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The functions {{formula:52b7e61b-4561-46f2-9500-338716b39878}} and {{formula:95f67947-a82e-434a-9ab6-46aa1c48b266}} are nonnegative, bounded and satisfy {{formula:a16c9fa5-5026-47c6-9ca7-7482b49d7798}} as {{formula:9d98a2cc-40ab-42e2-ab73-2e9585f0315b}} . Thus, without loss of generality we can and do assume that {{formula:f72dfa14-5c8e-4ad2-a9cb-bd9484e133df}} is nonnegative.
Put {{formula:131c98a0-2d2d-40e4-9ea8-c35c14822ab6}} for {{formula:87a4576e-89e0-4ad6-9647-aefc528f689e}} . We shall show that
{{formula:700d12a4-3e3e-44e3-8cdd-cb03934b3e21}}
Fix any {{formula:63e8011f-718a-4b34-9be8-4f1258edb220}} . Then
{{formula:08150f33-87de-4881-b4ad-967dfac67a57}}
follows from
{{formula:fab8a762-b85f-4b28-a4fd-ad9bd0198460}}
Observe that the usual requirement of continuity of {{formula:fb437c9b-4086-41ea-9b95-9292ea944b5b}} is not needed here, for the measure {{formula:7a3b4896-bb4a-4e31-b34c-8a5031192390}} is (absolutely) continuous.
There is a constant {{formula:35017184-783a-4e6a-9011-0bda30ede598}} such that {{formula:585271b6-83bf-4065-98a5-fcd25802292c}} whenever {{formula:f3c83150-983a-4a04-a905-2e78b52600b4}} . With this at hand we conclude that
{{formula:0b9f6a78-5725-45fe-b60a-a67e04477327}}
Further,
{{formula:3be29d5b-028c-46bf-b6e5-c4bdc9920a49}}
as {{formula:90652ac3-7030-45ef-843c-6a24936f6825}} ,
where the first asymptotic relation follows from Karamata's theorem {{cite:7729f6089ca9b2ca698ba2ccf89a40b60d615efc}}. We infer
{{formula:670977fd-314e-451b-b776-7dc540db40b7}}
and
{{formula:3147b972-6dc0-4344-87d5-1e720cf67502}}
Sending {{formula:2d91d1e8-b079-4a28-a627-23e9c28ec65d}} we arrive at
{{formula:7841403a-b652-4c80-aed0-6bc3959f2071}}
For the lower bound, write, for any {{formula:cdc3bd39-7773-42dd-888a-825d705a1f5c}} ,
{{formula:10414be0-83b4-4b25-8a87-dee0118ec17f}}
Sending {{formula:b3a1a831-2ce1-4e9e-8622-ef11dee80178}} we obtain
{{formula:4ea10516-d316-4081-8b57-e02ad8d1c334}}
and (REF ) follows.
Starting with
{{formula:f7228af9-bf3c-4cbd-b5a6-f1361bbb6704}}
and arguing analogously we also conclude that
{{formula:79335db2-1914-4030-a1b3-ca547b80796f}}
Combining this with (REF ) completes the proof of the lemma.
| r | 42741908c0e6341dc6f709d5698ca380 |
It is also interesting to compare higher energy neon and iron lines from our CGM data to the {{cite:2a7468024d38888bc098d7b1295c0e8bbe5bfc46}} results as a check on the existence of our hot component. While there are hints of neon and iron lines in the XQC data, the presence of those lines in the XQC data is inconclusive. Line strengths for Ne ix, Ne x, and Fe xvii were calculated for the HaloSat models and compared to the 1999 and 2008 XQC observations. In both cases, all three lines were found to be below the noise level of those observations. As such, the relatively short duration XQC observations are consistent with our relatively weak hot component.
| d | 6324f4c167e1a72ed6c69d9bd90618e8 |
In this section, we present numerical results to evaluate the performance of the proposed hybrid beamforming design for mmWave MU-MIMO systems with DSs.
For comparison, the classical hybrid beamforming for DSs, i.e., Mink-L1{{cite:2012ba02d280f46e529ffe1091afdb081b64ebdf}}, DHBFFor fair comparisons, we only consider the fully-digital beamforming obtained by the SVD of user channels as in (REF ) instead of the PDD method.{{cite:73cd89869a62a65c95054c1da841fe9d8c253b6a}}, and LowCom{{cite:6c43adf0351b29ca2d1095c7ffe6a20b9e0dc6f5}}, and that for FSs, i.e., SDR-AltMin{{cite:5b54c01701d8a38a7a26008e7d2f9bfa7953c9cf}}, are used in the second stage as benchmarks.
The hybrid beamforming for mmWave MU-MIMO systems with FCSs in {{cite:8288ce6b365ad24c31d9614ab763d3c090606e7c}}, termed HBF-FCS, and the fully-digital beamforming assuming no IUI, named FD, are both considered.
| r | 086dfe682ffe08deb2747ef69c8a12bc |
Achieving these goals will require the development of a simple but versatile tool-set that might be useful to the community for inspecting and editing models in diverse research or industrial areas (similarly to Grad-Cam {{cite:3c754722a54363b72df4508a7b36eb8674857730}} and Bertology {{cite:10972236ffc18aceabe9d021ef6fd65025189ac2}} and many other helpful visualization tools found to be relevant by DL practitioners).
| m | 525a11bd48867f202277a99cb6134f2e |
In addition to the model proposed by Huang et al. {{cite:91852d785d7f1d2cf26abaa7d0f4fd557a0dd1c5}} we add the local affine transfrom {{formula:c93c22cc-32a9-4340-84b6-fe9723c65e83}} also known as the photorealism factor of the content image calculated from the Matting Laplacian matrix proposed by Levin et al. {{cite:08a68e63ffcafd043d67c161554e240a2192c55d}}.
| m | 37ef9319e62ee2e3e72a7923ca1a7b74 |
DIM {{cite:e8d3d0408d7d91ed090e870df3c1917080d7c442}} relies on a stochastic transformation function to craft adversarial examples, which can be represented as
{{formula:84154381-7ead-4ea0-9652-b18009750021}}
| m | 0e913b60775a4367d729339cba53cf78 |
Quantum simulations of fermionic systems on digital quantum devices can be challenging due to the anti-commutation relations of fermionic operators. More specifically, in order to carry out such simulations, one must map anti-commuting fermion operators onto Pauli operators, which naturally obey commutation relations.
The most commonly used mapping between fermionic and spin degrees of freedom is the Jordan-Wigner transformation (JWT), which follows as a natural consequence of the second quantization formalism of fermions {{cite:87b5ba1567246e596376e8506f91b01000f9a544}}. After choosing a fermion ordering in the second quantization formalism, the JWT maps each fermion operator {{formula:d062cbb7-db17-4f40-95ec-08ec9abbcae8}} onto qubit operators {{formula:9f48822f-def0-4492-ad8a-db2f1bde272c}} , where {{formula:f7882f70-8cb1-4c12-9333-b4613a1b05d6}} are Pauli matrices applied to qubit {{formula:865f223e-92ae-4e13-8967-ca721ac00a86}} .
The operator chain {{formula:a89846c8-8ddf-41cf-bc45-dbb174cafeaf}} is commonly referred to as a Jordan-Wigner string, and is necessary to maintain the aforementioned fermionic anti-commutation relations. Typical physical Hamiltonians of fermions on a lattice (such as the Fermi-Hubbard model) consist of spatially local operators such as the hopping operators {{formula:5a6808a1-3961-4f16-bfab-aa64ffd10150}} , where {{formula:6eb1177f-2d62-4807-82d8-653e16265095}} and {{formula:01aa004b-327b-4324-b5e7-f763e140cdbc}} refer to fermionic modes on neighboring sites. Even though these operators are local on the fermionic side, under a JWT they can become non-local on the qubit operator side {{formula:81b0f721-7419-47b5-b14e-255ac01aa0d1}} . The operator string {{formula:be9f00e6-1219-4744-8f5f-d67d6f6d2634}} appears when the sites corresponding to modes {{formula:32243944-e5f5-42a7-b035-9627b8c01b55}} and {{formula:84cff211-adc1-46bf-a9a9-f06cf257b8de}} are not adjacent in the chosen JW ordering of the fermionic modes. For example, in the case of a 2D square lattice of size {{formula:8e438727-f18a-48d7-9c7d-16946e4ed5f3}} , the lattice sites are often assigned an order according to a horizontal snake-like pattern. In the latter case, vertical hopping terms will generate Jordan-Wigner strings with sizes up to {{formula:8c7f3079-b823-4365-9ee0-faeaf643dfc6}} {{cite:8f7360beb06e65180f78ea9ca7039128bc6f68c8}}. The non-locality of the Jordan-Wigner strings become increasingly problematic as the dimensionality of the system increases {{cite:f4cb7c6bfd00c1f1e52acfe6d446d20fae471ce0}}, {{cite:39d29a2837d42799bcf0a349c9ab35c0e2024851}}.
| i | 8c1cc27d0c1b8519ed6d6f64addaa6b9 |
In general, the optimality-gaps are rather large compared to results obtained
e.g., for the TSP in {{cite:afd9372c9bbaa675dbef0eda44b838d2f2686988}}, {{cite:b1c8433bf8b8017266edd2ea064182fc1832cbca}}. Thus, it
seems that directly using existing graph convolutional approaches for
successfully solving the pCP may not be possible. This could be due to the
min-max objective function, which makes it different to many other existing
COPs on graphs. We think the problem can be an interesting
benchmark problem for the machine learning community as potentially new graph
convolutional techniques or other advances need to be developed in order to
obtain improved results.
{{figure:76bedc0c-f522-452c-9836-8fefb796aa19}}{{figure:e75e1a8d-42a0-4dbf-a727-37f4bb322ec9}}{{figure:7332e927-314d-47c7-83e4-ac1cd4f4fc95}} | r | 8aa337747e1e8f03ed82991973902eef |
Overall, the results presented in this manuscript are encouraging to the authors for future work on extending the approach to 2D and 3D problem spaces. Such scaling will result in large tensors, however one can leverage the sparsity inherent in PDE discretizations and utilize common tensor decompositions such as the tensor train decomposition {{cite:ca47931cb5bcc514d7177a30f17646716546977b}} for a dramatic computational speed-up. Other future directions include extensions to the case of a system with additive Gaussian noise, second order expansions of the dynamics, and novel methods to handle the sensitivities that arise in the discretization of the backward process.
| d | e015fc15e8d7a7b713ac621dfd4af660 |
and then decoded using a recurrent neural decoder followed by a multi-layer perceptron (MLP). As suggested by Bahdanau et al. {{cite:54d5a0f746754445c40ee0d31b7f26319274bb3c}}, in order to allow the decoder to attend the entire encoded sequence at every output step, we are using an attention mechanism. At every output step {{formula:8c21c16c-ac5b-476a-85f1-79160d06d705}} , the decoder produces state vectors {{formula:eb371cba-8908-4972-9efc-7650accf2a07}} and output vectors {{formula:f69e96a1-aa81-40b8-a696-faff341ec27f}} , based on the previous step context vector {{formula:049b8f90-2355-478a-a744-259870dbcf55}} , the decoder state vector {{formula:9cf43ace-aab3-4de1-88bd-0e3cae2d8499}} and the predicted visual frame index {{formula:11a40403-9c73-4bc1-9276-91989268c04e}} . The latter is obtained by an MLP that is applied to the output vector {{formula:6b9f6ea1-dea4-404a-8d20-7817ed060c1b}} and the context vector {{formula:58b5162c-6601-4327-be5c-60a6d60bb771}} .
| m | c8803ce1d43045d3de46c08568b83891 |
Finally it is worth mentioning that, an ambitious (and broad) objective along these line of thoughts is to understand the connection between different learning scenarios to dueling bandits,
e.g. feedback graphs {{cite:6d84e8a4709ac343f6dc28143231630676eacf1d}}, {{cite:c608fce0ae840bea86b0edef3d804e0122b6fa00}},
partial monitoring problems {{cite:e8b45998313d2df293c8cca07ad0f592d4588f77}}, {{cite:2239ac5bc4104c6ef68e013b46d964d6a71982ff}}, {{cite:3544f9862e0869973f8d25ac3095a5d79969aa57}},
markov games {{cite:ca61920b38921d33012a8a344e60db50339f5928}}, {{cite:ccf060ac55c15a959a0a1826d52c1d9ce749ac83}}, {{cite:0ebc44b2d6b84e25b1361b7be95273d17250d55b}},
etc. The obvious motivation being to understand how far we can re-engineer the existing results from related learning literature to solve the online preference bandits problems.
| d | 6b637387c7a00df3dcdec0e9d415a3f3 |
The classification algorithm {{formula:266ca0cb-eaa5-46a8-a922-e4a7311ec576}} we have used is {{formula:4a3e6307-a9de-410a-aeca-2fb7824f35ab}} -Nearest Neighbours {{cite:e32f035650aeb62d4abe07cbbc732b7527e1e8fc}}. Four popular evaluation metrics are used for classification tasks; these are, accuracy, precision, recall and F-score (also known as F1-score) {{cite:b30a5fbace03ea6ddcff897aa1b11452d731ce26}}. Accuracy is the overall performance of the classification algorithm, precision is the ratio of true positives over the predicted positives, recall is the ratio of true positives over the actual positives and F-score is a trade-off between precision and recall.
| m | 51a9b12a9dc48d1c0dca9eb9446861f4 |
To compare the perturbations generated for different NR-IQA models in a more intuitive way, we visualize the absolute residual images (i.e., {{formula:fcbb25a1-c40e-47b9-bf31-8ae72c582d3b}} ) in Fig. REF , where DISTS is used as the image fidelity measure in Eq. (REF ). The primary observation is that the difference in perturbations provides useful clues on how they extract quality-aware features. Specifically, perturbations for BRISQUE {{cite:b7d6920e48ba80624dc62e76cec0e2af3b432d19}} mainly emerge in smooth and textured regions, where manipulation of individual and product of locally normalized luminances is much easier, as a way of cheating the built NSS model. The learned codebook in CORNIA {{cite:22f902d440f576a70131187422a0e636888e7c92}} contains many Dirac delta functions of different locations and edge filters of different orientations, for which the selected texture and edge patches from a test image give the maximum response and thus are used for quality computation. This may explain the perturbations in Fig. REF (c) are concentrated along the edges and in strong textures. The blocking perturbations in Fig. REF (d) appear primarily on the objects (e.g., the lighthouse and the fence) and along strong edges (e.g., the image borders due to zero padding in DNNs). We believe this arises from the spatial pyramid pooling {{cite:6037dbc58fcb27db3e88bac287696a03b1510b17}} layer used in Ma19 {{cite:3079019e24e9b54e8217516a6067a110b3dc8adb}}. When the pyramid pooling is replaced with global average pooling, the perturbations by Ma19 resemble those in Fig. REF (e) by UNIQUE. In addition, compare to BRISQUE and CORNIA that only accept grayscale images, the perturbations by Ma19 and UNIQUE occur in all color channels (not shown).
Finally, nearly all pixel perturbations are less than {{formula:cd34b754-985c-421a-b800-b2a0c37b8b56}} , justifying the effectiveness of our psychophysical experiment to identify counterexamples that are below JNDs.
{{figure:3d972daf-2717-4ac4-8a8f-9eb3fcaa4b9d}} | r | 1716889f11d436a5850fd7a058a74672 |
Several measurements of {{formula:1cb134eb-258f-476f-b2a2-f261d0915824}} at high {{formula:b558750a-9a25-4ef8-8928-c7b1e597a151}} for different {{formula:f1f77954-889f-40fe-9baf-fae59f2a2d4d}} {{cite:3804fd0d2abf615749aeeaae89e87024de60ea21}}, {{cite:a6b343cdaba6838977e9b1e233f4dc84a39bf652}}, {{cite:f0b30ff7f2e2798b02a0f20e9d170127946a30ba}}, {{cite:de4692b90272ed515aef4c79b22a7ddbd11f3c8e}}, {{cite:8ee8249af6e4d8344589a217c7b4ae24fdc3c049}}, {{cite:f6608d0478f862654f9165c5c1c41a766528d515}}, {{cite:47800f6f24dd4b254ea1630fc320fdcfdcb2754b}} support the formation of a dense partonic medium in heavy-ion collisions where hard partons lose energy via a combination of elastic and inelastic collisions with the constituents of the sQGP {{cite:967636d6993d5697672f6c1ced0ec12a3dccc6dc}}.
