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where {{formula:c7b16489-e6ff-4624-96be-1670f460fb90}} is the Thurston measure on the space {{formula:b0f67f95-0fec-4739-9370-60fc02aaaf4a}} of compactly supported measured laminations on {{formula:6414d928-851d-4a8f-b81e-058dc5c23b4d}} , {{formula:2acccb16-da41-4034-b608-283ff6dfa4ac}} is a constant depending on the type {{formula:140943cf-3d25-4f9b-916c-bf736b02c37c}} , and {{formula:e3004a7e-ef09-400d-b174-292265ba2c40}} is a constant depending on the topology of {{formula:069c95bb-527c-4567-bb77-628e5db04c3b}} . We refer the reader to {{cite:b3377a1c5840eb03c073f4a16855783197b54e3a}} and {{cite:0bb6c6065d83dc539db649bbab8b333a06042e25}} for details of the constants, and to {{cite:2259992fdd7e035a02f392288d7b19faf8f16ff0}}, {{cite:030f3fb3950eaf237455fcd46dc0bff67e965c5b}} and {{cite:5586b72927377d5d587bac664bda6f3b543db59f}} for a background on {{formula:c7826bf0-012f-4098-a8c3-af3f101974ee}} . Here, {{formula:76dc920d-0fd0-49b0-87a5-dbe15994816d}} denotes the {{formula:296c57ea-ec8d-414d-aee9-03077b3a1b20}} -length of the geodesic representative of {{formula:d3bd51ea-c1bd-4336-a356-4aa9c0fd8321}} . Mirzakhani first proved the above result for simple multicurves in {{cite:b3377a1c5840eb03c073f4a16855783197b54e3a}}, and then again for general multicurves in {{cite:0bb6c6065d83dc539db649bbab8b333a06042e25}}; also see {{cite:2902ffe1872fe69c53e09ae5d22af7805ed1c574}} and {{cite:e931ffca52fa090a40362374a3893a7895c7365c}} for an alternative proof of this theorem.
| i | 8809fafb8ee2a3affd58f1be9a4519db |
One important application of Eq.(REF ) in the hard string scattering
limit was to reproduce {{cite:f283e8e9bfb8cfc06f3336ff3e286afd32440c41}} infinite linear relations with constant
coefficients among all 4-point hard SSA ({{formula:58b7ac85-cf8c-475c-a3ab-800b80bced43}} ) and solve the ratios among
them. This high energy symmetry of string theory {{cite:0a4c9cb9110a572e7e5a89753cb14c18e91f8b01}}, {{cite:5c52a860dcd4a2811b086d037576c3194bdec727}} was first
conjectured by Gross {{cite:164eced05d8808061297badc56c80851ea029d82}} and later corrected and proved
{{cite:64bedc97e1c5c1c7848ad0c29dbfa345f94ba087}}, {{cite:f1f4b5a2cd042040a91dae1e57811eec44ecd00e}}, {{cite:3931fc9901cbd2e7dadd53a56ba60fa5a06d4e66}}, {{cite:4bc5ec61ac9ccb467e33016b1fb68a971072bd2b}} by the method of decoupling of zero norm
states (ZNS) {{cite:aaafcee919f6283705c935959c393fcdd23a525f}}, {{cite:f6c358d0ea24566ce1ca9d56b498bcdd5c5d9d58}}, {{cite:aa464d618311913ff119ad04195e1a86678f1e5e}}. ZNS was also shown to carry {{formula:f124b25b-6506-474f-98c4-a22f6349342c}} symmetry charges of {{formula:2be6ee3f-8e5c-4137-a5e0-ba77d29159b1}} string ({{formula:6154af0d-a17b-4c85-8448-8e6d54b4eeca}} , {{formula:92f5e8e7-5e52-445a-8f11-9e5f843ce285}} quantum gravity)
{{cite:4e6629fc415819cd4811e243654685628b890f38}}. See the review papers {{cite:9f03ab50c28c0a29a4b3218028ac8bdd73623cb3}}, {{cite:e3395dbe32848ae196650b50a9e4ba2fadb2b32e}}. More importantly,
since the decoupling of ZNS or stringy Ward identities persist to all string
loop orders {{cite:b6ff924701a47ecc08a1324adb02f9603e8d1ced}}, it is conceivable that the infinite linear relations
obtained in the hard scattering limit for arbitrary mass {{formula:21d44279-2f0d-43c8-8635-19540be5a7ac}} levels
for 4-point SSA are also valid for all string loop amplitudes. On the other
hand, one notes that these linear relations are not shared by amplitudes of
quantum field theories which depend on polarizations of the scattering
particles {{cite:a81fa506ffc6dd8d97d48c11acf0222ec33ca703}}.
| i | 1e412448318c3640bbf51bdbdf81bc75 |
We evaluate multiple-shot attack {{cite:68160e20a985787f610c265c73cbebba241a10ec}}, which means that the attackers perform attacks in multiple rounds, and the malicious updates are accumulated to achieve a successful backdoor attack. As mentioned in Section REF , we perform a complete attack in every round, which can show the difference between DBA and CBA in a shorter time {{cite:950228f559be89594ba1e93b13b216dec175f5a2}}.
| r | 2c1e98453fb76a3bde1bb9c631b7cede |
Dataset: we used MNIST {{cite:055025cf991bfcc0611e20f9296b6aeafdb730c7}} as {{formula:13cdf72a-6288-4bf0-a170-c54068b2a264}} and SVHN format 2 {{cite:ff0a8b1ba793ef04668dbf10a0be3ef865cb994c}} as {{formula:dac005d1-9919-4c7b-b632-d99db28690a3}} . MNIST contains {{formula:829f82b2-e7ef-4757-bac3-78fc5528caf1}} binary images of size {{formula:77e6d868-c0a6-4098-9e03-85c35754e24f}} for training and {{formula:37c27a2c-61fc-4fab-907e-018ebe3bb71c}} images for testing. SVHN contains {{formula:4c599182-0b1b-4902-acbe-e4bc067f235b}} colour images of size {{formula:37ecd3e2-9a32-4405-909e-577091d08fb1}} for training and {{formula:754613c6-cc8c-4bcb-9e65-8d13231d90b4}} for testing. We chose these two datasets for the following reasons: (i) they are designed for the same classification (10-class) task; (ii) data are drawn from different distributions.
| r | 7b5ce6bfa2f2bf4384c486e23b46df9b |
We conduct an empirical evaluation of the proposed methods against state-of-the-art gradient-based methods (PGD given here and FGSM in the appendix) for various NN architectures trained with different approximate inference methods, including Hamiltonian Monte Carlo (HMC, {{cite:24ce2a32eb5d09d25f0875a2c089095d02437998}}), Bayes by Backprop (BBB, {{cite:beb466d9910c798a4a2fe6f225455441127dc3a7}}), Variational Online Guass Newton (VOGN, {{cite:af08f39e664c21a8b5d3d7a1e65c53f3260ee504}}), NoisyAdam (NA, {{cite:263a2f1a04fb31401a7a83141d31e4f7b804f9b4}}), and Stochastic Weight Averaging - Gaussian (SWAG, {{cite:eaabd857632c0a2b545f0da1dca0f4bc4e723930}}). For each of the BNNs discussed, we select the prior distribution based on the Glorot normal distribution {{cite:88f81063d53948b7ea059e16cae915ee65daea50}}.
For MNIST we fix the strength of the adversarial perturbation {{formula:6edd3b33-af46-4b00-8905-28185e322a4c}} and for FashionMNIST we instead consider {{formula:90826ac4-723f-4808-95ee-5ee46a38061d}} . For each PGD attack we consider 5 iterations with 1 restart. We note that each iteration of PGD requires estimation of the expectation of the gradient via Monte Carlo integration making this setting as computationally expensive as 1000 iterations of PGD in the deterministic case (assuming 100 steps for the Monte Carlo integration).
| r | f363498460d0b346f4deafec2741e5c9 |
Since the mechanism of the QLD is driven by the unstable cyclotron
waves, it is important to investigate the effectiveness of the
instability and the corresponding growth rate. {{cite:cc818ba0833aca46f486d1bc08b92912c3f8efe0}}
has shown that the increment of the cyclotron instability is
given by
{{formula:ad1a9262-8f2a-4c8b-9372-e3cc36be9467}}
| d | 995fd75f0d5a91b64a2f8603e7edcc67 |
The projected power method {{cite:7bb9c1afc53507fda0a02ea88fc56372d84662ff}} suggests to replace the global normalization (REF ) by an entrywise projection onto the group.
Specifically, the {{formula:b1c29662-6a7c-4f87-985a-44132cd1752d}} -th iteration reads:
{{formula:dd25a555-449f-4d37-b7c4-4f75350454a6}}
| m | 597909b8e1b666b772d527394acb4163 |
We address the machine learning problem of predicting values of a target variable given a training data set in which the target variable values are known. The training data set needs to be representative of the underlying population, and its size must be large enough for the machine learning model to accurately learn to predict the target variable. Yet, in applications like personalized medicine {{cite:681d961bced8c095074a9c9cd652bd7d84f3ced7}}, {{cite:ab23d9f544cd2a349ff87ea3d2296a4963702a69}}, {{cite:4836b4576331713ebd243c97d16e4c778ca9131d}}, brain imaging {{cite:76898679640cac50c2d3e15ca21d7ac33ce5643b}}, {{cite:34b052fe9f025dd64f9db9b2d59829a5a7569118}} and textual document categorization {{cite:da7c284dfb1433236c5abe72115f5a0585b0fb5c}}, {{cite:6fd254d04d788add8988be769dec7779aef1caa7}}, {{cite:80655d0d63983a1e0512ec66a92c771204db30c9}}, {{cite:7ccbe3e33555be21f9f36edbb0490b48eb86d6b4}}, {{cite:3ff7106700fa4b196ceb88af7c53f1d25ee5bca6}}, the number of features by far exceeds the number of samples, leading to the “small {{formula:d58cc870-dcff-42ce-a584-d8ba58127f9e}} large {{formula:f22ea6c2-4371-48eb-addf-c9b6df3e2cba}} ” problem {{cite:f17775f2565da2b7073d9a57b904d17517d2c326}} where classical models inaccurately predict the target.
Fitting regression models for this problem requires regularizing the model's regression coefficients {{cite:4bb3ecd8b262b1ba392ba02db388bb14def82024}}, {{cite:4f7cd276504f144fa144927a9fa7c1e1d9324a0b}}, {{cite:0c83cb260267dec77d54add8286408f52520b73c}}. Typically, the level of regularization is tuned by estimating a hyperparameter from the data, but this neglects prior information that could be available on the problem, the prior information referring to any knowledge of the problem the user may have before inspecting the data.
Yet, knowledge of the features' effects on the target could significantly improve predictions {{cite:8fe0aec7d1f91603a447bf1fba1823cd54bf6c46}}.
| i | cfa9ec5f1874bb383c4457170081d0dd |
Conventionally,
a mechanical mode can be said in its quantum ground state when its thermal population {{formula:aaa3b842-321e-4e81-86a3-33e1da41b3e0}} , which can be achieved by lowering the temperature {{formula:0c3ad50d-21fc-44a3-903f-c5c5bacf7cd7}} .
Alternatively, the high degree of control reached within optomechanical systems enables the use of back-action cooling {{cite:38855f8aa0cd42dda3bb5e817e4467e32b1bd842}}, {{cite:c32337b4c948356295829d0777de564c182b8dba}}.
This comes at a cost: the mode is strongly damped by the light field, while the surrounding bath remains warm {{cite:a20e5d21bb59d71163a24c7afd5c62d38981e69a}}, {{cite:5e631c550105077c96bc69decf375df80395fc53}}.
GHz acoustics has been passively cooled to the ground state using conventional dilution cryostats {{cite:f878095c8dd6008faf1c35229f06784b553ab830}}, {{cite:bc2fb418713dd8ec9c651ecdba189062ba8c7274}}, {{cite:5d845f0d35591e5abbc80a1ab72c3fbf65f9ca86}}.
However, these systems are limited to extremely small centre-of-mass displacements (zero in the case of breathing modes {{cite:f878095c8dd6008faf1c35229f06784b553ab830}}, {{cite:5d845f0d35591e5abbc80a1ab72c3fbf65f9ca86}}),
even though they do contain a very large number of individual atoms. Hence, they are not suitable for tests of quantum decoherence and collapse theories {{cite:f5ba412b42c1687693ec07e838efcbc236577212}}.
| i | 3f35772c185f0c6d6565d88687638eae |
we obtain a real and continuous function, which is also bounded away from zero. The resulting operator {{formula:89e56a6f-f704-468a-a8ff-1ce18459ac82}} is invertible and therefore, since the finite section method can be applied (see {{cite:e1922b7f32b82e87e42d16511671dff5cc67ac9e}} for example), the related finite Toeplitz matrices {{formula:7724b1c2-6659-4d70-89d9-b1987d131913}} are also invertible. Note that {{formula:0b9b6788-7e7e-4a68-b0cb-8849a1830763}} can be thought of as the quotient between {{formula:02868b36-9bca-48a4-891f-2b52943f9daf}} and {{formula:0160d6b2-f608-48fc-ad22-dbaa7b203a35}} , which is similar to the preconditioning process of the ill-conditioned matrix {{formula:be1b4a5d-1def-43af-8687-ec4590d9face}} used for example in {{cite:b7198500f3536d662af034e2e1aafe051a814f97}}, {{cite:56090593f8873edac7d07addd2a26485e6c93c5b}}; for a general account on preconditioning in a Toeplitz setting see {{cite:3783ef20425125199a9359eae41a3da83241628d}}, {{cite:91ce4a5041750b453391cce913a206dc2964f7ee}} and references therein.
| r | 1658fabc864de51eb80895057c4c490c |
The fidelity between the initial ansatz state and the true ground state, the flatness of energy landscape around local minima {{cite:f354ead13813f7f4a392a3f7e4cbc8401e36ae7a}}, and limitations arising from the classical optimizer are the dominant factors which affect the shape of these distributions. In particular the flatness of energy landscape around a local minima can lead to a VQE result which is far away from the rest of the values, even in noiseless simulation.
