}. Therefore, extending studies on this subject can still lead to a wide range of applications and a better understanding of the behavior of scalar fields in this context can bring relevant ingredients in the development of new results.
| i | 804759dc71a5552934396b4b39cbe8dd |
We employ open source plane-wave code Quantum ESPRESSO {{cite:4cc280315043f67f458a9cfee6372d64a3915bce}} for structural relaxation and phonon calculations of carbon defects in monolayer hBN. We use the optimized norm-conserving Vanderbilt (ONCV) pseudopotentials {{cite:2ea97e3c6e0ef67858bd3c20fb4960e9a555162e}} and a 55 Ry wavefunction energy cutoff. We choose a supercell size of {{formula:cfcf5484-41fd-4b81-a30f-b6e3ea223d0c}} which shows good convergence as tested in Ref. wu2019carrier, Tyler2021-err, Smart2021wk.
Charged defect correction is included to eliminate the spurious electrostatic interaction by using the techniques developed in Refs. PingJCP, wu2017first and implemented in the JDFTx code {{cite:826426c18ea0050c368034673ed002122084f3bb}}. Total energy, defect formation energy and geometry are obtained with the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional {{cite:c58936d035a6829cdd535c091c536085553f53e7}}. The charged defect formation energy {{formula:9d7e82e4-acf2-44ce-a97a-94dd849b4d7f}} with the charge state {{formula:420bb0cd-ddbb-4e80-98de-3e3f7e2af8cf}} is calculated by
{{formula:df61952d-f1c8-4ede-9b92-03919127c12f}}
| m | 4df5d7073a2d300d913e65b59a1d9c83 |
To test our circuit pruning methods for feature preservation, we pruned circuits for features in an Imagenet {{cite:defe1686a38f8f9efbfafb15507efeb6046104d0}} trained Alexnet {{cite:936097ad33bf3c417d9f8bc17ae680c28c515458}}. We tested two versions of this model, one trained in the typical manner, as is available through the Pytorch modelzoo {{cite:a57443f8e0959b30931c5e4766b3ee3217365246}}, and one we trained with hierarchical group sparsity regularization {{cite:4ebed7ae2794c6c4f9fbc9fe6e0c9c5a65092f21}}. This regularization encourages groups of parameters (kernels and filters) towards zero magnitude during training (appendix). If we endeavor to find sparse circuits within a model, we reason it is useful to start with a model that already sparsely achieves the objective. We selected 20 random features from the last 3 of the model's convolutional layers on which to test our methods. For each feature, we average the activations it returns to a subset of 2000 random images from Imagenet (2 images per category). This is the value for {{formula:75613258-5387-4d2a-a54f-f047203d843a}} we use to compute kernel-wise saliency scores for each pruning method. As a baseline method, we additionally compute a magnitude kernel-wise saliency score, equal to the average magnitude of each weight in the kernel;
{{formula:41e5fff4-15ba-4cd4-b52d-7a7c2ce5085c}}
| m | effd60584d1ae4c1f7d05af89a0dd494 |
We demonstrated above how the pressure term in a perfect fluid
makes additional contribution to the energy-momentum of the system. During the Lorentz contraction of the system, when the system is accelerated from one inertial frame to another, work is done against pressure, which makes a finite contribution to the total energy of the system. Also, when a fluid system has a bulk motion, work done against pressure is positive on one side of the system, while on the opposite side, an equal amount work is being done by the system and this implies a continuous transport of energy from one side of the system to the other, thereby making a finite contribution to the momentum of the system. These contributions of pressure to the energy-momentum of the system, already present in the relativistic formulation of a perfect fluid, have remained shrouded in mystery, from a physical perspective.
