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The function class {{formula:53ca0ef7-804c-4510-9c1d-994008832fa7}} in this paper is constructed by the feedforward neural networks with the ReLU activation function.
Some recent results on the approximation theory of deep neural networks can be found in
{{cite:d15c45b5004ff5b0470c78ef35dbdb4df1a3e584}}, {{cite:367351b0bea8b5b9e2ab68bbd5d1534397b99bd2}}, {{cite:8ff1d04885f2296e2f5343b0e1fe31eb906eb642}}, {{cite:dddb3398c0300f1ee799aeba8932acb02eaa4a01}}, {{cite:a83edbeeda27bae8ffbc7c0a7f6f1747e9d82c5b}}, {{cite:152fcf2279a86826413a17da8561f6f4e00953fd}}, {{cite:15060bcd86772e66e952270537386f2e6b9f8792}}, {{cite:5658fd8acfa12d12610d003b7337a1a8b6b14342}}, {{cite:ce0b2b6072b41f2464d4e619e5c75c801b2a7452}}, {{cite:a080f5f3ff05848a1bbb4eb986582a8c354f9cb1}}, {{cite:398e968c9460ae7ede8dad097abd474f56b33349}}.
| r | 5129fe8a4451725a8b44c0fc08917b27 |
Lemma 4 (Linear convergence of an exact entropy-regularized NPG, Theorem 1 in {{cite:22afd7451b0a0f8cbec1fb223da2347088b71b21}})
For any learning rate {{formula:07ce353e-ffca-410f-bdde-a37764f2ba6b}} and any {{formula:d498d54d-d950-4b2c-b2e2-908c7cd4e46c}} , the entropy-regularized NPG updates satisfy
{{formula:7c8e64f3-08f6-4074-b387-2559a806554f}}
| r | e46cde520820a833baee7569202eb015 |
In GĂĄt {{cite:5e3576d842fd73c4db71fefd7491e7129d96d269}} (see also Simon {{cite:4bc137d678be00e4756987a0b52ecbc6a3519fbe}}) the following strong convergence result was obtained for
all {{formula:a893e393-75e1-488f-800d-c30aa869f0bb}}
{{formula:fa6f043c-4658-4b4c-84ae-65518333175c}}
| i | b5e67b66c4d0909cefc40657c58963c2 |
It is often convenient to consider covariant phase spaces, that is
to include symmetries along with the space (or space-time) generators.
Noncommutative {{formula:3a297922-1650-4ef6-be04-ea7766ea306a}} -deformed Minkowski space has been complemented with
appropriate momenta into a noncommutative phase space in a number of works.
It has been recently argued that this noncommutative phase space has
a structure of a (topological) Hopf algebroid {{cite:913fc2a5dd6f9d5345e1ed8bdeb48bfa1d0e5dec}}, {{cite:a1ba300d1a6c01ebfc7147a1fbffca55e6c0adf0}} and the
same for general Lie algebra type phase spaces {{cite:fe286bbed7ff0924cb784e9eda8c4c503fc96a25}};
the covariant structure
is however not included in those works.
It is known that both the standard and general {{formula:6fa87014-a309-4caa-ab03-07b39e1ede07}} -phase spaces
have a structure of a Heisenberg double {{cite:8588cf525a0687e86f5bc1315c98d1a5542e1af7}},
a Hopf algebraic generalization
of a Heisenberg algebra prominently
used in quantum group theory {{cite:d372b2c7758ef2d5b32107bc1e951b78ee2a7ee5}}, {{cite:dca43f7c104709ea352614a86a57546bfa06dc82}}.
Furthermore, J-H. Lu {{cite:012cabdf573b13801d96dc075baf79529aa33a29}} proved that
a finite dimensional Heisenberg double has a structure of a Hopf
algebroid. Her description can be generalized to some infinite dimensional
situations, including to the {{formula:1d752293-9037-4eb6-ae2e-d6596213f318}} -phase spaces; the advantage of
covariant phase space description as well as of Heisenberg double packaging
are among the main motivations for this work.
| i | 07fa1e546a0c0e3a80d936c3183990c2 |
Experiment Setup & Implementation Details.
We used two-stream I3D {{cite:d6473854efc3e16e56764ce8bb451c981b99653f}} for feature extraction, yet increased the stride of the sliding window to 16. Following {{cite:b0a02fabc984f384e2bf3d8d5fb97a0401cf664d}}, {{cite:b52c75290d9accd25dc89828f102398cdbc105b7}}, {{cite:28406126acbb1722ec9e5e06437981efd424f1ac}}, the extracted features were downsampled into a fixed length of 128 using linear interpolation. For evaluation, we used mAP@{{formula:5f1b68ea-2bfa-4b1d-aee6-23e07f07ef1b}} :{{formula:d52d8fa1-8b14-4192-891f-6b66ddbdf7e5}} :{{formula:55b6b150-d96e-4f9d-b470-5966d7354940}} and also reported the average mAP. Our model was trained for 15 epochs with a linear warmup of 5 epochs. The learning rate was 1e-3, the mini-batch size was 16, and the weight decay was 1e-4. A window size of 25 was used for local self-attention. Moreover, we combined external classification results from {{cite:5d775ddd2115278049283f4be4c70305bb62a7bf}} following {{cite:39d82c6c293988382ebc62921cff3c30f639f030}}, {{cite:28406126acbb1722ec9e5e06437981efd424f1ac}}, {{cite:200fdd98e629ca7ed3c8a91424249a162fc64ad3}}, {{cite:98949f04ec927b5de4a3a178403b8bb186f04e3a}}. Similarly, we consider the pre-training method from {{cite:00064fee402ff6ed2be523de03093636b037f02f}} and compare our model to the same set of baselines, including our close competitor of single-stage models.
| r | b0bf7432880d90f05d216d70fe5c8b38 |
The second line of work targets a large collection of unstructured text (such as Wikipedia) {{cite:c8c956ad1b0715d5241a66a0ea366e253fe9104e}} as the source of answers.
While the unstructured text is infinitely varied, open-domain question answering from text (TextQA) has advanced greatly in recent years {{cite:91a4fa5a6677050be03fc2bb30b74aafbe2212ba}}, {{cite:3bf826a66eaefa6a3fa503b0981fcf92eb524d02}}, {{cite:d7c722095f3423f3d46881194a4bb14db6a31c53}}, {{cite:dffb3f3cf78b1a3c6a4a9fb82785f2b6dd22d393}}, {{cite:fe6f265dd2f4ac58e24b3a1e1fcb9c35b93c5d2f}}, thanks to recent advances in machine reading comprehension and text retrieval.
| i | a456f6c7886ba87176502df56bd4fd1e |
Local Navigation Policy: Once a frame has been associated with a scene the policy is used for local navigation. Images are matched using graph neural-network based feature-matching {{cite:2da7f0fd69f063dde0b0f3d47aaad6ee1a452624}}. Intermediate images are said to have been identified when the matching score {{formula:2b45a42a-cbb9-4a66-9977-7593200b16d4}} calculated as shown in (REF ) crosses a pre-defined threshold {{formula:0f3bee24-1bbc-40e6-9e0a-c3ffa6138c31}} . The intermediate goal image {{formula:e447a790-cfb9-4c64-b487-6040d267e5be}} , is said to have been reached when the gradient {{formula:ea9075ca-6f52-4d02-a669-bcae9ea16853}} , of scores generated based on matching the current frame to the intermediate goal image {{formula:0f0324ed-6d18-4165-8779-6a3d688342b7}} turns negative and the product of the instantaneous matching scores and uncertainty measure of inference from RoomNet {{formula:08b9385b-8677-4cda-93b5-1f1b49607e67}} , over a moving window of {{formula:f68b2bd5-3154-440b-b795-40a00a4b807e}} previous predictions, drops below a threshold {{formula:728d1704-7580-4225-9765-963571368d22}} .
{{formula:4f4d27cf-23f5-4945-aa2c-6ff9e21fd03e}}
{{formula:2ec66f71-241f-4c64-bfb6-b6aaa0c9bfd5}}
{{formula:fa6ea8c1-5f56-4dbd-99fb-772bb3fe9738}}
{{figure:7128da00-5124-47c0-86f3-bfbf43934ff7}}{{figure:55374196-3531-4eed-bd79-6a2a7de2c07a}} | m | 3b1d1ca56beee69bbb10a4474dd815b4 |
with {{formula:30608ee7-9289-4713-bc87-63133b107da7}} carrying {{formula:18718954-b18b-458b-af3b-0ec5db3752c3}} and {{formula:183703e5-80fc-4a28-aa3a-22b9cc4d9e85}}
favored to carry {{formula:66f960c3-dde3-45b4-9768-30c4a4cd7d35}} . The masses of {{formula:0bed56a6-feed-4388-bbcd-ebeb8e5b2d20}} and
{{formula:c240f14f-6cfc-4a0a-973e-db77ac9f49b4}} are compatible with them being the same state, but
their measured widths are wildly different. For the purposes of this
paper, we assume that only a single light {{formula:538f57e8-5ea6-4fcb-80f9-78a5e880bff9}} state exists near
4.0 GeV, the discrepancy in width measurements perhaps arising from
effects caused by interactions with the nearby charmed-meson
thresholds.This opinion is not universal. For example,
Ref. {{cite:df1e37d79c3db1651ab6479bc0210f53e7436137}} treats {{formula:79767647-894d-4851-9ade-e890c36faf0e}} and {{formula:1ac50e4e-a1ea-4d8e-a8e4-49d10d6f1bf0}}
as separate states belonging to distinct SU(3){{formula:993d8ca0-c31f-4048-a559-9f8dbb4350cd}}
multiplets. LHCb also observes a baryonic
structure {{cite:3b5262e6578a33f332bda1a7353c0dc6629de5f0}} {{formula:1f71204c-9e67-4d14-9a07-a6f084570451}} decaying to
{{formula:e1421ff2-5a02-4af8-ba72-d2ed00cc70cf}} :
{{formula:99b720c9-9cfa-4307-9e94-b7313677b7b0}}
| i | edb050cf3ed6dc40f2840420652e3533 |
Private information retrieval (PIR) is a communication protocol presented in seminal work {{cite:4ee0c524b2b211c34fb7b3709d597df79273aeb3}} and is devised for the secure use of information stored in databases. In the PIR problem, a user wants to download one of the messages from multiple databases. A user sends queries to the databases and needs to hide what message is being downloaded from databases. Recently, Sun and Jafar {{cite:5cbbfb3a87621f0393d5f6038a41b5ba375b48e3}} characterized the information-theoretic capacity of PIR and presented a capacity-achieving scheme. Since then, many studies on PIR have been actively conducted for diverse assumptions and environments {{cite:042abcefcea84178dd0e9c88d1fbe81d8486b4e4}}, {{cite:3bfadc68836282ff507864c2a5757eb5b1c1ec5a}}, {{cite:30c04be68d51748ee96d856d01da661710fe0c2b}}, {{cite:244ffd923147cf44208c0e3cb8bfee423f0af502}}, {{cite:dc67cb30b70c76204b01f366963ee18212e8dd8a}}, {{cite:5198ba66df9858ea511ffcc0d2ae88c5b63ce79f}}, {{cite:3212ec45a499661b404f30b0d3e9d1c1f971bc40}}, {{cite:962caecc1a60f6f8e8bae959ca37493abf607bf5}}, {{cite:b1cbacd27e3a5817a021933aba350fc6694acf64}}, {{cite:180885f228a8bce7759b5654b7c2c3359a88ffbe}}.
| i | ca95b9e24b60db2079e9bcb85a9a1b72 |
Policy gradient methods {{cite:6fb83a96586c47f3c7839f21aad1f9681f8d1802}} are a popular choice for a variety of reinforcement learning tasks. Suppose the policy {{formula:168361e6-5306-439b-b65f-954356f8eb9f}} of an agent is parametrized by {{formula:7aecf977-fc78-4343-a0b4-5f7d6d5fd1f0}} . Policy gradient methods aim to maximize the objective {{formula:f4181039-c1d0-4250-8d78-dd4449873752}} by updating the agent's policy steps in the direction of {{formula:d88534ea-dee4-4a5f-a14c-da5b49fe7954}} .
| m | 98fb1d39db5d2924ce904b2c37837014 |
Generative methods learn to generate new data with similar distributions to obey the distribution of the observed data. With the ability to learn latent representations, the auto-encoder (AE) {{cite:99d2875de197253aab2c9a1c7baeb7d94fe90e12}} is widely used. Vincent et al. {{cite:03e97aed3cf16086c63a39ea18ab63da22a79d40}} extracted features with AE based on the idea of making the learned representations robust to partial corruption of the input data. Kingma et al. {{cite:752bc4760a8414ca9a3e955573b68708e247b9e7}} designed a Variational Auto-Encoder (VAE) to infer and learn features with simple ancestral sampling. Besides, inspired by the residual connection network {{cite:78a5261fd48f4ed11076d7e6368725d9ef8a8f6f}}, Tran et al. {{cite:e3afec78ee667b27e0bd64868872c6a78a24f3a8}} proposed a Cascaded Residual Auto-encoder (CRA) to impute data with missing modality, which combined a series of residual AEs into a cascaded architecture to learn relationships among different modalities. As for the Generative Adversarial Networks (GAN) {{cite:a6a3871fb4a698206bc6373dad96838c42e12084}}, Shang et al. {{cite:e0d1e9e3cc2d0543259b83d167584b3b359d5e26}} treated each view as a separate domain, and identified domain-to-domain mappings via a GAN using randomly-sampled data from each view. Besides, the domain mapping technique is also considered to impute missing data. Cai et al. {{cite:20025419724af00a4e4683f663ca686bdc16a0f8}} formulated the missing modality problem as a conditional image generation task, and designed a 3D encoder-decoder network to capture modality relations. They also incorporated the available category information during training to enhance the robustness of the model. Moreover, Zhao et al. {{cite:87151bf424185085913799b85af9d188e69610be}} developed a cross partial multi-view network to model complex correlations among different views, where multiple discriminators are used to generate missing data.
| m | 222a354d05f5899786723ec18bcbd25c |
The class-wise vulnerability of the SI {{cite:66d73a79cb88288eb6b5dfe3d86457e1fe7cb7b3}} against the FGSM, PGD, and CW {{cite:cceff7ffb4d3b29c215d08507950b6a5e69f61c6}}, {{cite:c3fccf0ff9253b92c42d2bf0bfc9f109ecfd1a1a}}, {{cite:3519d381d3816b9d84b2d65e2bb04bb34bae094c}} adversarial attacks under Task-IL setting of continual learning is depicted in Figure REF . The first and second row depicts the class-wise vulnerability of the SI against FGSM. Similarly, the third and fourth row shows the class-wise vulnerability of the SI against PGD, and the fifth and sixth row presents the class-wise vulnerability of the SI against CW. The first sub-figure in rows 1, 3, and 5 presents the SI average performance under standard evaluation of continual learning. The degradation under untargeted adversarial attacks is depicted in the second sub-plots in rows 1, 3, and 5. Furthermore, the following sub-plots show the decline in average performance as a result of targeted adversarial attacks. The headers of the sub-plots bring attention to the targeted labels. The x-axis represents the task number while the y-axis shows the average accuracy over 10 runs.
{{figure:644d34cd-8192-4d88-b093-020c3d6d7ca0}} | r | 1d95faec8bb16ea5caa6b317f5e8ab3b |
In this section, the numerical results will validate the performance of our proposed scheme. We assume that uniform linear arrays (ULAs) are deployed at the Alice, Bob and Willie, respectively. In contrast, HR-RIS uses a unified plane array (UPA) with {{formula:3fae5b47-16de-4f9f-9a11-fc093c4c6d22}} elements. Furthermore, assuming that there is a half-wavelength distance between Alice, Bob, Willie and HR-RIS arrays. We consider a two-dimensional coordinate system, Alice, HR-RIS, Bob, and Willie are respectively located at {{formula:328c8641-f75d-4ebc-b770-e12b5fe080c9}} , {{formula:737c8a9a-584d-4b97-8834-fc045cf509a9}} , {{formula:18bb5395-3a5d-471b-99bb-31e106b0d5b0}} and {{formula:255444b1-197f-4ef9-8ea0-0f47dc028267}} . All channel realizations are drawn from Rician fading. The path loss of a link distance {{formula:809d607c-b1ae-4c41-be1d-9224c5a15487}} is given by {{cite:f3fbed596678a924b990ac566f5c38c9c5ae4085}}, {{cite:bfa55d5edfb28b5e091b909be35adb4bc83eeebc}}, {{formula:d01b3abe-2730-45b5-a9be-f860477fc495}} , where {{formula:b3386776-0ea7-4806-994c-f09fcbd8fd96}} is the path loss at the reference distance of 1 meter, and {{formula:d17d0191-1417-45a4-a0d2-ec7e2a880e60}} is the path loss exponent. Specifically, the path loss exponents are set as {{formula:fa7dec95-1737-4ae1-b1f2-6d8ff7e236c2}} , {{formula:36fbacb8-32bc-4b26-a081-9eb83e7d58b5}} , {{formula:c31fb571-7cc8-4b0e-b309-d8ad49373ab3}} , {{formula:3547afd5-10a2-4aac-ae35-b13215e786f5}} , and {{formula:890ea206-ced9-4b59-8cab-caa10d894abd}} .