{{figure:e76692c6-e197-44b2-9cc4-d20734f21c18}} | r | 22785fb964d0b9f93ae37e1600310cf1 |
We compare the proposed algorithm with one state-of-the-art image-collections based 3D face reconstruction method {{cite:0f9a41ce618e9482f427811c3ab288075bcb01c5}}, using its pretrained model.
We quantitatively evaluate the expression disentanglement consistency by calculating the lip LMD on 100 video clips of different speakers randomly sampled from the test split.
For {{cite:0f9a41ce618e9482f427811c3ab288075bcb01c5}}, we report two results, one with person-specific attributes estimated preframe; the other with person-specific attributes aggregated from frames of high confidence.
For the proposed algorithm, since the E-Net does not regress person-specific attributes during inference, we report one result obtained with the mean person-specific attributes and two results obtained with person-specific attributes randomly sampled from trained share matrices on trainset.
As shown in Tab.REF , for {{cite:0f9a41ce618e9482f427811c3ab288075bcb01c5}}, the results obtained using aggregated person-specific attributes are worse than the results obtained using preframe estimations. It indicates that both expression and person-specific attributes are adjusted for lip fittings on most frames. In contrast, the proposed algorithm results are more consistent, indicating that non-rigid facial morphings are consistently ascribed to expression, thus less affected by changing person-specific attributes.
| r | 981a0002cc0fde8a3547a17ed466aadf |
Define the Fourier transform of {{formula:2c1c16a7-5188-4659-9a84-9d7cf97dbcfc}} coefficients, {{formula:2a61544f-2367-402f-a801-a438db714752}} , and of the operators, {{formula:974db012-dccf-4558-8b4f-32cdf7d65467}} ;
and assuming {{formula:78c8ecad-4763-4be5-ad6d-1fb106201d55}} is real and symmetric, equation 39 from {{cite:2fd60f257d212f3caa50237a2decd689e565db14}} writes
{{formula:d8680880-cc98-47e8-a9b8-ea8fe09da82f}}
Use a binary oracle {{formula:6e791823-49f4-4725-9775-8868bc6161ac}} such that {{formula:12806f22-1b34-42f2-8648-d42267025668}} . Then we can implement the phase operator
{{formula:72f61d72-01ad-42dd-9534-0493d2d3ce1a}}
| m | 89f7eb5d45f1689dfa9f32516bc9eeb0 |
Remark 4
It is a well-known fact that asymptotic stability of the synchronization manifold is guaranteed in lossless networks when the magnitude of the phase differences {{formula:dfd86908-91c7-44f6-8dae-a398cea9ffa6}} at equilibrium do not exceed {{formula:020d907f-268c-4b27-8e77-c3bc397b9ef0}} {{cite:a94847c8860187e5abf575ccafddd5136cdf6860}}, {{cite:525cb6a337f6c94d7a628ffa4571b6c50b419e07}}, {{cite:6520ab280e4e994bb5793520410b7bf5c1351428}}.
However, the presence of the
phase shifts {{formula:6f16a9b5-6bd6-4489-a78b-ca8c47eda4fe}} in (REF ), as revealed by its equivalent representation (REF ), imposes additional constraints on the values that {{formula:a500c503-0c7a-40bd-bddb-096556ef9a84}} can take to guarantee frequency synchronization in blacksystem (REF ). This provides insight into why power networks such as small-scale inverter-based microgrids can often encounter stability issues.
For these networks, the resistances of their couplings (interconnecting power lines) can be significant
and thus {{formula:d6d73cbf-4fb2-40bb-8e13-2ce4a2806c08}} can take large values close to {{formula:bbbd1517-90b7-413a-b079-bca636671abc}} . This results in high resistance to the flow necessary for synchronization since the conductance {{formula:4d9757c2-b81a-486c-a148-d81cc2118599}} responsible for inhibiting synchronization is large, thus explaining why these networks can often encounter stability issues.
| r | e513841b91a2a288b5ca43f565b968e7 |
Tie strengths play an important role in the analysis of social networks, characterizing the relationship between individuals and providing insight into how those involved will interact with each other {{cite:7e8ac0e6028081d317c4170c4e0b378a46a32577}}, {{cite:7eed1c528c9db9b40d05cd42fdee5635150291d6}}, {{cite:c2f69c392754bdecae0360014c091682f04a5182}}. While past works have delved into predicting tie strength {{cite:0b01cd18f55ded602e1e29b4870212c4dd41a205}}, {{cite:e18491d9fc1fc8487cd9f1babe64e2f0cd86bb67}}, there has been limited research into the forecasting and subsequent analysis of tie strength that evolve over long periods of time. The paucity of this kind of research is in part due to the difficulty in collecting data social ties as they change, which is typically done through surveys. Additionally, many past works tend to implement tie strength measures that depend on many platform-specific attributes. In this paper we address both problems by introducing a system that converts easily collected communication data into continuous tie strength values with machine learning. We design this system to be generalizable, depending only on the communication data and a sparse number of ego network surveys. Using a small set of modular questions, we extract social tie rankings from the surveys that we use to train our predictive models and predict the social tie rankings. The trained models can also convert communication data to continuous signals over time. Given the nature of these signals that are generated by our models to predict survey rankings, we can interpret these values as continually evolving tie strengths. And with these values, we can analyze the relationship dynamics of social networks.
| d | 8843fbef99cdcbdb6d66ca8fcaff1cb0 |
This paper accounts for behavioural variations among agents using Rényi divergences and their associated variational bounds. These divergences are Rényi relative entropiesThe Rényi entropy provides a parametric family of measures of information ({{cite:a94a128e70ca44a2362a5e42ade292cd53921096}}), and satisfy similar properties as the KL divergence ({{cite:a94a128e70ca44a2362a5e42ade292cd53921096}}, {{cite:b28424996ee82837bcee703707a44d6eeaffbaf6}}). Rényi divergences depend on an {{formula:5d802ab0-00fd-42a9-b913-3f6b5807b255}} parameter that controls the strength of the bound and induces different posterior estimates about the state of the world. In turn, different beliefs about the world lead to differences in behaviour. This provides a natural explanation as to why some people are more risk averse than others. For this alternative account to hold, we assumed throughout that agents sample their actions from posterior beliefs about the world, and those posterior beliefs depend on the form of the Rényi bound's {{formula:7d300c56-dd7f-462e-a8dc-0c44004a1ffa}} parameter. Yet, note that a similar account is possible if actions depended upon an expected free energy functional ({{cite:c9d47ad4c2e5b92eefd65c5d3eb88cb0c0b940f2}}, {{cite:b729066585470b79661a1c9cabc677b9d3826bdc}}, {{cite:00af1116134bf3268b24f30e8b6dc2568d3ed650}}, {{cite:eae3136192634e47e712621eb52f3d617fe98a1f}}), intrinsic reward ({{cite:fe494e4c605482dbba8b69af8d6e2c90a9060bae}}, {{cite:65ab48b0a5331e84715b7288a7b33e87454826a7}}, {{cite:8c0a547d342bc1b58e43c9842987c5f9d97bd454}}, {{cite:7a3c588c3d7c068c5ed8b68418686af40dfbebb3}}) or any class of objective functions that incorporates beliefs about the environment.
| d | ba6f3f90fb83de0cf5bcc05896bf4a6e |
There are many open avenues for future research. An emerging field of research in science and engineering is scientific machine learning (see, e.g., {{cite:b3dcc68905a4501a59addf5daa74bdc44629d994}}), in which a primary goal is to infuse empirical knowledge and first-principles rules of processes in the course of training neural networks. We hope that by incorporating such information and physics while training, one learns models using fewer data (otherwise, deep learning approaches are data-demanding). Also, the autoencoder would be better interpretable and generalizable. Furthermore, finding suitable designs of an encoder and decoder is a concern though there are enough intuitions by deep learning experts to find reasonably good designs. Moreover, we mention that despite our effort to avoid computation of the time-derivatives—which is dubious for noisy measurements—to obtain a continuous quadratic model by fusion with a Runge-Kutta method, our approach still may show poor performance. However, one can execute a de-noising step to remove noise from data using, e.g., the techniques in {{cite:39a2221e0f3ca8626ebefe7097feeeee1623c822}}, {{cite:fa876fcf72d76913cb8ee959169bd86e20d578f4}}. Last but not least, finding the intrinsic dimension of the low-dimensional embedding with the desired properties plays a crucial role in the performance of our approach. So, to find a good estimate of it, thus leading to the most parsimonious representation, would require further research.
| d | 748a9dfcaaa1e0c1399c25403c6699bb |
Comparison with other F-V losses. We compare our proposed FOP against various losses typically employed in F-V association methods.
The first is center loss {{cite:bf46e856a9f6da5a364134ce17a14048c61a84f4}}, and is adapted by {{cite:7a707f9bbd3de28eb0f362db72f9529d6c11a537}} in a single stream network to learn F-V association for cross-modal verification and matching tasks.
The second is Git loss {{cite:74cf5119a53a37d2db3d3eed1149ce1f571791f3}}, which in addition to center loss also maximizes the intra-identity distances of embeddings with other centroids and has shown effectiveness for verification and matching tasks.
In implementation, we simply replaced our orthogonal constraints loss formulation ({{formula:7735f319-4cb4-478f-a621-b1badf9be705}} ) with center loss and then Git loss while keeping all other settings unaltered.
The third one is Contrastive Loss that is adapted by {{cite:9dc56f1435a2dd6f01510ddb25e85b823ebf0706}} to associate face and voice of a person in a cross-modal verification task.
The last is Triplet Loss, that was leveraged by {{cite:ad26fe1589769c20ea9d8ab328179d78877dbfcc}} in their face-voice association framework.
In implementation, we remove our FOP module in the overall architecture and plug first contrastive and then triplet loss with hard negative mining strategy {{cite:a9b7e4ac6aadf7b483977796427a80961a76e92d}} while keeping the rest of settings fixed.
| r | 30d9ecc0934fc1aff48e97d75cb3d622 |
Proof.
By applying the descent property {{cite:c9f1c07600d91c542065afcbe541c5446587aef9}} of the projected gradient algorithm to the primal update (REF ), it holds that
{{formula:bb51c7ba-a48c-4df3-918b-117f108098df}}
| d | 5f4501e90535e1d74c21a22eaefec237 |
Based on results from dynamic system {{cite:efaa1c2b5e515c606e12c5804fa9b9bcd35056c9}},
Lee et al. {{cite:699a7d12fa28ba4e9f8edf93bd6e74ffcd1ad194}} first established the global stability of first-order methods for unconstrained optimization, i.e., they can avoid saddle points for almost all initializations. More precisely,
the first-order iteration method {{formula:d6ddf2d1-bc4a-4b55-8527-0c669e14acb4}} almost converges to minimizers under the assumptions that {{formula:b971b0a4-e37a-4aca-b259-b7b19c0a20d1}} is a local diffeomorphsim and the derivative {{formula:aab91cee-9da4-4a78-8538-b941b0c076cb}} has a negative eigenvalue at every strict saddle points. Mathematically, we have
[{{cite:699a7d12fa28ba4e9f8edf93bd6e74ffcd1ad194}}]
Given a {{formula:5daa3e14-9b4c-4185-93f5-4afa1875d92b}} -dimensional manifold {{formula:214c0616-f3de-4154-8af4-d85e755fc74d}} , and a {{formula:ee86d5e6-01e4-4a19-8c52-ae14833c3746}} mapping {{formula:d4a63792-91c6-45d3-9a9e-f61d112916d8}} , the set of initial points that converge to an unstable fixed point has measure zero,
| i | b9daa3e401b9462609c098d5bef21019 |
To have a better intuition of the trained CNNs, we visualize the feature maps of CNN 5 and CNN 6 before the last layer using the t-SNE method {{cite:bd7ee5d959a0c19eb57b8eaf96eb7a6fb0f6ac9b}}. The feature maps are vectors of length 98 for CNN 6 and 64 for CNN 5. By the t-SNE method we reduce the dimension to be able to visualize them in 2D. Figure REF shows the t-SNE representation of features extracted by the CNN part of the network (Fig. REF A), and by the whole network (model CNN 6- Fig. REF B). It is clear that combining the CNN and MLP networks has led to a better separability of the two classes of LDS and FDS.
{{figure:74060b98-f94b-468d-977c-b055c525c9da}}{{table:44094d4d-8ac4-4131-b651-94de881b3897}}{{figure:542ec509-da7c-4fb4-b75c-22c019f0a376}}{{figure:1f3fd4dd-1db8-4d9b-aef7-d4087c5b7c47}} | r | ec5568763617d16bb4e30752172fd21f |
In our paper, we try to establish the global existence of the mCH equation (REF ) on the line
by using inverse scattering theory. We find that extension of this approach to the mCH equation
will confront some substantial difficulties, which are much different from the NLS, AKNS, derivative NLS equation {{cite:4ba3b9e9598376874e60b76037f82b317f6999a9}}, {{cite:222447ed083768d25322f23742471a665b8e9059}}, {{cite:4941653bd7657071bfb520078eabc99018e614f9}}.
For example,
| i | 449e27e555887eee043622f2c830ef03 |
It is of interest in the above to know what are the restrictions
on the symmetric matrices {{formula:3ccc1308-4d95-443e-ab6f-2a06d31a56cb}}
and volume fractions {{formula:6b8e91a7-fab4-49b7-ada5-2d64f0ef9e72}} for which we
can find periodic E-inclusions.
Let {{formula:5becec26-8187-4c62-bb66-8028b5047134}} be a solution of (REF )
associated to a periodic E-inclusion. Using {{formula:98235ad8-4058-45d9-9631-fd0c70aaca1e}} estimates for the Laplace operator
we see that {{formula:13f4275d-9da9-4c3c-8420-144ad0e39e02}} is in fact bounded in {{formula:4a8059bc-68e8-4c64-b4ba-68437acdf65c}} for any
{{formula:a1bbc49e-e7c1-442d-a27a-d5fcc942b521}} since {{formula:1332f56e-fe2a-48fe-870b-25933b337f9c}} is bounded in {{formula:2c3478df-b4b4-49a6-a69c-9e8311358dd6}}
(Gilbarg & Trudinger {{cite:64ecf5a04baec4a8cbb60395837acd366aa9afa9}}, page 235).