Results from {{formula:b2410b28-b79f-4da8-b575-6f224a9f51a5}} collisions at {{formula:b9c92862-a3ca-4459-b8f6-f5410fabd656}} TeV showed that within uncertainties, the suppression is the same for pions, kaons and (anti-)protons {{cite:61532163aca65f6ced34920ab1cf3680ffc20f54}}.
Moreover, the inclusive charged-particle nuclear modification factor measured in {{formula:36c5f75f-670a-44ea-a308-268fdfdfaf21}} collisions at 5.02 TeV shows that the suppression continues to diminish for {{formula:ebe3bff3-7ee1-4904-99cc-1c0227de1d9d}} above 100 {{formula:2f1b0626-d3bb-444b-8941-dbf941d52437}} {{cite:90cbe3470a541daa1b0682342458309da428914e}} while the suppression of jets saturates at a value of 0.5 {{cite:03fdb440aab72d1baad04945402b1ca03660ad4d}}.
Particle production at high transverse momentum has also been studied as a function of the Bjorken energy density {{cite:531151cd96920807848348af3d57893b58047ba7}} and path length {{cite:64c0fa6860dc58889e006832f866b575a48bbf12}}, {{cite:175bbc16f136a8ed2f81b2e3b2685793614741d6}}, {{cite:13d0e0260928518492ff861f3c461af33d129360}}.
The results show interesting scaling properties which can be further tested using LHC data at higher energies.
| i | fdacbb76fe7d957777f3e807dfe00171 |
Keeton and Petters established a completely beneficial framework for computing corrections in a standard asymptotically flat metric theory of gravity {{cite:b0bd54e09f346e07e42011040adf1702785e5300}}, {{cite:a53f9a9a6beeee4e78371660391a04cd131ee1f8}}. The central focus is to illustrate a way to manage lensing in computing gravity theories using PPN corrections upto third order.
| m | c54b9d69b78a6dffe3e9d99c257283b9 |
In recent years, researchers have made relevant calculations and studies on the proton mass radius using vector meson photoproduction data.
In ref. {{cite:c6ed9657e3c2d909fa8bf741f49bc15be5acef26}}, the gluonic contributions to the quantum anomalous energy, mass radius, spin, and mechanical pressure in the proton are studied by analyzing the near-threshold production of heavy quarkonium, and proton mass radius is calculated as 0.68 fm. By studying the near-threshold differential cross-section of the vector mesons, one work {{cite:f7380bd1b8fa046a9e7693ed8694f254614783fa}} get the average value of mass radius is {{formula:900b8a01-c66d-4932-870b-9e3ed8e5f415}} fm, according to {{formula:2c011418-5bd4-4c22-9dd7-cd781bd173ee}} , {{formula:78ea3e15-16ef-4ecb-b3cb-ec0389baa9b5}} , {{formula:7dfe4e2e-a4ce-4346-bb7c-3141d6aa6ab8}} experiment data {{cite:26c808761c79569404c7f274cfc8443b4fd51926}}, {{cite:2b4037443a54d2c9be656e3876baa8467a5e5eb0}}, {{cite:1ed98a513b9a375c4321efebecc6c9f40359bc28}}.
Kharzeev calculate the mass radius is {{formula:a8ee9cf9-1753-44a8-9b61-75f59fd25e23}} fm {{cite:a697d85886aa77270a94d162a65f424a47748e7e}} according to GlueX data of {{formula:28e544e4-eeae-4756-96c4-dfbbf76e71d1}} photoproduction {{cite:26c808761c79569404c7f274cfc8443b4fd51926}}. One noticed that the proton's mass radius is smaller than its charge radius, which may mean that the mass distribution of protons is tighter than the charge distribution, and different interaction forces correspond to different proton radius.
| i | d2c74f66ab3213601eb91bededcf8a90 |
The Belle II detector {{cite:895013b29631ee460ad7129a72f9b9f2f2c9d5f6}}, {{cite:0e726e518b2fde4f7bb23bae185ff081d92315f7}} at the SuperKEKB accelerator complex {{cite:c404aaf26c0a2096d9b5ef519e3dd1ac433903c7}} is a super-B factory covering a wide range of exciting physics topics {{cite:6c8c984b3a47d5249da1373684ca678edfab4a14}}. To achieve the project's research goals, a substantial increase of the data sample to 50 ab{{formula:1af0a007-2627-4021-92e0-9db1f12d536d}} is needed, and for that, the luminosity has to reach the ambitious goal of {{formula:e615a927-f9a1-4652-8637-fb7e0289066c}} cm{{formula:21730409-ca43-4d9f-9d10-4aae7c98b37d}} s{{formula:c951105e-61a2-4731-9953-e42b4fc1ffd8}} . The progress towards the design luminosity is accompanied by research and development of the accelerator, detector components, operation methods, as well as their upgrades.
| i | 0b1873390b8f05751798b6e704fcb68b |
The generalizability, which enables an algorithm to handle unseen tasks, is fruitful yet challenging in multifarious decision-making domains.
Recent literature {{cite:e77782bbd6697c190f9a980ee224b42fc83f5ab0}}, {{cite:2108239e5d2d462c81dfa52757e0a088af4b54ec}}, {{cite:166d1882e69d97cb1035eb2128dac86239706e6f}} reveals the critical role of reasoning in improving the generalization of reinforcement learning (RL).
However, most off-the-shelf RL algorithms {{cite:7c694f05b82c360b7cc0614361b0897bce9b4712}} have not regarded reasoning as an indispensable accessory, thus usually suffer from data ineffciency and performance degradation due to the mismatch between training and testing settings.
To attain generalization at the testing stage, some efforts were put into incorporating domain knowledge to learn structured information, including sub-task decomposition {{cite:11f58e7c46f5f21c80d027a7cc99c66b6b94bd59}}, or program generation {{cite:23d4ee69cf04487d03d779cb2b802a14f3035ce8}}, {{cite:f0bd6bd9c2fb5c524d724685c045282cd46c1fec}}, {{cite:50bda10475cab5f553513fe1a70b1e350ca341a8}} and execution {{cite:7f9cc532305ec09987a3f20378e775120453538f}}, {{cite:7f58d0a1b335be54f5c2667f8596846dbc2a0f07}}, which guide the model to solve complicated tasks in an explainable way.
However, such symbolism-dominant methods heavily depend on the re-usability of sub-tasks and pre-defined grammars, which may not always be accessible in decision-making tasks.
| i | 6eaeab2bb7745f5d797eccee4baff137 |
The demand to process vast amounts of data generated from the high frame-rate, high-resolution cameras has motivated novel energy-efficient on-device CV solutions {{cite:16b509a1c2b3a83badc55e36e7b5f581ac22ae12}}, {{cite:6bb1b26f878bde7ff66bcefa618fae89784a4da8}}, {{cite:e1efea7975ed149947009afb08c59928334ad92c}}. Visual data in such cameras are usually captured in analog voltages by a sensor pixel array and then converted to the digital domain for subsequent AI processing using analog-to-digital converters (ADC).
Hence, high-resolution input images need to be streamed between the camera and the CV processing unit, frame by frame, causing energy, bandwidth, and security bottlenecks {{cite:e1efea7975ed149947009afb08c59928334ad92c}}. In fact, this energy may actually dominate the total energy incurred by the CV processing, particularly with the range of effective model optimization techniques developed by the CV community {{cite:5cd48a31abf047ebf23db1cc36243b240685e9da}}.
One such technique that we adopt in this work is the conversion of the traditional networks to one-time-step SNNs {{cite:a40535ce72c504d055e0f52f015ca0063bdb6642}} (no temporal overhead) that achieve high sparsity and avoid expensive multiplication operations, thereby improving energy efficiency {{cite:bc79793e4f148bcc9a6a34eeeaa9b74c34c654eb}}, {{cite:2ad22da6ef17d1d033c934026d025aed65592c91}}.
| i | 5f868a27cae3614ff19009c26902e683 |
There are many physical and biological processes in which the mean-squared displacement of the particle motion grows only sublinearly with time {{formula:3312ed88-fdb5-4ecf-8cd5-4c04ea110125}} , instead of linear growth. For instance, acoustic wave propagation in viscoelastic materials {{cite:19dce4dc76fbea831f171a53bc1173b7044619c8}}, cancer invasion system {{cite:208053b8675edf95dd2ef5695eb43b2709f798cc}}, anomalous diffusion transport {{cite:e633ec1b4e501c55c0bd2e0e78cf1d2360aa0b6d}}, which cannot be described accurately by classical models having integer order derivatives. Therefore the study of fractional differential equations has evolved immensely in recent years.
| i | 6148c0b6cae71b568c5acddab89edd5d |
Following {{cite:9b0286183efc633718ab32bfc0a89dc61dca4cd8}}, the cubic term {{formula:41bd6daa-ebb2-460d-b152-4028b7e57e5d}} can be reduced to a quadratic term with an additional ancillary binary variable {{formula:aeb05eff-59da-464d-a9f1-a653f1b2d90b}} , i.e.,
{{formula:21094476-32f0-424f-94d0-9a333deb26d9}}
| m | cf6cb323b66f7d0a4f44f1eb71767455 |
However, there are various sources of noise and wavelength dependencies that could complicate the interpretation of such assessments. A more comprehensive approach would be to analyse all wavelengths simultaneously, and indeed computational mechanics offers approaches for multi-variate datasets, as well as for continuously-valued data {{cite:f704e35919ef2b074eaf05378f214288bbc55301}}, {{cite:a692b9d6133c16a3d025e06e60158a2de551be07}}, {{cite:691b2ab6270e6d87111aa0080c0486d1da20f075}}. Additionally, while statistical complexity quantifies the size of the minimal predictive model of a process, the Shannon entropy rate quantifies the degree of randomness in the process, or the rate at which `surprise' is generated {{cite:8089480fa334b74eeec5a654020b0149f633c560}}.
| r | 88f3d90f7b6ce048877a3680912af9c6 |
In section we show that by changing the meromorphic (3,0)-form on twistor space we can obtain a range of inequivalent actions on {{formula:7567d9da-8a9c-4c55-9b38-03d375df5234}} for the ASDYM equations. These include the action obtained by Chalmers and Siegel in {{cite:9936a047573ffcdef61a6190263db8ec992e3ca0}} and an unpublished action of Mason and Sparling appearing in {{cite:55d6d61142e69f00defa70836c977eb6f904b1f5}}. We also show that by choosing a meromorphic (3,0)-form on twistor space with zeros we obtain 4d theories which are not equivalent to the ASDYM equations, but nevertheless yield 2d integrable theories under symmetry reduction.
| i | e25423b4424e5d46f360f4c7f4edcead |
We further evaluated the transferability of the searched cells by ITNAS on other three benchmarks, , CNIC-10 {{cite:6ee93fbfefbfde385f2669367fa0059ffa49ab70}}, CIFAR-100 {{cite:4759348b282e6dbbb6d774396a363d5e964d57fd}} and SVHN {{cite:d15d52b469cf055b250aa6409db0fdd87a26ae52}}. CINIC-10 is an extension of CIFAR-10 via the addition of downsampled ImageNet images. It contains {{formula:6eb5a358-f53d-47a2-9b66-002146465d9f}} images of 10 classes. CIFAR-100 contains {{formula:0c2eb742-0201-4e42-b751-11dd91e93bb3}} images from 100 classes, including {{formula:e92375f6-cb00-485f-a97f-86416b619a4c}} images for training and {{formula:ef8d457b-1d87-4af2-af55-3fe28af6507b}} images for test. The image size is {{formula:83f5f992-367a-49fd-a84a-ec83cf520037}} . SVHN contains {{formula:53683471-7697-46f3-971a-46920f88dcbc}} {{formula:9f647a5e-df36-4234-ad97-d1e1248b1968}} real-world images of 10 classes of digits and numbers from natural scenes. For a fair comparison, we adopted the same network configuration and hyper-parameters as ASAP {{cite:f254c2de77a1e1af1a0db78372146d578c01c558}}, except from the searched cells. The results of ITNAS and SOTA methods are summarized in Table REF , showing that the cells searched by ITNAS can generalize well on other classification tasks and outperforms other cells searched by SOTA methods. In addition, ITNAS sets a new SOTA on CINIC-10, , {{formula:6e33e3b1-37d3-43d7-a138-e0a5007c7816}} classification error.
| r | 1f193360e0d58388b261a32d70d389d1 |
Our work in this paper may be pushed forward in following directions in future.
Firstly, one may check the inequalities of {{formula:17a7de29-1842-4dff-ab1e-84d2303a2554}} in time-dependent bulk gravity, which could improve our understanding on the dynamical properties of {{formula:a414583a-e454-427b-863f-ca013e98e2f3}} . Secondly, it is very desirable to apply the algebraic method proposed in this work to explore more inequalities of {{formula:7982925c-214f-48a9-9990-16688be9e93f}} , especially holographic {{formula:43156622-1192-4349-abd2-36e6f0f083bc}} inequalities such as MMI, which might impose new constraints on holographic states. Finally, it is also very interesting to consider the inequalities beyond the leading order of the holographic entanglement. For instance, one may take
into account the bulk corrections to the holographic entanglement as discussed in {{cite:c36da61e011dcb23453e1e5953405eb498f58ee2}}{{cite:93461853d74d2b59466630cd78795dcc0d8035b0}}, and then check whether the behaviours of those inequalities would be changed.
| d | cc174253678a23adbcf97671f30533f5 |
Due to the above-discussed relations, the steady RDM is approximately commutable
with a renormalized Hamiltonian {{formula:12fa9001-6871-4d9c-b339-579b557029a3}} of the central system, which includes certain averaged
effect of the system-environment interaction.
As a result, decoherence may lead to a preferred basis given by the eigenbasis of the renormalized Hamiltonian,
even under a dissipative system-environment interaction.
This phenomenon was observed numerically in certain specific models previously
(see, e.g., Ref.{{cite:bb639980ac28cc1afdf6b739a855f01c7584d449}}).
Beside the field of decoherence, results of this paper may also be useful in other fields
in which properties of steady states of small quantum systems are of relevance,
such as quantum thermodynamics
{{cite:a09b29ef2663df082fc3dc17b99ef5cea29d120f}}, {{cite:3b8d4859eb3ba54662918b91b3ca52b0041440cf}}, {{cite:08980cf6129de1e961a2a780c794b25b5c461764}}, {{cite:7a8b45119b647bd10cb03d6f956796d6d6565988}}.
| d | 1c4128ee8745c8ba32e409825b3615a7 |
where in the last equality we have used the sequence of primes
arranged in increasing order. (For complex values of {{formula:e39ad71a-3e59-448b-9fc6-b2de37ffe144}} , by
{{formula:59f36eb7-97b3-4e42-a2aa-d6c7ca84e7c8}} we mean the main branch of the logarithmic
function, defined by the usual agreement: {{formula:c57d44ce-70d4-4bad-a8c9-fb2acfc227dc}} if
{{formula:0428f25e-df77-435b-bf1b-810882f9cd16}} ). It is clear that {{formula:57b404d8-dfb9-4954-8a42-ff4e8d1051c3}} is analytic for {{formula:bb7b677e-d453-48c1-b90f-98c34544b75e}} .