{{figure:c8f18668-1cfc-49cc-ba60-f38cda7b2e76}} | r | 89b85f8e36ad25c275e963272c6cb7f2 |
The result now follows by Lemma 1 of {{cite:1f45f0c0ebe1badd3d2cbd3f2d6c489fca0ee005}}.{{formula:52b50034-26aa-4e94-9629-700d39e9e076}}
| r | 98b39e4928a7d2290351208479a38c15 |
The premier promise of holography is to uncover universal phenomena at strong coupling, and explain these phenomena in a qualitative manner. Several such examples are listed at the end of section . We should ask whether there are similar examples with magnetic fields. The answer is in the affirmative. One such example is inverse magnetic catalysis. As discussed in detail in section , improved holographic models generically exhibit this phenomenon for sufficiently small values of the parameter {{formula:1d1540e1-90b4-4b59-a0fa-1d4bef23d9fd}} in the {{formula:0a41582d-c733-483c-81e3-19c845e61ab3}} potential of the DBI action. Interestingly, for larger values of {{formula:278ff388-b4e8-4f64-850f-a56323467c4d}} for which IMC disappears, the quark-anti-quark potential profile also becomes unphysical. This is an example of how holography can relate different phenomena in the same theory by requiring overall consistency. The model also points toward a possible explanation of the IMC phenomenon by relating it to backreaction of B on the background geometry, which was suggested in {{cite:3d751630305e077ff7154b733716596d55b79a98}} as the holographic analog of the “sea quarks” {{cite:ccdbbaa0a7d7dcb214c1ef303e027e3e683deed4}}, {{cite:5f93ea0a5dbf49b51ba539c50bcf89673ef6eb3e}}. We did not cover here another universal feature of the holographic model, that the chiral condensate tends to decrease in an anisotropic state even in the absence of B, called “inverse anisotropic catalysis” {{cite:1533076fa2b727f6d266610b420dea7a32d6a342}}, {{cite:250b5d1e0980d9d28369d8e42401b8ba44de6ae6}}.
| d | 7f8841f78f79d49b1fd1e4c992015efd |
black
Figure REF illustrates our evaluation setup using the cycle-accurate NeuroXplorer {{cite:9d08cc4537c761d9d157616e20f448095285e24a}} framework.
This framework is validated extensively against the DYNAP-SE neuromorphic hardware {{cite:465b014c6c865330af82311eac958d270d48d2f6}}, {{cite:0dbab28aa0e554f00f73ca4017d7bc927d286cb3}}, {{cite:f2cfd68f7d263057d0e9cff6925f77c1a32e657b}}, {{cite:e7e25bec95b0212066be3c2427d7e641e0c6bdab}}, {{cite:86ef769c06a9789e8d38eb6d3ea177fc42c80c90}}, and can model the architecture of other neuromorphic hardware platforms such as Loihi {{cite:6b189e18bf975eebea27f20bd39301de294ee235}} and TrueNorth {{cite:a0d28d8da61c87dc5b17bf268b1762671f9abe0c}}. NeuroXplorer
can simulate multi-compartment neuron models and 9-parameter Izhikevich and leaky integrate-and-fire (LIF) spiking neuron models. Additionally, NeuroXplorer can model Non-Volatile Memory (NVM) synapses such as Phase Change Memory (PCM) and Oxide-based Resistive Random Access Memory (OxRRAM). NeuroXplorer also models the spike delay on the shared interconnect as well as the delay in propagating spikes through the synapses of a crossbar {{cite:9d08cc4537c761d9d157616e20f448095285e24a}}.
The mapping and scheduling results obtained using DFSynthesizer are used in NeuroXplorer to estimate energy, accuracy, and throughput.
{{figure:e53a4026-6085-4df7-8692-24e06799e8a7}} | m | 1f467b01df7960b5f9470b01e8130a9d |
Datasets: We demonstrate the effectiveness of the proposed model in two open-sourced dataset and one private dataset: ORCAS dataset {{cite:5cf515f03c23f451e6bd152e7095cee63a241a81}}, Yandex click dataset {{cite:025fd9208dfa078e2a89a941952ac23c4255e1d3}} and the real interactive dataset from a large e-commerce website (https://www.homedepot.com/). ORCAS is a click-based dataset associated with the TREC Deep Learning Track. It covers 1.4 million of the TREC DL documents, providing 18 million connections to 10 million distinct queries. The Yandex click dataset comes from the Yandex search engine, containing more than
30 million search sessions. Each session contains at least
one search query together with 10 ranked items. The private Interactive Dataset (RID) is a 3-month search log. In this dataset, the users normally search for several queries. For each query, the search engine returns a list of products and then the user can interact with the results by clicking, adding the items to the cart and ordering. Table REF shows a sample of the data. Additionally, with the products' ID, we can further find the page of the products and extract the text features. The features list can be found in {{cite:820a8ee811535af75501ee06f4a1705d22eacef8}}.
{{table:53d09fc5-9428-4ed1-bf19-bdafa395955b}} | d | aa48ce46a4a915de54ee12383e6be9c4 |
In this work we introduce valuable new methods for studying deep reinforcement learning, and use them to discover new results about the optimization characteristics of popular RL environments. Reward surfaces provide a useful overview of the reward structure of an environment. Loss landscapes have already been used in debugging tools for computer vision tasks {{cite:44cac719890be5ffd9903437c932c73ef4d65a91}}, and we hope that reward surfaces could be similarly useful in debugging RL systems. In particular, the reward surfaces for sparse environments allow us to see large regions of flat rewards, and extreme evaluation noise at individual points. Gradient methods cannot optimize flat surfaces, so solutions to this problem are constrained to either modifying the reward structure (e.g. curiosity or bonus-based exploration methods {{cite:9779606f40a61fef71284b8415fb105c7f6a50cd}}, {{cite:b55016a4e79bddd76d943d885c52ffb4afe39adf}}) or condensing the action space such that simple exploration methods are tractable (e.g. DIAYN and related work {{cite:48e854c1151ef74326ca96e32fed149fb053c3cb}}, {{cite:8f452ea9b24eb40f5186cef194ffb771fb0e8d01}}).
| d | 71ccf493add1d01a4e5417e34e05c214 |
We refer {{cite:096193f4de577fdffe415af5729a300240907c96}} for the proof.
{{formula:935062e6-4f42-437d-8009-9253b3d43177}}
Lemma 4.2
For any complex number {{formula:5d31c7eb-08f3-4bff-8848-5a8986789491}} , we have
{{formula:e3b8d886-83e5-47ec-ad19-eaf9b259956e}}
This is the duplication formula for the gamma function. The next result gives an important bound for the inverse of the Dirichlet {{formula:ef69f43f-065c-4b6b-8ea6-7e07a3290253}} -function.
Lemma 4.3
Assume there exist a sequence of positive numbers {{formula:d2fbce3b-aa9f-4949-9420-1291dcf27f3c}} with arbitrary large absolute value satisfying {{formula:f6aab711-122c-4a68-a09a-d996cca85ec6}} for every non-trivial zero {{formula:054d4500-a979-4ce9-bf7e-c51ab5262d38}} of {{formula:15a90659-549b-4749-a49b-cbcfa347821b}} , where {{formula:cb42a53e-8062-4edf-bd9c-6d5a6a63ecae}} is some suitable positive constant. Then,
{{formula:e951bb96-cd74-4f4c-9236-c31c84a2682c}}
for some suitable constant {{formula:0440de66-acdc-4e2a-87c4-d6dcbaccda30}} .
| r | 7bf765150b3f5d60451446575ea2b7a8 |
This paper takes a different approach to {{cite:3afb8b5bce22091852481700bef9d3e0d28153e3}}, {{cite:bac827f4dc0a851322c705fb2e24523f2ee61946}}, {{cite:a8ab0ca41ad9917ea7874ff776cbe1c2daaed904}}, {{cite:5fd6d69e5c4463a7612fe60e23534eb9a525cd81}} to establish an achievability bound that applies to finite block length codes. The contributions of this paper are summarised as follows. Following important preliminary details in Section , Section revisits the implications of the LPD constraint on the input signalling density. It is shown that the LPD constraint can be recast as a constraint on the chi-squared distance between the densities of the adversary's observations conditioned on transmission and no transmission, similar to {{cite:3afb8b5bce22091852481700bef9d3e0d28153e3}}, {{cite:bac827f4dc0a851322c705fb2e24523f2ee61946}}, {{cite:a8ab0ca41ad9917ea7874ff776cbe1c2daaed904}}, {{cite:5fd6d69e5c4463a7612fe60e23534eb9a525cd81}}, but without using Pinsker's inequality {{cite:edc8afebeedbde82366892c1f07a56cef141adcc}}, Taylor series expansions or bounds on the natural logarithm. Using this relationship the spareness factor, defined as the probability of sending a non-innocent symbol, is derived in terms of the block length, LPD constraint and chi-squared distance. In Section , Gallager's error exponent {{cite:11fbee22b2a064948960bc31fc47f42d267b189c}}, {{cite:bc286965acaedcf496ea6c7c68f98dcfb72a76a3}} is lower bounded in terms of the sparseness factor and the exponent of the density of the non-innocent symbols. Combining this result with the constraint on the sparseness factor, a finite block length lower bound is derived on the number of bits that can be transmitted with non-vanishing LPD and decoding error probability. Interestingly, in the finite block length regime the bound indicates there is an optimal block length that maximises the achievable information rate (bits per channel use), i.e. the achievable rate increases with {{formula:96f2200b-6a61-41e3-a04e-0e1fe488ae1c}} until it reaches this optimal block length and then begins decreasing at a rate proportional to {{formula:ad4bb971-0d94-4bc9-bed9-a674a26cd580}} as a result of the SRL. In the asymptotic large block length regime, the lower bound can be written in terms of the mutual information of the Rx's channel similar to {{cite:bac827f4dc0a851322c705fb2e24523f2ee61946}}, {{cite:a8ab0ca41ad9917ea7874ff776cbe1c2daaed904}}, {{cite:5fd6d69e5c4463a7612fe60e23534eb9a525cd81}}. In Section , the utility of the finite block length achievability bound is demonstrated for the well known binary symmetric channel (BSC) and AWGN channel {{cite:24e1632a20580d4869530f6bbc484f8785554beb}}.
| i | 7a2422063b451c954d82a0a27897af89 |
In addition, the main challenges of diagnosing TB with chest X-ray images include the low visual contrast between lesions and other regions, and distortions induced by other overlapping tissues. Sometimes it is difficult for radiologists to recognize obscure diseases.For CTD, previous methods mainly concentrated on disease classification {{cite:b6625ab53f111c5779ebca6ec14ae77b46a072b9}}, {{cite:7f071452c188308059d4f823fdbd9fb65a0542e8}}
, and several recent works have taken a step forward to detect disease regions under weak/limited supervisions. They can be grouped into two main categories: the first category {{cite:3125cea0ba548e6f6f6b0c1b3521517e038cc436}}
resorts to convolutional neural networks (CNN) trained on the classification task and output disease localization results through calculating the category activation maps {{cite:fa273127ced086874af17b5ea66ceb6a6702e81d}}; the second category {{cite:0ff69abb6a2d045834b883a45620c94c07633323}}, {{cite:63c8c55aac42ea4de87a8863d00e7d735205b070}} uses the multiple instance learning to directly yield categorical probability maps that can be easily transformed to lesion positions. However, the performance of these methods is still far from clinical usage. Effective WSL algorithms remain the boundary to explore.
| i | 3d30c8cadda4ae5d659f218fa0bc9bb4 |
Comfort loss (Comfort): the mean comfort loss value for a chair generated given an input body shape (in kilopascals; lower is better).
Poss loss (Pose): the mean pose matching loss value for a chair generated given an input body shape (in centimeters; lower is better).
Frechet Distance (FD): the Frechet Distance {{cite:a662351a99b386d664770ff7b826bf8712f0b3aa}} (evaluated in the feature space of a pre-trained PointNet classifier {{cite:475868eacb2e394bd39a18efcaf4144424fd1837}}) between a set of generated chairs and a set of chairs from a held-out test set (lower is better).
| r | 0967867ce7ca84fc7dd1d9d19d32d726 |
Lemma 3.3 {{cite:96252ac4943d9fc043a0de79c212a10b2b1c5ff9}}, {{cite:e491596df8bccde99d89c9afb58943ad3e157f9b}}, {{cite:d6fd4d53da71b31d70900cc748bf6450a3463772}}
{{formula:868a52de-fb5a-4804-ba49-c24d890d55a4}} ; {{formula:cc4c6b39-f9bc-4773-b59f-cb7190c30977}} ;
{{formula:a9110b62-31c4-41cc-9853-8cc993f6724f}} .
| r | b6f63945a17ab0d4e1dbf261e42508f8 |
Let {{formula:8e575dc6-9c3b-4c36-a0dc-eba71f6d3717}} be a kernel, {{formula:0ed2ea1c-82f7-4887-8743-f3d6472ac5fb}} the corresponding RKHS and {{formula:fb8e1644-608b-4a2f-bc57-c49404c97f18}} be paired observations. In Nyström KRR {{cite:d6f3cad9ca0b75246b1c79ade0b5c42e6d2eb448}} we seek to minimise the empirical risk over a finite dimensional subspace {{formula:f2cffb7d-25a5-4069-b3a4-8f3f819cbced}}
{{formula:43a22ed4-4c5b-4f59-a398-1c814957b129}}
| m | a3f59035f4112ec56806325bdb34b2b4 |
In this study, we replace the hidden layers of the MLPs (see Fig. REF ) by the NODEs (see Fig. REF ). The input layer and output layer are the same as in the case of the conventional MLP-based EDMD-DL.
Also, the parameter update scheme shares the same idea as that of the original EDMD-DL {{cite:11d25439264cee357825bed0fd6a2420bfe67108}}.
Algorithm REF shows how our proposed method is performed. The hyperparameter {{formula:d388c4af-7701-4764-99b2-f35c4281cc0c}} is the tolerated error in the finite-dimensional approximation of the Koopman operator.
| m | 0e0be7b6953665b42366a09efa1b8941 |
There have been many recent advances on the theoretical properties of sampling algorithms for approximate inference, which changed our interpretation and understanding of them. Particularly worth mentioning is the work of {{cite:427f9e67737a71639cd345c3a67b28eddb82ccfd}}, who reinterpret Markov Chain Monte Carlo (MCMC) as a gradient flow of the KL divergence over the Wasserstein space of probability measures. This new formulation not only allowed for a deeper understanding of these methods but also inspired the inception of new and more efficient inference strategies. Following this direction, {{cite:fc88373647b80bdaec6eecbeb9dc74bdef5b47de}} recently proposed the Stein Variational Gradient Descent (SVGD) to perform approximate Wasserstein gradient descent. This method belongs to the more general family of particle optimization variational inference (POVI), where a continuous density {{formula:0ad42ff8-dcbe-4ab1-9247-3b5c4fa22e37}} is approximated by a set of {{formula:54c4edca-cef9-41aa-b276-34f2c6ee6aae}} particles that evolve over time towards the target. However, a solid understanding of its behavior in the finite particle limit beyond the mean field convergence analysis {{cite:63d4f2015338fd66be2e84462267a85d5854fe7a}} remains elusive. What is more, there is empirical evidence that SVGD suffers from a degeneracy that compromises the particle diversity under these conditions, making them collapse to a small number of modes {{cite:486948cdc5b6768004fb61db64ea6a85b928f1d6}}. In the following, we discuss how an annealing strategy can significantly mitigate this issue, encourage exploration of the significant modes, and yield better samples from the target density than standard SVGD.
| i | 8805ebe88bb5422cacf2cdbf901f985b |
The total transverse rapidity of the {{formula:c2da7216-1102-4e6a-804a-a0f2b8333497}} th azimuthal bin is the summation of all particles' transverse rapidity in an event, and its average is {{cite:ba44e304cf0f7c5c383561aca6e1503d92725d56}}, {{cite:2197f44d75a453d379ccac63d4296dde6137acb4}}, {{cite:8b7c854f849842d28e9eaef9fecd815e6d2bfaaa}},
{{formula:4030d5e1-2c80-4b01-85d8-a7c366cbfaf7}}
| m | 84db59dce60321930d298a6335dd5b21 |
Controllability issues for nondegenerate hyperbolic equations have been a mainstream topic over the past several years, and numerous developments have been pursued (see for example {{cite:26078d72a32cbf2c618f56c3600eca385a67346b}}, {{cite:942cc503fb1a9eb82f3a7e12356ae383b01a7aa1}}, {{cite:69a6e7a4d8953ca739fda0803ce848cb2790ee57}}, {{cite:4307b3c7ca7f9474a4841424ddcc325d8c567aad}}, {{cite:9039c3802fce54bce448106096a452e03122856b}}, {{cite:109ab807cfda30ec92685b84c7fd66110cfe8634}} and the references therein).
| i | 771aaf1cc9a56fd32f0e5a62206b4274 |
Deep-learning-based methods have gained superior popularity in recent years. Inspired by 2D image denoising network DnCNN {{cite:013a7583dba379ffb37b1d4055815c18a081da9d}}, Chang et al {{cite:5d8cf5037c6f4efe5fdd8dc052d090692e1275a2}} proposed HSI-DeNet that learns multi-channel 2-D filters to model spectral correlation. Yuan et al {{cite:039306487c634989e35fc91c1f72ebb2b0066057}} introduce residual network structure with a sliding window strategy for remote sensed HSI. To further exploit the spatial-spectral correlation, Dong et al {{cite:a0141e51a35385d263189a8ea6a1fd140dcdaace}} designed a 3D U-net architecture. These methods have been successfully applied to different HSIs, but all of them lack the flexibility to handle HSIs with different number of bands using one model. To address such issues, Wei {{cite:d2912460acbdef74c16f101d9a4486fbf07e32b8}} et al proposed a 3D convolutional quasi recurrent neural network (QRNN3D), which uses 3D convolution to extract spatial-spectral correlated features, and then adopts a quasi recurrent network to integrate information from different bands in a global perspective.
| m | e1ea4c3ce3080a50454d3404abf0acbb |
Our time-averaged spectroscopy shows that absorbed blackbody model provides a good fit for the burst spectra yielding an emitting radius ({{formula:cae1e83e-4b85-4b98-87d0-da9026eade15}} ) of {{formula:3d41b652-f679-473b-89fb-ed01dbe8fd5d}} 2.3–6.8 km and blackbody temperature ({{formula:7c0c0ab0-8787-4926-890d-2e727e481ca8}} ) of {{formula:68397b21-300f-4c45-a3c1-bd54d692b585}} 1.6–2.0 keV. Similar studies have been carried out by {{cite:25bba282c12c5a85aec910d4a58dda86193927c9}} for 4U 1636{{formula:64d9f6eb-c11f-4de0-88b9-d2ec30541b05}} 536 SAX J1747.0{{formula:bdef5eaa-356a-4dc7-b70c-a1ccd0b0cb0a}} 2853 and their radius and temperature values are in good agreement with ours. However, there is scope for an additional model component such as powerlaw, perhaps due to varying temperatures during bursts or plausible deviation from ideal blackbody behavior. We also analyze using the {{formula:0bfe75d7-baae-41e1-a654-902b0063f690}} method and find that the spectral fit improves. The {{formula:bc4ea9aa-eb8c-4a23-9957-012b15bf5102}} values suggest a
substantial contribution from the persistent emission. Our time-resolved spectroscopy do not show any evidence of photospheric radius expansion {{cite:6dd9333cefc629010ebbc2bedcabb7fab82b509b}}, {{cite:896dcec65d9f90e5d7a2d57897bb1063c35eae75}}. However, we would like to add a caveat that the possibility of radius expansion cannot be ruled out due to limited statistics. In most of the bursts, the {{formula:b5b68933-b24b-4998-891e-78cbd58b1a6d}} values are {{formula:1f79e0d7-c4c5-4d63-aa00-a10d96ff5abf}} 5 close to the burst peak suggesting enhanced persistent flux at this stage.
| d | 6555cff8d7e0afb18130159084d6981d |
Betweenness was extended recently to link streams {{cite:036364996f0bcf5c5e73a4590467d71bde78f3e4}}, a family of formal objects that model sequences of interactions over time in a way similar to the modeling of relations by graphs.