Then we can rescale it and get a sequence {{formula:06a698da-f349-4888-be88-0f0c8d04605c}} for an open bounded domain {{formula:111e36de-5428-4cf1-8f87-4ee54b018168}} .
The corresponding sequence of gradients {{formula:84030424-3742-4d1b-8446-76416f8274e5}}
is bounded in {{formula:2088ac15-576f-4343-87f8-ecac59553edf}} for any {{formula:b932df06-a945-42a2-9c5d-fe935a38c3dd}} . The
study of the gradient Young measure of the sequence {{formula:a8872546-6537-4879-b747-c895ca2f3d6c}} gives
natural restrictions on {{formula:3140217c-fa0e-4422-b29b-f0d5106cc8a2}} and volume fractions {{formula:b4f843ac-597a-4676-b9b7-c61b0778e056}} . For this and
other purposes it is useful to define the concept of a sequential E-inclusion.
A sequential E-inclusion is a homogeneous gradient Young measure that
is generated by a sequence bounded in {{formula:3c179f3d-7778-46ce-87b7-8f64f90a4284}}
for any {{formula:a0d6b0fe-39b4-4c88-a9dc-81b330f28312}} , has zero center of mass,
and satisfies
{{formula:546cee15-3844-411b-a368-98bdcc5181a4}}
| d | babbaddc843aac052b5cbaae2329cf3d |
In the form stated, the converse to Quiggin's theorem is not true. However, if one requires norm-preserving extensions in the vector-valued case too, then the condition that {{formula:b17b09b7-f98b-4a3f-8ea1-67023b29e8c1}} has one positive square is both necessary and sufficient.
This was proved by McCullough {{cite:220adb9bebcf2c20191f054ee7752e2c5dbb74a9}} in a different context, and put in a unified context in {{cite:087187395f3ac495c6300f6b411f59f181b25d68}}. See also
the paper by Knese {{cite:b9a7140ce2af42502122873ef5cb07a8468affaf}} for an elegant proof of necessity,
and {{cite:e4fa053ad97caac117ab069fb2c169d83e047856}} for a discussion in a book.
| r | 131cf4f90b785c7268d6d6a17820495d |
The proof combines ideas from the case of constant-coefficient homogeneous phases due to Ou–Wang {{cite:55e16caf0d8cc44e8abf528489a8922a9864cf82}} and Gao–Liu–Miao–Xi {{cite:b80c41226577baa0df1e3c503b4bacf203568fb4}} and variable-coefficient non-homogeneous phases due to Guth–Hickman–Iliopoulou {{cite:2826ba59b25ec5334af6cf834ab605638ae19e81}}. We digress for a moment to describe the tools we will use and put them into context. Bennett–Carbery–Tao {{cite:6970a82e5fcb643f804409c6e6f39fa2d6d2f7d3}} delivered an important contribution with sharp {{formula:2dffc4ce-9945-425b-b69d-cc5937bc57fd}} -multilinear restriction estimates. We note that the multilinear estimates were shown as well for constant-coefficient phase functions as smooth perturbations thereof. Bourgain–Guth {{cite:348b2273373fa108b5de19ed9ba003aa45098e1b}} devised an iteration to deduce linear estimates from multilinear estimates. Guth {{cite:86c03426bfd7bc589b29653f9fc8c396cf954d07}} observed that the full strength of {{formula:771d6161-eeee-4f0b-b78b-65a5b630ceaa}} -multilinear estimates is not required, but a slightly weaker variant given by {{formula:609dfc2d-74c8-489a-a1c5-adece03d96c9}} -broad norms suffices to run the iteration. He used polynomial partitioning to improve on the previous results in {{cite:86c03426bfd7bc589b29653f9fc8c396cf954d07}}, {{cite:57aa0414069b670b293b22c11e70d089d6256d32}}. The idea is to equipartition the broad norm with polynomials of controlled degree: After wave packet decomposition, one finds that either the broad norm is concentrated on “cells" or on the “wall", which is a neighbourhood of a variety. To oversimplify matters for a moment, if the broad norm is concentrated on the cells, then sharp bounds follow from induction on scales. If the broad norm is concentrated along the wall, then we are morally dealing with a restriction problem in lower dimensions, which is amenable to another induction hypothesis.
| i | ddd545a3cfea6a2e266b7e8f3bfe43a1 |
In all chaotic maps, we took (see section REF ) the same
initial conditions and the parameter-values detailed by Sprott.
The corresponding initial values are given in the basin of
attraction or near the attractor for the dissipative systems, or
in the chaotic sea for the conservative systems {{cite:8c56556860ba6a9480d503305b12f17e3853857f}}.
For each map's TS, we discarded the first {{formula:b2833424-7fcc-4fdf-b7ce-9fd620a24312}} iterations and,
after that, {{formula:83da1595-bc87-4477-b00b-80751b11971a}} iterations-data were generated.
| r | f795e7fe260b1fc133200e04baf15e10 |
A number of past works have aimed to combine low-rank approximation with quadratic trace estimation {{cite:9fc899f757370f29211328aec5d507fdc4f20dad}}, {{cite:647493c68bcb379525edf3b6d5a7b06ad9c518b7}}, {{cite:37ba4c9f12678ab99cab6b21c0eb3e4ebee89b19}}, {{cite:024465a29e3035ec18b4dc3592343db9c9b39dda}}, {{cite:1864d1e237a01fdd106cd1da4341b6ccd6f45c38}}, {{cite:11bee02349084245b93978028e2d6504442610cc}}.
Perhaps the most well known is the Hutch++ algorithm {{cite:37ba4c9f12678ab99cab6b21c0eb3e4ebee89b19}} for approximating the trace of an arbitrary implicit matrix {{formula:ec57020d-31fc-4400-af33-1d83cb3a24ec}} .
However, Hutch++ does not take advantage of knowledge that matvecs with {{formula:55d98069-0bc4-4adf-a8f9-3666d1b7911c}} are to be approximated by a Krylov subspace method.
Moreover, at least in its original form, Hutch++ and related variants must be run separately for each implicit matrix.
This is in contrast to simple quadratic trace estimation based Krylov subspace methods which essentially produce a quadrature approximation that can be used to approximate {{formula:a82e760a-5b0e-468b-b32e-7ef839ee5f14}} for many functions {{formula:46c1fd24-21f9-44b7-8194-9b301487496b}} efficiently {{cite:07e507919b6aaedb2f16b6bfb9a348772cc10df8}}, {{cite:2968fb52bdffab2e436d4eb54b6f72158cd4f25a}}, {{cite:5dfb99f405d72b7cd73dead36e8b4e8767361923}}, {{cite:aaf18a5dfbdfcb975d673be60a9b515f1a62129e}}, {{cite:9cd79e8fc1ad2a517b1873d11a4ff9d41c7ff4e3}}.
| i | 03181b7538645da5dbc42064dff609d2 |
Theorem provides some new information concerning Algorithm . Firstly, Theorem improves the known convergence factor in the literature; see our discussion in Introduction. In addition, it investigates the convergence rate for a step length in a larger interval. Secondly, it does not assume the second order continuous differentiability of {{formula:5445f3af-fb76-44b8-bcb4-3e359964779e}} , which is commonly used for deriving a local convergence rate; see {{cite:71227bde4da9e528cf327aaaae09260b5e5356ae}}, {{cite:8545fe0eceb0f9c7a8404b215130b1a921a0f339}}, {{cite:5e1296de72939b7627b8c0629715786b859323f8}}. Finally, the given convergence rate incorporates three parameter {{formula:8a420cff-eb23-48bb-ae29-b34ca96f4d96}} , {{formula:b3e9db2e-ce9e-49aa-a691-46e031e8252d}} and {{formula:7d2f038e-076a-4065-8757-ffe23157b9fe}} , which is more informative in comparison with the results in the literature mostly given in terms of {{formula:a08154e7-b79a-45ef-8130-81d51b8d71ac}} and {{formula:f9a64393-2df8-4975-9e0b-02d4e40613e9}} ; see {{cite:c35af28ab81f29d4998121cdde87f12a2c4cf039}}, {{cite:5e1296de72939b7627b8c0629715786b859323f8}}, {{cite:f839e727a7cbe4dea23a08a174036c63965ce549}} and references therein. Even though if one considers {{formula:4dc19dcc-4cb2-46d8-9985-a70895039aec}} and {{formula:4825bdda-f231-4c19-9bdb-37087a72f344}} , convergence rate () dominates (). This follows from that for {{formula:07c19df0-0f7c-429c-94b2-f32a87fc821c}} , one has
(1+4L2t2-2t)-(1+12(3L2+2)t2-(L+)t +12(L-)t(Lt + t - 2)2 + 4L2t2)
| m | b4aff16e9a9d1869f9e9073491ac6141 |
Intuitively, roles can be reflected in the network topologies, for example, leaders are corresponding to hub nodes of cliques and bridges between groups are corresponding to structural holes.
In fact, structural role identification has been studied for decades. However, despite their achievements, most traditional approaches {{cite:629d81bc97d93ad4c0253b95b1691459eb1e7e55}}, {{cite:7b3ec57aa2b317ef480c29b427c1f0dc570d8184}}, {{cite:1c05c55c131f52866e1f346cffae3bb78afc7168}} require computation of multiple complicated graph-metrics, such as PageRank value {{cite:c3da5d0713aeaca1fde7c4703cd2977d1a27170b}}, structural hole value {{cite:1f2202b613ed4a5e3de78ae24f2163c0a229ab23}} or clustering coefficient {{cite:93af4af37bd4d5e11ad6b663145b5b0aaeca0e5b}}.
Thus, these approaches are often ad hoc and time-consuming, making them hard to extend to massive networks.
| i | 822b9fc6d5ed2954e4d63f6ac784958a |
Table REF shows the performance of networks trained with different loss functions.
We found no clear effect of this parameter on performance.
Adversarial training did not outperform the other loss functions either,
despite an expected behavior during the adversarial training and good discriminator performance.
This experiment corroborates the idea expressed in {{cite:5a27e9fc6782b79377359d21de9738cfb0f6e171}}, {{cite:51673fa3b059df9263067c0470afa4e7e64d25bb}} that
data variety and annotation quality are prominent,
and that the gains induced by those innovations are sometimes hard to replicate on custom datasets.
Our cross-validation experiment showed high score differences across splits,
and showed that the split we chose for comparing strategies was particularly difficult (one cross-validation split averages a Dice of {{formula:fbc353ea-e6a3-4da1-9c35-91148c658bcb}} on both T1 and T2). This also corroborates the idea of prominence of data on performance.
| r | 381fdb929fafa9b785b58905baa5259f |
Our work suggests that the distance between the average encoded state and the maximally mixed state may be a reasonable metric to quantify how well the quantum encoding preserves the features in quantum supervised learning. The result on the encoding concentration also motivates us to consider how to design PQC-based encoding strategies better to avoid the exponentially decayed distance. An obvious way this paper implies might be to keep the depth shallow while accompanied by a higher width. Still, it will render poor generalization performance {{cite:b37059de70fbcdb9bb581683e19ab618786ff2a3}} as well as the notorious barren plateau issue {{cite:8ab64b11cf9ca6993b66807d13863c7e16e6dee7}}. Therefore, it will be desirable to develop nontrivial quantum encoding strategies to guarantee the effectiveness and efficiency of quantum supervised learning as well as quantum kernel methods {{cite:95b6e24ff7c9f3124b2467b7cef1788799590447}}, {{cite:099bb91c88a68b4f665f8b67edd3ac5283e1f8db}}, {{cite:2f04800bce8e85df1298e3becd7a2d3e072ffff4}}. Recent works on data re-uploading {{cite:d01c7d0e4b7928a71a9a332051bdf504a7661002}}, {{cite:218577132942a1247d839d794c4fe80d61e07696}}, {{cite:a52f29302a774de4d3b5d6ce89418cb05c63dea2}} and pooling {{cite:b37059de70fbcdb9bb581683e19ab618786ff2a3}}, {{cite:505739d75927f2ffda9e6c04b4ada629ea4ec284}} of quantum neural networks may also provide potential methods for improving the quantum encoding efficiency.
| d | 59e50e7547eff64c29f391c0ccd93512 |
While adopting state-of-the-art channel optimization directly can be costly, one may consider using cheap pruning methods and adopt a Prune-then-Grow strategy to carry out width optimization. We compare to magnitude-based channel pruning: network slimming (NS) {{cite:4997d399bb81d555d1c2d2362e08efc29ae1688c}} that prunes channels based on the magnitude of {{formula:99f77236-dcc3-4b59-bf3e-e1607542f731}} of the batch normalization layer. NS-{{formula:b9e7a579-a0f9-458f-af60-757da031adbd}} w-{{formula:d2c509e0-c5fc-43ff-923a-f76c29fbe754}} e follows a three-step procedure: train an {{formula:e6003fb0-cb34-4b5b-be1c-b7b2cdee33e8}} wider network for {{formula:4f339558-4054-4a92-93fd-b1154e3b2d32}} epochs, prune the network with global {{formula:db596769-7464-4bc2-99c3-ad93432a7ec8}} ranking, and re-train the pruned network using full training schedule. The induced overhead for width optimization lies in the first step. The comparisons with NS for ResNet18 on ImageNet is shown in Fig. REF . Using DMCP directly is indeed the most expensive one, but it has the best performance. Our width transfer achieves similar performance compared to DMCP with overhead lower than magnitude-based pruning.
{{figure:5a5da61a-f1c5-47e5-8517-53776fd063c1}} | m | 960c0f6bbeabf76cad43eb73ab97e255 |
The Lyapunov stability theorem {{cite:9bea6a5a43a42e58a128467b3c9d6cddb42998ab}}, {{cite:daaf34f62e926c18cd222b9ae9577c61cd69ac2d}} presents a sufficient condition of stability through the construction of a certain positive definite function.
| m | 9eb41e4644c87e5154b7a9e66d9ce740 |
The transductive setting has been the norm in the literature of learning causal relations {{cite:12ccf89d24f10a7b7333334cb1ada8ffdf9bbfe2}}, {{cite:d57f37bd4e868d989721477e1189b2287bcac599}} in part because the conventional setting of learning causal relations is similar to that of supervised learning. However, in observational studies, the ground-truth causal relations may not be used to train the algorithms even during the training phase. In addition, Guo et al. pointed out in {{cite:c2c6ef2cb9f8ec75302df2e5ec900565c59c1d83}} that most of the existing algorithms can only discover the causal relations among variables that can be observed in the training data. Hence, it remains an open problem to develop causal inference algorithms that can be generalized to unseen variables, i.e., an inductive evaluation setting.