Moreover, Fabry gap theorem immediately implies that the
circle of convergence {{formula:c18d1073-0346-4287-b1f1-8de12535685a}} is a natural boundary of
{{formula:7fceded7-aa07-45f9-aadd-81064dc70b46}} and {{formula:f096baaa-aa02-4d29-9f4a-f5f8f80e0189}} . For the sake of completeness, we state it below
and refer the reader to {{cite:1dabe3568d8e23a37fa68e67b7a1ce1d20b2ba72}} for its proof.
| r | a96bd2accaa594940f5627ba3037b88a |
Depth Estimation with Learning-based methods: Our depth estimation could be improved for both better depth accuracy and faster processing. The recent NeRF {{cite:c7e713af22edce6aa245944478e81eef8f3aac40}} could provide a clue to improve this. Although, we observed that naive NeRF has converging issues when we train it with 360° images, which we believe the issue is related to the MLP network. The main idea of NeRF is to use a learning-based method to learn the representation of scene. The scene information is still described using similar techniques from the classical MVS, such as ray sampling. When performing ray sampling the images will be converted to 3D points, thus, the format of the image does not effect the result of this process. Furthermore, as 360° images have advantages of FoV compared to normal perspective images, the use of 360° images should improve the result. Thus, replacing the MLP network in NeRF with a more effective learning structure, and use the improved NeRF for depth estimation, could be a good next step to improve our pipeline.
| d | efbf1f4f0201eb6a9e51df19c329d73f |
Theorem A.4 ({{cite:7f216b0ba91b4cd0369d48a78ad6ed145aafa3be}})
Let {{formula:0d1e43cf-5593-4323-a601-20f6411ad4f5}} slowly varying and {{formula:24ca6a42-139f-49a6-806f-cdda818c27ef}} . Then the following statements are equivalent.
| r | 7f370a59e7a1ccfcb3d5453ff0b0bfe4 |
With the popularity of learning based methods in the field of robot learning, learning based terrain adaptation methods also started to gain significant attention due to their effectiveness and robustness ({{cite:453ecc642a2ae976c2d72a78fc526d91a5d48c1b}}).
Terrain adaptation was initially addressed from the perspective of online learning where the model parameters were updated continuously in the execution stage ({{cite:c9fd70cdbc2d9ea6de69285c52d893d9e84d707e}}).
Although successful, these methods lacked the ability to adapt on the fly with the changes in unstructured terrains.
This led to development of open-loop control methods that generated navigational behaviors according to the terrain characteristics ({{cite:286433b852adb94ed986c4b6bd15eb5ae3aa6dd8}}).
Reinforcement learning based navigation was employed to generate stable locomotion patterns for terrain adaptation ({{cite:e5eda280943330803dbc54b3b22b25465e860131}}).
Techniques based on inverse reinforcement learning were employed to mimic expert navigational behaviors to achieve near human-level maneuverability ({{cite:6e1931d0f575f6c78dccf7a08057c4bbeefcd72d}}).
More recently, an approach for terrain aware apprenticeship learning has showed promising results for ground robot navigation on unstructured terrains ({{cite:e396bb168a98763e7632cd59818839b8a243d705}}).
| m | 43922cdf0c7e5650bc51250f58f6ab07 |
In order to make an universal approach, we apply redundant sampling strategy in our scheme. Redundant sampling means to acquire more samples than the size of imaging resolution {{cite:083cded02348e589638225886c218750c012a0aa}}. It is widely used in phase retrieval problem as it can provide more independent equations to determine the unique solution of non-linear detection equations. In our SPI scheme, redundant samplings can be achieved through dynamic mask modulation, and the advances of high performance spatial light modulators (SLM) make it convenient for the experimental implementation. Finally, solving Eq. (REF ) from redundant data could have different approaches. For examples, semi-definite programming {{cite:cd95c38690371f76102e1570d3ed135bc9db8468}}, {{cite:b3ca76dbad9486078cc5fdfe8bbd60d534b8794c}} and non-convex optimization {{cite:c287b3cceb91374e6bdf7e69f84c200399c6101c}}, {{cite:61ca6c6dca06f9c1cb1ba52131fb9aa0f1a42b68}} are two classical schemes. In our work, we tried out various algorithms with both simulation and Experimental data. Based on the comparison of different reconstruction results, we adopt truncated amplitude flow (TAF) algorithm for its performance both in recovering quality and calculation speed. TAF algorithm is an outstanding non-convex optimization algorithm that apply a generalized gradient decent method to minimize the loss function in a phase problem{{cite:c287b3cceb91374e6bdf7e69f84c200399c6101c}}.
In our work, TAF algorithm can work out reasonable reconstructions with various generalized objects, even for those with steep phase changes. Previous work has reported that a {{formula:68461275-ae8f-4f8b-995c-4316444cb5b3}} sampling ratio is the minimum requirement for determining the unique solution of a complex object {{cite:3805ec8036efc11c00a9374cfa97f30ebd5e860c}}, {{cite:7109018d9ee315a46a2116e93d08b24d0922add9}}. In our scheme, we will show that a {{formula:cc7a8ad5-4a2e-4aa4-936a-7fd4bda21968}} sampling ratio is able to generate a clearly reconstruction. If we take into account that each pixel of the reconstruction contains two variables, this is almost a reconstruction in a full sampling condition.
| m | 0f461f5f89b26c6ddf69cd2ce2271a14 |
We take quark suppression into account by multiplying the Boltzmann distribution by a global “quark suppression” factor, which is smaller than unity.
The anisotropy parameter {{formula:9f6b3e65-a3a0-49da-9634-32a42be2edd5}} and the quark suppression factor are computed as a function of time using QCD kinetic theory {{cite:a7a971fdb49c648bc83e2c53e5653d276e701d90}}.
More precisely, we use QCD kinetic theory to evaluate the pressure anisotropy and the fraction of energy density carried by quarks.
We then match the anisotropy parameter and the quark suppression factor to these results.
Note that we could have used QCD kinetic theory to calculate directly the quark distribution.
The reason why we choose not to do so is the following.
There is by now strong theoretical evidence that the evolution of the pressure anisotropy is fairly universal {{cite:bba047fab2b71bef6d797e9d23e7cf8e6142a77c}}, {{cite:bd69d1b18c0ab3896888f29577badb672d253517}} and does not depend on the details of the microscopic dynamics {{cite:469ab558b3a5e0c90defdfc59e13c52b1d4a2d78}}.
We therefore believe that the results we obtain in this indirect way, through a minimal distortion of the Boltzmann distribution, provide an efficient, transparent and robust way to investigate the dilepton spectrum.
The only free parameter in the calculation is the viscosity over entropy ratio {{formula:abe2cdb8-5186-4775-93e8-c341c1260c54}} , which is assumed constant, and fixes the normalization of collision rates in the kinetic theory calculation.
| r | 25c053b35600cf0183b08f0dd4492d59 |
A great advancement in object detection is carried out by YOLO stimulated models {{cite:48817f8e17b4f5df578a871e05d642009244bae0}}, {{cite:c59a774e3eb700d187a7dde798dcf4a3ec903214}}. New features: Weighted Residual Connections, Cross State Partial connections, Cross Mini-Batch Normalization, Self-adversarial training, Mish Activation are used in YOLOv4 {{cite:499f6b846aa91cc43794d7550a06617add89b1b6}}.Tesseract 4, a latest released stable open-source OCR engine has Unicode (UTF-8) support and it has the ability to recognize more than 100 languages. Tesseract 4 has a new, neural network-based engine specifically Long short-term memory (LSTM) based neural network.
| i | d7c499182f859a69133079a146a13317 |
Label Distribution Matrix Learning.
Inspired by confident learning ({{cite:be9406d0a71c495f63b4444ad9872d35f8f2211a}}), we develop a matrix of label distribution with a Gaussian before estimating the uncertainty of the labels.
For the data distribution of each label value, we use a Gaussian distribution to delimit the distribution rather than other multi-peaked distribution priors, and numerous kinds of literature have verified that this approach can eliminate the uncertainty ({{cite:1350ae275df75e7150ed76ee31333cfe762f5024}}, {{cite:9e3984c1fac505646013417b5cf02af27c375204}}, {{cite:d2f02aefe440caece7c3cf21a4867b5c298dd2c5}}, {{cite:b2f5d01faa45a06c4d7d2c851693a30785e21c9e}}).
Furthermore, to capture the global correlation between labels to generate a standard label distribution, we employ a self-attention mechanism to model the label distribution matrix.
To obtain a label distribution matrix {{formula:9a7c9772-df8b-4967-beca-e4fa83b00e27}} , we need a latent feature {{formula:3f30f0a5-55d7-401a-87ed-1ecc0ad7d26b}} from the SNN and a coordinate matrix {{formula:99140548-d014-464c-88ea-11151f725e8a}} (GCN denotes the graph convolution network) that passes through the graph convolution network.
Specifically, first, we initialize a matrix of coordinates {{formula:fc325f94-dfb6-470f-8433-1dcb5bc55cd8}} {{formula:7f39ab13-642b-4d76-9ae7-121c010fa3a6}} based on the functions (torch.randn) provided by PyTorch.
{{formula:e4ed0f9e-a18b-49ff-adc6-30134c67af87}} denotes the number of nodes and 64 denotes that we assign one feature vector to each node, with each feature vector sampled in a Gaussian distribution.
To build a graph structure the data needs information about the edges, where there is an edge with no direction between the nodes.
So far, we built the node with the edge information and have the ability to integrate it into a graph to input into the GCN.
Our GCN includes four graph convolution layers and four activation layers, where the activation function uses ReLU.
These four graph convolutions include 64, 128, 256, and {{formula:53733e44-2fd2-4818-9fe4-1b36b2960876}} neurons respectively.
There is one key message to note, the output matrix {{formula:799395d4-a24b-4c3a-abb7-60b8fccde9b9}} of the GCN is filled (torch.repeat) with the same number of samples as the latent feature space {{formula:e4fa91b2-d2fc-4036-ba7b-d7d8192cefa2}} .
Then, we use {{formula:54f46497-4119-4cbc-a0f9-ac197d6a9f18}} to look up the table in {{formula:a43a8f38-ab3e-4100-81a4-ccf0899dc24a}} to obtain a matrix by using flatten operations.
The {{formula:d0757696-3423-447d-a9cf-7617a731d4c2}} label distribution values include a {{formula:15a5bf57-8a09-4248-b798-768ec154bdb5}} vector to form a label distribution matrix {{formula:d02e3b90-8465-466e-9b67-7a19e97f4197}} .
Each vector is constrained by a designated Gaussian distribution {{formula:295ef9e6-ffa1-4736-b32f-b48421f672ca}} with parameters whose mean is the value of the label distribution and variance of 0.5.
Finally, this matrix is squeezed by using a self-attention algorithm ({{cite:7a05eabf4e8e1c1fc1d490bf72d6edbdc76043bb}}) to obtain the corresponding label distribution for the samples.
| m | fb1c9586d8174c5043426a6f4dfe98ca |
Swin-UNet {{cite:9d3c6184025b97b34cb3d05706ceb64250887e10}} used the Swin Transformer in the encoder with shifted windows approach. The image is split into several patches and fed to the encoder extracting spatial and global features. The decoder uses a symmetric Swin Transformer consisting patch expanding layer to create the mask. The source code is available at https://github.com/HuCaoFighting/Swin-Unet.
| m | 55c666e96177c699c90ebb1738462ec4 |
Our results suggest that training can be more effective if each module is trained separately with other modules already trained; similar to what has been found in curriculum learning {{cite:98313e59315d73fde22ae792028dd7fe3520500c}}. Also, freezing the feature extraction layer after initial training and using this layer for training other modules, shows a considerable reduction in training time. This indicates that training of complex learning systems should be accomplished in a structured fashion, i.e. training simple modules first and independent of the rest of the network. It aligns with the paradigm of bottom-up learning approach where complex behaviours could arise by generating and combining simple ones {{cite:3ce64196ac29c895d380a4de62223b0239619906}} of which motivates the adoption of Brook's Subsumption Architecture {{cite:6489ac9e425aca9d9ab32725b46d17a5946786c9}} in this work.
| r | 7a8b109e2c84c63462ee8a400397d25a |
It is possible to change the definition of entropy, such that
maximum entropy applied to the transformed measure of entropy plus
the direct constraint {{formula:4ee8d130-5b58-4410-b2c4-4294b03e3bdb}} gives the correct answer
{{cite:eacc17744d0b79c9120c91a18bc3948e828d13b4}}. The resulting probability
distributions are of course the same when transforming the
constraint or using an appropriate matching transformation of the
entropy measure. We discuss the mathematical relation between the
alternative transformations in a later paper.
| d | cff316fd55db6321f1d71872d8538423 |
The increasing demand for high data rates to support emerging applications (e.g., vehicular communication) has induced numerous research challenges in high mobility networks {{cite:03aa2b243c148fcd3da511a77db17c6e78e45477}}. Millimeter-Wave (mmWave) is a promising candidate for these applications to support high rates {{cite:99229219ccc90054d0a4e522cb4d8f7ce29cb2c5}}, thanks to its large bandwidth availability {{cite:d430316aa6f627f3e580628561932e616188248d}}. In a dynamic vehicular environment, the transmission from a multiple-antenna base station (or generally a relay) to a vehicular user equipment (UE) depends on the spatially correlated channels {{cite:857820efdea988056808ebe7e164ef9c3197530f}} which are determined by their relative positions. Since each relay’s location is different, each relay will experience different channel characteristics towards its UEs. As such, having a fixed pre-defined beamforming codebook for all relays will be inefficient. Instead, there is a need for each relay to learn its wireless environment
characteristics (i.e., channel covariance matrices), then construct a matched beamforming codebook according to {{cite:6b9410972b3d97f519abd76d9ccf957cc4274302}}, {{cite:8fecfc58f28f9dbec71769c2f169a31c5d4635ee}}, {{cite:1008853d1259e3c0cee864c75fa4ed3c37bb4e58}}. Learning the spatially correlated covariance matrices can dramatically reduce the network overhead needed to design an environment-aware beamforming codebook {{cite:1008853d1259e3c0cee864c75fa4ed3c37bb4e58}}.
| i | 41b647ad1b2921d1ad0a1488030431d4 |
HumanEval {{cite:6102d242d74bdf5f16324313920fe7f543f4359a}} contains 164 hand-written code generation problems. As mentioned in Section , the evaluation metric is pass{{formula:f94129e3-822c-4d61-858d-f49b5108f093}} . We use the same parameters as those used by Codex, except for the stop sequences. The stop sequences include \nclass, \ndef, \n#, \n@, \nprint, and \nif. We generate 200 programs and apply nucleus sampling using {{formula:e3d14c86-fe2d-43ff-96ac-aa607a71e8bf}} . As in previous work, we try various temperatures (from {{formula:255fdb58-c024-4217-80ea-d8811404d598}} to {{formula:72027520-4520-4e75-87cc-d618a74dcdb1}} with the interval of {{formula:4f2ba67c-1b7a-4cfb-8450-9b41543f9051}} ) and report the best result for each {{formula:1fc01088-3c29-4316-b580-24e093e8044e}} .
| r | 17aee403bf8f49dc4135550ae4e409f8 |
We note that a different notion of dimension was considered earlier by Linial, London, Rabinovich {{cite:681ddd5d774d4c463e40b71ae55302540a86baa7}}, and Linial {{cite:1ff6faceefbde36a15ab3506f0e35223953f1b98}}, namely one defines the
dimension of a graph {{formula:7909e5b2-995a-4822-850c-39ceb9941644}} to be the smallest {{formula:a35f1e61-380a-4fd7-8fcd-3572d6a28842}} for which there is an embedding {{formula:6c6957aa-039d-4821-a4f1-b2eb455da7a8}} so that {{formula:5e906ed5-919c-4217-8d07-456744bb2ae7}} for {{formula:1857e292-1ff6-408c-8440-d4567481cbfa}} and for some {{formula:f544b8db-a998-4e56-ac8f-650b00b599e0}} ,
{{formula:7a8860e2-781e-4b87-8866-4f9c6d4c8aa0}} if {{formula:f01c815f-1e01-40b3-880d-8df074dfa31a}} are adjacent.
Krauthgamer and Lee {{cite:72bdfae4a7f8de276ea6cbf750bdc7250fced54a}} showed that graphs of polynomial growth {{formula:00eccb6c-b9a7-4d47-b5d8-1b2a866ca60b}} embed in this sense in {{formula:6f85f2d9-7f22-45f2-91d3-803630bdc548}} . Bonamy et al deduce from this in {{cite:2b3361c4af4f15c17538dbf3c630c4e76fbdf42b}} that graphs of polynomial growth {{formula:f4533d03-dac0-4464-b25c-7b296d0638b2}} have asymptotic dimension
bounded by {{formula:2323dc1e-20c3-4fca-a523-391a96777832}} . It is further shown that graphs of superpolynomial growth can have infinite asymptotic dimension.