They are equivalent to other objects like time-varying graphs (TVG) {{cite:88208903571737965d2073d6d35c055fd21071dc}}, {{cite:cca69e83758fc7d5d90006de1be8c12311d2463d}}, relational event models (REM) {{cite:cffc6fa4872743ae51b3b3f74e69da3ece40bbef}}, {{cite:21e588c4435e17214ec5f91298c8aebbc605e800}}, or temporal networks {{cite:3a17a28bc5568c274f3f6f442475c299600bdbd5}}, {{cite:86b38451ce74ad4765da673bc0357ba1c3b7b341}}, with an emphasis on the streaming nature of link sequences. Various temporal extensions of beweenness were introduced in these contexts, see Section .
| i | 6a817f1ba02c2d5cee565eab4be1a8e7 |
Numerous works have been addressed towards the task of SISR {{cite:3ebfc21623d3cc9efc516dc2346894a820adbc17}}, {{cite:7011e7b9cf8dfb56e553b60251e6466361e12a96}}, {{cite:43c892b20f39938464bef687d955cf10a82fcbd2}}, {{cite:10d6434c2e87462ad371817992ab32e2de446464}}, {{cite:4d777fde008cc7bc468f83ad2da63cd0d80e95cf}}, {{cite:6d28a19c096094a18d3ce671deede381d3efd31e}}, {{cite:363bd538287af6c407509f53092fb840076d3ceb}}, {{cite:0e1fd1d09add296c80aedd1d3a197e9437fbddb2}}, {{cite:2cea2e4180fa7b238230bac32c679db5fdb9e5d0}}, {{cite:4ea029499938b0c59d13fd38130b7fad79101563}}, {{cite:2feb2801fd796212ceeda3d662139e9918d35872}}, {{cite:bdc6f57c515f81167bc4f5883db0f9bd6a4b7c5d}}, {{cite:b3bd72189a69de7aa6da553dbff08257df9ce76e}}, {{cite:4e81be105bc3697747a0eed5b441aa6e61385c62}} and real-world SISR {{cite:28700e86337a18889f7f794df7c371043ca518af}}, {{cite:03137f269fdabdd5ef202a6b717c559d1ebfb629}}, {{cite:606292efcba60cc98f7c6ecd88e3295888ed293a}}, {{cite:f0380439d33c6cbbcd9a2888f9de58df7a06a14c}}, {{cite:075cff9ee76559b69c281fe985374ba0ecfc7fc4}}, {{cite:04493f4fb218bea8cc41684e2a3e362d1d4b06e1}}, {{cite:ea7cde6c6055c22f0999819329b7f212447558d1}}. Due to the ill-posed nature of the SISR problem, the existing methods have limited performance to recover high frequency details through single image learned priors. Besides the development of the SISR approaches based on single image priors, the recent works {{cite:b8c1835929b972b3b196713f6254ef7fdaeac33a}}, {{cite:19d08e3628433c36df46fd2fdd52315978ee8014}}, {{cite:3d802f5ec2352dafdb4d440c6b0b951ba3a36237}}, {{cite:374def4f5cb3e4bef923a942e55d9929764f6634}}, {{cite:abbc908ed85e10613c1c147952b6c564ba6f7b2a}}, {{cite:6ffb449e6aeedbc4c7f11c46db0b62182e355f33}} have demonstrated the potential of MFSR methods that aim to fuse multiple LR frames to reconstruct a HR output. However, the deep learning based Raw Burst SR methods are black-box data-driven approaches with larger model size, while our proposed scheme (RBSRICNN) has the merit of interpretability and small model size with good reconstruction results as shown in Fig. REF . Our proposed scheme exploits a powerful image regularization and large-scale optimization techniques by training a deep CNNs in an iterative manner to produce the final SR output with an iterative refinement of the intermediate SR estimates.
| i | a1769fa058c94ce52a2e53e5ef16d7a7 |
This paper is concerned with the study of anisotropic Besov regularity estimates for parabolic partial diffenential equations (PDEs). Regularity estimates in Besov spaces are always important since they determine the convergence order of adaptive and other nonlinear constructive approximation schemes for the corresponding, unknown solution. In contrast to this, it is the classical Sobolev smoothness that determines the convergence order of more conventional, uniform schemes. We refer e.g. to DeVore {{cite:89d19e029f9fb3d432c5dbd527b20bdb7dd1c14c}} and {{cite:d0036ccf92895bb5c26088ef014c1f91e3b4eecc}}. For elliptic PDEs, a lot of results in this direction have been achieved in recent years, see {{cite:d0036ccf92895bb5c26088ef014c1f91e3b4eecc}}, {{cite:c0a84617b0605ab3dd34a92ae2b43f22e79b5757}}, {{cite:6c61baacda0576ae78b89bc8daa124efb88540d2}} and many others. In all these cases, the Besov smoothness was generically higher than the Sobolev regularity which justifies the use of adaptive algorithms. However, most of these results are concerned with isotropic Besov estimates which fit perfectly to the stationary character of elliptic partial differential equations. Quite recently, also Besov regularity results for parabolic PDEs have been investigated, see e.g. {{cite:d5544568f3ab0609b8d007f10d97c5d5c2fa19c1}}, {{cite:24b371f8cbc2155c774670aa2861c0f97ebfed99}}. In these works, the authors derived time-dependent Besov regularity in space. In particular, they determine the convergence order of space-adaptive numerical schemes such as classical time-marching schemes for parabolic equations. For good reasons, in recent years the development of numerical schemes working on the whole space-time cylinder has become more and more important {{cite:b0827628004ed73dfe8fa182455e7a6d5d3c6c9e}}. In many cases, these schemes are simply more efficient. However, if we take the whole space-time cylinder into account, then anisotropic structures occur, since we have (in the simplest case) one derivative in time but two derivatives in space. Therefore, anisotropic Besov spaces might be reasonable choices for the regularity spaces. First results for the heat equation have been obtained by Aimar and Gomez {{cite:06e6b2c248252d5e52d2fe723095e05a85907e1e}}. The results in this very interesting paper rely on a certain interpolation technique in scales with {{formula:4edb242d-bdc5-4d31-811b-1d2f87feacaa}} , which naturally limits the applicability of their approach. Therefore, in this paper, we follow a different line: In the meantime, it has turned out that a very efficient way to establish Besov regularity for the solution to a PDE is first to study the regularity in weighted Sobolev spaces, the so-called Kondratiev spaces {{cite:743fceab06d817659de001619da721ff71160873}}. The reason is that very sharp embeddings of Kondratiev spaces into Besov spaces habe been derived. The whole program has, e.g., very efficiently been carried out in {{cite:c0a84617b0605ab3dd34a92ae2b43f22e79b5757}}, {{cite:24b371f8cbc2155c774670aa2861c0f97ebfed99}}. Usually, Kondratiev spaces can be used for a very precise description of the singularities of the solutions. For our purposes, clearly anisotropic Kondratiev spaces are needed. Therefore, in our setting, the following tasks have to be solved:
| i | 6e3facbae23d8e976f99ff1fc54b3965 |
There are a number of avenues for further work. Firstly, one could
apply the SCH operator to different Yang-Mills solutions, and
see what general conclusions can be reached about their possible
SCH groups. It would also be interesting to look at how to
match the holonomy and its single copy in gauge and gravity theories more
generally, which might help in extending the classical double copy to
more complicated cases than are currently possible. Thirdly, it would
be nice if the SCH operator could shed light on
non-perturbative aspects of the double copy. In particular, we note
that the SCH operator is matrix-valued both in colour and spin
space. It thus rotates vectors both in the internal space associated
with the colour degrees of freedom, and also in the tangent space of
the manifold, which is associated with kinematic information. Might the single copy of the holonomy then have something to do with BCJ
duality {{cite:3d2ded75f25487ba36f2402c8d27751a78db3a32}}, which links colour and kinematics in an
intriguing way?
| d | a0dfb053ff7b673e80dad117d5f3c463 |
Multi-agent reinforcement learning (MARL) extends the decision-making capabilities of single-agent RL to include distributed decision making problems.
In MARL, multiple agents are trained to act as individual decision makers of some larger system, typically with the goal of achieving a scalable and effective decentralised execution strategy when deployed {{cite:f9fa394b446c57784d8640050f74346d824d0b76}}.
MARL systems can be complex and time consuming to build, while at the same time, be difficult to design in a modular way.
This modularity helps to be able to quickly iterate and test new research ideas.
Furthermore, despite the added complexity of MARL, it is crucial that these systems maintain the advantages of distributed training.
Often the core system implementation and the distributed version of these systems pose two completely different challenges, which makes scaling single process prototypes towards deployable multi-process solutions a nontrivial undertaking.
| i | 1b5c746fc2164ec51d05da8e3e210070 |
In this paper we have studied the vacuum zero point energy in a black hole background. We are interested in the limit where the Compton length of the fundamental field is much smaller than the black hole horizon radius, corresponding to {{formula:35f62b12-750a-4e5f-8dd6-d001bc58dc59}} . We have demonstrated the validity of
Eq. (REF ) in a black hole background, both for the near horizon and
for the far observer. In addition, we have demonstrated the validity of Eq. (REF ) in the Nariai background as a specific limit of the dS-Schwarzschild background. Our result is inline with conclusion in {{cite:fbb6ac2d85f69292e6e81c045b6d2d7be7320741}} where the validity
of Eq. (REF ) was demonstrated for a general curved background.
| d | 40846499bc57122ab53dc9c3d19d85d4 |
Exemplary {{formula:757d0bb6-ede4-4b5e-9080-a9d5e2b4dc41}} -band light curves the F- and 1O-mode
of a donor-turned-AC model
with {{formula:250a4bad-80b7-485e-8644-dd4559fa2e63}} at {{formula:739fb0df-c6d9-4881-96c8-804bb4b498cd}} , and {{formula:26eb0691-7e28-45cd-b4c0-92615fd524a2}} K.
The F-mode's I-band amplitude is {{formula:ce05632a-1258-4682-a34c-21d0134dca97}} mag, the one of the
1O mode {{formula:3be3d49b-17b6-48f4-ac4a-029c370ec335}} mag. Keeping in mind that no fine-tuning was applied,
these amplitudes compare decently well
with what is observed e.g. in OGLE IV: {{formula:d02c7e20-e4e1-4669-9ef6-2940edad7f2e}} for the
21 F-mode ACs with {{formula:2d85da10-83a9-4521-9a63-9040df8f72e8}} and
{{formula:bdaba048-60dd-4534-b9b0-4d58c6fc78e5}} for the 14 1O-mode ACs with
{{formula:8e02a338-6133-4c8d-9dbc-456bfff9717a}} .
Preliminary RSP computations have been performed on models fitting the
binary scenarios as put forth in {{cite:6c9e8e6611730b2352655b46a9c2a75f647ed40d}} and on envelopes
appropriate for the single-star scenario of {{cite:27ffb634b20ff90f5803e0961ad00273ea84c846}}.
Figure illustrates exemplarily light curves obtained for AC-like
envelopes. The particular case shown belongs to a model star of {{formula:5cf3f634-8743-43ed-941b-e3314ef34ea6}} at
{{formula:1d3e2712-0f35-42c2-af10-0abaa1669fce}} , {{formula:00be3a78-3f4d-452f-bcff-782311675612}} K, and with a chemical composition of
{{formula:fc8edc57-7250-4b91-a6c1-c167ef4e16d8}} as appropriate for the binary-scenario of a
donor-turned-AC case in {{cite:6c9e8e6611730b2352655b46a9c2a75f647ed40d}}. The fundamental mode has a period
of about one day, the (red colored) 1O mode has a cycle length of {{formula:b45be280-ead0-4295-a6d0-f3cfa70a2141}} d.
Asymmetric light curves, with Sk and Ac somewhat enhanced, of 1O modes were
encountered frequently in all scenarios except for the merger model, which was
also contemplated in {{cite:6c9e8e6611730b2352655b46a9c2a75f647ed40d}}. In accordance with the 1O's
luminosity-perturbation node at a depth of around {{formula:3d83041a-9085-4e6e-be4d-42665bf118b3}} K, the more symmetrical
merger-model light curves acquired low Ac and low Sk. In the respective period range,
the computed I-band amplitudes of the 1O pulsations are on the lower side
compared with observations reported in the OGLE database.
| d | aa502bf0ea18d4a9b4196c84a1b79b84 |
Undirected graphical models, also known as Markov Random Fields (MRF), provide a framework for modeling high dimensional distributions with dependent variables. Ising models are a special class of discrete pairwise graphical models originated from statistical physics. Ising models have numerous applications in
computer vision {{cite:45d81d93fcc4a5f62fe9a15f831a578dd357ff72}}, bio-informatics {{cite:c8274b029871a928a075429d4cc8602eed2e9db7}}, and social networks {{cite:505d6325023bba83000b4940b36f45aa7a25c9af}}. Explicitly, the joint distribution of Ising model is given by
{{formula:a67235c9-a467-42c3-98ff-eb0dc72df59f}}
| i | b18261fc6f79fbf6350b974104456c21 |
Transformer-based methods {{cite:4042a8c7b0e10adcc6366ef71c7bc39fb390f81e}}, {{cite:09274bb1d4f87feefdb97db4fa769c79307ba03d}} have attracted more and more attention and achieved great performance in person ReID. For example, the pure transformer-based method TransReID {{cite:4042a8c7b0e10adcc6366ef71c7bc39fb390f81e}} achieves a significant performance boost over state-of-the-art CNN-based methods. However, there exists a large domain gap between ImageNet and person ReID datasets because 1) The image content of ImageNet and ReID datasets is very different {{cite:08545c80993acb77cf67a523cae7e48e5a261a50}}; 2) supervised pre-training on ImageNet is focused on category-level supervision which reduces the rich visual information {{cite:89ebdab3cc7f188539129c8e5c96806191232998}} while person ReID prefers fine-grained identity information. As a result, Transformers need to be pre-trained on a larger-scale dataset ImageNet-21K {{cite:aa0b9c9dd21b48130c1207e462cb73bb0ac689c7}} to avoid over-fitting on the pre-training dataset. To bridge the gap between pre-training and fine-tuning datasets for better transformer-based ReID models, this paper tackles the problem from the perspectives of data and model structure, respectively.
| i | 07fdba2e74ade2cecb33a40b862697df |
For the problem of counting points in thin spherical shells (Subsection REF ) we recover the bound (REF ) of Landau {{cite:e30658afa530d7be39b022923e1099b9d2ca7fab}}, see also the comments after Theorem REF .
The problem of bounding {{formula:4f6c865e-b93e-461a-afd6-f5b441d6ae2e}} norms of eigenfunctions was prevously considered for rational tori, that is {{formula:e6bf5908-a53e-476d-8f21-86445cfac9a0}} where {{formula:1c06508b-f42a-4440-97cb-b322b8c46fb6}} . Our results do not improve the bounds of Bourgain-Demeter {{cite:b34895c7cbc76ab173e65a436d338bc45d8133f1}} in this case. For generic tori, eigenfunction bounds are trivial; the natural analogue of bounding the {{formula:a47e2a81-cb50-47c1-84a0-d5376df73c64}} norms of eigenfunctions is to bound the operator norm of {{formula:0114b4bb-c824-4bc7-9c22-9c0c83abf57f}} , and this question does not appear to have been considered before. For any torus, that is any {{formula:26143714-d5b3-422a-b6e1-e337a0730ba0}} with {{formula:016980cb-21eb-4057-a68c-2ce4d69821dd}} , we obtain from Theorem REF below the bound
{{formula:94fed37b-660c-4eef-a3e2-5b0a8f60caa2}}
For the problem of proving uniform resolvent bounds (Subsection REF ), it proves the desired estimate up to a subpolynomial loss
{{formula:b740dd5f-029f-4266-82dc-e08a97b12347}}
if {{formula:255c5507-dd10-4b7c-9d46-4c06bea9c5de}} ,
or if {{formula:5ab3bc38-bbb3-4e82-82b9-f1756e9132a8}} and {{formula:5ec70c7c-8f86-4e17-a999-68250aa0847a}} , improving over Hickman's {{cite:778128f5d362425d1947ae16755863dc34ebc105}} result that {{formula:6bf0e82b-9e40-45a2-8cd1-3a224a316a68}} .
| r | d86c264f941d6fcc394d7ebca2194ad6 |
In this way, one can think of Inflation and Quintessence as of the two different sides of a coin or, after the introduction by
Peebles and Vilenkin, in their seminal paper {{cite:80a3650d98119ff6d6887037a1bf3c471320ace0}}, of the concept of Quintessential Inflation (QI),
as just a unique kind of force, which describes both inflation and the accelerated expansion.