Furthermore, the combination of observational and experimental data may provide with unique opportunities to identify a model, that under various assumptions, can extract some true external cause-effect relationships. There is a recent line of research {{cite:6e25066cf38c7c2102f04c8bae37ebb8ba085209}}, {{cite:557ebb6c9426fb0a9ea6a3db613b61762bba9c11}} focusing on learning causal relations from the combination of observational data and interventional data with some selected variables. This is promising as it may overcome the limitations of using pure observational or RCT data. To this end, learning causal relations with the combined data can be reduced to an easier problem where the goal is to identify a certain set of interventions.
| d | d3647b5a38a3fc8697ad877050f44ae2 |
The simulation results for optimizing objective (REF ) are presented in Figure REF , where we compare vanilla decentralized (no compression) algorithm with our proposed compressed optimization procedure using {{formula:1b360bb4-3246-47a0-977e-acf6ffc525aa}} {{cite:da3d5c54eeb5513e41a6e6fef0c72c093aff3cf5}}, {{formula:f3ba97bf-225d-4bd2-aec5-7f7d68aabcde}} {{cite:a7fb82ba9052d5de07bf70efdbc723c72189328b}} and composed {{formula:459da755-3e25-4e6c-9030-f1595a381eea}} {{cite:e89d1e40e08feb7930ad8e69bc94c1537f00049f}} compression operators. Schemes with `Bandit' in parenthesis indicate those implemented via Algorithm REF for the case of gradient estimation in bandit feedback, and via Algorithm REF with sample feedback otherwise. Figure REF shows the relative cost gap for the objective given by
{{formula:fa37aa49-8f53-4b57-a2bd-2a19e7a6d580}} , and Figure REF shows the difference of the parameter from the optimal value normalized to the latter, given by {{formula:dda2aaa7-a183-4dd1-a4cf-33501ad09d18}} for iteration {{formula:a3477728-1527-494a-84d8-8bc3180ff002}} . From these figures, we see that schemes with compression, including the ones implemented via bandit feedback, effectively perform the same as uncompressed vanilla SGD to minimize the objective. The benefit of our proposed scheme can be seen in Figure REF , where we show the relative cost gap as a function of the number of bits communicated among the nodes, assuming precision of 32bit floats. To achieve a target relative cost gap of around {{formula:95440a52-566c-4964-9b19-96d5f1a6c0c7}} , compressed schemes use significantly fewer bits than vanilla decentralized training, saving a factor of about {{formula:fae5f1e1-f383-43be-bd09-d0528d08385d}} with {{formula:1f457890-e4f7-4f05-a8b7-4576c93fefad}} compression, factor of {{formula:e7e9ce24-6369-429c-9276-bb4aee2dec32}} when using {{formula:fdf9f068-35e5-4954-8ef6-bd77f641e700}} compression operation, and a factor of around {{formula:4b811017-ab71-4c7a-80d5-183cd7702485}} for the composed {{formula:c744b88d-f2e7-4346-b66d-818807cd936a}} compression operator. Further, in Figure REF we plot the value of the constraint {{formula:35da4370-7176-4a29-8bb7-50b280e2d1ff}} for a randomly chosen {{formula:827aea3b-fd93-403c-94dd-a51760a8f45f}} and {{formula:09984c21-adf4-4978-a5af-3fb44e44b7b3}} . The constraint value settles to a negative value, which implies that each scheme arrives at an objective value lying in the feasible space of the problem (REF ).
| r | 7739238d8cd5020fbcd97c2e6529adf3 |
One of the most challenging open problems in theoretical and experimental
investigations in Quantum Chromodynamics (QCD) is to determine the phases
diagram at finite density and temperature, and especially, to shed light on
the confinement mechanism. Asymptotic freedom in the ultraviolet (UV) supports the melting
of Hadrons at high energies when Quarks and Gluons should be liberated, and
relativistic heavy-ion colliders allowed to realize high temperature
deconfined hadronic matter {{cite:c7b558337993faf1ee378655dd94bf0a33f9edbb}}. This phase is relevant, for
instance, in the analysis of the core of compact stars (see for instance {{cite:c3bd5e95b7bc474abe469b66d1ada515202dd3b0}}, {{cite:d35542dc33bed0cee2ce3c5beb7d5c91fe5d085e}}, {{cite:843cf47f57d7091fa8939e67f10aea2deb79a4cd}}, {{cite:8e8aa4aaed99e8fe3baa1a5820cd695c3cd2e83d}} and {{cite:66570bf580dbef2bbf6d8655294ed8801a3d3926}}).
Unfortunately both, in any heavy-ion experiment and in the core of
compact stars, QCD physics is dominated by the non-perturbative effects (see
{{cite:f2b599364332cbbdb4869d58c1ef99a67a3f2887}} and references therein). In order to get insight on these
difficult problems lattice QCD (LQCD) simulations are effective {{cite:3e621aa48e0b4b677f21174a3c9efca4512b900d}},
{{cite:412bc842cc3c12300ee4a3f918c9a8bca829dcd0}}, {{cite:7ddbbf0a2f85f4dfc52d47d19d15334d5bcf946f}}, {{cite:74efaf4a9468ff6b7a7a28ee709731a05edd018a}}, {{cite:06e2391d631bbfd7a06f18c0b14623333ba6e764}}, {{cite:3e01d3d9560f4c604a1273be6687ec6bbde17beb}}, {{cite:dad2d6900f5615d7413c1f83e099a0eba176b9bc}}, {{cite:1d50fcee68a3533401d3492163c8d30572cb3ef6}}.
| i | 3c536d7f9442261111386ce590691878 |
Fact 2. For {{formula:d88e64e0-f84f-444a-9ebd-bc809c6c1dc5}} , the first return time to 0 we have (cf.
Feller {{cite:89b5ecf5693f1f5f6c12308271174383119799cb}})
{{formula:60cc27ea-1f81-43eb-9f30-bdca988d984c}}
| r | b6387cedcfc4c631f97e04455884d143 |
We will make a detailed comparison with the supervised baseline and state-of-the-art SSOD methods, including CSD {{cite:81f9b8f60372e3d7e860af84f1ea84439adf582e}} and STAC {{cite:387c0489773ea1559e12ac452d53db7504596ff7}}. The detailed results are summarized in Table REF and Table REF .
| r | 6e214a760c5eeb0bc0ee8e7a2e914f44 |
The results of this study show that the best performance is obtained by Noisy DQN for base approaches and Averaged DQN for the proposed method. The novel improvements and extensions were implemented to DQN, such as Double and Duelling DQN, but these two extensions could not perform better than DQN. A general assumption about these extensions is; Double DQN and Duelling DQN methods have better performance than DQN, as shown in {{cite:4e70fb9a7319816aca441189ed3bbcefbbb36fbf}} and {{cite:be4df6bd196fa397d853baab96ab7a8d03439cd5}}. However, this is not consistent in all environments, as seen in {{cite:4e70fb9a7319816aca441189ed3bbcefbbb36fbf}}. Reinforcement learning approaches distinctly depend on the environment and action space of the agent since everything is built on the interaction of these two. According to {{cite:4e70fb9a7319816aca441189ed3bbcefbbb36fbf}}, Duel DQN showed -100% worse performance than DQN on the Freeway environment in which an agent attempts to avoid other traffic participants and pass through the highway. In this environment, similar to our case, the agent has only three actions and avoids collisions. As a result, Duelling DQN is not always better than DQN. In limited action space, it shows reduced performance compared to DQN. The advantage of the duelling network lies in its ability to approximate values efficiently. When the number of actions is high, this advantage over single-stream Q networks increases {{cite:dd67b1b508e1b4766e94b09076db869a517a182c}}. It shows superior performance if there is a possibility of the agent having multiple actions per time step, such as the Atlantis environment {{cite:2dbee79f7ad92093d568fce23e82ac30e0b4aaa7}}.
| d | bde319a87c50704964d374020348b417 |
To the best of our knowledge, there are few truly unsupervised methods that can work only with the image being inspected, with no prior training or information about normal samples, as shown in Table REF . In order to compare our proposed method with the state of the art, we use MVTec AD {{cite:0133bd9b3894681221d68049eff42620068d0cb8}}, a recent anomaly dataset that simulates faults or anomalies in industrial conditions. The MVTec AD dataset contains several subsets, divided in two categories: texture and objects. We focus on the texture category, as we are interested in the detection of low level anomalies. Also, one of the subsets has special importance for us,
as it considers anomalies in leather samples. MVTec AD also provides several non-faulty images, which most of the state of the art methods use for learning the normality. In order to extend the comparison, we also include the baseline methods, even if they require to train on normal-only samples and the comparison is not completely fair, in their favor. Results are shown in Table REF . To perform the comparison, we use the area under the receiver operating characteristic curve (ROC AUC), as it is the most widely used in the literature, and enables us to compare with state of the art results.
| r | 4ac8dc5f9bb54a174b63627c2ee75daa |
The optimized adaptive response possesses high sensitivity (large {{formula:a30c2196-f40e-4cd6-afd9-6286e9b4bed2}} and {{formula:120c0f26-7aec-4d6f-81c2-824fe4f6d95f}} ; Table REF ) consistent with experimental results from E. coli {{cite:3f68767a7b823cbf6f5bcbf407064015abd0b987}}. Furthermore, {{formula:97f223ec-b481-4911-a887-4e7d93ad8c12}} , the rate at which the bacterium stops tumbling, is high, which is in line with the short tumbles observed in real bacteria {{cite:cb25107c5e549e3467f4dd0fb39a241395550a2f}}. In contrast to real bacteria, the optimized bacteria have a lower {{formula:052160da-9643-4eca-8c93-458ece77cd45}} , and thus tumble less than real bacteria when attractant concentration is increasing (Figure REF c, red curve, {{formula:cda7134b-4276-49dd-84ca-3604759883cf}} ). This may be an artifact of modeling chemotaxis in a one-dimensional environment: in a three-dimensional environment, tumbling may assist the bacterium in finding even steeper paths to attractant optima.
| d | 567f3cbd9b00c5c2531114d3e63f040d |
If the cumulative distribution of the measurable polarizations favors
the SO model,
the globally ordered magnetic field would be advected from the central engine.
If we understand the strength of the magnetic field in the emitting
region from the luminosity and the spectrum of the emission,
we can constrain the strength of the field at the central engine.
If the geometric SR/CD models are favored from the observations,
it will be established, independently of the afterglow observations,
that GRB outflows are not spherical but highly collimated.
If the CD model is favored by the observations, we may constrain the
distribution of the parameter {{formula:cf9f46f6-f052-459c-876d-c1ef3514ca9d}} of GRB jets.
The CD model needs a dense optical/UV photon field
interacting within the relativistic jets {{cite:47b9d42f12746d02e539099977d013066a0d2815}}, {{cite:1cf3fa40b98e5c54f8f9c5c15f52b02c381d5f95}}.
| d | 3c913bda05d3fce78b5ff8c554658aba |
Unlike previous ML-based proposals for TE (e.g., {{cite:7aa6567b40854cec64ad119fd1a7d170b91bb85f}}, {{cite:208d253150d6b2cf70e69f78ad56ec73a96b1c2a}}, {{cite:0be0392e4f0b1d66617a4df8bfc8f628aded22ec}}), the combination of MARL and GNN allows us to handle topologies of various sizes and structures in a distributed fashion; and more importantly, to achieve combinatorial generalization over the information exchanged by agents in the network, which is naturally represented as a graph {{cite:aa6fb6e2f0b02b8afe328a7b1f80852c040bbe54}}, {{cite:527adcb72edb574d5fb72d055cef76c8a9a7c6f0}}.
| i | 1564ace36246080c79604b53ef9a03c1 |
Our result also has significant consequences on the kernel machine side. Path kernels provide a new and very flexible way to incorporate knowledge of the target function into the kernel. Previously, it was only possible to do so in a weak sense, via generic notions of what makes two data points similar. The extensive knowledge that has been encoded into deep architectures by applied researchers, and is crucial to the success of deep learning, can now be ported directly to kernel machines. For example, kernels with translation invariance or selective attention are directly obtainable from the architecture of, respectively, convolutional neural networks {{cite:9e40db8251bf89b8b8b8ab553c67fc488b5accd3}} or transformers {{cite:f07cddb2b8b4617410ec555a5c8fce6d3904326b}}.
| d | 4c461293c8180a65d11874b2c1c9b58b |
In a recent landmark study, De Fauw et al {{cite:423f0646c8776cd6ad6dc50dbfb590eaac76ab9f}} proposed the idea of using device-independent representations (segmentation maps) for the diagnosis of retinal pathologies from OCT images. However, the study was not truly device-independent, as, even though the diagnosis network was device-independent, the segmentation network was still trained with multiple devices. Similarly, our approach may not truly be considered as device-independent. While ONH-Net is device-independent, the enhancer (on which ONH-Net relies on) needs to be trained with data for all considered devices. But this is a still a very acceptable option, because the enhancer only requires un-labeled images (i.e. non-segmented; 100 OCT volumes) for any new device that is being considered. After which, automated segmentation can still be performed without ever needing manual segmentation for that new device. Such a task would require a few minutes rather than several weeks/months needed for manual segmentations.
| d | a66a7cb782fddc5344bd9597acb7ee96 |
Our proposed ultra-high resolution image segmentation framework follows the three-step procedure as shown in Fig. REF ), which is consistent with the common practice applied in prior works (e.g., {{cite:db8bd1ed1d1b5f8c1c5223ad9bc09c0ee3e48e27}}, {{cite:f73660919314bf76225c82bbefd1ca36839971ca}}).