Of course, if the liquid is contained and one includes the contribution of the container pressure too, then these pressure terms get cancelled in the expressions for energy-momentum, which then behaves as a 4-vector under a Lorentz transformation. However, in systems, where the liquid does not have an external container, and may be self-contained, like in the relativistic description of a spherical star or the cosmological model of the Universe expansion {{cite:215a6cbac3cc9bb3091308ce3e80139cb4a19c5c}}, {{cite:7e31dc14e08ca4ee93979e4468f4af15ae5be830}}, one has to use the fluid equations, including the pressure contribution to the energy-momentum of the system.
| d | ae2884239c8fa7b62a74a6bdfd3db948 |
Related work The only other interpolation scheme we are aware of, that is proven to be statistically consistent in arbitrary dimensions under general conditions, is the recently proposed weighted interpolating nearest neighbors method (wiNN) {{cite:b47e1bc0e7f520fcc76856093fe5084d7e81db84}}, which is also a NW estimator utilizing a singular power law kernel of a very similar form but with two important differences: a finite number of neighbors {{formula:8a107f7c-1d39-4cea-a676-49ce208c41be}} is utilized (rather than all data points), and the power law exponent {{formula:940fc080-d219-4c70-b32d-9cfec291c1fc}} of the NW kernel satisfies {{formula:99d5f04c-dadf-4bd3-b636-cde763723cb5}} rather than {{formula:8f4d1fc8-feca-439a-a377-c11cc2fe72c2}} . To achieve consistency {{formula:bb9f8f70-f05a-4ba7-9484-1932a8bb5c60}} has to scale appropriately with sample size. Despite the superficial resemblance, the wiNN and Hilbert Kernel estimators have quite different convergence rates, as we will see from the results of this paper. Also worth mentioning is the Shepard interpolation scheme {{cite:3e1a773c942f87441016d5a46f224bdbf10d54dd}} originally proposed for interpolation of 2D geospatial data sets, also a NW style interpolating estimator, though used in the context of scattered data interpolation. In scattered data interpolation {{cite:c2f7dc70e79bd89f46641670478030be01637ede}}, the focus is generally on the approximation error (corresponding to the “bias” term in our analysis below). The approximation error of the Shepard scheme has been analyzed {{cite:2b834613a7a639c369a002bb71dfc06a4d98c477}} but as we will see below the risk for Hilbert kernel interpolation is dominated by the noise or “variance” term. In contrast with wiNN or Hilbert kernel interpolation, other interpolating learning methods such as simplex interpolation {{cite:b47e1bc0e7f520fcc76856093fe5084d7e81db84}} or ridgeless kernel regression {{cite:b3eabdcad9d97f1254922ace1632ce3c4a67fcd4}} are generally not statistically consistent in fixed finite dimension {{cite:9a056e7a834a2d52d859ca4ac18e106a3f679138}}.
| i | 125d8ffce1c88f11446b08e83b88fc48 |
and
{{formula:600ae26c-d1f1-44bc-8882-4d4f1e01c7d6}} . By the definition of the minimal operator {{formula:77054a66-b93d-4455-8ad0-6f0f00476302}} , each vector {{formula:7f910226-f45d-47b5-a2ef-c2ca12a85594}} is approximated
by finite vectors {{formula:38c43f5f-a182-47d8-b21d-f4429e1b4cc2}} in the graph norm of {{formula:832ccbd1-e028-4647-98f0-b99957dd6e84}} .
Therefore estimate (REF ) remains valid for any {{formula:46a4ecd5-b2ac-4d0b-8f00-7cad9e1af5f3}} .
In particular, this yields the inclusion {{formula:900f2eef-682a-48a5-b789-20750f391d5a}} , hence {{formula:c3b6a3fb-541c-4b68-9d7e-b03e36a7ebb8}} .
Since {{formula:146a9e59-ddf1-4969-854c-cbe9bc637c79}} , the Kato–Rellich theorem ({{cite:7470a0199f6b24a88ad7f1cef38c00d12bacf1c0}})
applied to estimate (REF ) yields {{formula:994c8a7b-7b3a-41ea-84a1-c0ac91bc3be6}} .
| r | a754e9328e720638854b251f6c329db3 |
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