The idea of a unified picture of the Universe connecting the early and the present accelerated stages is possible,
through the introduction of a single scalar field, also named the inflaton, as in standard inflation, which at early times produces inflation while at late times provides quintessence.
| i | 79514857714c7c77419847ad95dfe595 |
Markov-chain Monte Carlo (MCMC) techniques, reviewed in Section REF , draw parameter {{formula:43a68f99-bf33-4b47-9824-4b895ff00187}} samples from the posterior by using a Markov chain with {{formula:4d90a826-b39a-479b-a003-d43f8e68a47d}} as its invariant, i.e., stationary, distribution.
We employ two such methods, namely Hamiltonian Monte Carlo (HMC) and Langevin Dynamics (LD), in the comparative study of Section .
Variational inference (VI) techniques, reviewed in Section REF , approximate {{formula:f7aaa97f-ef24-4217-bb63-7d873a8a4291}} by employing a variational distribution {{formula:f3f07ffe-aec6-4e30-910e-de0981f5c999}} parametrized by {{formula:91fffbb1-2105-4642-af6b-754cc50a2152}} , that is optimized by maximizing a lower bound of the marginal likelihood of Eq. (REF ).
Mean-field VI (MFVI)
utilizes a factorized Gaussian variational distribution.
Monte Carlo dropout (MCD), which is reviewed in Section REF and can be interpreted as a special case of VI, first requires standard training with dropout {{cite:8ab9e4a27b95275e78735fe87977c3561757d13f}}.
Subsequently, at inference time {{formula:21ab9a44-7067-4da4-8c1e-bdd27f7b8570}} samples are drawn by randomly dropping for each sample a fixed percentage of the NN parameters.
Laplace approximation (LA), reviewed in Section REF , involves standard NN training, and subsequently fitting a Gaussian distribution to the discovered mode {{formula:37b1cb11-cd20-4782-b44f-d7ccdae02ab0}} , with a width determined by the Hessian of the training error.
| m | 7766edba6323f12f3793357f74da8f9f |
Aiming to enhance the performance of QKD systems, it is essential to develop ultrafast clock rate QKD devices capable of delivering high secret key rates for widespread applications. However, even for GHz clock rates, QKD transmitters exhibit intensity correlations {{cite:dd938b334febac7e87b531bf0316b68e60af8237}}, {{cite:d6caf618d980e202e449ab00441c80c497e07f5c}} that invalidate standard decoy-state analyses for parameter estimation. As opposed to many other source imperfections, only limited solutions were known for this security loophole so far {{cite:d6caf618d980e202e449ab00441c80c497e07f5c}}, {{cite:a01419c2b721879809a624732b4dc0a68fd1f45b}}, {{cite:37ef97fd83eb3ce5953e024fa7e142c5b4755d58}}. In this work, we solve the problem by quantifying the maximum effect of intensity correlations in the security of QKD. For this purpose, we introduce two experimental-friendly security parameters that allow to characterize arbitrary correlations in the intensity modulator. Importantly, our technique builds on a result that we refer to as the Cauchy-Schwarz constraint (recently used in {{cite:cde1f5389b2b6e068de5c9f42fe3a6cf274c50d6}}, {{cite:d20b82229cc517891089404a797d3bd5a0a4dac3}}), which provides tighter bounds on the indistinguishability of non-orthogonal quantum states than the well-known trace distance argument {{cite:ef30d8a5f6f4661ba724de2ee9f59ba7a7a7308a}}.
| d | 52abf78ea056267def7c03de3bc3afaf |
The only long-lasting foray into classical measurement seems to be the body of work surrounding Maxwell's demon and the foundations of thermodynamics. The demon was first conceptualized by Maxwell in 1867 {{cite:e4cb2eb5e1cd8baa01905ab651729d8f55d7c736}} as a “very observant and neat-fingered being" capable of monitoring the molecules of a gas, and, by opening and closing a small door without exerting any work, of sorting the high-energy molecules from the low, thus creating a temperature gradient. This amplifier of fluctuations, if it existed, could then be used to run a perpetual motion machine of the second kind, violating the second law. Writing in 1929 Szilárd {{cite:b06a1901070015935f3f32643868fa977fecf550}} realized that, to save the second law, somewhere in the measurement process entropy had to be produced. Soon afterwards von Neumann {{cite:8aa60759c9a56ed4ae1a8010fd39db689c938724}}, in his reading of Szilárd, pointed to information acquisition as the key step incurring entropy cost—a claim that would later be developed by Brillouin {{cite:2e8463b687fb08c07b22e0fb6e187c8b76e2643c}}, {{cite:01ed3aff16593c8fb211c7f1e9d5514684bb1e91}}. Building on work by Landauer {{cite:221a836299d3d5a467a782b11aff2854e508dbf4}}, Bennett in 1982 {{cite:94aaa30e63b8ff8099a910720be5e946a5b1fde5}}, {{cite:ccb4cd188738a37e56169a10760e4ec75eebb0db}} argued against Brillouin, pointing instead to erasure of the measurement record as the key step incurring entropy cost. This 150-year-long inquiry seems to have finally near a close in recent years, with the realization that the entropy cost of measurement can in fact be traded between the acquisition and erasure steps, as reviewed in {{cite:763585d97aebd7db93ef2e4c5a850ba94efca124}}. Crucially, in the absence of a mature theory of classical measurement, the latter rigorous analyses had to rely on quantum measurement theory to settle the problem. Earlier attempts had it worse: with neither a mature classical nor quantum theory of measurement available, most of them proceeded by contradiction; requiring that measurement (whatever its mechanism may be) not be incompatible with the laws of thermodynamics.
| i | 9d9c395b1a27294023cb7fba31b3d866 |
Several limitations of this work warrant further discussion. While DeshadowGAN has performed relatively well on baseline OCT images from healthy eyes, we cannot confirm that its performance will remain the same for eyes with pathological conditions such as glaucoma. This is because deep learning approaches respond unpredictably when the input is very different from its training images,{{cite:d6f3b7666e7215e763221f3e684ad34ee3f7e07e}}, {{cite:2001b33da696c0573d2f2ff0b0f2827928647d65}} and `pathological' training sets may be required. Furthermore, DeshadowGAN was trained on high quality multi-frame OCT images from a single Spectralis OCT device. It is unknown if the algorithm would be able to perform as effectively if applied to OCT images obtained from other OCT devices, or OCT images from the same device but with significantly less or no signal averaging. Similarly, each scenario may require a separate training set. We aim to perform further tests to assess all possible scenarios.
| d | 4e12dc38b9aff31fc9f9aac9f9dbb41e |
The kernel Stein discrepancy (KSD) {{cite:9757a0c66a15e7680da80dec6ba0b2978a1bda62}}, {{cite:ef5a7049dfbd48d6ec55561a201c67e114f8e36c}} is a kernel-based discrepancy between probability measures. It provides a convenient approach to measure the divergence between a set of samples and a target probability measure which might only be known up to a normalization constant. The construction of KSD combines the Stein identity {{cite:6ec3fc3bdfcb41f7349e6f51f6429dc1e0ba6243}}, {{cite:dd23f928d79a12148a1af3b5f65adec8290b19fe}}, {{cite:54f39818fe97b9251b0f431956b28142601ea61b}}, which provides a set of sufficient conditions for a random variable to be distributed according to a given probability measure, and reproducing kernel Hilbert space (RKHS) theory. Through the combination of these two tools, KSD has become an effective and generally-applicable tool in computational statistics and machine learning. Applications range from assessing MCMC output quality {{cite:b8135048ee61d363b42e90de109ee6fc86cd0075}}, post-processing of MCMC output {{cite:47312e6ae86de4731b61def067e2d2baed754a15}}, goodness-of-fit testing {{cite:9757a0c66a15e7680da80dec6ba0b2978a1bda62}}, {{cite:ef5a7049dfbd48d6ec55561a201c67e114f8e36c}}, variational and amortized inference {{cite:bc0357c35e37fe257bd3d783214abcabf7a9fd13}}, {{cite:63146ceeaa3c344afe693b0994bf60483127850e}}, generalised Bayesian inference {{cite:78269eba814fce19c914688ffc07fb00b9b099e8}} and generative modelling {{cite:0796d9b016e0191deb268b65c37c3a332d55af59}}. For a recent survey see {{cite:0b17f1a56283ebcd78015bc8ad3e19f9d0cb0d08}}.
| i | c8270374eec8dabc3e01f52890ad4b44 |
An interesting discovery was made by changing the periodicity of spacetime or adding boundaries {{cite:ecac2f5c5cdfedae5b1aa2960b309419ec76fd17}}, {{cite:c024936809d38bcb144de3796ad2c02a16e52f4c}}. When we express the entanglement entropy in the path integral formalism, the reduced density matrix and the entanglement entropy can be defined using the partition function on the {{formula:2dba5a42-791c-40c3-bdef-eb278fd55030}} copies of the manifold glued along {{formula:bab554ca-27ab-4632-ac2b-d9fcf3e9da33}} at the fixed time. We consider Euclidean time and space direction.
When the subsystem {{formula:d737ec11-257c-4f01-8d63-9fd66e0e0a52}} is a single interval along a space direction with a periodic boundary condition, the entanglement entropy in 1+1 dimensional CFT becomes {{cite:5bba5dbd3c91d1341d319ff6f2f150132f048292}}
{{formula:cf5e4335-5e16-4b83-ba74-8bbea28671ad}}
| i | f63383ca4c1302d203faf03255b296f2 |
Cahn-Hilliard equation was originally
introduced {{cite:133f8ee2481ed5388d7d373aa4df51584529baf9}}, {{cite:d3bc9f833c7a1ac42357cfa759da2dac0270e3d7}} as a phenomenological
model of phase separation in a binary alloy and it has been
successfully applied in different contexts as a model which
characterizes phase segregation and interface dynamics. Applications
include tumor
tissues {{cite:09469590d1b7e1806f3958048cf6bb4512095cb8}}, {{cite:70f04276b2f00a83c3b44335f37de6d8b900d719}},
image processing {{cite:0d7236b4a1dc1aedc49f44ec8695b920506dcc18}} and multi-phase fluid
systems, see e.g. the review {{cite:107f59a32fe5efa3408c2f1bb2d448b15bc286ba}}.
The dynamics of this equation comprises a first stage in which a rapid
separation process takes place, leading to the creation of interfaces,
followed by a second stage aggregation and development of bulk phases
separated by thin diffuse interfaces takes place. These two phenomena
(separation and aggregation) are characterized by different temporal
and spatial scales which, together with the non-linear and
fourth-order nature of CH, makes efficiently solving this equation an
interesing computational challenge.
| i | 9f9a75b60d94f91d0b2670085332262e |
In order to prove Theorem REF , we need the following two lemmas. The first one is an immediate consequence of Dedekind's theorem. The second one follows from {{cite:8422a01d8afe35696e0ff70726293853c9a87f93}}.
| r | 312c7074674c6b444a8a9d7a8e40959f |
The system architecture, as shown in Figure REF is composed of multiple object detectors (face, nose and coin), convolutional neural networks for landmark identification followed by a stage which combines the results of landmark identification stages to compute a recommended mask size. The face detector is the entry point for the system, as all information that is required by the system is contained within the bounding box of the face. In this implementation the OpenCV implementation of the Viola & Jones algorithm {{cite:ceed1781a2b7b4949dbaa35043387ec26f10f730}} was used with the pre-trained front-on face detector. For the nose and coin detection stages; the Dlib implementation {{cite:3842b74eabb43fb249d32ae0a6ef50d2c2238189}} of the Dalal & Triggs HOG based detector {{cite:bfd0b5dd794d603891c821c3a3aa7f354ee62f84}} was used, training the detectors using a subset of the noses present within the MUCT and PUT datasets as well as a sample of the coins within the generated dataset.
{{figure:0acc58a9-3461-434f-aff5-803a12ce71b7}} | m | 0b1f5b7b67118a234554d6c51eccf156 |
Our MCMC examination of the first six DM halos in a completely uniform framework of input data allows us to produce {{formula:008b8ddc-b1da-487a-b371-02719c18406d}} and {{formula:ef289000-348b-45a7-ad4a-cba40a1b1f1d}} values for dSphs in agreement with the literature. The most discrepant result is {{formula:9e3fad11-5716-48c5-a5b4-fbb71776a208}} for Dra I, which is offset by a factor of {{formula:ea6db37b-ab4c-427b-bc5c-bdda2bcfdaa5}} 4 from e.g. the value given by {{cite:3deff45a6fac09e71256340da515d41f9feed808}}. Nevertheless, CLUMPY is only able to perform a spherical Jeans analysis of the DM halos, thus not taking into account additional uncertainties arising from a possible halo triaxiality ({{formula:fbf3e5b0-3765-4132-9a19-f4ff2b9f0064}} 0.4 dex). We also note that, within the analyzed data sets, the dSph Tri II is potentially observable with CTA as a single targets in {{formula:ae0e74e8-1ffe-4085-a308-d4a2c6e82708}} 100 h integration. However, the limited statistics available on its stellar kinematics (which is also possibly contaminated by binary stars {{cite:118b4db4abc53b81797e4fdff82eb09bd398fef7}}) prevents to draw any firm conclusion, again emphasizing the importance of collecting good and clean stellar data for such targets in order to evaluate them as viable candidates for DM searches with Cherenkov telescopes.
| d | a2df164a73fb54f3f13c06bdfb46f64d |
Depending on whether the exchange integrals {{formula:506119a7-e468-4c7f-85c6-2ce221888577}} are considered as isotropic or anisotropic there are two possible scenarios. In the first, one notes a striking similarity of magnetic ordering patterns of {{formula:f5a5b11a-97f9-4b6f-9cf4-fab276a83a92}} and rare-earth metals Dysprosium (Dy) and Terbium (Tb). The latter elements acquire incommensurate-helical order at their particular {{formula:b1f40a3a-3a5a-4fa7-97f0-62d4d213a88e}} featuring temperature dependent {{formula:3e89fc1a-f4ea-4363-bc12-0841ada0f070}} and ferromagnetic transition, taking place a few degrees below {{formula:84dce573-b2ca-4d26-9243-83d6aca22480}} . By keeping aside itinerant-magnetism peculiarities, generally important for Dy and Tb, the ordering phenomenology itself can convincingly be interpreted {{cite:bdbc8539a6282902ae162f3f755063148fddd5d1}} on basis of an interplay between the isotropic exchange integrals and temperature dependent magnetocrystalline energy. Closer examination of the driving force responsible for ferromagnetism of Dy and Tb showed however that magnetostriction plays perhaps a more direct role than the temperature dependence of single ion anisotropy {{cite:95dbd040ed62b02eae108a7203a8ee24b0289578}}. Whether magnetostriction sets in at {{formula:976727b2-d40d-48bf-86ea-51482bcd6fc3}} in {{formula:7d0c3f25-8ae9-4b84-a365-6c35e069922d}} as well is not fully resolved as yet. A high-resolution diffraction study is needed to detect magnetostriction-related structural changes in vicinity of {{formula:de17df15-bb14-45f0-a958-6d5ac062247c}} .
| d | ed7d8a778baeb0e3c06d262caf899e01 |
Answer retrieval is to find the most aligned answer from a large set of candidates given a question {{cite:1ddcc204dca6400c00921884b679f8fa93805932}}, {{cite:3e6d4b85bf420bc8b666844d1d787b38d95d77e5}}. It has been paid increasing attention by the NLP and information retrieval community {{cite:d234fb91cd8d10ca6035dd3350a48e92b489b849}}, {{cite:fb2e2272eca9d71f0ca933ed60103415966d5ad0}}. Sentence-level answer retrieval approaches rely on learning vector representations (i.e., embeddings) of questions and answers from pairs of question-answer texts. The question-answer alignment and question/answer semantics are expected to be preserved in the representations. In other words, the question/answer embeddings must reflect their semantics in the texts of being aligned as pairs.
{{table:0a24402a-7c58-48d2-9d15-9c23b219ed00}} | i | 96b5560d3bdc309c405d0ecb2e911062 |
Table REF provides an extensive comparison of the iteration complexities — including both upper and lower bounds — of PG and NPG methods under softmax parameterization.
As suggested by our result, the iteration complexity {{formula:8236ed12-53f1-496a-ba65-19225909c479}} derived in {{cite:fac541e2b3463ec38d45df5528feaaaf2a0dbb9e}} (see Table REF ) might not be as rosy as it seems for problems with large state space and long effective horizon; in fact, the crucial quantity {{formula:6aa876ee-c06c-4e48-b3b5-835e5a271b36}} therein could scale in a prohibitive manner with both {{formula:37da8b96-3712-49c1-a2ad-cfb6b736c6b7}} and {{formula:59a405f0-327a-4952-bfd6-e34569b0b107}} .