First, given an ultra-high resolution image {{formula:150627f4-84b1-4263-a1b2-30ba1746e264}} with width {{formula:1a4ee3f9-f54a-4cb7-b24c-490692c911eb}} and height {{formula:2bf685c9-6402-4613-a8f0-e80210f34e7b}} , we evenly partition it into {{formula:158e8d22-ada7-4454-af11-44b0bacf6a9b}} local patches {{formula:a2a0afbd-fd6c-4360-ad7d-30d50a237ee1}} ({{formula:8c6810c4-4a10-45be-86d4-c0a2d73e019a}} , {{formula:d76883a8-5a85-4719-8842-4e04164fad8b}} ) with width {{formula:7674d284-cfc5-4daf-baba-d83b53976bd9}} and height {{formula:8c3aa3b1-7e9d-4359-b17d-a8a5ff385a55}} ({{formula:8fc5c9ea-fce2-4fe7-927e-2910bb7957a6}} and {{formula:96bcf559-d165-47ef-ba1a-838ffc3aab33}} ).
Next, a local semantic segmentation model computes the local result for each patch. Last, we merge the local results into one piece as the final high-resolution segmentation mask.
Our main contributions rest in how to generate fine local segmentation (the second step) and refined results that can be seamlessly merged into a high-resolution mask (the third step). As follows, we will elaborate the technical details.
| m | 3bd7a66c24220a3684321910c24df40b |
The proof of Theorem REF used the
compactification technique of Section to
show there is R-tipping in the nonautonomous system (REF ) by computing codimension-one
heteroclinic connections in the compactified system ().
A similar approach has previously been used on a case-by-case basis to compute critical rates in specific examples of R-tipping {{cite:42db0a1db8fa9ae3440d4957627ebc5b9117f652}}, {{cite:0f8fd3620e5055e7564f1dd51d28770ac5a33a99}}, {{cite:9b80e0b2227f129509b48a3a0801a1b645e0e1cc}}, {{cite:9d4a521632eee6f8fae6e562abef58d41c6f1538}}, {{cite:706078950e64d67c9b52936c22cbc01a147c864a}}. We show here that connecting (heteroclinic) orbits of () can be used to:
| m | b7f9f0e615402442ccd446e0e66fda8d |
We can observe that the jitters in a video are highly-unbalanced, where most frames suffer from slight jitters while long-term significant jitters will be accompanied with large biased errors.
SmoothNet can relieve not only small jitters but long-term jitters well. And it can boost both smoothness and precision significantly.
Specifically, unlike low-pass filters {{cite:263ffc226ec20026dae3e596f9b8caaaa1abeb54}}, {{cite:d1ab5a00e8caa7840ccb44c81be1ce05bf3d826b}}, {{cite:a105c49202c30dcda83a2b7398324aa543b599d3}}, our method can estimate the high-frequency movements well, like the action Posing (3d_pose/smooth3d_SubS9_ActPosing_Cam0_SmoothNet.mp4).
Finally, we observe that some ground truth of AIST++ is not quite accurate and smooth, especially for the 6D rotation matrices from SMPL fitting with less constraints. Instead, Their 14 skeletal 3D positions are more precise from multi-view 2D keypoints and camera parameters, which will be more suitable as the supervision. Meanwhile, SmoothNet is able to cross modality to smooth results from 3D positions to rotation matrices. Moreover, the data-driven models, like VIBE {{cite:b6599eb4faaea7c389743d8e02961da2e81c4a65}}, are basically no back bulge, illustrated the red arrow in Figure REF . Thus, our method can benefit from both the precise 3D positions from the ground truth of AIST++ at training stage and the relatively better estimated rotation matrices from VIBE as our inputs at inference stage to obtain more precise and smooth results.
| r | 4836534862ed325fc9190605e97a6a67 |
Implementation Details.
We adopt ResNet32 {{cite:313423244e1db145d03a9d1ad986ffecbe08c8d6}}https://github.com/arthurdouillard/incremental_learning.pytorch as representation model architecture on CIFAR-100 with 64-dimension feature space.
We trained the model for 800 epochs for each task using Adam optimizer with a learning rate of {{formula:1702a3e4-f93a-43ef-bd21-3799e4f93a38}} for the initial task and {{formula:c96d6fc5-341b-471b-9d40-d46741fbf176}} for the others. Random crop and horizontal flip are used as image augmentation.
Following {{cite:6bcf4920f9108a533402cea8a61b21bb67e95eed}}, we adopt pretrained Google Inception {{cite:fdab13930519f9bb3775cc4fd7e8284cc15d6549}} as representation model architecture on CUB-200 and Stanford Dogs with 512-dimension feature space.
We trained the model for 2300 epochs for each task using with Adam optimizer with a learning rate of {{formula:7f245a0d-c772-4a2a-8264-d1634829ae71}} for the convolutional layers and {{formula:a24f2795-d82a-4c11-9b7a-08b326524e76}} for the classifier.
Random crop and horizontal flip are used as image augmentation.
We adopt Recall@K{{cite:a956b5d7a92742bae536a9b00db1ad73abf592b4}}{{cite:160b51bdadc61ac54cf83812e4b946975dc0d21e}} as performance metric using each image in the test-set as query and the others as gallery.
{{table:99e28cf9-1891-4785-8d95-faddc565c467}} | r | 64b10ac847bed7c4f62cf77e9a9d84aa |
To evaluate the architecture modifications, we chose BERT {{cite:a450814bad95b0b3f95935f126f3a817cb6e6482}} pre-training and fine-tuning. The large dataset and challenging training objective mean that task performance improves consistently with model size {{cite:ce3432022cc8dd1e35eb2e79db969353610fd358}} and the risk of over-fitting is reduced. This makes it possible to clearly distinguish architecture modifications that benefit efficiency.
| r | c58f435518b84bbd29caebda5626bae7 |
Motivated by these observations, we propose an open vocabulary object detection framework that can be trained without human-provided bounding-box annotations, by taking advantage of the localization ability of pre-trained vision-language models. As shown in Figure REF , we design a pseudo bounding-box label generation strategy to automatically obtain pseudo box annotations of a diverse set of objects from large-scale image-caption dataset.
Specifically, given a pre-trained vision-language model and an image-caption pair, we compute an activation map (Grad-CAM {{cite:0f2e91eedb51e7a87ac0c12eaf00b78b94eddded}}) in the image that corresponds to an object of interest mentioned in the caption. We then convert the activation map into a pseudo bounding-box label for the corresponding object category. Our open vocabulary detector is then directly supervised by these pseudo box-labels, which enables training object detectors with no human-provided bounding-box annotations.
Since our method for generating pseudo bounding-box labels is fully automated with no manual intervention, the size of training data and the number of training object categories can be largely increased. This enables our approach to outperform existing zero-shot/open vocabulary detection methods trained with a limited set of base categories, even though our method does not rely on human-provided bounding boxes.
| i | 6d607ef7b8a53e870337cd4586145318 |
{{formula:3c3f2970-69f6-4832-8a41-250ecb33310d}} Comparison on 12 Most Frequent Classes of EPIC.
Since the data distribution in the EPIC {{cite:b126be848c038f1faabf88bc213f5231e8e44dda}} dataset is highly unbalanced, e.g., the number of samples for some categories is less than one percent. The experimental results are more affected by the classes that contain a large number of samples. To verify the effectiveness of our method in the case of a large number of samples, we compare our method with others on the twelve most frequent classes. The experimental results are shown in Table REF . Our method outperforms all other methods, implying that our method can better locate the region where people interact with objects in more samples.
| r | 54ea8e265c2f8b4b49848897f8b9f4b4 |
In Loop Quantum Gravity (LQG) the spectrum of the length, area and volume operators are famously discrete {{cite:2065d1f78a8d545a918b0ed1f3316eea26326268}}. Discreteness of time may arise in a similar fashion from this theory, although nothing has been proven yet.There is also a debate on whether discreteness in the spectrum of observables survives the implementation of the hamiltonian constraint {{cite:e82205af2e90b3dcfef9389c54ad3d42150de52e}}, {{cite:a07f694ad1c67b694852db748b7eadb915933b84}}.
| d | 8e2c22b24814e34c0891b90972c7a641 |
Main Contributions: We present SLICER, a new SSL algorithm for learning general-purpose audio representations from un-labeled audio that simultaneously learns instance-level discriminative features and performs online clustering in a one-stage and end-to-end manner without any extra overhead like an offline clustering step. In general, offline clustering does not scale well with large-scale datasets as they need to perform clustering on the entire dataset at each epoch {{cite:a5d96e6061067c3c94df47323ea637440bb87eee}}. In contrast to prior methods, SLICER learns a deep network that outputs a matrix where rows and columns correspond to the instance and cluster representations, respectively (see Fig. REF ). We achieve this by projecting the input audio log-mel-spectrogram into an output space that is equal to the number of desired clusters centroids. We build this on top of the student and momentum-teacher learning paradigm, where one out of two identical encoders is updated from the momentum of the other {{cite:72d74c6d4f8e09656bdd6a7273bd8a7fa4a75053}}, {{cite:09ec00faeb5dc1da7112bdad28040b60244263d4}}. Moreover, for instance-level learning, we use a symmetrical cross-contrastive loss where each encoder calculates a separate loss by sampling negatives for each of the positives from the output of the other. A pictorial representation of our setup can be seen in Fig. REF .
{{figure:76d9b801-589e-49b8-8738-d241da80f666}} | i | 515845a63db2ab18a4f8cb0d84e961aa |
Progress towards this conjecture {{cite:1fa8e25a33309e394573079bfebb0a29e66e93d2}}, {{cite:a795bdc1a2b4f5d233796a330b0345e23ea2fcbc}}, {{cite:5dd49eff7bd20898c39e471818a067abf863d24a}} culminated in the work of Bourgain and Demeter on {{formula:68e99562-3070-4b04-aec4-112f54a4f053}} -decoupling {{cite:b34895c7cbc76ab173e65a436d338bc45d8133f1}}, where the above conjecture is proved for {{formula:fc258219-703a-4504-80d1-2cef7138e950}} and {{formula:59f41de3-3b61-420b-8ddc-7126b5569e87}} .
| r | 0c6161a5240d84716c82fff756ec39f5 |
The problems with applying sampling-based inference to GroupMatch designs with trajectory replacement are quite distinct. Here the primary issue relates to the unknown correlation structure for repeated measures from a single control individual. The literature on matching with replacement provides estimators for pairs that are fully independent {{cite:e8c5a100cbb0d6d3e998ec6f85964abc17b70b58}} and for cases in which a single observation appears identically in multiple pairs {{cite:9e14b413d6a9e7b6ab869e85767229912d457135}}, but not for the intermediate case of GroupMatch with trajectory replacement where distinct but correlated observations appear in distinct matched sets.
| m | 03fd6c31709d7e3a193dbe91fbe40331 |
Calculations' details.
AFLOW {{cite:c90460554a25090d910654e6f07fae7683ef0499}} leverages the Vienna ab initio simulation package (VASP)
with all calculation parameters following the AFLOW standard {{cite:71f759a8daf68735d8dc22dc71ab6285a69fb4f6}}.
Exchange and correlation were treated with the projector augmented wave (PAW)
method {{cite:50bb371b2545ff9e37e4d6b91abb87a02ea00d63}} in either the local density approximation (LDA) {{cite:b22adba38b5be859deef00b316fca59927d90e93}} or
generalized gradient approximation (GGA) proposed by
Perdew, Burke, and Ernzerhof (PBE) {{cite:77882c7c572a20b07a3d65e594ddf9a60c6644f8}}.
The cutoff energies are chosen to be 1.4 times the recommended maximum cutoffs (ENMAX)
of all pseudopotentials as set by VASP.
| m | e7c7de0d64a2031f04746f72f0eea6a1 |
We study separately the cases {{formula:50512487-1c45-4807-982a-6f2009168003}} and {{formula:933a7790-d713-4cb7-8635-03e9e8dcd5fb}} . For {{formula:26f37c0f-102e-46ce-af5f-ce22f2651533}} , we have that {{formula:fb0c2998-cfda-4c7a-bacb-12dc92046ee6}} , so
{{formula:587f9ec4-ddb0-4154-a878-da041fed0b78}}
Since {{formula:a628e532-c1f4-4e7b-b63d-e6fd39f7de6e}} , from Remark 9 and Remark 11, it follows that {{formula:c500f4e2-c5d6-4459-a854-522a3353305d}} for each {{formula:4ec0b93d-83a7-4850-aefa-ec725b11dd52}} . Now Theorem 5 in {{cite:dc0a16aa44eef4234c791f8557bafa958c89c5fa}} gives (REF ).
The proof for {{formula:b0fc5a84-7e90-4bf3-8d48-4b44654a8b3d}} is analogous to the proof of Theorem 1 b) in {{cite:7a5cf82b7f667b678997413c0b3c2f139910978b}}.
| r | 4c65a22962ffed681aa17124187424fa |
In fact we did run a test for the “Stochastic binary quantization" method in {{cite:e231e7169650e9e966492e40f36a892e429f7832}} on ResNet-50+ImageNet over 16 EC2 p3.2xlarge nodes (per node batch size 32) as it is the computationally cheapest methods proposed in the paper. Though it is showed that conducting random rotation over the gradients can improve the compression error, we only care about the computational and communication efficiencies of the method in this particular experiment. Per epoch runtime results are shown in Figure REF .
{{figure:2353a6bc-526c-44ba-9c49-9f7034877118}} | d | 89d8f7bc7b9d444f3e5c9ce1636d65fb |
While the above calculations provide transparent intuition on which to base algorithm design, our proposed algorithm is the stochastic dual accelerated method (SDA) presented in Algorithm , which involves a more sophisticated (but still simple) iteration. In particular, it relies on Nesterov's accelerated gradient method {{cite:de44fb0266d346cf225bcea06e9710d766b829c9}} with constant step-size, used in conjunction with Polyak–Ruppert averaging of the last {{formula:d34652d5-aafb-4b8f-b716-dcad23109518}} iterates {{cite:96d4a5c0a9278ca9864357cd82bf13d8697203ab}}. SDA is a stochastic variant of the single-step dual accelerated algorithm proposed and analyzed in {{cite:c5bc77d0c3dd9c57d04388bd05b47e25a0fc7572}}, which was developed for smooth and strongly convex distributed deterministic optimization. While both algorithms are similar in spirit, the analysis of SDA uses completely different techniques, since it applies to the stochastic setting for a special class of quadratic functions, as opposed to the deterministic setting for general smooth and strongly convex functions. The analysis in this paper builds on a dynamical system representation of the algorithm and relies on explicitly studying the evolution of several relevant linear systems, and may be of independent interest.
| m | a02e34b29acea9a8471f2f13d5edc69a |
LDAMP{{cite:487eee8e8e792d6c8e68fbc2107b8f976df28213}}: An end-to-end reconstruction network built from the unrolled iterative image denoising process by replacing the model-based image denoisers with neural-network-based denoisers.
| m | 425a2d56c657343f5af286fba6af3d80 |
Different distillation methods.