Benjamini and Georgakopoulos {{cite:5bb723f7b84818e4f2f939474af35bde2dda17d5}} show that planar triangulations of subquadratic growth are quasi-isometric to trees (and so they
have {{formula:924b7a81-5dd2-4639-8e66-24680e75fcd4}} ). Tessera in {{cite:4b6311a400fdaef6913f85e7108532dbd5089da2}} studies geometric properties of general graphs of polynomial growth.
| i | 54b72cbc17f38981c29d6d20ea83d7a8 |
Imagine that you want to endow an autonomous driving car with an optical system that can localise and detect road signs. This system must be robust to light changes, sensor noise and distortions, occlusions, and variations of the sign. Alternatively, imagine a system that localises the heart in Magnetic Resonance Imaging (MRI) and Computerised Tomography (CT) scans. This system needs to be robust to any changes in imaging process, scanner, noise, as well as anatomical and pathological variation. Regardless of the application domain, the current deep (supervised) learning paradigm indicates that we must present to the system as many examples as possible to make it robust and learn what is unnecessary, or nuisance {{cite:413d701a302b9160d5f885df16d63b70396ea072}}, e.g. the angle between the camera and sign or the patient being placed rotated in the scanner, as opposed to what matters, i.e. the location of the sign or of the heart.
But in reality, collecting and annotating enough data to cover the real-world variation is an extremely time-consuming and costly solution, hence not realistic. On the other hand, algorithms trained on existing annotated data exhibit drastic performance reduction when deployed in the real-world settings due to the data distribution shift {{cite:b0f5eee9a3b66318dff66c3fa83623157dd8f50a}}, {{cite:f8c4fb37b4a7aecf8634ff68bffa5acb2f134f48}}, {{cite:977443ed1f1b721a46af678f65b8d6d160cea281}}.
| i | 01f24d5d629456f46050a21bfc7ebd4e |
We closely follow the analysis for the current constraints in the model from {{cite:3327694765f9ef99a1e5726dc69231db3d9fcfd9}}, {{cite:67e706cbb6ace7463c8028dbc6de069696ca64ae}}.
In particular, we take into account the theoretical constraints on the scalar potential,
the collider physics from the LHC including the signal strengths
of {{formula:b662bf71-4467-40aa-89a3-06f36e350abf}} {{cite:873d3764e56bb3110461bbf0ead57c0b3d8ccc30}} and {{formula:434bd07a-7bcd-4749-b51b-612a08fa5cd5}} {{cite:f1f94e8d8bcd982274080708c8080b623b0942f4}} from the gluon-gluon fusion, the constraints from the electroweak precision measurement at {{formula:468765df-4c80-4116-aeb2-ab6a0d86b56f}} pole {{cite:2b6d2cccb0171df9a13742a45f7a304e46645e53}}
and from {{formula:7a81c64b-cea5-47e5-8695-f7b2861b1de8}} {{cite:824ede1ecc839bc9035b5f54c0596ccf3bb8ddd0}} and dark photon {{formula:cce7ecfa-799f-45b9-9f71-dc962a257e07}} physics (see {{cite:23a29893fee8817cfb88c3ab6d224fc2130ac906}} for a recent review).
To take into account the new {{formula:c788bdd8-1d8d-4d0b-9350-b0e6914418b6}} boson mass measurement at the CDF II,
we adopt the recent global fit values for the oblique parameters from {{cite:183a48d8855c82ecbba5d88dd46a518053b325ac}},
which are given as
{{formula:c40663b4-cdd0-41f3-9164-932f1ea0128c}}
| r | 3573f927b85c0a17a4840468c53bcf54 |
At the other extreme are positively correlated tests. Fig.s REF , REF both show that the smaller {{formula:afb95309-7e68-4034-9240-7e6afdc09a5b}} is, the closer conservative confidence gets to the confidence under the i.i.d. assumption. Indeed, when {{formula:fcb6ddb8-e0fb-4805-84c4-5588247cbd59}} is zero, conservative confidence grows to certainty as the number of successes grows (see appendix ). While the larger {{formula:aa81ba9e-96dc-4089-8480-5b697c980803}} is, the more conservative the confidence becomes. Here, confidence in positive correlations (i.e. large {{formula:bbba7e6c-0d40-4b81-bada-a391b778ec12}} ) may be due to pessimistic reasons for the failure-free tests – i.e. “success clustering” can occur even if the software is unreliable. The tests could be unrepresentatively “easy” for the software to correctly respond to, or the test oracle is incorrect so failures aren't detected {{cite:d4dac2972f29ecde4ba5db7065986c52d8885eac}},{{cite:a1f757af55eba2bfb40a6f7f4414008c546b6b08}}.
{{figure:a8405a76-6e64-4b80-8486-43fa4b1de2c3}} | r | 1f253852f3b626cb4954735aa652c899 |
Miniprot broadly follows the seed-chain-extend strategy used by
minimap2 {{cite:867c7b51ff70e6941d0193938929f5d97e58454c}}. It indexes the genome with open
syncmers {{cite:382ebe77421f06547543bfa57881120027c78260}} in all six open reading frames (ORFs) on both
strands. During alignment, miniprot extracts syncmers on a query protein,
finds seed matches (aka anchors), and then performs chaining. It closes
unaligned regions between anchors and extends from terminal anchors with
dynamic programming (DP).
| m | 7534c18c085d73446f8e465573afba37 |
In our case the reconnection site of the mini flare at the base of the jet has been identified in a tiny bald patch region transformed dynamically in a X-point current sheet which explains its multi-thermal components {{cite:0c835c3a364accad72aa262f43ac151826eb9c82}}. The electron beam input should be sufficient to power the thermal flare observed with Balmer continuum excess. The estimation of the non thermal energy is based on the size of the deposit electron area. This is a relatively unknown variable. The site of reconnection may be smaller than the IRIS spatial resolution and the energy input per unit area is may be underestimated. The spectral signatures of the mini flare have been identified as IRIS bomb spectra {{cite:c52248db49a603bcffc62190f62bde1102ea2c84}}, {{cite:bb7e30e78c1c7a3f0aa23cc1525321a08189111b}}, {{cite:c4dbe2f8f96dfd5392f528d29798a5f2b1fcc00e}}, {{cite:695800bbb398ad2647433cb59a9b622d85d3e609}}. Such structures can be due to plasmoid instablity which creates tiny multi-thermal plasmoids not resolved by our telescopes {{cite:64a00dd5240eceb6ee93a5a78b38a2c64db9ee84}}, {{cite:faf3b89fb69993771edf7278a58d44f2c1b75228}}, {{cite:4d315cfe29ff02d8db139525215ff7ebc18fea8f}}.
| d | 9aec4c4245a74297d9619ca14f439206 |
1) Quantitative Results: Table REF shows the MSE and average running time achieved by different methods. It can be observed that our method achieves the lowest MSE (i.e., highest accuracy) on 9 scenes and the second lowest MSE on 2 scenes. We submitted our results to the 4D LF benchmark {{cite:d6e1722ccd9bdeaef485f9c40e19fff2799d6f75}} for a comprehensive evaluation. Among all the 91 submissions, our method achieves the first and the second place in terms of average MSE and average BadPix0.07, respectively. Readers can refer to our supplemental material for additional results.
Note that, our method only spends 0.034 seconds on each scene, which is faster than FastLFnet {{cite:36cf0fb7e0d16c0b893f6eb844a08ffdf215c808}} by an order of magnitude. The high accuracy and efficiency demonstrate the superiority of our OACC.
{{figure:38ae0ec2-3838-404a-9034-ad20d062d066}} | m | 6c0adaf2f33872b0af98c06b5ef48988 |
We present two new notions of
efficient enumeration kernels by replacing the demand for {{formula:538c7ced-286e-4276-b270-68b70cfaf9a5}} -delay algorithms by
a demand for polynomial-time enumeration algorithms or polynomial-delay algorithms,
respectively. We call the two resulting notions of enumeration kernelization
fully-polynomial enumeration kernels and polynomial-delay enumeration
kernels. Our paper aims at showing that these two new definitions present a sweet spot
between the notion of full kernels, which is too strict for some applications, and
enumeration kernels, which are too lenient in some sense. We first show that the two new
definitions capture the class of efficiently enumerable problems in the sense that a
problem has a fully-polynomial (a polynomial-delay) enumeration kernel if and only if it
has an {{formula:8ddf98b4-1912-4b63-983b-16c266d78250}} -enumeration algorithm (an {{formula:4e16e83d-bc1a-40ec-93e5-a1b7da03673f}} -delay enumeration
algorithm). Moreover, the kernels have constant size if and only if the problems have
polynomial-time (polynomial-delay) enumeration algorithms. Thus, the new definitions
correspond to the case of problem kernels for decision problems, which are in {{formula:a5f144ae-dab1-4ce7-996a-719af391dbed}} if and
only if they have kernels and which can be solved in polynomial time if and only if they have
kernels of constant size (see, e.g. {{cite:593026f562a706ae95f49132a79c6e4de6423a19}} or {{cite:cd30755a077be5200d1ab206131456bb6844bfed}}).
| r | d88fd25c16c3ee002b1f47d57a62cdd5 |
where {{formula:434d7ae5-3e6d-4ff1-ad23-fe6e57f8ca92}} is the step counter for how many times the agent has visited {{formula:9e59db76-3836-44ff-8060-60b3dc7c4bba}} at step {{formula:a30459ed-f82c-4b8d-a498-d9dd68fb7340}} , {{formula:ba23c8d1-148a-4159-af3b-272811cbf51b}} is the confidence bonus indicating the agents confidence in its {{formula:b64d1c66-0d9d-4b8d-8251-316fb52d1804}} -value at {{formula:d9fcc2da-1481-49a0-8241-edcb0ce8d059}} , and the learning rate {{formula:acc4acc4-1fdf-4b9d-81ac-f58f2d37c72a}} is {{formula:04a4d93a-7f15-47d9-a6a4-4bd0516ed229}} .
This choice of learning rate {{formula:cdf1f777-8587-45b3-9bf4-2d234de641d7}} is crucial to obtain a total regret that is not exponential in {{formula:89b0eb52-009d-4ec8-8c70-229bbad4989c}} {{cite:c845c5942897c06a5967309846ef016a73ab3ce0}}.
| r | a5e7eb6a89b7e2fce8174fa79c5b6d18 |
Fig. REF shows sample segment maps and RGB images generated by our framework (i.e. TITAN-Net {{formula:35340e15-3d07-4bf9-8759-bbdcf6ee3c35}} Vid2Vid) in comparison with Pix2Pix {{cite:a33725aa1341cec1aa99afa021f1dfd52178657f}} and Vid2Vid (i.e. Pix2Pix {{formula:f3cec00c-03e7-454e-906d-12fd4b3f887f}} Vid2Vid).
This figure clearly shows that our TITAN-Net model can reconstruct more accurate segment maps, thus, has much better image synthesis capability compared to Pix2Pix.
For instance, the semantically important classes (such as buildings, roads, and vehicles) are reconstructed with high fidelity, as depicted in Fig. REF .
Note that since SC-UNET {{cite:172d080826919b1c6318e9dfdb96523af823f4eb}} does not rely on the segment masks, it is omitted in this figure.
| r | 97f7439821f4b5c29c1d0ed0fe316333 |
Our long-term project is the study of the influence of magnetic fields
on the radiation from IS using numerical simulations. In
{{cite:4a83782bfbf13a960e8d2b10a073a107678aa459}} we studied a large number of shell collisions
with different magnetization levels. In the present work we focus on a
limited number of shell magnetization levels, but vary other
parameters such as the jet viewing angle, bulk Lorentz factor of the
shells, and their relative Lorentz factor. The data obtained from
these simulations is used to categorize the specific effects that
variations of each parameter have on average spectra. These synthetic
observations are then compared with the second LAT AGN catalog (2LAC)
of blazars observed by Fermi {{cite:045b226fac3c29b36b2f2e87c09ce32869aa86b1}}.
| i | bbb16801fa30f4321e936815a79b57ca |
where {{formula:8107833c-ec9a-4d36-b8ab-7ca72dead27c}} is the distributions of the particle concentration in space and time and {{formula:5408e311-5637-465e-ae87-107566e857ba}} is the diffusion
coefficient. {{formula:f9a70901-5055-4f18-9de6-5f58166f12a3}} in the equation above is considered up to a constant, consequently it may also refer to the
concentration above or around the average. The
function {{formula:41e7b173-11ee-4326-a338-3443b600e1d7}} fulfills the necessary smoothness conditions with existing continuous first and second derivatives
in respect to time and and space and from physical reasons {{formula:6c6d026a-1ebe-45ac-a725-a9d325f29956}} .
Numerous physics textbooks gives us the derivation how the fundamental (the Gaussian) solutions can be obtained e.g. {{cite:ec892c50772e301160090addc4a6c57802ed2728}}, {{cite:7e341a0448b958b3da7a47cbf3f781edf2526b44}}, {{cite:cc387b24a309274908ba3d11bf7b35c56040378e}}, {{cite:2e7d969324965e7608773edc4f696b17e21e6321}}.
First, to dispel misunderstandings we have to express one thing clearly, the
regular diffusion equation has existence and unicity theorem for initial and boundary problems, but this is not contradictory to our forthcoming analysis. We will apply three
different trial functions (or Ansätze [this is the plural form] ) but neither the initial nor the boundary problems
are being well defined. The obtained results may fulfill well-defined initial and boundary problems via fixing their integration constants {{formula:a34814b5-519c-4a9f-948a-5ca2b318bfd1}} and {{formula:2d48a452-d5f6-4706-aab3-7aadb94376c7}} .
| r | 80cdcb3550f02168a065e331c884f3b4 |
Here the associated Hessian matrices of the Hamiltonian are assumed to have the same number of positive eigenvalues: otherwise there exist no periodic orbits near {{formula:4c68aac6-77e0-4a88-90b2-4464ea78625b}} on the same energy surface, as shown in Proposition REF below. Our theory is illustrated for a system with quartic single-well potential and some numerical results by using the computer software AUTO {{cite:bdffd290b755344c96857996331484a37d6bee24}} are given to support the theoretical results.
| i | 3b03f65b66207a0208598e8910632049 |
In this paper, we aim at answering three questions: Can the cost function proposed in {{cite:325eac949ef16b44091b76b4cfc0e0a7cf472e52}} be modified in such a way that the complexity of symmetry transformations in CFTs becomes exactly equal to the geometric action, including the central extension terms discarded previously? In this case, the complexity will simply be given by the on-shell value of the geometric action. This will hold the advantage that we may use the well-understood geometric actions to gain valuable insight into CFT complexity. The properties of the geometric action, such as gauge invariance under certain subgroups called stabilizers, will directly influence the complexity measurement. This leads us to the second question: Do geometric actions provide good complexity measures, in the sense that they are physically meaningful? Here again, the properties of geometric actions provide valuable means to address this question. And finally, the third question is: What is the relation between this notion of complexity and the path integral approach proposed in {{cite:7ab9ccde2642616ba26581bd60aa7dfb8e8c8af7}}?
| i | f63e1c34228326d8d6b67e92a0c18cdf |
where {{formula:05f63734-8f12-414b-b867-cf955e81a060}} represents the vector {{formula:e73935fc-cff7-4db8-a9c8-8e446713c2ec}} but without the component {{formula:938259b1-e2d9-44fb-b9f9-0853d281ceaf}} . This definition was introduced in {{cite:69d919689950c3efbf89f71cae25f182bec06458}}. It generalized the definition of {{cite:9d77f5525a4966df97e19d7f64059b04d413519e}} to multiple variables, which results in a causal map with the cross-induced cause-and-effect interactions between each signal, where the terms {{formula:aba90040-e37d-4ee2-bc7f-3f55a03d5475}} are set to zero. Furthermore, to assess these interactions, we normalise every causal effect {{formula:87d37fde-f0a6-4520-aff1-c266d85dcaaf}} using the {{formula:c5430676-f0e8-4673-8075-64c7cb7b7e96}} -norm.
| m | c6e29408ffc92c21774a994a4116fac2 |
Our presented model is a static model and does not focus on evolutionary aspects. Atmospheric escape can efficiently reduce the amount of surface water by high energy stellar flux [{{cite:1f5e67eb5c8757db4abd81e06943fbd74a3b53bd}}]. A reduction of surface water mass will shift the equilibrium state between magma ocean and surface reservoir according to Eq. REF , such that fractions of dissolved water outgas and are added to the steam atmosphere.