{{cite:fac541e2b3463ec38d45df5528feaaaf2a0dbb9e}} also developed a lower bound on the iteration complexity of softmax PG methods, which falls short of capturing the influence of the state space dimension and might become smaller than 1 unless {{formula:9411ab9b-051d-4396-930f-e02052633017}} is very small (e.g., {{formula:906dc944-9ae7-467c-88a7-3db9f1f4a60f}} ) for problems with long effective horizons.
In addition, {{cite:a9983a6d77aac601f6b053d31c99dd9a803b2eb5}} provided some interesting evidence that a poorly-initialized softmax PG algorithm can get stuck at suboptimal policies for a single-state MDP (i.e., the bandit problem). This result, however, fell short of providing a complete runtime analysis and did not look into the influence of a large state space. By contrast, our theory reveals that softmax PG methods can take exponential time to reach even a moderate accuracy level.
| r | 7256316f918b7606e4cbf310188918a5 |
These results incited us to revisit the emission of the HCN and HNC isotopologues in L1157-B1 in a more comprehensive and accurate way than was possible before. This study benefits from the unbiased and high-sensitivity millimeter spectral line survey of the shock region carried out as part of the IRAM 30m Large Program ASAI ("Astrochemical Surveys At IRAM", {{cite:21ebe1820746f0a19b2eb46f4c67514357d3d3e2}}). In order to better understand and constrain more precisely the impact of the shock on the chemistry of HCN and HNC, we have also investigated the properties of their isotopologue emission in the envelope of the Class 0 protostar L1157-mm, at about 1 arcmin away, which we took as a proxy of the initial gas composition before the arrival of the shock. The origin of the molecular emission was then derived from comparison of our observational results with the predictions of the time-dependent gas-grain chemical and shock model UCLCHEM {{cite:820558309eb947d393ba7cfbc0fae309515962d8}}.
| i | bea7fb5ddfc72a6a726b5ac3c740049f |
This kind of dynamics is known to generically lead to a
final state where the system divides into two groups
{{cite:0c9dcae598fa0068e80eb31f31b7b6ce75777d50}}, {{cite:7efd718172763e8b433f1944dd3b5ecee1bf4de1}}, {{cite:aca812bdfee2e43a158ae36fd9cb8bda90d044b8}}, {{cite:73ad0a546ba8d39593943bd46f61a479064b8b17}}, {{cite:d166c715ce5bc9f9988851b7c635ced601ba0ffd}} internally friendly but mutually hostile.
Such states are termed 'balanced'
{{cite:e0955adf82113e19788076d7d2ba84cc65fbae44}}. Here we abstract from the sociological interpretation {{cite:e0955adf82113e19788076d7d2ba84cc65fbae44}}
and focus on mathematical properties of the dynamics itself.
We are mainly interested in final states reached during the
evolution. In addition to 'balanced' states,
which are fixed points of the dynamics, the dynamics can lead
to jammed states, which are also fixed points but
they are not balanced {{cite:0c9dcae598fa0068e80eb31f31b7b6ce75777d50}}.
More interestingly, the dynamics also has limit cycles of
different lengths. The fixed points and
limit cycles can be used to classify states by basins of attraction they
belong to. The statistics of basins of attraction for small systems
was reported in {{cite:c921cf2d3500bf0658bd2f3c21e0846306346ff5}}. The aim of the present paper is to
explore properties of limit cycles, in particular of perfect limit cycles
to be defined below.
| i | be80e9e84f6d8b1f0a8d9f09ab2f3998 |
Currently, there is no doubt that computational simulations play an important role in the development of fundamental science as well as engineering applications.
Molecular Dynamics (MD) simulations and Monte Carlo (MC) simulations have been established to simulate the behaviours of materials in dense gas, liquid, and solid states at the microscopic, molecular level {{cite:5fa9c4dbb84fd438595a514ac04d2935e65585ab}}, {{cite:ce6eb0a94b45c3b166b297fa7ee4845a9a3b3be5}}.
The importance of these molecular simulations comes from the fact that they provide exact, quasi-experimental data on well-defined simulation models of materials.
The usefulness of simulations is also based on the fact that they can access data that cannot be obtained through experiments.
From the theoretical point of view, exact data on prototypical models are valuable for understanding the fundamental mechanisms of phenomena as well as for testing the validity of proposed theories.
In the past, molecular simulations have been employed to solve many important problems.
For example, in statistical physics, phase transitions, such as the gas-liquid transition and the paramagnetic-ferromagnetic transition, are among the topics that are most widely studied by means of computer simulations {{cite:159ba416d05b2bd949221eb42000e88fb4e8f9f3}}.
Additionally, to address the problem of glass transition, many previous works have relied on simulations of, e.g., the drastically slowed dynamics near the glass transition {{cite:13acf4b230b503863daaf1e1ef27ca4533c1d91c}}, {{cite:a2518afef6bca3656d68f0510b89107627ef036a}}.
| i | a24eba86fc20610e10fb796e0b5db0ab |
Sim-to-real transfer has emerged as a dominant paradigm for learning-based robotics.
Real world training is often slow, cost-prohibitive, and poses safety-related challenges, so training in simulation is an attractive alternative and has been explored for a number of real world tasks, including object manipulation {{cite:3d8b2d288464abb07a8e05d9227a66aa053be3b6}}, {{cite:c51dc0978f89ac42b2857f510cfc126e7066ce83}}, {{cite:46b7c8d4fea6b607f72d43a23b465ed946a38ca7}}, {{cite:1d7928216af45132bdf9f97ce4a53220c101977f}}, legged robot locomotion {{cite:d6cfa95c2a07bff012672462b74dba14e9d28351}}, {{cite:106624db16a49e20bf4ffebab67ef39d58ffc774}}, and aerial navigation {{cite:f4c3bdd1d8cacc26a30897e96e5ae7bac99c4ab6}}, {{cite:df042acfd7ad8b8d1b39e5ecdb15fe2377ad713a}}.
However, one element missing in this prior work is that the policies are not trained to be proficient at interacting with humans upon deployment. The utility of sim-to-real learning can be greatly increased if we extend it to settings where the trained policies need to interact with humans in a close, tight-loop fashion upon deployment.
One of the major promises of learning-based robotics is to deploy robots in human-occupied settings, since non-learning robots already work well in deterministic, non-human occupied settings, such as factory floors.
However, simulating human behavior is non-trivial (and indeed, one of the primary goals of artificial intelligence research), making it a major bottleneck in sim-to-real research for tasks involving human-robot interaction.
| i | fbbb58a8ebde5389f98803e4d1b5fbb0 |
Above we have described a principled generative capsules model. It
leads directly to a variational inference
algorithm which can handle either a mixture formulation or
incorporation of the DS matrix constraint.
We have also shown that this formulation outperforms the CCAE of {{cite:361a9e4996b4dc65e51380e2eef77a3bb3bca6b9}} on the constellation data generator that they used.
| d | e8904ce8ea6afa56bfe70136a8683e30 |
Recently, the North American Nanohertz Observatory for Gravitational Wave
(NANOGrav) Collaboration {{cite:6233864c0cc712ec9fb7b580bb867b45a5f422bc}} has reported an
analysis of 12.5-year pulsar timing array (PTA) data. According to the
analysis {{cite:6233864c0cc712ec9fb7b580bb867b45a5f422bc}}, a possible evidence is found for a
stochastic common-spectrum process which may be interpreted as a
gravitational wave (GW) signal with its frequency in 1–10 nHz, and its
average GW energy density {{formula:38e53fec-006a-4d3c-b9e2-d2bafadf660f}} with an almost flat GW spectrum
{{formula:8473a0ee-6c3f-49b4-a4fd-2c6a170cd78e}} at 1-{{formula:d7b98bee-ead2-4cd1-88ea-0be170a1ebcb}} level. Although
the observational results need further analyses, such as a joint analysis
with data from the other PTA collaborations (such as EPTA and
PPTA) {{cite:beef749a76d48d39a93dbd7f5e6b6ff5be124ea2}}, {{cite:02fc45ff63bb6bbc26f36a1ed56ca7d2afe81b00}}, {{cite:658cf573d56694cf69655c366e9fe3a943720dea}}, the potentiality of its being a
stochastic GW background (SGWB) signal has aroused keen interest of
theorists {{cite:09e6a58d1c7a4725e1e8cab07e83f586e6e5e668}}, {{cite:40cedb79474efaff9de14fe1213998e8a43040ad}}, {{cite:41577fdae04276272b00f54f18cd8acf59d45742}}, {{cite:e6acf0ab10fe36e1c3943cd2120b88f10f4ce7cf}}, {{cite:9b8857fb470ea716e31244bd9ee0ebd3aab9664b}}, {{cite:01eb3e9962f1db3b66cd347b7716d6b5e65174d0}}, {{cite:7dc2cef0a2667da0f4309c2135f00de1e4440305}}, {{cite:9b3d4d0444e47dfcc0f8e1c5dab342326f721d45}}, {{cite:01c50666c7beddc7085c92c895e759da52e50f99}}, {{cite:9b05b09035252db1d22327d8e146ac8c0771df20}}, {{cite:861ac4bfb4f2666514f22400072768aa798b8f9b}}, {{cite:4cf6222430fbcef61a2feb780669a1f01bac8e66}}, {{cite:4f2e01fb302ec6b1e3aa22d77747186a93dab4f0}}, {{cite:53a046b22bc5373d163f3d9e2f25007d445d603c}}, {{cite:98d4689072dc0631d79ec1f6a647cabe62ae9f28}}, {{cite:203532d39756dc8483968af334b19fcc2a4815ce}}, {{cite:9ab410f13e94e4bfa0f782ecdfce2a8bb3595fd4}}, {{cite:9e95ebb457fdad73cd1f12f85c7c6240a1cad2c0}}, {{cite:d38234d363ecab613fd9658a0cf6982eb9cd03ce}}, {{cite:9bcb21774f1d213f7cdec0b27f0f6605e157dafb}}, {{cite:e00f3d9cee1f600e3f3d7d63b0b5203fdd17440c}}, {{cite:dbc99b855d0e5a8e146132cad6bd418cce4c8135}}, {{cite:c70ce1bbdd9abcf16fca908e567f3f1438529e36}}, {{cite:96e20c922e320ee0da2b6e12500c5c95bf758dea}}, {{cite:823259b2e1ace0dacc2c2e18890a4e8c82cd9d26}}, {{cite:a8693951b9fbc330a876214b0564654bd3f40213}}, {{cite:55b3e6fbaca1a40d8e24139464bce4bb653d1d0d}}, {{cite:45a9c3c35768ca9b659c690a051f3d4a520f0842}}. On the one hand, one may explain it as a potential
SGWB signal by considering different astrophysical and cosmological
sources. On the other hand, the possible SGWB signal could serve as a potential new
probe to studying new physics.
| i | 30e06d394f7367efc6977c55f19f200f |
Step 3: Querying the Human. We elicit preferences over trajectories from the human in the loop, by querying
pairs of attacking trajectories, ensuring that queried trajectories actually exhibit different behaviour (differently from past work on preference elicitation, which samples trajectories uniformly at random {{cite:2c85dd75795829d57976c1dca253c167409cb7a1}} or based on the uncertainty in the reward model {{cite:b1392dd8b0dec26bbcbf97e78ff98ef2eaeb66ed}}).
| m | 208e4a8ff181201510b502881385eb8e |
Style transfer to 3D models resembles video stylization use case, however,
there are specific features worth separate discussion. In this scenario we let
the user select a camera viewpoint from which a 3D model is rendered to get
image {{formula:5b1b471c-e7b5-4457-b94d-423308730d99}} . As the network {{formula:b7e06044-6573-4265-97d6-0f7d22d3b509}} is sensitive to local variations in {{formula:b7ed749f-8051-4d15-8a07-ae4c4f2abe58}} , it is
important to avoid larger flat regions which can make the translation
ambiguous. Due to this reason we add a noisy texture to the 3D model to
alleviate the ambiguity (see source render in Fig. REF ). An artist then
prepares the stylized counterpart {{formula:4bf36450-e138-48f4-92f4-1ac332787ebd}} and the model is rendered again from a
few different viewpoints to produce {{formula:4d08eb50-aaaa-4116-a8db-fde1a50448d2}} . Using those inputs, weights {{formula:11260a01-75f2-4e9e-9f9d-b5656967407d}}
of the network {{formula:e2668ded-68c0-44a0-bab9-61a148badf7a}} are optimized and the translation network can then be used
in an interactive scenario where the user changes the camera viewpoint, the 3D
model is rendered on the fly, and immediately stylized using {{formula:51059322-d523-4f51-aca9-fab2588a96c2}} . See
Figures REF and REF and our supplementary video for results
in this scenario. As in the video stylization case when compared to other
techniques {{cite:bee08583eb0ef04106c37ae3812e7df2f8654f84}}, {{cite:44f35adf1f53f3202a6f26023af9fb6b43775a3f}}, {{cite:887437800ac4aaa898b42f07fc1e41fc9bf2ff6b}}, {{cite:e93961a74e02c526abf3d1b4b6a882e3960c6c56}} our approach better
preserves the style exemplar (c.f. Fig. REF ) and implicitly maintains temporal
consistency.
{{figure:9fb22e69-9914-4a85-9d00-1b5b17debb18}}{{figure:2ed540e2-5fb4-406a-9c9f-533d20ba0106}} | r | d30b139d951d8ded2d6382e56cf2245a |
The study of topological insulators has developed into a vast research field {{cite:71a2585315d00b441c647db65599a1463a0de54a}}, {{cite:d7f9300bd21fdc38c8ed97f454eb63e3714c8d83}}, {{cite:a344ded25cf64d72abcd0f81f6cf9ffe4fd76fc7}}, {{cite:4b8be4aaddb03d55db0ef26c6783d1aa1dd7663f}}. A conventional {{formula:1b54e429-9354-4cda-8695-23d73d3b3a85}} -dimensional topological insulator features a nontrivial bulk topological invariant defined for the valence states below the bulk band gap, and it has protected gapless states at its {{formula:facf2b22-f6e1-4877-b166-2ffd97ecf7a8}} -dimensional boundaries. Later on, it was realized that with certain spatial symmetries, there could exist a class of higher-order topological insulators (HOTIs), in which the gapless states appear not at {{formula:9518916e-db9a-423c-926d-050a89500df9}} - but at {{formula:d89a54d2-0d6b-4c23-9483-eb4713ab484f}} -dimensional boundaries with {{formula:7348b75b-efb7-4ba1-9ee2-191676378db4}} {{cite:94db63125adda31c251bdb96f2532f1722e5937a}}, {{cite:313d592e32f6b72311c803db88ffa887cb0cd51a}}, {{cite:d7ce9614a4cac17e9330e356cb38ae26dfc0abd1}}, {{cite:1ae222fdd9abc0d01f4311ff8bee6bae1beb946a}}, {{cite:bc1a4d89ba75e10829d043ec656a827998640614}}, {{cite:6b8186acba5df221ee53c4ce6e45f28ba2c6763e}}. For example, a two-dimensional (2D) second-order topological insulator would have gapped bulk and edge spectra, meanwhile, gapless excitations occur at its 0D corners.
The concept of HOTI has attracted great interest {{cite:2fbe0e74bb129d144cc1bf9dee8ba9fbe1d8c0e8}}, {{cite:32dc15726c81156b6a2bcf756bb65578c63cf81e}}, {{cite:86b4295fdd71dc03c590f208950cd8c9282b3c2f}}, {{cite:55bd13a8507c1badb06d0a3ee8ab97139d758c2b}}, {{cite:a36ef88f581590cbc71ccce71a81525c387a0df9}}, {{cite:a3a1ea61be7561efe33b467022e4d9d182a50e03}}. Unlike the conventional topological insulator, a HOTI does not necessarily require the spin-orbit coupling. In other words, HOTI can be realized in spinless systems. Thus, its impact is not limited to electronic systems, but also spreads into bosonic and even classical systems, such as photonic/acoustic metamaterials {{cite:4600d62c7e683aacd98666f7d8e14c18cf20b670}}, {{cite:fde8a3097709616589d1a124cf201f3415e31eed}}, {{cite:31e536166436c7917fd3ac202f7e30aabad7ac9f}}, {{cite:ff23db16a8d97251001ddd7adbd2f975882f6757}}, {{cite:498efd72935f11c825fbb4bb473fc0b2e198e543}}, electric circuit arrays {{cite:1a3e512542241514436754d992b9bd89c5a62216}}, {{cite:b055322555cdd1787dd4e7522117c677ad670330}}, and mechanical networks {{cite:85d9988b10badcc927c68abb7b7232e4ec239685}}, {{cite:fabf0bd7113270a0fcf70348bac27b9842966f53}}.