We also compare MTD loss with other knowledge distillation methods, namely knowledge distillation (KD) {{cite:fb1bc133d9d95b96330471e11b66898eb8208efe}}, relational knowledge distillation (RKD) {{cite:74d6229ec1a6a47c49ff7e2995c190495651663c}}, MiniLM*, LAST-FitNets and SEL-FitNets.
Since direct training with MiniLM {{cite:556e6e29189c514c1eb06b5838e8b4cb7a6bb5cc}} does not converge, we use the loss of MiniLM combined with {{formula:8588aed2-48a8-4039-be2a-9a95f6b1ab19}} for training, denoted as MiniLM*.
LAST-FitNets and SEL-FitNets are developed based on FitNets {{cite:7908c228ec345be27cf5214cf99eca05904af913}}. LAST-FitNets uses the last layer representation of each Transformer block as the hint and the guide layers. SEL-FitNets denotes we utilize the best layers set (8) in Table REF to distill FitNets.
Other hyper-parameters will follow the best settings in their paper.
We replace the MTD loss of MTDVocaLiST with different losses for comparison.
Table REF shows that MTD outperforms other distillation methods in most input frame lengths.
Take input frame length “5” for analysis, training with only {{formula:b18e1406-2ce2-4292-bb56-4ddbae33247c}} is the worst, with only the accuracy of 71.36%. Compared with KD, RKD, MiniLM*, LAST-FiNets, SEL-FitNets, MTD loss improves the accuracy of 10.62%, 5.43%, 5.89%, 0.68%, 8.32% respectively.
Other input frame lengths are with the similar trend.
What is in common for LAST-FitNets, SEL-FitNets and MTD losses, is that they all distilled Transformer layers, but MTD loss is better.
To gain a deeper understanding of this phenomenon, we conduct further analysis below.
| m | 169d03b7568f6a67f021ab54fe6738e8 |
First, to see if similarly embedded nodes have similar structural properties, we perform the following analysis:
(1) For each node {{formula:5474075d-562b-40da-98bd-468928a157a0}} in graph {{formula:57a0792f-9450-48f9-8db1-9350963dfdbb}} , we calculate a property of interest {{formula:13f0bff0-95f7-450d-bda5-7863b19cc237}} . We consider four properties: degree, PageRank (with damping parameter {{formula:aed4f2d1-d298-4700-aebf-80b9a4ecc24f}} {{cite:c8f67607b13d957892aecb31579323623b69ea30}}), clustering coefficient, and betweenness centrality.
(2) We identify {{formula:b39e328d-4f0e-4703-9d47-b2b8cf7f0cf7}} 's {{formula:4bbdaa36-cbeb-4dc2-9cb3-255eb6d66e3d}} -nearest neighbors ({{formula:909a77b5-adf5-4779-9781-c4ad3208f77c}} -NN) in the embedding space {{formula:499ff336-7b6a-46d8-88f0-7ee912c4103b}} using cosine or Euclidean distance, and compute the average value for each structural property, {{formula:80115d0b-217c-42ac-8a95-27dec0d0a805}} .
(3) Per property {{formula:27417e5f-387a-4184-a96f-bcb2799cf47e}} , we calculate the Pearson correlation between the structural property of a node and its {{formula:f432d85e-2ec2-4a3b-a28d-82b54ece9dbf}} -NN across all nodes.
{{figure:9955341f-4b59-4a5a-9472-1fd9ae7c7b33}} | m | eb2212230bd1466108d5d07b36dda55d |
resnetbackbonecompare compare the two methods using the same teacher and student's backbones. It is obvious that LAD and CoLAD are superior to LD in all cases. Moreover, our LAD/CoLAD is very simple and can be adapted quickly to any single-stage detectors without architecture modification, and not restricted to Generalized Focal detector {{cite:cf16b804d0bcbbea92699e2a64a95c73faa44824}}, {{cite:8eacce3d210df91e77b12c4c5499ec9965c60015}}. This shows how flexible and effective our method is compared to other distillation methods, such as feature mimicking.
| m | 61fc18bcc71897b91982315f08501c3b |
In previous work on uniaxial pressure tuning, it was observed that, sharp superconducting transitions were only seen near zero pressure and near the Van Hove pressure, where {{formula:66e6026a-eed4-4495-bc7a-3dca347d5c43}} depends weakly on pressure.
In contrast, at intermediate pressures, where the pressure dependence of {{formula:80ae656c-a4a2-4339-a396-671eea6b406a}} is stronger, the transitions were considerably broadened due to strain inhomogeneity in the samples.
In order to perform a meaningful study of the critical fields in this intermediate strain region, we took several steps to reduce the effect of strain inhomogeneity.
First of all, we screened multiple samples from different growths by ac susceptibility to find suitable samples (large {{formula:1e7d5441-28f1-46e6-abca-718e42a71c87}} and a narrow transition, indicating low internal strain inhomogeneity).
All the samples we investigated were grown by a floating-zone technique {{cite:1681315f23c1e766848ca426387b5995bbfb3e3a}} and showed a {{formula:84a1a591-90ae-4c85-95e4-f764c1cf8029}} close to the clean-limit value {{cite:9c92ebc090c0a069ed42cb4bc2fa8aaeef4d1ba1}}.
Figure REF (b) shows ac susceptibility data of a piece of the same rod from which samples 1 and 2 were taken.
The sharpness of the superconducting transitions in magnetic field, down to low temperatures, points to high quality of the crystal, with no apparent effect of ruthenium inclusions {{cite:9582d3fcda3822dba517f0061745ace43ff8ae06}}.
In a second step, we shrank the size of the ac susceptibility coils so that only the most-homogeneously strained region in the center of the sample was probed.
We used a pair of concentric coils with a diameter of {{formula:a7fd71a9-d362-4d1d-9115-fc7b80a61cb4}} m, which was placed on top of the sample (Fig. REF (c)) with the ac field along the {{formula:9f19e8e0-9263-4312-8675-6e50518203b6}} -axis.
Finally, we used samples with high length-to-width and length-to-thickness ratios, reducing sensitivity to the end regions where the applied strain is inhomogeneous.
The bars were mounted in a piezoelectric-based uniaxial pressure cell, as described elsewhere {{cite:3d52e51d743d54db38732358639817ae797d36f2}}.
{{figure:9ff4b1a8-143f-4321-b036-76f19c5ce108}} | r | 79cf1d002e5c159972796979cc341ffe |
Thermodynamics can be derived by using a statistical description of nature. However, how to give such description in quantum systems still remains an open problem of fundamental importance. In particular, several attempts have been made to describe the work statistics, after the two-projective-measurement scheme has been originally proposed {{cite:9c322929469ce227dfce429b06ccdf7cad4ee432}}. For instance, among these, work distributions have been defined in terms of a work operator {{cite:c6aeeb85eb0d3cdff4542fd213d230bdc7ff3798}}, gaussian measurements {{cite:a87cb6b9ed533487f63629c2186da827c0d674e6}}, full-counting statistics {{cite:8d9faf31ae67750659fe357fa47be71d30366a49}}, weak values {{cite:820ffeb491f6c74ad0cc2517af110df470fe83a4}} and consistent histories {{cite:ed1ed20fdeda06167dc99b6a5ae067e5553eeca5}}.
In particular, the two quasiprobabilities of Refs. {{cite:8d9faf31ae67750659fe357fa47be71d30366a49}}, {{cite:820ffeb491f6c74ad0cc2517af110df470fe83a4}} can be viewed as particular cases of a more general quasiprobability {{cite:96a5700ca3455342d21a1d7251bd3d2bca52a04d}}.
To briefly introduce the problem, we recall that if the work performed on a thermally isolated quantum system is equal to the energy change of the system, then the two-projective-measurement scheme fails to describe the work statistics in the presence of initial quantum coherence in the energy basis. Basically, in this invasive scheme, where two projective measurements of the energy are performed at the initial and final times to infer the work statistics, the first measurement destroys the initial coherence in the energy basis.
A no-go theorem {{cite:1dbe241747dd69a7b2863a951a77d08eb0a8826d}} states that there is no scheme having a probability distribution of work, which is linear with respect to the initial state, such that it reduces to the two-projective-measurement scheme for incoherent states and the average work corresponds to the average energy change. Thus, if these latter conditions are satisfied, we have to look for a quasiprobability instead of a probability. As shown in Ref. {{cite:b9110564f982282ff13855c87ee804f11e4695dd}}, this can be related to the contextuality of the protocol. Now a fundamental question arises: what is the quasiprobability of work which satisfies these conditions? Going in this direction, a class of quasiprobabilities has been introduced in Ref. {{cite:96a5700ca3455342d21a1d7251bd3d2bca52a04d}}. However, this does not exclude the possible existence of different quasiprobabilities. Here, to give an answer we aim to deduce what the work quasiprobability is, starting from some fundamental conditions. To do this, in Sec. we introduce a general notion of quasiprobability in analogy to the well-known Gleason's theorem {{cite:41d7aac5ba58fae02a8a4dc7a3fb5edd56dc5b3a}}, starting from Ref. {{cite:1279036727eb29938b0d66fc97bc4a4a1cc2d044}}. Thus, in Sec. we use this notion to naturally define a quasiprobability of work, and we determinate its form if some conditions need to be satisfied. To identify the quantum features and signatures of the work statistics, we discuss the contextuality of the protocol in Sec. . Finally, we summarize and discuss our results in Sec. .
| i | 673c416c1a1c85a4877ebf17f43dfa19 |
We propose a new method for predicting accurate egocentric body pose by leveraging the estimated scene geometry. An overview of our method is shown in Fig. REF . In order to train the scene-aware network, we first generate a synthetic dataset based on the GTA-IM dataset {{cite:b6473723a1d091de474324c8e09bad93ee65fae5}}, called EgoGTA, and an in-the-wild dataset based on the EgoPW dataset {{cite:be7e1c343a7a54679bf8f1c6cda7ae4f215106ba}}, called EgoPW-Scene (Sec. REF ).
Next, we train a depth estimator to estimate the geometry of the surrounding scene and introduce the depth-inpainting network that estimates the depth behind the human body (Sec. REF ).
Finally, we combine 2D features and scene geometry in a common voxel space and predict the egocentric pose with a V2V network {{cite:b1cfb5131f5b6157599bc240edd93153f6949b2a}} (Sec. REF ).
| m | 224bf5dcd77ac0d0ec72f87718d42817 |
Events aggregation.
Instead of relying on raw asynchronous events, recent literature has shifted toward aggregating events together to build synchronous events representation. Common approaches range from simply integrating batch of events (constant-count) to representations involving stochastic modelling of events {{cite:ee48d04f35a3a577f41156cca28dfcc41984c579}} and temporal sparsity {{cite:0a71159bb7af58da5e6b30867cfe5f52a61994fc}}. As temporal information is critical in 3D human pose estimation {{cite:cd35cc1da1593c7927b14459c50439b276944138}}, our first question is to understand if 3D Human Pose Estimation benefits from specific spatio-temporal representations.
To provide an answer, we compare constant-count representation with spatio-temporal voxel grids {{cite:0a71159bb7af58da5e6b30867cfe5f52a61994fc}}.
While constant-count simply aggregates a constant number of events into an image, spatio-temporal voxel-grid preserves the timestamp contribution of events by building {{formula:5724e9b9-f8ae-40ca-94f4-3a83307dfcac}} temporal bins and have been already adopted in image reconstruction {{cite:e69e4e885e0ba5512cc7e1ddd0c02171caf1f16f}}, {{cite:dea2b66c157c25b9e57029759146ed4ba6e1888a}} and depth estimation {{cite:ed44081ac74b12e42924f748ca58941b0d52d631}}. Given a set of N events {{formula:6383f8a3-ef82-4326-b38e-92ad30d9d65b}} , we compute {{formula:0b1bd663-b4a8-4123-92b1-c1c07428d7f9}} as the normalized timestamp of event {{formula:5c118da5-ff5b-4ae4-9ecb-1f723bb6a0dd}} into range {{formula:68880be1-819c-466b-9157-ba8899fb7d94}} . Each event {{formula:33b9d3f4-dd8f-49dc-9438-630a074cfdf1}} contribute to each bin {{formula:43a9cb6e-0fb6-4a7c-a709-9fcd6b582640}} of voxel {{formula:2d48ec8e-0a69-4caf-8176-6ad1cc741f1a}} proportionally to its normalized timestamp {{formula:fdfc003a-924f-4a24-ad1f-8b1b826331a3}} , as:
{{formula:4fb5c059-6f3b-4d82-a2ef-82de8c852607}}
| m | 00e10d01ef9cbc2714f5fed6fce1c459 |
Theoretical modeling: Mechanical properties were obtained from the generalized stacking fault energy (GSFE) {{cite:c64a8f8b7809c54d94abeae80a316b2ade9cd1bf}}, extracting its parameters from DFT calculations as implemented in the VASP {{cite:f4a5fc376d63b93b1f9a9f187534753e4e3b45d6}} code. We used the r{{formula:cb399007-65db-4fec-bcce-e2956a640919}} SCAN+rVV10 exchange-correlation functional {{cite:3fbc1745f26650e8d98c4d86ab894ef50b8c3839}}, a meta-GGA functional that accurately describes structural and electronic properties accounting for van der Waals interactions {{cite:c9e2de217af44d87705cfef54e571f8180d9510e}}. All calculations used projector-augmented wave (PAW) pseudopotentials {{cite:58d3b27826101ac666bab2577b84b694cf319c41}}, plane-wave expansion of the wavefunctions with an energy cutoff of 292 eV, k-point sampling by {{formula:cca706cb-4b11-4da0-9156-1ed4a04520c7}} -centered Monkhorst-Pack meshes, and electronic self-consistent convergence of {{formula:935b20d0-c3ae-466c-8f3e-a6b44419d79e}} eV. Atomic positions were relaxed until Hellmann-Feynman forces were smaller than {{formula:6b79cbd6-1771-41e1-8c9a-3974b58f87a0}} eV {{formula:e4116548-b908-45e1-a37a-6d0d7615d9fd}} . We add a vacuum layer of at least 15 {{formula:fa1d9d0e-28dd-4136-9a4b-c48f6df1828e}} in the z-direction, and include dipole corrections. First, we obtained the optimized MoSe{{formula:1ab60974-17d4-4ad5-aa3e-a1983cd940a5}} -WSe{{formula:ec44a0ce-13c3-428f-ab4d-58d76395b1db}} heterostructure lattice parameters as {{formula:2a588ff3-d9fc-4be0-8019-b0c15d608061}} and {{formula:ecb35ede-59a8-48cb-8f59-b2eff58f8348}} for the R- and H-stacking, respectively, and then we calculated total energies including vertical relaxation for a grid of 9 displaced unit cells, where one of the layers was displaced along the in-plane diagonal relative to the other. For the R-stacking, the calculated interlayer distance between the metal atoms was {{formula:ed3d8382-f95e-4b4d-bc8d-69c48b49a1a1}} and 7.15 {{formula:c32c9bdb-9ebf-4735-8629-ff1459bd67d2}} at the minimum and maximum energy stackings, respectively, and {{formula:b2eb5091-ec1d-4486-b46e-5ca9ea47b815}} and {{formula:336f000b-460d-41cf-8a6b-e750dbf67f8d}} for the H-stacking. The resulting fitted GSFE is shown in Fig. REF d, e.