A planet with water in its magma ocean (scenario C) will experience less water-loss compared to a planet with only surface water (scenario A and B). This is because the partitioning of water in the interior [further decreases the upper-atmosphere water mixing ratio due to condensation {{cite:3b0a880eaa5ae5bf03d501d70155d88d01b7a924}}]. Hence, high solubility of H{{formula:c454a2bb-886d-4710-873d-202f25311e99}} O in magma oceans may enable its safe storage over long time spans. Time-dependent coupled models of magma ocean evolution, outgassing and atmospheric escape are necessary to tackle these questions {{cite:9a5ad28cca6f17f906e72f80adc955d513fabe88}}, {{cite:721c7feb72884ecc59168df822fa14ec6f47bddc}}.
| d | 74e15f8d649da87b4c233b035ae206de |
In Algorithm REF , we aim to find a saddle point of {{formula:9675f4b3-05f1-4063-96d8-d8675ae1e575}} using the alternating gradient method. This approach is adapted from the Algorithm 1 of {{cite:5f05fddb00b5cae8f25d64644e47ad6ef99f8167}}. The authors show that their Algorithm 1 converges geometrically to a saddle point under suitable conditions.
In the alternating training process of Algorithm REF , updating {{formula:d7c1dbe6-7a62-4ab4-808a-856c927e8716}} is a 1-d optimization problem when {{formula:99162655-d7ae-4045-a1b5-89ba57cb4147}} is treated as fixed for any step {{formula:15567c28-9973-4fe7-a045-60b07e165055}} . Hence we can also directly find {{formula:c182d15d-eb7d-439a-947d-9985c525fac0}} instead of performing a single step gradient ascent on {{formula:c82335ad-43c5-4c90-8de6-3f71b889cd84}} . By Proposition REF and REF , {{formula:fb235e19-c992-4738-b1ac-5f183e11bbae}} can be viewed as a (biased) Bridge estimator of {{formula:b8693142-e7dc-436a-8ab9-d8d3fb8aee87}} given any choice of {{formula:1c576faf-e9f5-4c5f-b008-4a659dfd9dc6}} . However, such estimator {{formula:a3dab147-2fe9-44dc-8b4f-2bb652dfd7b6}} is not reliable when {{formula:5a96e09e-bda2-41f9-8c91-f728d41ca679}} and {{formula:ce193546-46a3-4ba4-bb00-bb08eb7d0b00}} share little overlap. Therefore directly optimizing {{formula:2823e279-ddb8-49f1-945a-792d0e2fbedf}} at each iteration {{formula:57d70691-118a-479b-959f-2ebb08940abb}} is not always necessary or beneficial in practice, especially at the early stage of training when {{formula:8c205bba-aaa9-4875-8f28-a7e512204ec4}} is not yet a sensible approximation of {{formula:f503c7d3-011b-4cd4-89a7-9656fd870460}} . In addition, the gradient ascent update of {{formula:6d32cbb1-6e92-4268-adb5-05e4608f5cf4}} is computationally cheaper than finding the optimizer {{formula:273008c6-7e9a-4edd-a9bb-2efb5c119776}} directly. Therefore we follow {{cite:5f05fddb00b5cae8f25d64644e47ad6ef99f8167}} and use the alternating gradient method to find the saddle point of {{formula:e7a40431-458b-46b8-ab8a-4174aa7bb77d}} . We only recommend optimizing {{formula:e2322150-c6e4-49d3-8031-f033dbaefde8}} directly in Algorithm REF when we know {{formula:7750cbfa-3789-4812-8f50-904b49ec8b5c}} and {{formula:a41a3894-fb1a-4520-bb3f-7af150986cfd}} have at least some degree of overlap.
| m | 411a0d7905dd9202e508e6f1023c6a0c |
{{formula:092ad0cf-b8e8-410f-8357-89d5c8c057e5}} is the erosion operator.
Solving the Eikonal equation {{cite:71313ca9c5cd37b53e97cb1a5e440c78bc7ce4c6}} by computing the distance transform by
| m | 3038e16afe8dba84af206ceb5763c7cf |
Evolutionary graph theory {{cite:8d03d7a2190500d8b7a8d097b54e1ea294dadd4e}} was introduced as a way of adding spatial structure to the stochastic evolutionary dynamics considered by Moran {{cite:26e66d1f31a06f15677c9bf4854370d2f567ea75}}. Analytic results on these stochastic dynamics focused on idealised cases of simple graphs {{cite:c3bdaacae5e019b4e76a8aae5cd68b1986c54e3d}}, {{cite:e1125de2222866bf09d830bd5d200a39c62a25a9}}. In order to study arbitrary graphs, methods usually follow certain restrictions, such as focusing on the evolutionary process under weak selection or infinitely large populations {{cite:d67789695b203a1d18c118c792917c4a3bb12263}}, {{cite:66f7beb28a6f47a4988c26f6467a21e6e8111dd0}}, {{cite:f503c681238a23eccc45c18f7f6fac2f8f30b1f8}}. Alternatively, individual-based stochastic simulations give very accurate results but are limited by computational time {{cite:3ed6e079c7b59c34073ebf0ec131b923f7fbf163}}, {{cite:0b658083b165586cb2f6064fcb0c7f5b88d85c59}}.
| d | 281dd3fa5085b17995bc3dea9f0110ce |
Although the LATE estimation in our specific setting has not been studied before, some existing methods can be applied.
We discuss the advantages and disadvantages of these methods especially in terms of accuracy and model selection.
Since the true value of treatment effects is not observable by the fundamental problem of causal inference {{cite:0582aead8db81cd9b92ff3e72df431a297828494}}, model selection and hyperparameter tuning are substantial issues in practice {{cite:f2603ad9824c43d3ccabb3c06c3bebfb3a5f4184}}, {{cite:c0cef73c20d5f66cdaf866058f773eb06c825c9c}}, {{cite:075e680fd1988ef87df7294ca79c20b99e66accd}}.
| m | b6a0b5f351dc16c899f9d10bae1f66e9 |
In recent decades, the research of electron-positron pairs created from vacuum under extreme external field is one of the hot topics.
The existence of positron was first predicted theoretically by Dirac in 1928{{cite:173d38aeef94308a30a6cf014d50ad528fff5551}}. Soon after that, it was confirmed in the laboratory by Anderson {{cite:a1b355f490ec0682d91cd480b3e7607b6fa953f0}}. After pioneering researches of Sauter{{cite:d487fed30a5823d2ec9d17f66e1e3f7beacb9e4f}}, Heisenberg and Euler{{cite:ef60a8e707bbd0cffb49849b6f076863cba9b963}}, and Schwinger{{cite:c07665b18d7750e35edb405c7acf317621f70883}}, several research methods were developed, such as proper time technique{{cite:5ceee45171560cb63c74121705efd6251ad94d90}}, {{cite:d514bc7a443a663e832c6aa3de388c48277a8f6e}}, Wentzel-Kramers-Brillouin (WKB) approximation{{cite:bd704cd4b767cd49dfb401e0f16ed520e45d71cd}}, worldline instanton technique{{cite:8bf7c3e93337ab8d03ace59e67df88cdd84ab444}}, {{cite:5b3f800ddee6ecbd4c4346e7f20cbfe4183ae558}}, quantum kinetic method{{cite:49ade8b9096f579226109c45134542a3cd56ecb8}}, {{cite:86fe5f0ca65554b7400a90f2905d55db4cc392c8}}, {{cite:1fb55d8647fee43ed97e22665a2a9999019ed332}}, {{cite:1be3c89843549aea3197870e4b8292277ad8197e}}, and the computational quantum field theory{{cite:3c3f4fef1a412f429902941eaaa6ea4beadac176}}, {{cite:bbb7aebb6a1ef7f1299cd7a68bb3d1a78bae680c}}, {{cite:a573e92407d4a19ab84c783ce5ad953fce71bea6}}.
| i | 3ebe6d0c02f36741b44e9e076c7d9f54 |
Regarding classification, the learning representation is used as the input to different classifiers. In this work, we apply linear (Logistic Regression, LR) and non-linear classifiers (k-nearest neighbour, k-NN; decision trees; random forest; support vector machines, SVM; nu-SVM; and multilayer perceptron, MLP). Due to space limitations, we do not describe the classifiers here, but for the interested reader, we refer to {{cite:7cb82c900d4f015a503afbcf13c0df1d9df7b9b2}}.
| m | bbd9ef7d3e75b62c0a7382a2078b45fb |
A considerable amount of research has been undertaken on both communication-efficient FL {{cite:a3f88f91826185c83147011a75a4ef3b71271f03}}, {{cite:64fb36ef0788c6bc03b37a5e6f972fe1f6878ed9}}, {{cite:5127deaeffd334b73e6926127b24557e8eb9f3f3}}, {{cite:ef0db112b677e6825e2e5f9c9a683175a0cdc388}}, {{cite:831f67902c5bd9dd8b266e1cade1a6c351219007}}, {{cite:f743989ee797cedcbd2ebd05e5a1a2f75f772f34}}, {{cite:000c2e257a64b27b18a51b50c37cd71c4a3fafd1}}, {{cite:a2076f798d929959092ce81302ba450f04305311}} and asynchronous FL {{cite:e53391b5af507c0351cbef09c6eb0d97d4569bd6}}, {{cite:ce09faf98e988acac7e30523ac4f9bc4f5f98990}}, {{cite:a3b9eba66285bbf2a020006cf0cd98970c862a3d}}, {{cite:137a9a33b534cc187f4190a455a6366000581e9d}}; however, there is little work combining the two aspects into one. The works in {{cite:fe9c5605e65d14840d3b1b394807d583f29d2cf4}}, {{cite:ef0db112b677e6825e2e5f9c9a683175a0cdc388}} reduced the communication overhead via compressed updates on the client-side, but they did not address communication needs on the server-side. Aside from the accuracy cost associated with this projection method, it also adds an extra computational burden, which is not appealing for low-battery clients. Moreover, the work in {{cite:ef0db112b677e6825e2e5f9c9a683175a0cdc388}} did not consider asynchronous settings. Although the work in {{cite:7ab51f88ffd0315d0173f15d29862e764d2e6181}} reduced the communication load of the clients, it is specific to deep neural networks and does not provide a mathematical analysis of the presented results; in addition, the asynchronous setting considered do not include communication delays. The classical federated averaging (Fed-Avg) {{cite:a3f88f91826185c83147011a75a4ef3b71271f03}} reduced the communication in FL by selecting a subset of the clients to participate at each iteration. However, because some clients may participate sporadically in the asynchronous setting, we do not intend to discard any participation by sub-sampling the available clients. Another option, explored until recently only in distributed learning, is the partial-sharing of the model parameters {{cite:497e56db93b106c0364ab6e964c51d13860a128e}}. The partial-sharing-based online FL (PSO-Fed) {{cite:5127deaeffd334b73e6926127b24557e8eb9f3f3}} introduces partial-sharing in FL, but only in an ideal setting.
| i | 9774f7c54275a3487fb2c31f14debb74 |
Firstly, by adding a simple JN regularization term, our model obtains the best mean accuracy on Office-31 and Office-Home, and the best per-class accuracy on Visda-Home. Compared with the USFDA SOTAs {{cite:fabc3e6985ca0fd121109974c5108c6427cfbdc4}}, {{cite:242fc877a17182bf2cf1464d5e757cbce3b6abbd}}, {{cite:c75b97703f7a5cdc7256e7b112154f160f4f188d}}, we achieve the best/second-best results on 5 out of 6 individual tasks at Office-31 dataset and the best/second best on all 12 tasks at Office-Home dataset, respectively. For large-scale synthesis-to-real VisDA-C dataset, we achieve the best/second-best class accuracy among 9 out of 12 classes. These results obtained from a wide range of datasets with different sample sizes demonstrate that our model is capable of reducing the target risk while solving USFDA to great extent.
| r | 5de82eb84a1aee7728d1c244a1e051ff |
The study of the Lipschitz regularity in the {{formula:f22701b8-244c-4d6b-beca-7c4f3b12aab0}} growth context started
with the papers by Marcellini {{cite:f510bf52f04ca5892c78d9a8ee55f4662d008d43}},{{cite:ddd4d2d39ddc294cf6a9e4879a92a0c1fea8587c}} and, since then,
many and various contributions to the subject have been provided, see the
references in {{cite:2436cab3b01b5b03a44467b1d3789951ee6f71f7}},{{cite:b7c5d4e357a75113f4a22d4eecf415a0b3181a51}}. The vectorial
homogeneous framework was considered in {{cite:308a286cd934512c867fab726337630f6951729a}},{{cite:06e215d4d7a911595ced24b7f2b0c0e876d78dda}} and by
Esposito, Leonetti and Mingione {{cite:1b747131cb39dad84fc5ccc48d6476ca3b54eb79}},{{cite:09d657334014144cfefdfa98324ecb6de852b43b}}. The
condition (REF ){{formula:fe22282a-c4bd-4ac2-9e54-1b969a00eae8}} for general non autonomous integrands {{formula:54902994-7f07-4db4-a340-6280ed995679}} has been first introduced in {{cite:5722800376b1c1b95922d5058a9b52eccf1dc00e}},{{cite:a661aa680d6b6748d19ea7c5fe59b899183a7f24}},{{cite:80397fe134d2a363020cfd15eab85eea1b527e78}}.
It is worth to highlight that, due to the {{formula:6bfe06c3-dffe-480b-b441-b4f696875bc9}} dependence, the study of
regularity is significantly harder and the techniques more complex. The
research on this subject is intense, as confirmed by the many articles
recently published, see e.g. {{cite:199db21aed98f21e0093dbf7afb00e92ab56cde4}},{{cite:46f5eab6a703a66d74320aa6b62cd9a227d76150}},{{cite:61b126d7a2b3fa9de5c59a209f99c33353c3d97f}},{{cite:8272d3eaa3f07644835b2ce851ef438206e29744}}, {{cite:c0b33a4b384e60c2043036c5524f5ef1c69fb387}},{{cite:aade678d4fee95675eb6b194e7f6b7bdd7e3d5d7}},{{cite:b7c5d4e357a75113f4a22d4eecf415a0b3181a51}},{{cite:9edd947f1c65386e1d76fe0b4be7ec8aa0656cd0}},{{cite:b8c8a2f0a21269effb50c8f2458f4613af8538d3}},{{cite:e11f1ef8d0a052d6fa28bbda52d28c22d65af462}}.
| i | b6f45c49c5521dcfba621567b7bca06f |
Neutrinoless double {{formula:d1933b65-c405-45fe-adbe-e912f7fa0298}} decay ({{formula:16de52bd-7be8-49f3-9b14-7914d49b5385}} ) is the process in which two neutrons in a nucleus convert into two protons by emitting two electrons and
no neutrinos {{cite:5fb2cb0ff1af52549f2722882ff2b49dbc5300e1}}.
This process is by far the most sensitive laboratory probe of lepton number violation (LNV) and
its observation would prove that neutrinos are Majorana fermions {{cite:5feb0445c0f1753b0c9070740f980eaf1d49d858}},
constrain neutrino mass parameters, and provide experimental validation for leptogenesis scenarios {{cite:3a56c166b26cff1c57a309b74da3f69fc6ceeda5}}, {{cite:abee18dc50a5cfa775b08c2091cbe5196e7a0480}}.