| i | 215036063213f371f791c282b1a102a8 |
The testing and benchmarking of QAML models involve selection of datasets, generation of adversarial attacks, implementation of classical and quantum ML models and a systematic investigation of attack transferability and defence. In this work, we investigate QAML across a diverse set of well-known image datasets, including both grey-scale (MNIST {{cite:4da83a1208260fb612101ad71bd16735289a73cf}} and FMNIST {{cite:7a2d89ceb169ddb5615503471ad0bd5afbd08a45}}), and RGB colour (CIFAR {{cite:4a3ecf0b3104bf150ebde725086dd5409cbfa246}} and Celeb-A {{cite:2c29af4d71388fac84d1b5916479573bb7e8185c}}) images. While we use all ten classes of the MNIST and FMNIST datasets, although not a limitation of our work, we restrict to binary classification (ships vs trucks) in the case of CIFAR in order to reduce the computational burden of training the large quantum classifiers. The classification challenge considered for the Celeb-A dataset is to determine whether the pictured person has black hair. Example images from each of the datasets are shown in Figure REF (a). After the selection of datasets, we implemented three different types of adversarial attacks: PGD {{cite:e717799bb7a7b5cb23390170089ce93c2ea7f84c}}, FGSM {{cite:d7eb59406fbded67ec1f8344d668b660d25962ad}}, and AutoAttack {{cite:a63a0642acf38ff40adae0590723ad3d79665306}}. These are some of the strongest attacks commonly used in the classical ML literature to test and benchmark the adversarial vulnerability of classical neural networks. On the quantum side, our focus is on standard quantum variational classifiers (QVCs), while on the classical side we consider convolutional neural networks (henceforth labelled as ConvNet for simplicity) and the well-known neural network architecture ResNet18 (henceforth labelled as ResNet for simplicity) {{cite:4a5d95a70d6711dcec40ade89bcbd8a931018567}}. The architectures of ConvNet, ResNet, and the QVCs are schematically shown in Supplementary Figure S1. We load the images into the QVCs with the method of amplitude encoding {{cite:456db08ed729d4ca2f50e84bbc0c3dda9216d632}}, which can access the entire, exponentially large, Hilbert space of the quantum computer. We are therefore able to encode the 28{{formula:9702038a-f099-490c-b21d-8228a43957fc}} 28 grey-scale images of the MNIST and FMNIST datasets into 10 qubits, and the 3{{formula:f232a21f-99e5-4a14-9442-dabbf11b95e1}} 32{{formula:ae46c97b-5bac-42ba-83a7-b9e93524c2f7}} 32 RGB images of CIFAR and Celeb-A into 12 qubits (as {{formula:596f2d9a-65d7-4987-afcd-2d161744bbd2}} and {{formula:32ef89b8-5676-4a34-99fc-c8fb89861332}} ). After encoding, the resulting quantum state is processed by a variable number of layers of parametrised (trainable) single-qubit rotations and entangling CZ gates (refer to Figure REF (c) and Supplementary Figure S1 (c)). The QVC networks are labelled based on the number of layers in the architecture, e.g., QVC200 consists of 200 layers. Both classical and quantum networks were rigorously trained to achieve high accuracies (see details in Supplementary Table S2 and Supplementary Figure S3). We note that the learning accuracies of QVCs trained in our work are quite close to the outcomes from the classical networks even for complex RGB datasets (CIFAR and Celeb-A) and despite that the classical networks utilise significantly more resources than the QVCs. Furthermore, our primary aim in this work is to evaluate the robustness of quantum ML in the presence of adversarial attacks, and not so much on its performance for classification tasks, hence QVC parameters were not fine tuned for this purpose. Further details pertaining to the QVC architectures, CNNs, ResNet, and their training procedures are provided in the Appendix.
| r | e5e621f5cc6fce075ce09e6c05066c3a |
Here {{formula:cd19db8a-04e6-4e04-beae-30720d37ca24}} is the weight factor taken as {{formula:5f28e0c1-fea4-41bb-b490-39bae1f7f3a2}} of the particle for optimal resolution. The {{formula:4165a4a9-599d-49d0-ad1c-a3561415e9e1}} order event plane has a symmetry of 2{{formula:b38d485a-3e5f-4c2d-b829-bfe6ccd0639c}} /n and one would expect an isotropic distribution of the event plane angle from 0 to 2{{formula:a0cfd7ff-0a2c-4b37-8611-4177ffccd8f6}} /n. However, due to the azimuthally non-uniform detection efficiency of the TPC, the reconstructed event plane angle distribution is usually not isotropic. This is corrected for using the {{formula:8bd280f0-31b3-451e-ac15-6a3dd317544c}} -weight method, details of which can be found in the ref. {{cite:9a4c53ddd95f328d3e5224a90af9e4b7e7655bde}}.
| m | 8ed065756a8536ee400431996ec88b54 |
All graphs in this document are finite and simple.
Let us repeat some basic facts about strongly
regular graphs and bounds on their parameters:
Our notation for strongly regular graphs is standard,
cf. {{cite:a9e3f879fc7c531964555228dafb10ec17f2c04c}}, {{cite:427939ac97897e74539682c6510142637e502551}}.
A strongly regular graph {{formula:00baf3e8-ba77-44da-a8d9-ed6389ee120e}} with parameters {{formula:952ec68a-2b2f-4e35-ad3c-927820057000}}
is a {{formula:1cec5c5a-8b73-4838-b613-77fc6aaa3ada}} -regular graph (not complete, not edgeless) of order {{formula:2e802b96-07be-4137-a9c7-0c8e334c9239}}
such that two distinct adjacent vertices
have precisely {{formula:5fa5cd9f-017c-46fb-86ea-ca9b1b9b08ca}} common neighbors, while two distinct nonadjacent
vertices have precisely {{formula:d798dbcb-d65c-478a-b236-bb1fe30da1d2}} common neighbors.
One of the parameters depends on the others: For a fixed vertex {{formula:5ca51578-3b2b-4628-9f6d-78ed0eb70378}} ,
counting the pairs {{formula:2e5c3068-56a4-4a8f-8070-6175ba8fdc1b}} with {{formula:f2bd20a3-7d89-4f46-9b7e-9c635ab25ee7}} in two ways
shows that {{formula:ab0dc69e-9b56-4505-85ea-03db4600154e}} .
| i | 750d6d101c5801d89772d827872e0fe4 |
To confirm the superiority of our algorithm over the compared approaches, and especially LP, we suggest to use the Friedman test and Nemenyi test {{cite:201d9aaf451ab70fc54d4d298b674c591c911ef4}}. First, algorithms are ranked according to their performance on each dataset, then there are as many rankings as their are datasets. The Friedman test is then conducted to test the null-hypothesis under which all algorithms are equivalent, and in this case their average ranks should be the same. If the null hypothesis is rejected, then the Nemenyi test will be performed. If the average ranks of two approaches differ by at least the critical difference (CD), then it can be concluded that their performances are significantly different. In the Friedman test, we set the significance level {{formula:c850ca91-b335-423c-87e9-e8b859730fe1}} . Figure 5 shows a critical diagram representing a projection of average ranks of the algorithms on enumerated axis. The algorithms are ordered from left (the best) to the right (the worst) and a thick line connects the groups of algorithms that are not significantly different (for the significance level {{formula:3c74a6bb-e6e2-4554-b2e2-dfdce57a505e}} ). As shown in figure 5, OTP seem to achieve a big improvement over the other algorithms, in fact, for all evaluation measures, the statistical hypothesis test shows that our approach is more efficient than the compared ones and that the closest method is LS and then LP, which is normal, as both are label propagation approaches, followed by LNP and finally spectral clustering.
| r | 53e247d436b69100684fcd9091558632 |
with {{formula:6e77fa26-d27e-41b9-ad1e-0523027f51a5}} and {{formula:0231581b-a2ff-4e87-9e3f-e96bfa6f326f}} . On the left side of figure REF , we show the GW spectrum for {{formula:0f5147f6-6c67-4540-955d-2aea70153bba}} with loop size {{formula:278b650c-ec0f-411d-9621-3786e7211016}} and {{formula:ff5de391-ea4e-4c04-b7ad-e62c46438ddb}} . As one sees, that even for the {{formula:a4daa3b1-263f-43ab-85fd-bbe1cfbd3900}} , the mechanism predicts GW with a strong amplitude with a flat plateau which will be fully tested in the space-based interferometers such as Taiji {{cite:aba301f264853fc182d00bbf9be4f6cad2fa9ecc}}, TianQin{{cite:2fef96c13b5afa05bb5fb73eb78a9c827653631a}}, LISA{{cite:7ba36301b8bb46719a9cec90c7a4cae80b0390d5}}, BBO{{cite:d3802853f06896e12ab865eb3e5f624f31757b54}}, DECIGO{{cite:ef0cabb32baaae8c1eaafb7c4b76ff0360f474e0}}, ground-based interferometers like Einstein Telescope (ET){{cite:ff18fbf66e7d569e8f6536dde201eb72cfb43726}} and Cosmic Explorer (CE){{cite:e5d0b94d942def297dea3d546e457e15ebfa7093}}, and atomic interferometers MAGIS{{cite:b08268158bb7b28eed52887e2922b1389dde79ca}}, AEDGE{{cite:aaa4397a9d184033176c101ffea6cc7d0ea5ad86}}.
{{figure:6fc4c913-0d2b-46b1-9c5a-6b36c4c82f0a}} | d | b84c6fab8fedd36a6679e34a7c05e141 |
We can hence estimate
{{formula:d6006d8d-0117-4972-8e2d-02aed8583af6}} as large as {{formula:77f27102-2f4c-43de-9ed3-21cb9c33e297}} ,
which seems to be very accessible to the LHCb experiment. However,
there might exist other resonant decays to interfere with
{{formula:5a4646b8-db7e-48d7-949f-c256930e81d6}} ,
which would cause a complicated amplitude analysis. For example,
the amplitude analysis of {{formula:d729ce61-cea7-43df-87df-ab12dfa15ec2}} is complicated,
which is due to the resonant decays {{formula:b98ef79a-c2f1-44d9-940e-70ea358add70}}
with {{formula:bc2383fd-ee45-4753-b57f-0a82521f3a43}} , {{formula:dd4b20fe-458d-43b2-b345-8cc5951167e1}} , and {{formula:1df711c1-1dc0-4358-a679-5a8378dc7039}}
to interfere with
{{formula:77ba7704-830d-4c06-925e-a059e6b4098e}} {{cite:1e6cb89a1616d0c83bc9ff283925c7ea54a93498}}, {{cite:b89be47f47513deffbbb8aa80355b436bd292f05}}.
| r | 60f8e1bb696aa88b5a5c9477e2981245 |
The technique to obtain the effective action will be the Functional Renormalization Group (FRG) {{cite:7243f4b1a58e8253adb1ff462be5386b53cb7102}}, in the LPA approximation. We will follow the scale evolution of the couplings of the theory written up around the physical vacuum, containing also symmetry breaking terms. We also have to give an account to the changing vacuum, this will result a small difference in the FRG equations {{cite:2ccb202217e23bfbd41aef970e8f8a3c620fa64a}}.
| i | 1099f03081728ba1d3ddb460bbfff332 |
Audio-driven facial simulation technology is also attracting much research. Because little has been done to model expressive visual behavior during speech, Yong et al.{{cite:168838f73efe1eae0df7b02c67a546cae08c9de6}} address this issue using a machine learning approach that relies on a database of speech-related high-fidelity facial motions. Tero et al.{{cite:b4dde3ab8c1b7c9bf1c9a83897f6cca9fe280e8f}} drive real-time 3D facial animation by audio input with low latency. Neural network based end-to-end models suffer from slow inference speed, and the synthesized speech is usually not robust, i.e., some words are skipped or repeated. But, Yi et al.{{cite:158cb57bb859e802955bd9195345a1a4ae64c3a6}} extract attention alignments from an encoder-decoder based teacher model for phoneme duration prediction
| i | d51326eb9c76510ef4f0332f9ae8ad7c |
In order to constrain the allowed parameter space and investigate neutrino phenomenology, the model predictions for neutrino mass-squared differences {{formula:86527f87-8f8d-44d1-ab7b-79e8d2374c67}} and mixing angles {{formula:034cd22a-8a85-433a-aced-df446d8f353e}} are compared with 3{{formula:722adafe-cf63-43b1-a49b-de19cfe3d162}} ranges of the experimental data on neutrino masses and mixings viz., {{cite:f18f141714f9890c1f657914156e58b1f0ffed50}}
{{formula:be50105a-ca5e-4ba1-976e-24f17bc5c00b}}
{{formula:1efd723f-a1b0-4fd9-9fbd-93ae2ec58793}}
| d | 4676627e263cac60b633da1409ac7f67 |
For background on mixing times, cut-off, and related material, see,
for example, {{cite:a860f9f3a81a48b91d289126413d10351330c0c5}}.
| i | ba326e4eb83ba82e57c26857d5d1b94b |
DNNs has greatly boosted the performance of image classification due to its power of image feature learning {{cite:dd95789993ebba1a0ea1dc2b69f45db631cb8b90}}. The active retinal disease is characterized by exudates around retinal vessels resulting in cuffing of the affected vessels {{cite:d542f657fc1823cce32b2f82b6e104c4c1415451}}. However, ophthalmology images from clinical microscopy are often overlayed with white sheathing and minor features. Segmentation of retinal images has been investigated as a critical {{cite:709707713ea226f8ccad857c2ce22f5e56ed456c}} visual-aid technique for ophthalmologists. U-Net {{cite:4714e4a0c9e59c7ee84833e966beb199d8a00eaa}} is a functional DNNs, especially for segmentation. Here, we proposed a modified version of U-Net by reducing the copy and crop processes with a factor of two. The adjustment could speed up the training process and have been verified as an adequate semantic effect on small size images. We use cross-entropy for evaluating the training processes as:
{{formula:57160688-b542-420f-8414-bba83bdfb82c}}
| m | c399956c517f6e1e22f86dc6162287e0 |
Deep Neural Networks (DNNs) are prone to over-fitting and often tend to make overly confident predictions {{cite:e043b2c4af92b80b75f91ebbb1a70041d8837153}}, especially with inputs that are out of the original training data distribution.
Ideally, we would like to have a principled DNN that assigns low confidence scores to samples that cannot be well interpreted from the training information and high scores to inputs that are in the training manifold.
The ability for DNNs to say how certain they are in their predictions is particularly important for applications involving critical decision makings, such as healthcare and finance {{cite:08293e74cde0a273fc5a6b8d38f39b3814007c40}}.
| i | 1555184124d48dd92521384d8d0476d3 |
In this work, we investigated optimal methods for pair-wise binding
based on the VSA framework {{cite:4abfa09377222f2415d87d0352119120eba4f3cb}}, {{cite:dd4a0eb20b585bb111566fa875e51c3c865dc391}}, {{cite:20e38213b23825021cf417ee33b75fb9574f0ab9}}.
We first numerically optimized the binding and unbinding operators
for the best unbinding performance assuming only one pair is bound
to the composition vector. We found that the numerically optimized
binding operators outperform HRR, a popular method for binding (Fig.
2). Moreover, we revealed that there is a hidden {{formula:9e475254-48cb-4c60-821e-ab810ee9d239}} block
structure in the optimized binding and unbinding matrices (Fig. 3).
By analytically deriving a sufficient condition for a fixed-point
of the loss function, we show that the {{formula:2c092fb5-3149-491e-b88f-70606b90d990}} block structure
is originated from a matrix representation of the octonion algebra,
an eight-dimensional extension of the complex numbers (Fig. 4). Furthermore,
we showed that even when several pairs are bound into a composition,
the proposed binding method based on the octonion outperforms previously
proposed methods both under the dictionary decoding (Fig. 8)
and unbinding from an expanded composition (Fig. 9).
When there are many bound pairs in a composition, however, the advantage
of the proposed method vanishes, and even a random binding shows approximately
the optimal unbinding performance under a mild condition (Figs. 8
and 9).
| d | 3fffdf85cea5550292d94787bec0690a |
For our interventions, we used two different variations of the TS algorithm. For Weeks 1 and 2, we used a UR-TS Hybrid where the TS updating of the probability that an arm has the highest click rate used data from the UR participants too. This hybrid is called {{formula:2e872f5f-6eda-40c4-b7cb-4d02b9a9545a}} [0.5]-TS, because with epsilon (epsilon = 0.5) probability, arms are assigned using UR. This takes inspiration from past algorithms like epsilon-greedy {{cite:23b171c6e9d819c4a4ccdeb13bab2293632decec}} and top-two TS {{cite:ea258bd0328294caf2a68fb2b8507598ae98b301}}. This is interesting to investigate because scientists may want to get the benefits of obtaining data under UR (in case TS introduces biases {{cite:54851cab00dcccaeeb4fcba49b86eea0a6eec849}}) for analysis, while also then using that data to improve the performance of the TS algorithm. For Week 3, we applied traditional TS that did not use the data from the UR assignment.
| m | 7474dace756f3c2165cd22d1152ad5f3 |
Let {{formula:0246ad30-9f53-4147-b836-f4264664a866}} be as described. By the fixed point theorem in the appendix (Theorem REF ),
it suffices to show that {{formula:009feace-d628-4aea-840c-c578197559a3}} is an increasing concave self-map on
{{formula:d2018d0f-feed-452d-b7d1-37803d068269}} with {{formula:185dd40c-1272-4ee7-98e9-cb1c139fc59d}} for some {{formula:9898f50f-1fb8-4314-a271-7384304abfa7}} .
As confirmed in {{cite:6dadb5439a35b4bdd7fdb8c6271185ec5ac5ad9e}}, {{formula:44715b68-32f0-4cd5-9b46-570bb1dcf919}} is increasing and concave,
so only the last statement needs to be verified. To this end, we set
{{formula:8b1f23f9-ea32-4da5-8f32-057e85ff9564}}
Let {{formula:f81972d8-58de-4aa1-a66d-3d5920602461}} be defined by {{formula:346dfb91-5132-477b-918d-6a731dacdf97}} if {{formula:1c75283f-393a-44e4-810b-ce96a0ff83ab}} and zero
otherwise. We claim that, for all {{formula:18ab008a-a06e-41d3-8415-feeea5a2a7b1}} ,
{{formula:eeddae29-6a97-4cd4-9e85-0002b734ff71}}
This holds at {{formula:db8f1c25-95c5-434d-bd33-942d327c62c2}} because {{formula:e5c68b07-c7e5-4262-badf-027e4e82c2dc}} . Now suppose (REF ) holds at some {{formula:2c4c59bf-f18c-432c-9fed-110ca46c9ee3}} . Then, since {{formula:e3684b0e-f315-4899-aba2-0b3e51430f12}} is increasing, we obtain
{{formula:b4674618-d4d5-48ce-bf81-d9a179392a27}}
Since {{formula:e032792e-3bf3-4a0c-877e-b10f02c1751e}} , where
{{formula:b525a732-d6ea-4038-9a76-14c72d25edbc}} is a vector of ones, and since {{formula:df3de9c2-916f-4318-9bfb-b70848aacf23}}
by the definition of {{formula:04eadc6c-64a8-405d-a301-cb8e3f4b8745}} , we have
{{formula:77f8ef82-8bf4-428b-a922-250ad16a1180}} .