| m | fee26d04cdc90037e6adbdf1411ceb15 |
Incremental motion based approaches recover the calibration parameters using the well-known hand-eye calibration formulation, {{cite:880d9602a03fcc92451c29228aad2df8ffd9808d}}. The calibration was estimated between a gripper (hand) and a camera (eye) by moving the gripper in some trajectory, while exploiting the fact that the transformation between the camera and the gripper was always the same. More recent research has focused on extending the work to multi-sensor modalities by aligning the motion of each individual sensor. Brookshire et al {{cite:7f8677d84fc39a2a249a3cf2c1e7b7c03b71f34f}} utilized the DQ method {{cite:be88796ab84ea09455fa161336b5d5692edc7087}} to recover the relative transformation of two camera sensors mounted on a rigid body. The same principle was also applied by Heng et al in camodocal {{cite:81530d016f4fe5acd3eb3dd1fbc87e14f664e374}}. A more generic sensor configuration was proposed by Taylor et al. {{cite:7bbc253e27df698eae6e1a281013407343f6b64b}} for multi-modal sensor arrays calibration including 3D-lidar, IMU and camera by motion combination of sensors using hand-eye formulation. They also provided the uncertainty of the calibration. The same authors extended the work to incorporate the sensor's accuracy reading and estimated the timing offsets between the sensors as well {{cite:930522ebf82258069be75edbee22699fcec94baf}}. Moreover, overlapping fields of view was applied to further enhance the calibration when applicable. Jiao et al {{cite:7bc213102a284911cf78d4c8daea6b80154747b0}} exploited the hand-eye calibration of a multi-lidar system by motion alignment to recover an initial estimation of the extrinsic. A refinement process using point-to-plane features was then used to further enhance the calibration parameters. In their recent work M-LOAM {{cite:4a875aebc127dc8755ef906816b199efbd42635e}}, they used similar techniques with edge and planar features for the calibration refinements.
| m | c805664896ecb4c804fde35ec318eea4 |
Our methodology follows previous work {{cite:b9e8487c0736d7ee8e2cb00da00c7e3b40453fe0}}, {{cite:2035e98c3dc64d7b0c45c8194384ecf83dc9cf0b}}, {{cite:334daecccbf7372d996e258cda3cb9e4d5b8db83}}; we
work in the {{formula:53e1d8de-b982-49d1-938c-0c71dd51c715}} -{{formula:99475cec-9b8a-47b9-a77d-954f65a1ee17}} valence space with an inert {{formula:624a3683-1895-4c2b-b585-4e5a9f2590db}} O core.
Given an input set of two-body matrix elements (we leave aside single-particle
energies and any {{formula:a590198d-bb23-41ab-82ad-eb08f07c42ea}} -dependent scaling), which we write as a vector {{formula:fa5b0664-a8d8-4a1d-85f9-bd53867cc386}} ,
we can calculate the eigenvalues {{formula:052ea51f-9701-4bd6-80cc-3f6e18fe586a}} of the many-body Hamiltonian.
For this work the label {{formula:6c5cb135-0888-4c81-92ff-96fd36fd2eda}} ranged over
all nuclides with {{formula:bc81af9a-a952-48b3-8665-7915bdc73ba5}} and
took the ground state binding energy and the first five excitation energies.
| m | a227592e00b47e541baeaa2b8a512e09 |
We defined a new congestion model through diffusing particles with drift. A non-congestion phase and a congestion phase are distinguished in a phase diagram. We find different roughness exponents, depending on whether the congestion front forms reversibly or not. The roughness exponent for the immutable congestion front is found to be {{formula:d57f84d7-8eeb-436f-9193-6468c29a38eb}} and thus in the universality class of directed percolation depinning {{cite:f4412018d51e77f591e8d7e07fff9438d4024c07}}, {{cite:7911d5f8c8ecefca590dc4f7a4f69f8468ade9fd}}, {{cite:d875093169f2349c07fae8d1c8b01aa0ec0cdfe4}}, {{cite:f168713779431e0f8abe0dd75ff2db23e21bcd29}}. The roughness exponent {{formula:1d2547e8-617e-48a5-ba0f-c320b562ebed}} of the longest spanning, irreversible congestion front is remarkably small and we know no related universality class in two dimensions with the same roughness exponent. For the total immutable congestion front we find {{formula:b4e5c84e-477e-4f4e-b817-46409471ffa6}} , the interface thus being dense. In the limit of no lateral movement, where {{formula:a4af4f94-6115-4900-8256-bb4e1aba5016}} , all models are identical with roughness exponent {{formula:5eb51679-16fc-49f0-8d0f-ef899efe6753}} , being in the universality class of KPZ {{cite:e21d93f0a5dd2eb1e942076bc5faaa81008d10f0}} and ballistic deposition {{cite:08e0aeb6ced559ac12602e683d1d5d0acda08424}}.
| d | ebc6486214af823e0e8804c14e21fe14 |
Reconstructing trojans:
We tested feature visualization with a Fourier parameterization {{cite:be8bea28b3a4ee99f3263106ae2d103ffeaaf50d}}, {{cite:ad5d6cf595ac0723b80d7d5d6d311fa4d9b90cec}}, feature visualization with a pattern-producing network parameterization {{cite:ed4a5bda053676849841061978f2e84a45b1c461}}, {{cite:ad5d6cf595ac0723b80d7d5d6d311fa4d9b90cec}}, adversarial patches {{cite:99e138585dc8f83aff36a7793126b51ebf7fdc3f}}, robust feature-level adversarial patches {{cite:f7bbb96854c9bf8c5741947fc70eebf3c61bf489}}, and our copy/paste attacks.
We do not include any experiments here involving applicable methods from the Trojan literature that operate by constructing adversarial features {{cite:72191977475a49334ee38596f35b331535013932}}, {{cite:db828c7e2567e3967159ec657d21f72d62ebf80d}} because (1) the original papers on these methods found that while effective at reconstructing simple trojans such as single- or few-pixel ones, they failed to identifiably reproduce feature-level trojans and (2) we have also found this to be the case as well in our own experiments.
| m | ac2676b93820bfae1c8a07867935b82b |
To begin with, following Madelung {{cite:f7e7306d98920e7c7f99088ff9cdfebbbb003833}}, we have decomposed the Schroedinger wavefunction into amplitude and phase (see Eq. (REF )). This decomposition renders the usual Schroedinger equation strictly equivalent to the set of two equations (REF ) and (REF ) (the continuity equation for the Schroedinger probability fluid, and the quantum Hamilton–Jacobi equation, respectively). However, the advantage of the Madelung decomposition is that it bijectively maps the Schroedinger probability fluid into a perfect Euler fluid (see Eq. (REF )). This is useful because the nonrelativistic cosmological fluid qualifies as a perfect Euler fluid.
| d | 6c3ec272dd08eab17619554b80ee6600 |
It might be interesting to look at the fate of the inflated envelopes in close binaries, since {{formula:0eee9740-494d-405b-a41b-2ccdc78d3eba}} % of all massive stars are believed to interact during their lifetimes {{cite:52faf65d3f53a9e62e14b8a44492e68fe8b73f73}}. The loosely bound envelopes might help to stabilise mass-transfer in close massive binary systems, especially in metal-rich systems where this is expected to happen at lower masses. In close binaries, the hydrogen envelope is usually lost from the mass donor that bares its helium core and increases the {{formula:346882f6-0a71-4bca-9788-23e4f3991464}} ratio. Helium stars with solar metallicity start to develop inflated envelopes from {{formula:54848f99-0c20-4748-a529-d5df7ce3c0a8}} (see Fig. 19 in {{cite:e54aaaea6e56c07c73f0a2ad3f2112444853f40f}}). Massive Type Ib/c progenitors in binary systems are thus expected to have inflated envelopes {{cite:d767ff136777da122ea5ad52cf97a8af804dd96b}}.
| d | 8ba1e6aa1f0609b3b779824d7c5607e0 |
To alleviate the above conflicts, it is important to introduce a new modality transmission scheme, instead of embedding them individually.
Inspired by this, we introduce the idea of full-duplexOn the same channel, information can be transmitted and received simultaneously {{cite:3b8be6a1236cfa4d365e2ddffdc9272e1028434e}}. from the field of wireless communication.
As shown in Fig. REF (c) & Fig. REF (c), this is a bidirectional-attention scheme across motion and appearance cues, which explicitly incorporates the appearance and motion patterns in a unified framework.
As can be seen in the first row of Fig. REF , the proposed Full-duplex Strategy Network (FSNet) visually performs better than the one with simplex strategy.
To understand what enables good learning strategies, we comprehensively delve into the simplex and full-duplex strategies of our framework and present the following contributions:
| i | 07005dd7dbe05ede3d0ef200dbd756da |
Similar to other counterbalancing methods, it is possible to apply our proposed method also in multi-class settings, in a straightforward manner. Therefore, one can simply choose one of the existing divide-and-conquer methods, such the error-correcting output codes {{cite:828885d641e35d111c8733e0625e481c72d31785}}, including, e.g., the one-versus-one and one-versus-all approaches. Moreover, one can also apply our proposed method in form of cascaded classification architectures {{cite:901a2c8d6ff5a6a3700fcc786f64619e07179968}}, if it is possible to detect an ordinal class structure in the current classification task, as recently proposed, for instance, in {{cite:e814f383b3d163d0b87aa729c74fcecdf373aaf2}}, {{cite:a331cc2b8297fe7a6024b175e430bea22484b4b9}}.
| d | 5a1c24d36451a90fb2f8fdc2f4c2f167 |
The main mathematical aspects of the present paper have been presented previously in Refs. {{cite:4d3e857155d6f1c754ab07d99b3350eab47d6129}}, {{cite:5a1a6915871e9356d60cf414e99490fd95281def}}, {{cite:721a2652ff4e4bc530f54d699fa51585e7dc7e8a}}, {{cite:a439af457967f75efb93a1494b9be165532dc946}}, {{cite:17ebe9e111b4ee77ef4bc9f570589469b8df7cf4}}. A brief - introductory but probably helpful - summary of them is given in
Ref. {{cite:32a8939204275526f913d29a1cea86280bc274bc}}. Essential mathematical references are {{cite:3d45cffd9859327b9450f4859c11a65d741de34d}}, {{cite:e4e09ea641181d8922aa7b49ad40d68eacf6cb32}}, {{cite:188734ed4d04e1e9201b59667d77e57d3d380f57}}, {{cite:eda1bd8c8e9646ae4e85a466ce5a5f3be6fb899a}}, {{cite:e931f52e5fe110465f6be37945d5c56b74eeb746}}, {{cite:475ff9c100a1318bc36a20763a2f163f4a35337c}}.
| i | d8636497e52da08d2c765981f38b94f6 |
The step initial data effective hydrodynamic result is present in the literature. We quote {{cite:b6f89f436802ff55a34ebd1a3db4fcaa3c6a2b9e}} and {{cite:32bd09891a3d153777db66998111bd393109ec02}} (see l0estimate below) for this result. In fact, {{cite:b6f89f436802ff55a34ebd1a3db4fcaa3c6a2b9e}} essentially relies on {{cite:c6bc2b7f652dc714712e664447ecb42bf8a32288}} which uses Fredholm determinantant asymptotics as well as Widom's trick to establish the lower and upper tail bounds respectively. In general for determinantal models like TASEP, one tail often follows directly from showing decay of the kernel of the Fredholm determinant while the other is typically more complicated to demonstrate and requires tools like Widom's trick or Riemann-Hilbert problems {{cite:96306233694ab71d58eb08e1b3aabfc681371f75}}.
| i | b4169529f8777260c2ce794521ff326a |
We employed Yakhot and Orszag's scheme of renormalization without rescaling and obtained the renormalized surface tension and the strength of the noise correlation for the surface growth problem governed by the KPZ dynamics on a flat substrate. This scheme of renormalization is slightly different from the usual perturbative renormalization group analysis with rescaling that has been employed for dynamical problems by Ma and Mazenko {{cite:80ee87dc2c34de44715b3c9bf9e929e2ba2788ec}}, Forster et al. {{cite:43a834bc74fe10c45a2194e80bb6fbb5225ce1d6}}, and Medina et al. {{cite:c68857f3c2ce0d3b41cf105620022261ad6c7cf9}}. This method allowed us the advantage of obtaining the flow equations directly without rescaling by considering the iterative nature of the scale elimination procedure. This yielded the fixed point from the {{formula:4bb0d68e-9e5f-48e9-b71a-a32363ec62ad}} -dependent expression of effective coupling constant {{formula:637e13d1-495d-47cf-a933-bb18420ea41c}} in the limit {{formula:7eb2ed59-b001-4ef2-a7c6-f19adb62da58}} . Similar to the other calculations, the renormalized surface tension and the strength of the noise correlation are found to be renormalized in the same way so that {{formula:b11a6687-c528-4bd6-b04f-11a4cbb1b538}} is {{formula:7f5277a2-43ba-4e04-b87c-eb09e1414f91}} -independent, a consequence of fluctuation dissipation theorem for the case of {{formula:8c1fb237-4be5-44e6-95e6-91aa0cf9645a}} dimensional KPZ equation {{cite:43a834bc74fe10c45a2194e80bb6fbb5225ce1d6}}, {{cite:f54fb50301465df67562db67192377495939e3fd}}.