If {{formula:03dd160b-f269-4e05-a7e4-205ef2e7f534}} decay is caused by the exchange of light Majorana neutrinos, as we assume throughout this paper, the amplitude is proportional to the effective neutrino mass {{formula:2b61716e-18a9-427b-903d-de62bc3e1c86}} , where the sum runs over light neutrino masses {{formula:d85e1db6-8063-4a3d-87a8-de558a25b853}} and {{formula:2fe70581-d6e1-464c-988d-fe7cebe30b0d}} are elements of the neutrino mixing matrix. {{formula:eabc17d4-a894-48dd-b23a-4d8d5ca5e052}} decay is a complicated process encompassing aspects from particle, nuclear, and atomic physics, with the interpretation of current experimental limits {{cite:c1a14bb23043785316bbe06fa9fc9f40601234e2}}, {{cite:a629ca533f754311d47420bf2093523f2cd65b09}}, {{cite:79622c0ae64a5fc8adfa1a83c486e12340594d3f}}, {{cite:6c0b2972ea3557e0dec088ce76b9c47c26033212}}, {{cite:2871b362b57492927103d37d6175965b40ff3992}}, {{cite:6b034a25a7a8471502f3b48b281e12bf0bd56868}} and of potential future discoveries limited by substantial uncertainties in the calculation of hadronic and nuclear matrix elements {{cite:3b976046112b5e679f7befb1458cad668fd991f0}}, {{cite:d827f165007273542748888946cb294f311d2581}}, {{cite:49a3739b9a82a94e5732b3ec1ddf00bdcb67368a}}, {{cite:5cfaccceb613f2217a48a262d552ac1773cb0a22}}, {{cite:02edd148281089f2002cd8cdacff91ddd6105add}}, {{cite:98861867005e8726edacbfb97a9877cac281f4b4}}, {{cite:b41a532f618e50542babe32c6c52dbf3b09e33f7}}, {{cite:95dce097bc857f44f6055940d2075d407f5941d2}}, {{cite:05dbecbc9f0d1f46c90784219bac2fdc10e4b6b1}}.
| i | c201d3f29ba6d5446914b2c87a93ffb9 |
Our proposed MNP-TMD quantum nonlinear oscillator could be further coupled to an optical cavity, facilitating its use to construct nonlinear quantum photonic devices. Recent studies demonstrated a decoherence-free operation of a system combining an LSPR mode and an emitter {{cite:607189a91612216fc729de7f128a47f9b7e10492}}, {{cite:3b5b75cb02936ce7eb6b0f06c45d23a90c01c656}}. For example, one can couple our quantum nonlinear oscillator with a cavity. In this case, one can consider the following Hamiltonian
{{formula:90f540f5-ceff-4da7-9b26-d4bf757899fc}}
| d | 152325cea7d6a99fdc2bf5d150307402 |
Several multi-equation models for two-phase flow can be found in the literature, resulting in at most two mass conservation equations, two momentum conservation equations, two energy equations and an equation that governs the advection of the interface.
In {{cite:feb18ccb0e07fc19d606f2036b52d40a90fab009}} a hyperbolic seven equation model (2-2-2-1) is considered for the simulation of two-phase compressible flow.
The energy equations are omitted in {{cite:77bd50928b16dae111044b6a2ab3939b294a6ad7}}, who therefore consider a five equation model (2-2-0-1), and in {{cite:d699d5cc9e90f158ef2a76a061047058d38bef17}} a six equation model (2-1-2-1) is considered where a momentum equation for the mixture is considered.
| i | 1271e16bfa1a82ecec5033d0b49c062e |
We follow the suggestion of {{cite:6a61a5ab933572840c25d34e4de3e4af01dc66b6}} for the configuration of {{formula:04ded6b5-f4f9-4b78-a401-6bdf3e6cad1c}} and set {{formula:1221e7fe-0908-4255-b1ed-0bcd08da3f3d}} to 0.1 (if not stated otherwise).
| m | 8554ec8ec938cbd60ef9bd413db53fcd |
Quantum key distribution (QKD) is a cryptographic task that allows two distant parties, Alice and Bob, to exchange secret keys and communicate securely over an untrusted quantum channel, provided they have access to an authenticated classical channel.
The first QKD protocol, BB84, was proposed by {{cite:8c1803f4b405bfe2dd64d789013949232d0935d6}} more than three decades ago and the last 30 years have witnessed staggering experimental advances, making QKD the first quantum information technology. With the advent of quantum information theory, {{cite:26117ecfa8ddd48e0611b8d5f38dbb37127d480d}} offered a fruitful new perspective on quantum key distribution by casting it in terms of quantum entanglement and Bell nonlocality and it was quickly noted that the original BB84 protocol can be seen in this light as well {{cite:b485a498dbafcc79cd9d362203d7c88739b64e95}}. This new perspective was particularly useful for the development of formal security proofs of QKD.
| i | 25c4ee6a03432e9c20bf92a80dafcad0 |
In this paper we provide a rigorous study of the problem considered by Anderson, in the case of the Lorentzian cone metrics corresponding to the Hawking–Page solutions of {{cite:a9f9280918034f041c72f522f9e6d31fecc51e6d}}, in order to investigate the possibility of constructing {{formula:1968417d-d057-48ff-aea5-d96d045306c6}} -dimensional vacuum spacetimes with naked singularities. The Hawking–Page solutions are the 1-parameter family of Einstein metrics on {{formula:88143141-01c9-406b-b410-c336f3d6606e}}
{{formula:f64cfdae-102f-490d-b85e-413d9703e668}}
| r | 89013272e10b35845c7a34ff1a5d29b0 |
To explore the suitability of chiral structures for information recording, we
have chosen cobalt samples with DMI for our study, based on recent works on
these systems {{cite:35c85c012959732007213c0fa97fda02272aef7c}}, {{cite:70a1cdac565feac150945982ab514ae74d0d942a}}, {{cite:5e29466f9bbcb3c02edd3049044ce05a101e1237}}. This will also
show us another perspective of the claimed topological protection properties of
skyrmions in finite systems: in confined geometries the boundaries play a major
role on the skyrmion stability. Accordingly, based on
[Sampaio2013], we define an 80 nm long, 40 nm wide and 0.4 nm
thick stripe, which we discretise into a 320 by 185 spin lattice with a lattice
constant of {{formula:03b07273-e8ac-4c2f-b9b4-ed18cb977e07}} (see Methods for details). This system has an
interfacial DMI whose magnitude we vary and a strong uniaxial out of plane
anisotropy. The DMI in a Co based system can be obtained by stacking the cobalt
on top of a heavy metal with a larger spin orbit coupling and experimental
techniques have been proposed to tune the DMI
magnitude {{cite:70a1cdac565feac150945982ab514ae74d0d942a}}, {{cite:64ac88d7870e9c4223aa729ed288e210aeae3137}}. At the time of publication of
Ref. Sampaio2013, there was no experimental evidence of the Co
samples under study, thus the magnetic parameters are based on standard Co
material. Correspondingly, the atomic layer spacing is assumed as
{{formula:b943277c-5563-405d-b68c-5e05fa5db25c}} and a lattice constant of {{formula:eda7001d-12d4-4093-a2f8-4091c26b50da}} . The
atomic arrangement of an FCC cobalt layer has an hexagonal
structure {{cite:efedcd8f1ad17e1be5ca2cde6e528dcd38128adb}}, {{cite:35c85c012959732007213c0fa97fda02272aef7c}}, {{cite:f836bf8d026f5061aa5bd8b82882d8cd50dcfb92}}.
{{figure:3cb6d557-864f-4a48-b53c-ef1d6492812b}} | m | 16e42dd029313b0c6816716aadd13637 |
In Table REF we test the influence of the quality of the flow method by comparing RAFT {{cite:803e52df6e756796914b474fbc34758ed6253e48}} and PWC-Net {{cite:0edf2265774ac3aa83aae8276714b81773c961e0}}. In addition, we simulated less powerful flow methods by simply fitting a homography or an affine transformation to the predicted RAFT flow, and using these fitted transforms as our flow. We found that using a correspondence-wise loss with better quality flow methods produces better downstream image generation performance.
{{table:7ffa3ec1-261e-48c1-8448-5f3aedbab270}}{{figure:16398148-b683-49cf-880a-8cbf9107e652}} | m | e8af9c6e03f4cd2add1f9920e3bfaab3 |
The observed results to date are seen to be in excellent agreement with predictions from the exactly solved models.
Early on, the prototypical integrable model–the Lieb-Liniger Bose gas was realized to reveal ground state properties, local pair correlation {{cite:18a2e15e234a9c8d75ce7a4b39a6df3e79a03b31}}, {{cite:e6f6b4e099e7e8b6d62f122001c6c705c41f9490}}, {{cite:01a562e3b76eb920604892912e176dce38f25cde}}.
Subsequently, the Yang-Yang thermodynamics and quantum fluctuation in the model were observed {{cite:cdef20488f57d8eca55388b24327c2147238161e}}, {{cite:691b21cb9336873997c25c4cef626e038153fb7d}}, {{cite:2647b963199b9970b4d2ac45e2efe4504e02f9e9}}, {{cite:191655d0cc038f5db4cf250c8a226f388df4371b}}, {{cite:164db6ffe314f12e13dd0383c02288790ca04af1}}, {{cite:0e75f45539dd5bc266165e9b5fe19d05fea6fd2f}}.
Based on theoretical prediction of the fermionization in the Lieb-Liniger gas {{cite:f2a8c092cc0fafde92cd29c714fa6632a7c073fd}}, {{cite:995ee0f16d02a83c66b3256a01179a95d5ed1f2d}}, the novel super Tonks-Girardeau gas-like state was experimentally realized in {{cite:60cdb047a24963820d3ea2c0bcc490b670e96f61}}, {{cite:5ec71cc5728d0dbf17e93a5a3f5d7a76f59692c4}}.
Observation of the quantum degenerate spin-1/2 Fermi gas {{cite:9a0ff67972701620a08689865190fd2c77dc4200}}, {{cite:e0ddab6560635060553894eea53ef6a6eae2f0a1}}, {{cite:664818325458dfbc11d5d7078bdf0f9299fef5d7}}, {{cite:d8bcd45f145bf9a50f893b84d454a3ebe3cbdee3}}, {{cite:413660de5edd94ffdd61efa7aebfb60c05827df9}}, {{cite:65d0741e89b06b9753be406b10ace38950a289d0}}, {{cite:da35928567a8c1247323b26082e3271307e66090}}, {{cite:eab28113f689a0e0c126d3542d8bc38d62d683ab}} and SU(N) Fermi gases {{cite:64bc8845948aa1063cb1ad5d8f7af262ba3fff7b}}, {{cite:12cf9d2c2cd7f0e4741a24fe2352a9477bb9beaa}} are having high impact in ultracold atoms {{cite:356f780cec98035b4ad4e7cdc9adbff6255b8814}}, {{cite:c87999bc639cd5a132d2e88fb33a5aba55b3f45d}}.
| i | 918cb2dd677260854074e31fd0549fc1 |
Methods based on homogenised mixed cells and volume-of-fluid reconstruction, along the lines of the approach described in {{cite:408dc18b88e3ec9bd0fea712b189b23ab89ffec5}}. These methods underpin many well-established and legacy multi-material codes.
Ghost-fluid methods such as {{cite:5f70145c99c441c7b327d42e138b7d540e663dfd}}, {{cite:e9df894b954d0fe17fa20a10cef2aa25db867adb}}, {{cite:004fd465512e3967928d5a6fdc4d3891b75f7e55}}, {{cite:aae6692a87e35447160ea41d1038f306c8b09391}}. Introduced more recently, these methods capture internal boundary conditions by extending the multi-fluid methods from {{cite:537159bffe7351013d5b03556416f2ff6c6b4213}}, {{cite:3816dfa662332d63f9d0ee5ac4ce45ca2649e365}}, {{cite:732041e6ab3860bdaf58e4d3ea7fb887825dff9e}}. The main drawback of these methods is that they are non-conservative.
Cut-cell methods such as {{cite:6b01eedbc671f210747e95cdd6795ee9a7e8b84a}} and {{cite:f84307c8dfc1c29e732f23ec7abb185ee2106f6b}}. These methods resolve the geometry of cells intersected by interfaces and apply a strict finite volume discretisation.
| i | ce13e650fd8feb6b82e16ae5e1cc7456 |
In this section we test our cross-learning framework on a classification problem with real data. Our goal is to classify images belonging to {{formula:443e07b2-76b3-46ae-a8c7-b99566ec5400}} different categories, and the problem is divided in {{formula:2720baa7-cabd-4250-8245-2c1c027648e0}} tasks corresponding to images belonging to {{formula:3e6fcb17-cd69-495b-a430-ba4bab171ab5}} different domains. Specifically, we use the Office-Home dataset {{cite:230077abad23f3b7dc443de2bd3f4cb62db8ff97}}. It consists of {{formula:183a30d9-16f0-49cb-bcb6-67bb05942de5}} different domains; Art: an artistic representation of the object, Clipart: a clip art reproduction, Product: the object as product for sale, and Real World: pictures of the object captured with a camera. The overall dataset contains {{formula:c4217ca4-c6c1-43c9-8f03-52b68411000d}} images divided in {{formula:ebe2a755-45db-4807-ba57-441c4d146a63}} categories, with five examples given in Figure REF , including Alarm, Bike, Glasses, Pen, and Speaker. Notice that within each category there are images belonging to each of the domains. The minimum number of images per domain and category is 15 and the image size varies from the smallest image size of {{formula:f1e8f132-31cc-4a8a-82b8-a8d9aba5e15d}} to the largest being {{formula:46a9d180-2486-40e4-8e7f-b274fc6e3647}} pixels. We preprocessed the images by normalizing them and fitting their size to {{formula:96d6fbdb-98c1-47aa-9004-3cac7cc16d09}} pixels.
| r | edc12ff841ab48a0b4e56daf571b5f66 |
We use BAO data from Baryon Spectroscopic Survey (BOSS) DR12 {{cite:337c5ab47fa53b53dbfed8007181acdb8f7252eb}} consensus results in three
redshift slices with effective redshifts {{formula:de8e6d32-1670-4905-a04e-f7143b57f524}} in combination with measure from 6dF
{{cite:e88d51c5fe753015267ff8983be934e0ce856e24}} at {{formula:bbaf2d7f-0a27-42d6-94bb-683274bb92d3}} and the one from SDSS DR7 {{cite:d8f692acdf56af692762f1a25998b3156aa466da}} at {{formula:fc70c3d3-2b84-4d0c-bc30-452d959c0d81}} .
| m | db9791eb19015bba378cbf3b27e6c786 |
[Proof of Theorem REF ]
The claim follows directly from the convergence results in {{cite:f2a151bcd776cfef538ea81e31a92c1468d3a7b0}} applied to the reformulation (REF ) of the dual oracle subproblem (REF ).
| r | 32510a85e502b77e3f203a50d24dc320 |
Identification of the maximum-likelihood grouping (equation (REF )) makes sense as long as the number of parameters stays the same, which means that the number of nonempty groups must remain fixed. If different numbers of groups are being considered, then the comparison between groupings must penalize for the change in degrees of freedom, for example using the Akaike information criterion {{cite:57609bc14b30f812c73940da8d5be60fdceae931}}. However, unlike the Bayesian approach, which directly integrates over the uncertainty in parameter values, AIC penalizes all parameters equally based on assumptions of independence and asymptotic distributions. Therefore, the Bayesian approach is likely to be more robust.