This argument confirms that (REF ) holds for all {{formula:70a6e3d6-7c39-476f-85e5-821aead54e41}} .
We now claim that {{formula:d858d2e7-9229-43c3-91d1-4a383b57d489}} . In view of (REF ), it suffices
to show that, for any {{formula:2bb43ef8-cde5-40b5-9249-5d0c3a9243d4}} , there exists a {{formula:5594a3ee-1d7e-485b-ac3a-f47f6f917b04}} with
{{formula:62a99e79-fc6b-480c-88da-a36aaacbb8f5}} .
Since every node in {{formula:d9e8cf70-51d9-43f5-8184-872298b99f72}} is cash accessible, we know there exists an {{formula:8e1fe988-dcb9-4e93-8503-45c62a710b04}} with {{formula:3414eb1e-0eed-4b1e-820e-622e831e89ad}} and {{formula:4cbd60b9-2304-46b8-a09e-e2fa88a1a912}} is accessible from {{formula:e9e8de5f-6ac6-47dc-804f-7ed35fa87bfe}} . For this {{formula:e04fdc96-8cba-4e48-8474-402d3bddd527}} we can
choose {{formula:b6e8234b-7e5a-47c6-9eae-8349c95599a3}} with {{formula:faedea21-ab08-4e0e-b8c4-9ba98900367d}} and {{formula:0e60e533-271f-46bf-8fef-71a65c81e2e0}} .
We conclude that {{formula:bcb92593-20d6-4bfa-9248-a0b5e6ebd4c9}} , as claimed.
| r | 8f9489b7e8f479556cdee582db0d9f41 |
We fuse the multimodal data sources in the following way as demonstrated in Figure REF : each satellite image data source is encoded using an independent CNN encoder (we use smaller MixNet {{cite:e913f12bbacb32830022cf050bb6a7d7b5ca102f}} for the simpler, non-changing Copernicus data and EfficientNets {{cite:9a18bdc7b715dd1a186f67f3244d6acc05092d57}} for the time-varying satellite images).
Time series gridMET data are fed into an LSTM {{cite:1ed978aeba897fc074bc9de35eed9778a9ea832b}}, while the non-time-series are left unencoded. The output representations are then concatenated into a single vector which is fed through a 3-layer MLP in order to directly predict the SWE of each 1km{{formula:ea2a06b7-0d7b-4ac0-a539-81c91e52386e}} cell.
| m | 345344702753d657ca69acc7c15a7f66 |
Criterion for choosing correlations: From experimental results, we propose to evaluate the reconstruction results using the pore-size distribution function {{formula:d1dba62a-4b8b-49fc-8774-9399bb666093}} as a surrogate. Specifically, {{formula:ecb258f2-037c-4c08-b666-e37992898482}} provides the probability that a spherical “cavity” of radius {{formula:e1d1a519-c3fd-4f4f-b900-dcd764364e8d}} can be entirely inserted into the phase of interest centered at a randomly selected point in that phase of {{formula:cd7c4ccf-4c61-4fa8-958f-2bf57fa84e3f}} {{cite:2b3046cecb70336725afdbe51e82721a9fe27fb5}}. {{formula:118bb498-65a0-4a2f-8196-5939a9a9d4eb}} was originally introduced to quantify the void phase in porous materials and was subsequently generalized as a generic statistical descriptor to quantify disordered heterogeneous materials. Since the porous phase is hosting all transport processes such as fluid flow and chemical diffusion in the porous media, the function {{formula:07b003f1-423e-4fe0-aa77-27c6a5e8753d}} is shown to quantitatively related to a variety of transport properties including effective diffusivity, fluid permeability and mean-survival time of chemicals {{cite:2b3046cecb70336725afdbe51e82721a9fe27fb5}}. Moreover, {{formula:59c9ef27-9018-4253-a83c-93f51fdffc64}} essentially provides a spherical measure of the clustering information in the phase of interest and thus encodes information on higher-order correlations {{cite:cc8f275b22f1410f1adbc777d45410405d798e61}}. In this study, we set {{formula:6f3bb8d6-da05-4628-a1cf-af5f39b221a3}} pixels and define
{{formula:9052f7e8-fb1e-4e78-abb0-2133c8119204}}
{{figure:ba9b9766-e103-4923-9922-bb98cb9b00d9}} | r | 3cf24313778375fa2b152e37cca8b4a4 |
In agreement with experiment, we obtain a negative charge-transfer insulator {{cite:ff231a0f66ab3dfd2f54567ac6115eef452109d6}}, {{cite:de8266316b664a17eb459f17ad6b34776f428322}} with an energy gap of {{formula:52b25b1f-7935-4d9c-9dfe-f911a815b7e4}} 0.6 eV (see the left panel of Fig. REF ). Moreover, our analysis of the Fe {{formula:16aee7b9-cfef-44c5-8334-44e933735a14}} Wannier occupations give a remarkable charge disproportionation between the Fe A and Fe B sites (due to a sufficiently different oxygen environment of these sites in the insulating {{formula:4b164124-44c5-48a4-a401-1dfb39bbf128}} phase, with the difference in Fe-O bond lengths {{formula:842d3494-39a6-4a3d-accb-8da129eee9e4}} 0.1 Å{{cite:0d5c22efc8b10e57da8920e1afd48e9392547a40}}, {{cite:36920dc38ceaca88641621757a2eb77caba5b2a3}}). In fact, at {{formula:b8b844e4-4706-4ba3-999a-d9c5b316082a}} 6.7 GPa the total Fe {{formula:579fb916-5db6-4af2-975e-cfb68560874f}} Wannier occupation for the Fe A site is only {{formula:5ecf04ee-5037-41af-97a4-2413637edba8}} 4.3, while for the Fe B sites it is 5.1, implying a rather large charge difference of {{formula:51cdead4-450d-4156-8a15-aaccb546f19f}} 0.8 electron. We note that this charge difference is about 40% of the ideal ionic Fe{{formula:b196c34f-dd1e-4cd2-adfe-36f1bf079a01}} -to-Fe{{formula:e9f6872c-b774-449a-a417-bf3901420163}} charge disproportionation, roughly consistent with the bond valence sum estimate of {{formula:2b95283e-f4e7-49f9-bfe7-6c35cfd1ae39}} 1.1 {{cite:0d5c22efc8b10e57da8920e1afd48e9392547a40}}, {{cite:36920dc38ceaca88641621757a2eb77caba5b2a3}}, as well as is in agreement with the significantly different local magnetic moments for the Fe A and Fe B sites (see above). Interestingly that previous estimates of a charge disproportionation in the low-temperature charge-ordered phases of the mixed-valence oxides such as Fe{{formula:0cacdbfc-03ba-40dd-920e-ae4a981d5e25}} O{{formula:dee475b1-f5e5-4d48-ad73-9f4ad1f707fc}} and rare-earth nickelates {{formula:812ac0e8-83c8-45bf-8752-2fcdc7133e5c}} NiO{{formula:bb2e7614-e13d-4b6a-be44-351c056efbe0}} give {{formula:5276a218-acfa-4b58-8fe5-7a0a1d55b1b0}} 20-40% of the ideal ionic disproportionation {{cite:448e89e50924a0f6662245fe6dfb395b2519a6c2}}, {{cite:6424a01606368b908ae28771cc93bdaede67a7dc}}, {{cite:ce660f28cc292ec1f622a2b6a5502973f153a692}}, {{cite:17a593fff273b19ef02ce87285f862bbcc265100}}, {{cite:b9542f1b6c0cdea0eda9d833dca5c35730424d3d}}, {{cite:a8efe4e8e2dd3253d1d90f3c0f9ed6fdab4a2bd1}}, {{cite:93851f009a59b6dd204c27ddda5f11dd72292156}}, {{cite:f336f9545608eaf5e14191c008846f37e4a18af9}}, {{cite:d5ae32a97ee21d52c8717bb603fda2d40042e441}}, consistent with our results.
| r | b90f599ccf155371c204914b17ace8f2 |
Our work is relevant however to more than just the FR thought experiment. Our results speak to unresolved issues in the Wigner's Friend paradox by identifying the state specific role a “memory” must play for an observer (rather than a superobserver) in the paradox. Thus, the transition between the two experimental contexts (captured by states {{formula:d67bd0ad-02da-4337-92b0-56d1b9beb2d1}} and {{formula:95b2f431-804a-4561-a486-c19c76674578}} respectively) can be interpreted as an assumption about the location of Heisenberg's cut {{cite:eda59c381fac480147aa3f356052e80bc8de7240}}. More precisely, it allows us to understand which entities/apparatuses must be considered as observers—the `ultimate measuring instruments' of Bohr {{cite:6594f84363c3db3e2866e6b3ee4f115e64bf695d}}—or included in the system described by quantum-mechanics {{cite:be05f802cfbba1ff81c8205127aaadf76419bf8f}}, {{cite:3d4be1617bb733cc9437c1f8d4fcc7b559572862}}. Indeed, for the friends to be considered as observers, their memory must, by definition, be preserved leading to state {{formula:9446a70c-b7a9-4149-b62e-f5db437fd250}} , while {{formula:c946ec60-46f7-4083-a593-277673b738b0}} requires the ability to alter their memory.
| d | fba58691f5bbc132d0235dd99e7756fd |
Gated Recurrent Unit (GRU): GRU {{cite:b02cc9df12e75eb029bca98a248326f2b693c62f}} is another version of recurrent neural network, but has fewer parameters than LSTM. It has also been widely used for stock prediction {{cite:132e08d8ebf44627cb1fca2eac2da01975fdf2d5}}, {{cite:145259ba9298baf7180862b935a6cb210e420812}}. This GRU baseline is same as the encoder network in our framework, but our method incorporates other components and training strategies instead of directly predicting the returns.
| m | 8c75fad1d085b208be6fc3014e7a147f |
Throughout this article, only win-loss scenarios are considered. For a standard Bradley-Terry model, typically two approaches to handling draws are considered: either by using ordinal logistic regression, treating win, loss, draw as outcomes from an ordered multinomial random variable, which can then be analysed via an ordered link model {{cite:860033e98edfdb77194175e9eb6bc738e595d402}}, see {{cite:7d95fa34bab558a02b25baac897270334fcbdc93}} which applies this to the 2008–2009 Italian Serie A football season; or via the extensions of the methods of {{cite:d21712faa03547b273512e2c23895e34d438a311}} or {{cite:b082b8864272edb5da9f9858ed0ab30de608b85e}}. With all these methods, certain “draw parameters” must be hand selected which can cause over-fitting. Moreover, they can impose additional restrictive structure, e.g., in the Davidson model stronger players have a higher draw potential, a feature which is not applicable to chess data {{cite:be9f97350a418d39f0a090c44307db0e32e9a8b4}}.
| d | 4ffbd4712bca5b14e5c7960aa81c4070 |
Table REF quantifies the Mean Absolute Error (MAE) values, the number of parameters, and the un-optimised inference times of the proposed network (with 5 folds), a UNet-like network (UNet Lite; see Table REF in appendix A for architectural details) with a similar number of parameters, a full UNet {{cite:87082f1f77d49cdb6d24208f2fec9f73d7afc4d7}}, and the CNN of {{cite:377125212c8c7b6e8af99c778b928ffaeb336d4d}}, containing about 60% more free parameters than the proposed network. We chose UNets as the benchmark because it is shown to be a very good baseline for such problems {{cite:5c371ffbdd547e886b47405dc22df16848af7231}}. Furthermore, most other works rely on a variation of a neural network with skip connections, so the UNet is a good common denominator. This comparison is made on the test data that was gathered for use in this project, as described in Section . The benchmark networks were trained using the same training strategy as the proposed network, albeit not in a greedy training strategy.
| r | be36d257389b3597594a240b9bfa00d7 |
blackAs shown in Fig. REF , the input size of point cloud {{formula:0e81ed60-4fd1-407f-bac3-a956b89d29c8}} is {{formula:59f5cc10-e43d-4719-a26a-a1590c7f03a8}} , where {{formula:630caf5f-faaf-4b2c-8b7f-96d63081e1f0}} is the number of points, and {{formula:51739a86-e7e6-495f-960e-0f10661011fb}} is the extra channels about RGB colors and normalized coordinates. The PointNet++ encoder module is composed of four set abstraction (SA) layers, while decoder layers are three feature propagation (FP) modulesFor more details about the PointNet++, we refer readers to {{cite:b037705a82da54abcaf882d0a2e02e2c3b211547}}. following with MLP layers, represents the segmentation head, grasp head, and collision head. The output size of these three heads are {{formula:5d6aa5fe-487e-4ef2-97bc-e630beea5e0d}} (semantic mask and instance embedding), {{formula:942ea58a-f95a-4807-9201-308e25cede26}} (graspable mask, two rotation vectors, grasp depth, width and score) and {{formula:084cd7df-7d68-40f7-82b3-f7489df61e46}} (collision mask).
| m | 5ad4880bac36cb8ba240fc9b21eeab51 |
Self-supervised methods aim at learning representations without the need for external supervision.
Absent explicit labels generated by humans, the success of these methods relies on the design of proxy learning tasks in which pseudo-labels are generated from patterns in the data.
These methods solve proxy tasks on unlabeled data to learn mappings from inputs to low-dimensional representations, which can then be used for downstream tasks such as classification.
This paradigm has seen major progress in computer vision {{cite:4af5e4dbe9ea6639a375595207628b6d9aeca550}}, {{cite:7344773f448244f896b8763ca01add915fd8d0c5}}, {{cite:c5b68e04bb640a83784dfc8523d364285a192ba4}} and in speech recognition {{cite:f2230579ccbde04e07dcccb7f05a8a4e2ca23171}}, {{cite:561f41f2be8acc8e32f84633b54fef083339ed2e}}, {{cite:7ee85f9dd3f25d69087a54231c3bff2d3e1d0cc9}}.
For general-purpose audio, including a variety of environmental sounds beyond speech, the majority of works are based on contrastive learning {{cite:73d2fb7653c04969db0d57c6f5a49c12a724d3d1}}, {{cite:ecb622352649ad7041c659294df6c21edd8d3f1b}}, {{cite:996c7e7fa60075d85ce28f957f65511ddbeefc14}}, {{cite:ff7de255b81634ac3cd7e952b4e3c43c3597a856}}, {{cite:9055d32533aac84bc83cbc2dec8fb4b91e97aa41}}, {{cite:729b63715a372c8f0e09c61f44d23bea87e2e4f8}}, where a representation is learned by comparing pairs of examples selected by some semantically-correlated notion of similarity {{cite:3ab815e9bfce61cb8ebf23f877500745762dfc1a}}.
Specifically, comparisons are made between positive pairs of ‘‘similar’’ and negative pairs of ‘‘dissimilar’’ examples, with the goal of learning a representation that pulls together positive pairs and thus reflects semantic structure.
One of the first works in contrastive audio representation learning uses triplet loss {{cite:73d2fb7653c04969db0d57c6f5a49c12a724d3d1}}, in which anchor-positive pairs are created by sampling neighboring audio frames as well as applying other audio transformations (e.g., adding noise).
The proxy task of coincidence prediction learns a representation to support predicting whether a pair of examples occurs within a certain temporal proximity {{cite:ecb622352649ad7041c659294df6c21edd8d3f1b}}.
| i | 3a1cc8d18f773cd45cf3baa4b4ffd245 |
We also compare FST to the Fair Empirical Risk Minimization (FERM) {{cite:eaf769cc64479285bbecccfef612c8a13451cd03}} approach. We use the codehttps://github.com/jmikko/fair_ERM provided by the authors. FERM, although a general principle, has been specified only for binary classification problems with hinge loss as the loss function, and equal opportunity as the fairness constraint in {{cite:eaf769cc64479285bbecccfef612c8a13451cd03}}. The code provided by the authors implements linear and kernel support vector classifiers (SVC) with an equal opportunity constraint between two protected groups. During our experimentation, we observed that kernel SVC formulations of FERM were computationally impractical for the datasets we used (adult, COMPAS, and MEPS). For example, experiments with the adult dataset using the RBF kernel SVC formulation did not finish even after waiting for 24 hours, whereas the linear formulation took only minutes to completeExperiments were performed on a machine running Ubuntu OS with 32 cores, and 64 GB RAM.. We suspect that this is because the kernel SVC formulation is implemented using a generic convex optimization solverhttp://cvxopt.org/ that does not incorporate any techniques for speedup specific to the problem. Hence we report results only for the linear SVC formulation. We also note that we use equalized odds as the fairness constraint in FST, which is stricter than the equal opportunity constraint used by FERM. These comparisons are illustrated in Figure REF . Clearly, our FST methods that post-process probability outputs from linear SVC (FSTpost, FSTbatch) outperform FERM substantially. We note however that the pre-processing variant of FST (FSTpre), which trains a second linear SVC model using sample weights described in Section REF , did not provide acceptable results. One possibility is that these sample weights, which are based on conditional probabilities, do not work well with the SVC problem formulation which is non-probabilistic. Nevertheless, in general we see that among all the four in-processing approaches we compared, only the reductions approach {{cite:e7610e77c93c94ac7b1c7c5565eb42c71822a078}} has performance competitive to ours.
{{figure:be6b16b1-612d-40d2-9e89-c3472fd69655}} | r | 8e7b47c44c7555cfee463cc0a479a680 |
Remark.
In real-world micro-video applications, multi-task learning framework {{cite:19a1ac4bc731a33507cf09ec88fd78af4b58dea7}}, {{cite:9d7b4bb4b7fb9abe57d7fd5ce6e492e073c91ade}} is usually adopted, which includes targets other than watch time, such as like, comment, follow, and so on.
Although these signals may not be affected by the duration bias, they are hard to collect (very sparse in the real world), while watch time is the most fundamental user feedback in micro-video platforms {{cite:cbc6c8616bf325973f7d7b3a7cd53bd09935850b}}. Therefore, our solution is essential and practical.
| d | 4420e687245ee0a034bdd84818692d6c |
Moser iteration (see example, {{cite:c0b3292bbf015cd6d2f72bca040bc5ea19746598}}) and {{formula:85f2defd-c199-48f5-9b76-182f217b1a98}} estimation (see {{cite:e9fdcfa2fb8c49de21fe4faa96067f4e69865c3c}}) yield that {{formula:91c3d7df-88dd-4b0d-a156-2c3e1cbeb9a6}} is smooth, and thus the critical point {{formula:4c22177a-2a47-4c81-8bc9-8889342a3de9}} is a smooth solution of (REF ). To this ends, we observe that for any function {{formula:99802474-47f6-4c78-befc-9922f7b3e810}} , which is odd in {{formula:c314261d-574c-4379-8b7f-152534eed3a6}} , we obtain
{{formula:0a794803-a250-49d3-9b88-69d58fab527d}}
| r | a165ef49e635a90018616ace3c1e2576 |
The charged-kaon production ({{formula:23878ebb-d4af-4b13-bbdf-35e9cc11205c}} ) measurement at MINERvA {{cite:3cb90c78ed0b3ec56405623670248aa2ce34244d}} experiment opens a new window to study the weak strangeness production mechanisms in detail. The weak processes that could lead to kaons in the final state are either initiated by strangeness conserving ({{formula:191de61c-a995-479a-a002-fddaed4d1e43}} ) or strangeness changing ({{formula:d6a02ac6-b9fb-46d6-a98a-b88bb2e2dbb0}} ) mechanisms. Although the {{formula:f9424308-662a-4c3b-ae30-120686dea012}} reactions ({{formula:317d49be-48e6-4821-8b53-0eda2972fcf8}} ) are Cabibbo suppressed compared to {{formula:9728f4f2-824b-434b-83eb-7fd51f164b82}} ones ({{formula:c63d4537-9df4-4568-8f60-cc0fc3267445}} ), the latter involve the production of massive strange hyperons ({{formula:62a98412-b14e-475b-8fed-19fcef01f782}} ), which pushes the reaction thresholds higher in neutrino energies. Therefore, below 2 GeV of incoming neutrino energies, the 1{{formula:e7b4f868-37bc-4afa-bd36-6857af51dfdb}} reaction is favoured {{cite:3cb90c78ed0b3ec56405623670248aa2ce34244d}}, {{cite:ed4320cded545e342734808844639b333b0343c3}}. In nuclei, final state interactions of the produced kaon are not very strong because of the absence of baryon resonances. However, kaons can also be produced in secondary collisions, rendering the extraction of information about the elementary 1{{formula:572eea90-6e77-42cc-bc4e-e302a0748027}} -production amplitudes in experiments with nuclear targets rather difficult {{cite:12f5f33ab42344170d84d53271c383f7563e67ac}}. As for several other processes, progress in our understanding of weak kaon production would greatly benefit from modern cross section measurements on hydrogen and/or deuterium {{cite:932700397b7fcda828f9d3315a4a67e1258d4b55}}.
| i | d913480e5c047a9f4f3eb4da706b3292 |
We have fitted 19 dipion {{formula:a82678f0-cc8e-404a-b99e-d8d5fc3267e7}} ranges(see Table I) using equation 7. We
included minijets up to {{formula:6e8022ae-378d-4a10-875d-3eb032f3d51d}} = 3 and resonances {{formula:09b5519a-1e88-4567-b5ab-2a0d7ff45487}} {{formula:011b6a2e-dc08-4bcb-84cc-ccd625239824}} = 0,
{{formula:b5a8cc62-4fb2-4efd-82db-8d2694ca068a}} {{formula:2093d785-f752-4c92-b56c-20df1b5d57e1}} = 1, and {{formula:938e57db-8638-4543-affd-ddf628ede2a1}} {{formula:a1dc519b-9aa8-4539-97b4-6c7dc6ad7ab2}} = 2. Using the arguments of
Sec. 3 of Part 1, we added the {{formula:45f90e10-cd7d-4303-bcd6-dbe0e6f9078c}} as a direct thermal term ({{formula:932329df-7d62-4e5c-9d99-c199924cd5af}} ) and
only the {{formula:0577d477-fa5d-42a9-81c7-c300686d1458}} interfered with {{formula:b690ddc7-0916-4d7a-8ecc-f1147ca70271}} = 0 minijet background. Two other
thermal terms are present in the cocktail, the {{formula:168954a2-0173-41a7-996d-4d1efe5c7f15}} and the {{formula:4a6b9abf-c277-42c9-bad2-7c1bd30fec5d}} .
All the thermal terms have an exponential behavior with dipion {{formula:2a51b395-625f-43d6-a788-6c67db326871}} and are
shown Figure 20. The spectrum of the minijet partial waves is obtained from
PYTHIA{{cite:771049a74c04a14db2ba5e384d2e10ee859b7887}}(see Sec. 5.2 of Part 1). We let the data determine which
minijet partial wave to add. We find only Swave minijet background is important
until {{formula:629f064f-7740-4b50-9cfe-f6880582d08a}} equal to 1.1 GeV/c. Above 1.5 GeV/c all four minijet partial waves
are used up to Fwave. It should be noted Dwave and Fwave are small effects.
We used PDG{{cite:73ae5b45d908a74beff5cd721b730117b3e0b9cb}} for the {{formula:a6f96c70-5128-4c44-8d6f-52ed1fb5eba7}} mass = 1.275 GeV and width =
.185 GeV. The {{formula:471746f5-dac6-4b3f-8ba2-8498a85ccb83}} was fitted obtaining mass = 0.9727 {{formula:86fb3a59-5a87-444b-9b71-3179500e78e5}} .0039 GeV and
width = 0.04512 {{formula:dc711b53-e465-4e1a-8c47-811d9a7c66db}} 0.01128 GeV. The {{formula:b2490d4a-659d-4966-b670-85f4af7c18ec}} mass and width used was fixed
because it was ill determined. The mass used was mass = 1.011 GeV and width =
1.015 GeV.
| d | 0ae1ee29a0b7125d4e607c947236ee87 |
We discuss two classes of theories. In the first class, {{formula:d637c582-0ae6-4601-aa38-666861d89981}} , Sec. and , we are able to prove the {{formula:c1c335c2-084f-4000-b517-feb7f7991eae}} {{formula:042050c6-c050-4223-a6bd-69e8da2f8832}} dualities using basic Seiberg dualities {{cite:48a3874b82a9108b0e572a8629d538af634c6469}}, {{cite:25cbc5efcb9470c680eea5fbdb28113b5eaf0e66}}, that is we use deconfinement and basic dualities sequentially, in the same spirit of {{cite:6f4aebc0a5878fbca108ad407ec38b6da88b6487}}, {{cite:8e3245ce6979e4755c3887114c759f021b05c25a}}, {{cite:c6402abe2ef442a7f998030094d3da24226f5df9}}, {{cite:eac4e0089e904d53c89f1d6fcc7c4b2650a16362}}, {{cite:9590f8160a7f925d8ba0178e6802efae735f7444}}, {{cite:513b1f4f6c508293963f1ff0bd764b02d6e6953d}}, {{cite:3ad04141e399f91316bd109d4f74759a4339075f}}, {{cite:54d112ec0ec09419076c3cf501cea4aa2150e32e}}, {{cite:3cbf1257b2043ff9a576d206cd913c446143d42c}}.
In the second class, Sec. and , we do not have such a proof and the proposed dualities are tested by matching the t'Hooft anomalies and the central charges. We conclude with section , where we discuss a set of theories obtaining by Higgsing the class {{formula:4e447483-3224-4776-bcb3-615c7521a89b}} .
| i | f921c12c159c1b77a8a855c67e16d91d |
We have established a variational formulation for the role of depth in random neural networks with batch normalization: The entropy of hidden representations increases with depth up to constants. Is this entropy increase achieved by a gradient flow in the space of probability measures? This question is inspired by the variational formulation for Ito processes established by {{cite:dcee86e310bcef5462fb1e8437c4de008b09ee8d}}. According to this formulation, the distribution of Ito processes, which obey Fokker–Planck equation, can be viewed as a gradient flow minimizing a free energy functional.
| d | fc3d941f0245e14449bb872e1abc837c |
A shell confinement model provides a new, unique boundary condition {{cite:1c3efa2d3d88b67b4ec37de3aa5bad91fea496a3}}, {{cite:40cec9d4667bdfe088249fd51a372e2d980f78f1}}, {{cite:dfb9455f35200fdd46a7bb932cf3756d4dcd76e8}}. An appropriate choice of inner ({{formula:289cba6f-d81b-4adf-bf45-78069e8d3739}} )
and outer ({{formula:1063a9a1-1b44-4a5c-8a32-c079728088ee}} ) radius of the shell can describe all possible radial boundary conditions so far reported in literature. For instance,
when {{formula:205cf4dd-8e28-46e4-a130-730483976ed4}} ({{formula:87aa5020-77f0-454c-9427-ea3273ebf4b7}} is a real finite number) it reduces to CHA. On the other hand, choosing {{formula:b554b6f2-fd41-4cf3-b7dd-2551da3de7ab}} ,
a free H atom (FHA) is achieved. When both {{formula:ccc35ce1-c219-4e54-b0b3-49a857f5a817}} are non-zero and finite, it is termed as shell confined H-like
atom (SCHA). Whereas, a finite {{formula:8aa244e1-ea79-49c0-a00d-4961d52aa3c0}} and infinite {{formula:426e2099-f04b-4a32-9eb4-7cd16a46f49d}} indicates left confined H-like atom (LCHA). All these four systems,
in general, are referred as a generalized confined H atom (GCHA). The nodal characteristics of orbitals of FHA have played a
significant role in conceptual development of degeneracy in GCHA. Previously, an attempt was made to solve SE of SCHA exactly {{cite:dfb9455f35200fdd46a7bb932cf3756d4dcd76e8}},
with limited success. Later, an accurate
numerical strategy {{cite:a6769dcc98212e3eb282a7c2f62cb46dd73d9f93}}, {{cite:1c3efa2d3d88b67b4ec37de3aa5bad91fea496a3}} was prescribed to emphasize the occurrence of incidental degeneracy in SCHA {{cite:40cec9d4667bdfe088249fd51a372e2d980f78f1}}. This new
degeneracy can also account for the presence of incidental and simultaneous degeneracy in a CHA.
The Kirkwood {{cite:7d21f1b75e47234a9608df596422ea459da3703e}} and Buckingham {{cite:fd6405f06096c38319f56e82846013b7f7f1871e}} polarizability were evaluated
{{cite:40cec9d4667bdfe088249fd51a372e2d980f78f1}}. Sternheimer perturbation-numerical method {{cite:0259ab015233fcc1836678a8b6163fc0dde38254}} was employed to calculate dipole polarizability in ground
state {{cite:40cec9d4667bdfe088249fd51a372e2d980f78f1}}. The Buckingham results are in good agreement with polarizability obtained via perturbation numerical
procedure {{cite:1c3efa2d3d88b67b4ec37de3aa5bad91fea496a3}}. The higher value of dipole polarizability in SCHA indicates metallic behavior of H atom in ground state {{cite:1c3efa2d3d88b67b4ec37de3aa5bad91fea496a3}}.
Eigenvalues and eigenfunctions of {{formula:b529335d-6251-4c90-9eb8-1b57f08688cd}} -dimensional SCHA has been examined lately {{cite:ba02bc7fc47976d73bdb603bcb6b63ae17efa5de}}.
| i | fc053d9c72a5ad16551a6ab0fd054351 |
We further investigate how our model pre-trained on ShapeNet can perform on scans of real objects. We use the Redwood 3DScans dataset {{cite:a8feb3e1e89a7c02ab3507d03a269bbf606cc068}} and test our model on partial shapes of chairs and tables, sampled from its depth images. Since the GenRe benchmark {{cite:2ff98b46f9c6ca603b22bd017424917d651491d3}} does not provide table data, the training data for the table category are generated by randomly sampling 20 views from ShapeNet meshes, following GenRe's procedure. Within each example, we present the real RGB-D scans and ground-truths from the input views.
| r | cc4d35783097fe2818718e67fe23d22c |
The physics of vector meson photoproduction is described, e.g., in Refs. {{cite:3f18647eb44c08c42cdbfc9401d5a68345089d36}}, {{cite:de8dcbf1b501082ed2e383575f722d34795b9fe2}}, {{cite:2c61eaffe47ecf1d9ab01d7b128565a3fa0d9235}}, {{cite:6f95b3d23eb3a84a64c49aa242362327a20bc7ce}}. Two vector meson photoproduction processes, coherent and incoherent, are relevant for the results presented here. In the former, the photon interacts with all nucleons in a nucleus, while in the latter it interacts with a single nucleon. In both cases a single vector meson is produced. Experimentally, one can distinguish between these two production types through the transverse momentum {{formula:7bc299cd-8684-49f1-8e35-580f5443ed66}} of the vector meson which is related to the transverse size of the target. While coherent photoproduction is characterised by an average transverse momentum {{formula:f13b163f-3706-4920-adc2-c146039d00a5}} 60 MeV/{{formula:c5756fba-6d68-4727-baa1-c115fa5432b2}} , incoherent production leads to higher average transverse momenta: {{formula:d91ccbb8-e39e-44ad-95a3-8ce6a5aa6a32}} 500 MeV/{{formula:a380591a-0419-401f-be11-cc4e1551efa4}} . Incoherent photoproduction can also be accompanied by the excitation and dissociation of the target nucleon resulting in an even higher transverse momentum of the produced vector meson {{cite:a8dd6f0bcb16350cf3250d0c87bcdb2f3df6f2cd}}.
| i | d8eaac063a63055531bc256d44d642c3 |
We find that datasets produced with Algorithm suffer from what is commonly termed the obfuscated gradient phenomenon {{cite:1bd281f6a597ce165390179dea84039d588e63d7}}, a situation where model gradients do not provide good directions for generating successful adversarial examples. However, in the past, this has only been observed with techniques that were either introducing non-differentiable parts in the inference pipeline or stochasticity to the model. Interestingly, we now observe this phenomenon from altering the training data alone and, even more remarkably, from data optimized using kernels.
| d | 2aa4a5b482beee0380b7986622e8c338 |
Collaboration naturally gives rise to challenges that originate from the fact that multiple users participate in inference. These include privacy concerns, due to the exchange of acquired samples; security considerations, as a malicious users can affect prediction; and communication bottlenecks affecting the exchange of information among the participating users.
The communication delay of our proposed collaborative inference approach is reduced by compressing the samples, thus conveying smaller volumes of data. We propose to carry out such compression by implementing vector quantization to the shared samples. The contribution of the quantization step is that the number of bits selected to represent the shared sample is controlled, resulting in overseeing the latency of the communication between the users, which depends on the capacities of the channels. Moreover, quantizing the shared features is likely to contribute to privacy conservation by the fact that the raw samples are not shared, but rather the quantized version of its extracted features {{cite:35141e670e4b854bd66ddf0c3b62026243bef88e}}. Security considerations can potentially be alleviated by incorporating Byzantine robust aggregation methods {{cite:1f5aa5dba1492f904422ff99ab786a36b39d4a40}}.
Nonetheless, we leave the analysis of the privacy enhancement capabilities of our approach and its combination with secure aggregation for future work. While we opt a learned quantization mechanism based on the VQ-VAE architecture in our experimental study in Section , edge ensembles can also be employed with alternative compression schemes for the exchanged features, such as the usage of universal vector quantizers {{cite:711ad2c9901381dc6daeaf7ccb5f6e735ff82f41}} or of trainable scalar quantizers {{cite:7ddc2fb2537425d7286849daafdf38f33b26c1cd}}.
| d | edfb54ec99dbca36360421b4c38fbd23 |
Before briefly discussing the minimization of the GL functional {{formula:116ee8e3-3525-4631-ae6f-e899324ff0d2}} , note that the matrix {{formula:56e2acd1-6444-475b-84c2-82eedac911e4}} needs to be positive semi-definite, as otherwise the {{formula:c3915ff3-33fd-4727-91cb-3fd999f9472d}} becomes unbounded below. This discards signed Laplacians like the balance ratio/normalized Laplacian introduced in section REF .
The minimization of the GL functional {{formula:f33ab9e7-a74e-4c0b-9f54-c75b63883720}} in the {{formula:af94d7eb-5229-45d5-a9b8-53d1b46100d2}}
function space
sense can be done through a gradient descent leading to a modified Allen-Cahn equation.
We employ a convexity splitting scheme (see
{{cite:a36c4745bbf6c2db4c464baf9e7aadf50ff0d5d5}}, {{cite:23270fbb3271335b57ea9a1765d7349fe7625b99}}, {{cite:ccb732f865378640d7cb1c4eb3e3f7442e2e7070}}, {{cite:f98b02a2126cfa4c7c13be0d743b126427bf9801}}, {{cite:0d1efbea8dbee4d5755bdc87be3be42eedb10039}}, {{cite:d2ba8e669a5127f645af491518ec1c4a6a8e79cf}}, {{cite:7e08ffff181bb8c33b971829c499d7ee2249af8d}}),
where the trick is to split {{formula:acd1d767-3a63-4891-b371-91fd7942a6dc}} into a difference of convex functions:
| m | c44196d87af1c88faba05fa6fa1cbc5b |
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