| m | 16c6e9bf11c868cabd6a39416e320dda |
In this regard, it is interesting to qualitatively compare the disk survival timescales of the binary b Cen ({{formula:0810b3cf-20ad-4a88-ad7d-7e8c9afd98d2}} , {{formula:c7aa7948-ffa9-4c6f-ade7-3d76afc2d23b}} ) and the single {{formula:64910f16-00ad-444d-b99e-8aa07d14a051}} Sco ({{formula:3f5cb185-820c-46ab-b35c-59468c13da6a}} ). While a naive comparison between b Cen A – expected to emit nearly all the X and UV flux in the b Cen system and treated thus as a single star – and {{formula:c61e10e7-ebf0-49f8-bb04-285e95a5a761}} Sco would yield a three times shorter disk lifetime around {{formula:61f32877-b175-4d8c-abf5-0d6c8783df21}} Sco {{cite:52da996e6dae089cc63f2203bf86c77a09e33e94}}, the actual ratio should be much larger due to an initial disk mass for b Cen related to the total system mass, hence comparable to that of {{formula:f26089fe-db36-431c-a57f-4755ad78904d}} Sco. Combining Eq. (11) from {{cite:628e76dad490d755923f1b3dabc5c0d1e957b079}} for the photoevaporation outflow rate with the expected ionizing photon flux {{formula:4d86f56a-6ec9-4a7e-aac1-16eb997c0b35}} for the three stars, the ratioWe interpolate between {{formula:82f89bd2-b8f7-4485-8964-0a23de23e7d1}} values for {{formula:b5e18926-c4ed-4e9a-b9a6-0215e3ad242d}} and {{formula:4c089fcf-6863-4363-97c7-ade237384a71}} {{cite:52da996e6dae089cc63f2203bf86c77a09e33e94}} and {{formula:a9975e38-628e-47eb-b3d9-0ba4ee67989e}} values for {{formula:a2a84d52-b309-411e-992c-437fd42621b7}} , {{formula:db11ac3b-370b-4678-af53-657cd5afc9da}} and {{formula:028f7337-95b0-4279-a093-3320407a15cb}} {{cite:09c4a4bd930b397a52ce50f66aec0c5ab27bd21b}}, deriving the empirical relation {{formula:01ca76eb-6eec-4810-a5ca-3b1e5ce46789}} . The b Cen photoevaporation outflow rate is the sum of the individual contributions of b Cen A and b Cen B. between the two disk survival timescales should be around {{formula:b1a3187c-7ada-49fb-8ec4-429ce1ccef14}} . While the impact of this on planet formation is difficult to be properly assessed, the presence of (at least) a companion with {{formula:98d910b8-dba7-4274-a183-4225124b991c}} around {{formula:44b590b9-bdf9-43db-b390-d3cff2c4cee2}} Sco looks much more challenging than that around b Cen in the framework of a CA scenario. Recent updates of the classical CA model, such as pebble accretion, have been indicated as a possible solution to the conundrum {{cite:5f7a3eb5e1fec71d1cd0023b344ceb7bef28088a}}Alternatively, the problem might be alleviated if {{formula:2043ccb3-51ed-4858-b27a-570e791f08cd}} Sco were actually formed by the merging of two nearly equal mass stars, which is possibly not an exotic case {{cite:d858424bd8069832a91567f783b3cda91d25324c}}. On this respect, it is notable that {{formula:92b3eaf0-00ef-412e-8a6c-40ab586d2ec0}} Sco appears to be a slow rotator (see Appendix ); in fact it has been argued recently that post-mergers should appear as slow rotators {{cite:1ddfd36c81eff05bb593feea6efed3e441264996}}, {{cite:483fb8ad4a68c7e8541601b62e59789ada6527e1}}. On the other hand, the same studies suggest that mergers might have strong magnetic fields, but there is no evidence for this in {{formula:97d01c1e-7a0a-48c4-bb13-ad0cd489009d}} Sco (see Appendix ).
| d | e360c3412e82521a4e9672d9fe1a0c94 |
Relaxing these
model constraints will not significantly alter our results for the
{{formula:f4dc0e09-462f-4341-b9a4-85cb8000c58a}} -operators, and transverse VBS in general, as long as extra
interactions do not induce very large mass splitting within the new matter
multiplets. Our toy model represents a variant of
natural dark matter models in the spirit of Ref. {{cite:c165813b1d2be11448f9e349db3436148d67ae2f}}. However,
we have only considered relatively modest masses, of order 1 TeV, which
would provide only a fraction of the observed dark matter in the universe.
In a less constrained UV-complete model, in particular when allowing mixing
with SM matter fields, direct collider searches for the extra multiplets as
well as their dark matter impact would be strongly affected by additional
interactions, leading to a vast and rich phenomenology. We were not interested
in such issues here but rather have concentrated on the generic loop-induced
effects of extra matter multiplets for weak boson interactions.
| d | db5051dd112b601c30cda4252f13f69a |
Typical application scenarios of UAV communications in urban areas, such as cargo delivery, traffic monitoring, and so on, their communication links are often blocked by tall building, which leads to severe degradation of channel quality. Fortunately, with its low power consumption and lightweight, the RIS can be installed at an appropriate location to reconfigure the propagation environment of air-ground links, thereby improving communication performance. Therefore, several works have studied various RIS-assisted UAV communication systems. In general, these studies fall into two categories, one for terrestrial RIS{{cite:edd21c788227e6937a36f701f57d095755a9086a}}, {{cite:0151ed2133215b73b2e9e12297deb3112af58123}}, {{cite:9931f4a75c2c07b930aa670164da31ab4dc90d2b}}, {{cite:3de344c02b1524ffc67dc521e9902b82164b277d}} and one for aerial RIS{{cite:3f78c177bfd229f331a79dadacef71e2bd67ca96}}, {{cite:7647b09e53eebf13f3477e31a9e0ac4be25f303d}}, {{cite:05aab2260276bcd26d976136124236aa3d24774d}}, {{cite:8a588021edba93b3fcf87d9dd8897db0d20df391}}, {{cite:170a62ab36e837bc441b520a967993cd161a8a52}}. For the first category, the UAV trajectory and the phase shift of the RIS mounted on the building surface are jointly designed to intensify different utilities such as communication coverage {{cite:edd21c788227e6937a36f701f57d095755a9086a}}, energy efficiency {{cite:0151ed2133215b73b2e9e12297deb3112af58123}}, confidentiality {{cite:9931f4a75c2c07b930aa670164da31ab4dc90d2b}}, and communication rates{{cite:3de344c02b1524ffc67dc521e9902b82164b277d}}.
| i | a51892448f4f8968a87f288e637f64eb |
where {{formula:c15807a7-8f29-4cee-b3d1-668c0961e362}} is the empirical Value-at-Risk of level {{formula:6bc61193-d922-48fc-9e57-ee1a1c82de1d}} , i.e. it is the empirical {{formula:edcf6050-d058-4f0b-940f-3020a1f1754c}} quantileThere exist several ways of computing empirical quantiles. We shall use the default method of Python NumPy package which corresponds to the method 7 in {{cite:7a525f8e68fecb524bf2932d3cff8ffd94a0a4b9}}. associated with the set of portfolio losses {{formula:3ddd4c25-37ce-42b8-b10d-1bab58d9221a}} .
| m | f7f3ef9c9ef85ef9dd979ad3449ad015 |
Another interesting issue to purchase is to include fermionic
and bosonic gauge fields with mixed indices.
There are some interesting works examining a deformation of the free action with fermions.
In {{cite:2eb494a7c3849b3e2c60b10f6c528457f83d1388}} a systematic analysis including fermionic gauge fields
was performed in the BRST-antifield formalismThe results were shown to be consistent with
those obtained in the light-cone formulation {{cite:2b6fbb027a16f49a10e6fc3df94566e1107bfe4e}}
and with one obtained in the tensionless limit of string theory
{{cite:ec705f716cdc674f5aaf10052204deea5027d11e}}..
It is interesting to examine actions of interacting bosonic and fermionic fields
including higher orders in {{formula:f92bc38d-7e34-4a33-8473-63ae711bdb0d}} ,
and to generalize them to those on AdS spaces.
| d | fe145ea3d806606a5a050a7da4755348 |
Generative adversarial networks (GANs) have been used to add robustness to adversarial attacks to the deep networks {{cite:b993c0051fc38030fdca04b9167b9e4aacfb8934}}.
Adversarial training can improve image segmentation by producing label maps that are similar to a target image {{cite:fabb9f4f9c357b322aa5964fb140396f29f6a517}}.
Adversarial networks have been applied in the segmentation of MR images {{cite:2edaea70c88e80859aed52d4876bbfe68141e6b2}}, {{cite:6e3e79c41f1b5b4a263273c83f262d94b8fbe720}}, {{cite:92859c64d581f970b4d38d1f2b25edb72c978c73}} where the datasets and the annotations are available. However, the application is limited since the adversarial training requires a large training set to train both the segmenter and the discriminator networks.
Lee et. al. {{cite:f2e1b6b3262d53c89d7208cf60407ada21efe1c5}} proposed an unsupervised image deconvolution method using a cycle-consistent adversarial network to improve the quality of blurred and noisy fluorescence microscopy images without labeled data. The adversarial network in DETCID models the inllumination as an adversarial attack without during training without increasing the complexity of the network during deployment.
| m | 7344ed3e552834cd18b0f22e1cef287e |
In this letter, we elaborated higher-spin dS{{formula:579ca266-5df7-490a-821e-ce4265d971f3}} holography by providing a concrete prescription to perform an analytic continuation of Gaberdiel-Gopakumar duality in {{cite:8a968cb21057809aeda25128056983cef9a48eae}}. Similar attempt was already done in {{cite:fc435a1c5ca1872f3c1785fc4c38fed5a672a79d}}, {{cite:440c14af8997409faada9ad372f1abad2ea82a78}}, but a modified version was analyzed here.
We then carefully applied the wave functional holographic calculation of {{cite:d521e80b80cd36e777fd652bafa270e679db3bd2}} and obtained bulk dS correlators at late time. The expressions are consistent with the previous analysis of {{cite:55b43ac6af335e6de718467231fa45e9994bddf0}}, {{cite:6e0dc797f8ca974153681d581aa962810b160310}} based on bulk Feynman diagrams in the in-in formulation, whose review may be found in {{cite:90ec6bbad113b8193ddd6e02e3610f817cfa7bce}}. Let us end by briefly commenting these two complementary approaches exploring the dS/CFT holography and where our results fit in here.
| d | 904e34b4f131e0ce0d2a3eb6c7acf8d3 |
Before we proceed, some remarks are in order.
First, an {{formula:259e0455-39f6-4cf7-ae0e-1334a0df62e4}} satisfying (REF ) can be found by a host of initialization procedures in existing methods. For example, {{cite:ca3b730b867df7d3d534f46cd9563a402e7d5bfd}} and {{cite:baee02aec56b1132e84e2f2e791920e8aa016cbe}} respectively proposed spectral clustering based initialization procedures that can obtain an {{formula:7a40f7cc-1d05-4e77-9f7e-17e9dde3f946}} satisfying
{{formula:9872274b-b76a-43c2-b145-66f502521850}}
| r | a6cdca270d1a8518973ec10b17a798db |
Under the above two assumptions on the graph, we have the following result (see {{cite:416528faf984bd68a21017d79e2487993bab798d}}).
| r | e9a56120847ba82ee072d89e686a2af6 |
The condition in Assumption REF –(i) is standard in random matrix theory and they are known to hold when, say, {{formula:bc3c8ea9-73f3-4c99-b1c5-655379ad0613}} is a convex function {{cite:d914709c87de8b10988fc44e6220a9050aa1cc63}}. The one-cut assumption is made just for ease of presentation, as it simplifies the Riemann-Hilbert analysis at the technical level considerably. On the other hand, the regularity condition is used substantially in our arguments, but is standard in Random Matrix Theory literature and holds true generically {{cite:a49dfe34a8564c5ad306fb92743cf2bc19509e81}}. Most of our results are of local nature near the right-most endpoint of {{formula:7c376261-ea23-4ab5-bf36-dbb68513a06b}} and could be shown to hold true for multi-cut potentials near regular endpoints as well, with appropriate but non-essential modifications.
| r | 13f41404e5c3b5358a9c466cba46a3ee |
The extragradient method {{cite:3f75499579bc8fc167658bac49c6b5e8d308a152}}
is one of the widely used methods for solving smooth convex-concave minimax problems
(see, e.g., {{cite:08abf771a2587cf4f561057afb1129177d0ee706}}, {{cite:84a4cf06179e9f742bf3e74b0082dd7a0c2145b4}}, {{cite:085ee09941d27ab5913aab1b91629c54dfbc7a27}}, {{cite:8e4b42de095c0698c4560d5a9d0014769da4d4f8}}, {{cite:bbe9a8625a589a8a7a4bffdf6f4f3eb6907026fd}}, {{cite:6b0fc82d145104ca33558105787579e15f37bd10}}, {{cite:583995c9c8caa6b6fda64d757c26883bb87eb0ef}} for its extensions and applications).
In terms of the duality gap, {{formula:8e2c1022-6c4c-4970-b770-b51f88d53dbe}} , where {{formula:65f4f81a-ec22-416a-b554-8014f9ab1137}} and {{formula:498ae566-3a62-4d8f-b0d6-ca321911bdec}} are compactThe convergence analysis on the duality gap of the extragradient type methods are generalized under
the unbounded domain assumption in {{cite:341ab1839035c5a26d04965ac0d77ae097f3c0b6}}, {{cite:a7c3c6632dd1a5470749dbb709b37c2321248846}}, {{cite:54db7fc9777c3134d71e53c7e695a17f73e86d92}}.
domains,
the ergodic iterate of the extragradient-type methods {{cite:17176f349a1ad417807fee82a278ff3e76b4b88c}}, {{cite:1729bce97e12c9842bb6ae19488db080f6ccf193}} have an {{formula:726a570f-ef64-4270-b177-f6b15abd4712}} rate.
Such {{formula:ba7b20a2-c6bb-4102-9a64-5c62e6fd8f0a}} rate on the duality gap is order-optimal for the first-order methods {{cite:30f56fc864706ec61a2ffa6a38808dfd913f0414}}, {{cite:5b5581372de02bad8e46844c5026ffa0b087bbf0}},
leaving no room for improvement.
On the other hand, the last iterate of
the extragradient method has a slower {{formula:0199c8b3-68b8-4376-8969-46015bd16cc8}} rate
on the duality gap,
under an additional assumption that {{formula:67f2b741-4acf-48bc-8120-7aa98f73bbca}} has a Lipschitz derivative {{cite:2b09359891ef30e17463be25cd51d6f44fe69d52}}.
In terms of
the squared gradient norm, {{formula:088cc256-ceb0-407d-a98c-44e4b1be019e}} , the best iterate of
the extragradient-type methods {{cite:3f75499579bc8fc167658bac49c6b5e8d308a152}}, {{cite:d246747e46b72f0317fbe11a6fd6ed1a87c6b9df}} have an
{{formula:4e3eae7b-b1be-44a3-8314-3620ab40f600}} rate
{{cite:7cd55fd22319b98a54af8cd702ffa22cfcd6306b}}, {{cite:7a2df94f074993c7d4efb4dde78ef971e1df9992}}, {{cite:c4832f024783c77cc0ed1dbd7b3e76bd81fbb3bc}}.
The last iterate of
the extragradient method also has a rate {{formula:7d490d14-f2c9-4fe1-9293-ebc31621ed29}} , when {{formula:a6471a6e-8a23-4b36-976e-0fc30282e45a}} is further assumed to have a Lipschitz derivative
{{cite:2b09359891ef30e17463be25cd51d6f44fe69d52}}.
Unlike the duality gap, the {{formula:7346ded2-ec6f-4fe7-98f8-1e5168b11f7a}} rate on the squared gradient norm is not optimal {{cite:c4832f024783c77cc0ed1dbd7b3e76bd81fbb3bc}}.
From now on throughout this paper,
we mainly study and compare the convergence rates on
the squared gradient norm,
which still has room for improvement in convex-concave problems,
and has meaning for nonconvex-nonconcave minimax problems,
unlike the duality gap.
| m | e00f9d689c206d7443c799f6f0fd904b |
Under the null of white noise, GARCH(p,q) effects are locally equivalent alternatives to ARCH(q). This is implied from the equivalence of white noise disturbances against GARCH(p,q) disturbances in linear regression models to disturbances of ARCH(q) {{cite:14bf4ce5d18da1033238e476da517f24403c9217}}. The tests for ARCH effects are generally valid to GARCH effects as well, thereby validating previous tests of ARCH models to GARCH models. To conclude the selection of model, various parameters such as AIC {{cite:986b5edfa6384b24cc53dc1797b98031191b7ed3}}, HQC {{cite:ab895cc6dc03672cc369fbc83c874c06bfa9e9f2}} and SIC {{cite:3948f1dcd7a0b4a4a0e0afde1bb1e89c448f13ba}} under normal (Gaussian) distributions are used to get the best fit. An EGARCH(1,1) model is proven to generate the best fit to model Funding Rate. The AIC, HQC and SIC of the models are listed in Table REF , where the EGARCH model has the most suitable Information Criterion.
{{table:1c33a19b-8c2b-4251-ad03-a46fbd71ef05}} | r | f6684b3f7e11c4ffca647f9a152e794e |
Lin et al.{{cite:2ed0ff45fb8807590f9e061f2990071443741d06}} showed that the thermodynamic properties can be estimated by treating the DoS
of a fluid as a sum of solid-like ({{formula:ab6a5e6b-f7ff-488c-8c38-e5363bfca246}} ) and gas-like ({{formula:1357900a-ec28-4f61-a365-eeaed75070d0}} ) contributions. Thermodynamic quantities for a solid can
be estimated by treating its vibrational modes as a system of noninteracting harmonic oscillators, as in the Debye
model {{cite:816e0bce3e1e7fa10c25575b7617b81fef8269fa}}. The gas part is described as a low-density hard-sphere fluid. The velocity autocorrelation
function decays exponentially for this model {{cite:816e0bce3e1e7fa10c25575b7617b81fef8269fa}}, and hence the DoS can be calculated analytically.
Thus, the calculation of entropy for solid and gas requires knowledge of the DoS.
| m | 7a13f844331189ea474004541d24a59d |
In panels j-l of Figure 1 of the main text, the density profile obtained by numerical simulation below the critical point is displayed. It was carried out on an Ising square lattice of size {{formula:d680d359-a1b8-4564-8d52-d391c23f0997}} with {{formula:07c19e61-04d5-45b0-af13-dac6c5be3f31}} , imposing helical boundary conditions {{cite:e462194cc05e478daa2085e618d50238b203c352}}. This means that the last spin in each row is coupled to the first spin of the next row instead of the first spin of the same row. This is computationally convenient as it allows one to store the lattice in a linear array. To do so we number the lattice sites from 1 to {{formula:7772db58-a6a6-4c74-b105-47cc3114b933}} along the rows, with the first row labelled 1 to {{formula:bfeedb0e-9b2c-4f3b-9ad0-5f0e4a52598c}} . Then the adjacency rule has a simple description in which the neighbors of the {{formula:acd506ee-b11f-45fd-8bbc-d40b8fdbc996}} spin on the two-dimensional lattice are situated at {{formula:064a00f5-749f-481d-93b7-dba86b77b70d}} modulo {{formula:afef0b2f-0d9a-4b9f-ae37-69a1b0528774}} and at {{formula:39e4b5ab-de12-40b5-b29a-80eb7050266e}} modulo {{formula:fe925f20-c249-478f-a72a-81396c7f13f3}} .
The density profile was averaged over 300 realizations, running for {{formula:a6f39854-4b8e-4406-b9ef-db3db3b78bbb}} Monte Carlo sweeps.
{{figure:0ca96812-5b13-415d-b78f-1eb202af8892}} | m | 01c7adc18d815598f09a185204c108c8 |
The features obtained in (REF ) are called scalar features as described by {{cite:3886c084fe62725eb09898371e75a312c783c909}}. In appendix § , we extend this solution to obtain outputs that are regular features represented by {{formula:661d150b-4044-4747-a1ea-28617e7b13a8}} in Alg. . Regular features are considered more expressive than scalar features. As proved in § , {{formula:0b362f4e-a33f-4a33-8b5b-97ab3ccc7c39}} is also equivariant. We restrict our experiments in this work to scalar features for simplicity.
| d | 48964ca4a8b1104fcacfe08cad7e5fdb |
Further, the joint minimization of the Scaled Lasso objective
(REF ) always includes computing an estimator
{{formula:07dba730-afc2-46c9-8214-14b9d442fcd6}} of the coefficients.
In particular, Corollary 1 in Sun and Zhang {{cite:fac30f2d026cd6aeb5a602b5517aafbe5e04270c}} also
guarantees optimal adaptation of this estimator at least under
{{formula:bdab54d2-127a-446c-be94-9f1ff4da6807}} -sparsity.
Ex ante, it is therefore unclear why one should apply our stopped boosting
algorithm on top of the noise estimate rather than just using the Scaled Lasso
estimator of the signal.
In Figure REF , we report the
relative efficiencies
{{formula:9bdfcecc-37f3-4983-bd5c-124ad0e52ff6}}
| r | 747560cd7d1aa96307dc170ece8f1fc9 |
The methods tested on compositional challenges of MWPs are mainly categorized into four families: (1) General encoder-decoder models, i.e., LSTM {{cite:205254cb5e0501b84d6f963fe781b03f6d6d1c8d}} and Transformer {{cite:828b8ff90913f82ea7b68de924958b3160e0da13}}.
(2) Strong MWP solving methods, i.e., MathEN {{cite:67ba778390316e7965b6c4177119c254c0bbc3f5}} and GTS {{cite:27b42d30c997922eac1719e418dc0e6c59e28569}}.
(3) Pretrained models i.e., BERTGen {{cite:f0f2e063bc23b17238dabde1f31eaa72c87e76a3}} and GPT-2 {{cite:3493940a349d3914203255360999d27e06cf27d5}}, which have been suggested to improve general compositional generalization {{cite:e96a54678a44762f67b07b34f6c313cdbea1bcb2}}.
(4) MathEN and GTS collaborating with our proposed data augmentation method (refer to as MathEN+DA and GTS+DA), which aims to improve compositional generalization.
| m | 9f9504678d6cced7afcc4d297f0d061c |
In this work, we investigate the superconducting properties of a less explored Re based pseudobinary telluride Chevrel phase Mo{{formula:5ee5b60e-3700-473c-8be4-2b164dbe089e}} Re{{formula:b765cf49-795b-454d-a565-f407ddad5de0}} Te{{formula:b9d7c931-d29a-4e61-920f-c1a3a291bcc7}} , where Re is partially substituted at the Mo site. This study comprises two different prospects; firstly, the presence of Re in the Mo cluster will increase the spin-orbit coupling strength (SOC {{formula:942b3f88-3923-40f6-b199-47c67a3f688b}} Z{{formula:348b2e0b-bbf5-46c5-9739-c41fe8634956}} ) and affect the phononic distribution by affecting the related interactions of the CP system. Secondly, this compound can address the ambiguity in Re-based superconductors around the possible reason for time-reversal symmetry (TRS) breaking. Such as Re{{formula:46de59a9-8b5a-4c7d-8388-f9d9c309a756}} X (X = Zr, Hf, Ti), a noncentrosymmetric family shows spontaneous field presence, breaking TRS, regardless of the element X {{cite:b37dbbacc4be5c457e88113762053221c040044b}}, {{cite:bc3b883e4bba38d263ba9a567bf15957b25c8c1c}}, {{cite:9005d6ac8c1899167b25bd3db3bd8ea448187eec}}, while the other non-centrosymmetric compounds Re{{formula:c0b4f155-ab69-4f57-9040-68d8e894a641}} Y (Y = Ta, W) and the Re-B system {{cite:0a6f847019589aefccfaa6c3a68be0e2ecf4173a}}, {{cite:edfc6ef4cc27c916bc845d94745b0ff9162bfcbb}}, {{cite:f8799890039b96dabf44341ee56d1e72d08d293e}}, preserve time-reversal symmetry. Furthermore, the uncertainty in TRS breaking presence in centrosymmetric Re is also intriguing {{cite:f66abfce12340e7791d6572fcd46b3ea6cab18e7}}, {{cite:c1a7f951366bf9bfed95844f972968ad92abfdf2}} and raises more questions about the role of associated structure and Re concentration in time reversal symmetry breaking. In this regard, investigating more Re based superconductors are essential and Re based pseudobinary telluride CP Mo{{formula:dc702086-0aa5-48d7-9b0f-67394339585a}} Re{{formula:6d7ac0c3-2d4b-457d-ba8a-41ba7a98a9e7}} Te{{formula:9a146be3-229a-4bec-99ff-6715cbaf9400}} , provides that platform with a new structural aspect and different Re concentration. We have performed the temperature-dependent measurements of AC transport, magnetization, and specific heat in different magnetic fields, which allow deducing the superconducting characteristics parameters with other electronic parameters of Mo{{formula:2d46fa84-7535-47e8-9eec-f0a1f655c42a}} Re{{formula:929096e0-fefb-4cf1-a77d-ad54ad78cb42}} Te{{formula:71c8297a-7900-409d-8c86-7e03c183ea7b}} . The extracted upper critical field value is close to the Pauli limiting field, which suggests the possibility of unconventionality in the superconducting ground state. Specific heat measurement indicates a moderate electron-phonon coupling with {{formula:5f749079-75c9-434d-842f-7eb5a44b2817}} -wave gap symmetry. Moreover, initial band structure calculations suggests importance of SOC on the electronic states of Mo{{formula:f69329ed-c791-4e39-b244-cbe9157fc2f9}} Re{{formula:3f139727-1a0e-406c-b1d7-d458d0dbd349}} Te{{formula:ea995786-268d-437f-a7f1-6b784172bd24}} along with dominance of d state of Re and Mo atoms in density of states at the Fermi level.
| i | 1c2c7f237e896b928795481e1b80f0c8 |
Here we denote an abelian Lie algebra of dimension n and the Heisenberg Lie algebra
of dimension {{formula:566ea1c3-d720-4f41-b109-d4c10f396af8}} by {{formula:b5e682c5-2304-4882-93b2-114fff3c3a1c}} and {{formula:2b95ed1b-0b73-459d-a267-f6339b0b58d5}} , respectively. Also, we use the following structures from {{cite:d9d4ba86a07fe5ce63a3fe7f32a719f31b626e8e}} for all nilpotent Lie algebras
{{formula:e7c6d78a-16bc-4727-b50f-aad13d464461}} of dimension at most 6 with {{formula:e55dfac6-1779-45c6-9cf4-37ed42b5ef54}} over an arbitrary field {{formula:f1688691-bcbf-4300-823c-7e1bcf6bcee6}}
{{formula:14e98606-d0bb-4318-91fb-11b661674df1}}
{{formula:79eefdc3-6603-4b78-8750-4a8ea6a524ef}}
{{formula:47c4cff8-4fb3-4fd1-8de4-bafd324fa7c1}}
{{formula:be1c04ac-dead-4605-8b17-f68ad4838144}}
{{formula:f794db23-895b-4b3b-8292-8e54354efa44}}
{{formula:dfe46d66-3e31-4c3a-8336-ba9bd268a15a}}
{{formula:4f56e037-d81e-4efd-80b0-07cce45a84ec}}
{{formula:0770ea0f-7c15-4632-8540-7a7bfd4d92fd}}
{{formula:c1d1bec0-ece9-481e-8ef2-377440199bf0}}
{{formula:c6689c68-a1cc-4691-bed3-0ff1d5be6a11}}
{{formula:6b1764a3-e0c1-47a7-a36c-2161fcd84368}}
{{formula:809de6f2-59ba-4c33-851f-e8f5548cfc62}}
{{formula:d880bb4d-f2a6-4d99-b565-8f700e8788aa}}
{{formula:37aad7e9-1198-4222-a194-8ad6c809603e}}
{{formula:4a6564ad-475f-4def-8fba-71d86b5bbdb8}}
{{formula:15b0f8b1-9276-4557-a9ba-8b99362a70e9}}
{{formula:272db14d-82d3-4a57-aecc-e815380857ee}}
{{formula:99aeb7b3-4f37-44dc-8e12-c2d17cf8d3b2}}
{{formula:aba32928-80bc-453a-b444-b3a3b3203c7a}}
{{formula:f009cd42-9acc-4863-a218-83ba8e0056fc}}
{{formula:8c4649e6-9c1a-4f2c-9147-826cd53a7241}}
{{formula:790e6a65-aa13-43ab-ba38-b5a428a94b6d}}
{{formula:2886c48e-9686-4a55-a7fb-d78282eda2b1}}
{{formula:2d3e3022-6602-47d9-8d49-5f9d04c5034f}}
{{formula:8e8373e2-48da-4e9c-aaa2-21ded7b6c29d}}
{{formula:cba9fecc-d01c-4243-bd85-caa1a34bc844}}
{{formula:221a8a53-75ab-4749-ae17-4c12dffa79ae}}
{{formula:d30b910d-ce2f-4330-94ca-a332415f6245}}
{{formula:92c94b4f-7ba7-4dc2-963e-9fb5e75ab916}}
{{formula:cf606408-0097-4ce1-9237-0e0b4ec98167}}
{{formula:a3d596c0-4810-49d8-90be-1c0b318ad0ff}}
{{formula:92f0d77a-9e18-45fb-bb3d-b2ae2fdbf4d8}}
{{formula:873f8288-fdbd-426d-b520-fd84425053c4}}
{{formula:b7622ae0-8ae2-4763-a37f-8169966f05a3}}
{{formula:71a51cf2-3518-4da2-b8e5-d4aa110585ec}}
{{formula:bec21703-28cd-422b-b69b-9adc9bda7cd7}}
{{formula:0447739e-fa17-4e03-9a95-f0e186d622a8}}
{{formula:b6466ef2-e9b8-4e4a-a16c-5237dcbf37bf}}
{{formula:b9e9af0c-2dcc-4644-8983-24a6d2f066b7}}
{{formula:889ebf28-5919-4e9c-8273-95ff2bcab88a}}
{{formula:e93dd581-1980-4739-bb21-12e002f52649}}
{{formula:be66749d-8b64-4fd2-927a-c87e63353687}}
{{formula:1274875d-badd-46aa-b44e-a74e4012a92a}}
{{formula:fb0ad434-95a8-4390-8c9f-7de7166e7093}}
{{formula:f016b4a9-de02-471b-b267-428b260f4268}}
{{formula:f10b796e-b362-450d-91dc-0798b0de012c}}
| i | 95e1c3d89dee41f34f2eb69220990727 |
Snake-based methods {{cite:7c81f7843799d165d95cfd83d923c5707a2ae904}}, {{cite:dce7f4774dd62d9443d1a1661e944501a8118667}} represent shapes as polygons in pixel coordinates and
deform them iteratively using circular convolutions. While these methods can reach good accuracy levels at reasonable speeds,
they generally make use of a high number of contour points, which can be costly in terms of storage on embedded devices,
especially compared to shape encoding methods described below.
| m | 28fe28eb57b96f6734e6617af7c88732 |
In the comparative ITS (DiD), we aim to identify the ordered treatment effect, or the average treatment effect on the treated (Ethereum), represented by {{formula:aa0307b8-7bec-412d-80bd-79966b16cffa}} , where {{formula:94386671-bc50-4eae-96c4-1beacd9f625e}} represents the expected outcome, with {{formula:31b04276-3911-4d8b-8941-d52b413bec4a}} and {{formula:dff74f86-bedf-476b-857d-c45031590faa}} . We use {{formula:766556e7-ded7-466b-9ba9-11665f5f477e}} to illustrate the treatment to get an airdrop reward with a low probability as in the Bitcoin blockchain; we use {{formula:25eb748f-cac5-46aa-9aed-77ec1f251b50}} to illustrate the treatment to get an airdrop reward with a high probability as in the Ethereum blockchain; we use {{formula:40463348-085b-465b-9453-0846c6a7774a}} to illustrate the condition when the treatment of an airdrop is not available. We use {{formula:5084a355-3d68-4a9f-8292-2c65193d282c}} to denote the time when the airdrop was available and {{formula:babd8710-0b68-4a36-86a9-9f330bcedf7d}} to denote the time when it is not available. This is equivalent to the local treatment effects discussed in {{cite:81a4c42c367ec72d91958eb9a8ee0cdf4d797963}}. We can re-write this equation such that:
{{formula:0045118c-8e9d-4bf6-ad9d-06b0827a5d30}}
| m | 7c6d09ccbaf3be234d097bc6412d1c33 |
Multiple seasons can be modelled together as if it were just one
season using the modelling framework we propose, as long as the game
rules, and hence, the definition of the events being considered does
not change. Another aspect of the tournament to note is the relegation
and promotion of teams within the league, which results in some teams
not playing the same number of games over multiple seasons. A
limitation of the proposed model is that the game periods are
exchangeable, because the likelihood is invariant to the order in
which the game periods and the games occur. It would be more natural
to allow for the team ability parameters
in (REF ) to be time-varying, especially over
multiple seasons during which team players and managers are likely to
change. Due to computational reasons we were not able to utilise most
of the data even within a single season and current work focuses on
overcoming this computational barrier using variational inference
{{cite:769ec13ed0841aac6c6cd62e2aa984971a540ff4}}.
| d | 12ffe4f1e519eef7bf3a9acbcc505f28 |
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