| d | 50d6459feafce6fa82bff8a0274a117d |
Similar to the celebrated {{cite:4250787df5a9bc53e1d09c44f09fa88303d28eca}} and {{cite:67a2108230df71762d46f69677a80a4251f16a01}} approaches, LLSM is formulated as a backward recursive procedure. In its first step, LLSM estimates the conditional expected option value via simulating paths. Based on these paths, regressions are carried out on the resulting option values. In contrast to the existing strategies, LLSM adds a variable selection step which allows an objective procedure for selecting the influential basis functions in the regression models considered. The corresponding regression result provides an approximation for the continuation value which can be compared to the early exercise value. Option values at different stopping times of all paths can then be evaluated, so can be the portfolio value as well as its VaR. Details of the algorithm for LLSM is summarized in Algorithm .
| m | 5cc44a2a472baf85ed617c530aa27822 |
This paper has focused on the conversion of dark energy into thermal radiation through technically natural couplings between a rolling field and a gauge sector. These kinds of couplings can also source another class of signals. Tachyonic instability {{cite:05126e728efeee453a25aaa16efce5b42bd00825}} can result in the conversion of the kinetic energy of the field into ultra-long ({{formula:f30a9d57-e54b-42fd-af3b-cf29ca20f539}} ) wavelength modes of a vector field. Canonical examples of such vector fields are {{formula:98a3a943-45d4-4550-93eb-1dc7494125bd}} gauge bosons and a hidden photon. Signals from the former can potentially be looked for using torsion balances/accelerometers{{cite:15e00c35695ae483e773f2f11e0cf73820b3c467}}. The latter case may be phenomenologically interesting - given the plasma mass of the photon, the hidden photon field is likely to manifest itself as a spatially coherent magnetic field in the universe and it might be interesting to see if such a magnetic field could be the source of the observed long range coherence in extra-galactic magnetic fields {{cite:f2b042ded0dc106d2a3f0de7d1e127617f2e5b46}}.
| d | cacc5b8d405e6b031577f81de9ae0e8f |
where {{formula:fa75c692-d3d5-4057-b2c5-8c1866a43a0a}} , {{formula:5ee6020d-b94b-4da7-8bed-7cab6a0eac43}} is an initial point, and {{formula:8de79e4b-1325-475c-a4f7-2859bee0acf5}} and {{formula:f79c18f5-8073-416f-b521-ef8ab7eece1d}} are two given step-sizes.
Here, we use two different step-sizes {{formula:65ed4a39-b5f6-4787-b326-8f5c1073bc75}} and {{formula:3e04ece2-ba18-4a45-b18a-96c9eed95caa}} compared to the original EAG in {{cite:d8d8c13ca1bc45d616ff5c889b3177148760eac5}} by adopting the idea of EG+ from {{cite:9c9909a1cfa70c6f5d687e48022505d7f2367020}}, see also {{cite:472bcfcb0d3a61aabddd14f82f75fc590eb32595}}.
| m | 91181f3a1ecd2112cc9a9c0d6ed63fa0 |
Korteweg - de Vries solitons are very interesting non-linear waves, which may exist
in many types of fluids from ordinary water to astrophysical plasmas {{cite:1ee112e972593e4a0627999bd6c7ccd314265a95}}.
In the last years
we have started to produce a new kind of fluid in laboratory: the quark gluon plasma (QGP).
This is a state where quarks and gluons, usually confined in the interior of baryons
(such as the proton) and mesons, are free to travel longer distances. With the beginning
of the LHC era, we have means to study larger and longer living samples of QGP and even the
propagation of perturbations in this new medium. In this context a natural question is:
can we have KdV solitons in the QCD plasma? In this work we give an answer to this question.
| i | 5e30345725c4da8b4f0f941cb9f56913 |
Topologically ordered phases are novel phases of matter beyond the paradigm of the standard Ginzburg–Landau theory {{cite:4ba1ed9506ba5c7419be550971f435bed0bbc0c7}}, {{cite:743f9e91bd3b85e105328aece9d05b677cc282ef}}, {{cite:bde79848cf6dabb5647a7c9eaca5a01f590bacb7}}, {{cite:bbe66638dbe9404addf3a0898d6c3a725cc39a66}}. There are many salient features in these phases, such as non-trivial ground state degeneracy (GSD)
when the systems are placed on manifolds with non-trivial topology {{cite:049a98dd5caad80f4c8c3c9b1864a865439b0df5}}, and fractionalized quasi-particle excitations (anyons) {{cite:8f37828b421d27a10c892e497381689acbf36689}}, {{cite:20ba271a7ca6a6730f4af881cefe8c704503b3ab}}, {{cite:4175305c3dfa85b03765ee97ad2b56b802ca16b6}}.
Topologically ordered phases have spurred a great deal of interest, involving different branches of physics. Examples are topological quantum field theories {{cite:a637d230a780e553bfca5ca6df620db6679a63c6}}, {{cite:71623d16707d7596508b49c14bac0e8c5ea46281}}, quantum error correcting codes {{cite:c1394e0b4684c95db541d2e367f9d2b20ca96f73}}, universal quantum computations {{cite:3a54b73ef8642caf938f2b9fed5271aaeca4c679}}, and the classification of symmetry protected topological phases by investigating anyonic statistics after gauging global symmetry {{cite:02aead5fb8e5f9cb1dad3ccb8e870b8bf3875e2a}}, {{cite:817b1abd4dc426b6dab3ccfb9d9642af06ccdab2}}, {{cite:45580316077ecd04a0ee2b1d183bb5b4798cee3c}}, {{cite:1be6ed175e64a07397940105f6d1fc8091196134}}.
| i | b3ae536c39ab38b294b233caba96ebbb |
In this study, we propose a deep learning approach to segment 30 deep brain structures from T1w MRI (Figure REF ). The method consists of a pre-processing step to transform all the images to the same reference orientation followed by a CNN with a 3D U-Net architecture {{cite:e8b895a4afa765f6602df8f798e3b40b1da6ceb5}}.
| m | f71e47356a7c7d7758e088e9318dc8b8 |
Language model pre-training is an increasingly promising research approach in NLP {{cite:04a2781326d52b4ba14cb7d6364342aa0c9011a2}}, {{cite:efe5fb07b628288b79111f8a607e54351ecbc15c}}, {{cite:e5342cdaba03943887f17bc916ee739116025f74}}, {{cite:33144dad89bf6ef6bc9a65e6af1f18554995448d}}, {{cite:6ef9e991a2f5981ff0bae19644d3f9ff88593c2e}}, {{cite:82c74e56c02479e990b51957fc0eff31fe3f1c6e}}, {{cite:4dbf3b94b02b6c727fc6f597a3d83fd695e51413}}, {{cite:0df1690aa78c533816eba717e03270f12b29a717}}, {{cite:37dd0488b956b13d221fd965254a8b8150e2673c}}, {{cite:29a54313dfe9c408af7949564dad94a7dad8b0ea}}, {{cite:27ae40e95a4b61a65d6ae02ee03733d71dbb8fce}}, {{cite:63b8af75cb9eb9b0f49aaa02e0f4c9c93b42c0f7}}. As pre-training uses unlabeled text, it can be combined with scaling model and dataset sizes to achieve better performance or new capabilities {{cite:45a8f9787e5cb6e378f34b56b97008518b5ca649}}. For example, GPT-3 {{cite:63b8af75cb9eb9b0f49aaa02e0f4c9c93b42c0f7}}, a 175B parameter model trained on a large corpus of unlabeled text, shows an impressive ability in few-shot learning thanks to scaling.
| i | 33ad649a57fb71155c9915e045b96b0e |
We identified a sample of 85 ULXs that exceeded a 0.5–8 keV luminosity of {{formula:4fd01bc1-b5ec-4399-9249-f04c97877e64}} erg s{{formula:fff9ebaf-4c2d-4da2-aa42-a67f73f67cfe}} in at least one observation, and determined their coordinates. We fitted the spectral parameters for the most luminous sources (25 ULXs with {{formula:a0dab5b8-4532-4a6d-9438-2c1e0d8b0ff5}} erg s{{formula:7441a084-6954-4a82-b363-67a0b91559ed}} ) and used their median power-law index and column density to convert count rates to luminosities for the rest of the ULXs, when they were too faint for individual fitting. We showed that the ULX luminosity distribution from our Virgo study is broadly consistent with the LF models from {{cite:1297368bd0e0ea259b1a029cc50f5dd3d8bf3d24}}, for a SFR {{formula:af28083b-7e5b-4eb1-99da-0488557f9118}} yr{{formula:3328f731-d6bb-4af9-8078-35bff0dfb1c8}} and a total stellar mass of {{formula:1c02e7e3-5c66-4692-926d-25d38a44f032}} 1.5 {{formula:7fd43380-c961-4a21-ad58-7086a99aa77c}} .
| d | 704e1ea125d8bfc0b1a3be49b0254387 |
We then evaluate and visualize the community detection results based on the social graph we have defined for the Bitcoin data.
First, we run the Elbow method in Ref. {{cite:f38dec820888c8f10c28f363bee98325f4d6e75e}} to determine the optimal number of clusters {{formula:72d6b0d8-b395-4c59-9b5f-0cc97e8e5858}} . Fig. REF (left) shows that the “inflection point" is {{formula:a9c76753-cbe6-414d-9c41-84f742b44c1a}} and thus we consider there are 5 clusters in our example. Interestingly, this is also roughly consistent with the results in Fig. REF although they have defined different edge weight. We then run Algorithm REF under a random initialization with {{formula:04297192-71df-447a-a73a-6c51efb55dae}} and find that the number of nodes in each cluster are 101, 78, 60, 27, and 13, respectively. A 2D visualization of the clustering results are shown in Fig. REF (right), where a machine learning algorithm called {{formula:e17a3739-944b-4deb-b1ee-e09d0b4a455f}} -SNE{{cite:c6568918a4ce78043d142a758721fb3d3fe2cc29}} is used for a nonlinear dimensionality reduction. The results show that the target users are indeed clustered in the compressed 2D space.
We use two parameters to evaluate the community results. One is the Silhouette score, which combines the two factors of cohesion and resolution to evaluate the clustering results{{cite:240644d0a6536ba6560f2e441c4c4b8a43eee6e6}}.
The other one is the Modularity score which is usually used to measure the structural of network communities{{cite:90f93380211600a4f35c810b2c33daf77c86e228}}. In this experiment, we have the Silhouette score {{formula:68f16a84-b3ef-48f6-b7de-59cdc27220c9}} and theModularity score {{formula:4c9fd01f-8827-4454-b0bb-55b9cfed9c94}} . Normally the Silhouette score is at a range of {{formula:9c3e3e17-87c1-47d5-a03d-ba78ffaeb83d}} and the range of the Modularity score is {{formula:548a6e43-0c73-404c-8e40-4a55eaba6e28}} . The more two scores approach to 1, the better quality of the network partition. The Modularity score around {{formula:ec700fc8-6581-4055-8741-36e9bb031588}} is considered as a good clustering result{{cite:ce34da99648a89da99b2e5633c69a093609fd3fd}}. We track the nodes of the gambling website and find that the gambling website nodes and other 55 nodes that had transactions with the gambling nodes have been all clustered into the same cluster. This cluster has in total 101 nodes.
| r | ba56b6949a84c39bb3a9def2430bd162 |
Movements of a robotic arm, rolling ball, or falling chain can be characterized by rigid body motion {{cite:cba85e806f97967bc527965a380459f50d4854b3}}, {{cite:06c92ed48831493f57800069dca4cef5ffea982b}}. Understanding the dynamics of the motion is crucial in several applications including robotics, human-robot interaction, planning, and computer graphics {{cite:0eecb7f5e1f09e528b905e460cee01311fba3e8f}}, {{cite:cba85e806f97967bc527965a380459f50d4854b3}}. Traditionally, the rigid body mechanics is studied in the framework of classical mechanics, which relies on either force-based or energy-based approaches {{cite:59ddc39a144944f6aefb5aeff0c34d4868e16124}}. Force-based approaches involve the computation of all the unknown forces based on the equations of equilibrium and hence is cumbersome for large structures. Energy-based approaches present an elegant formalism which involve the computation of a scalar quantity representing the state of a system, namely, Lagrangian ({{formula:669f4ac6-dd75-460b-ad1b-0733e03ad25d}} ), which is the difference between the kinetic {{formula:beba5c51-3e8b-4439-9392-e7d749a6096c}} and potential {{formula:913ece48-852c-40d6-8c15-5f5f6706d3b5}} energies, or Hamiltonian {{formula:5ffbd116-67c8-41c7-92d6-88520f755678}} , which represents the total energy of the system. This scalar quantity can, in turn, be used to predict the dynamics of the system. However, the functional form governing this scalar quantity may not be known a priori in many cases {{cite:17ec61a9631ece134cf11c09bdb6be86fe2e42f3}}. Thus, learning the dynamics of rigid bodies directly from the trajectory can simplify and accelerate the modeling of these systems {{cite:17ec61a9631ece134cf11c09bdb6be86fe2e42f3}}, {{cite:f61d535d38f9ecde0e05be950e1b449e04f20467}}, {{cite:a27747f1154b3ecd9de430a9d9e13bc252e72265}}, {{cite:c67effc777303f2427ccd016574b5d4ec6a25a8a}}.
| i | d62b6c13aab9a6ddb3de2a099b6c1c77 |
Global UniBlock vs. Perceiver {{cite:1595feb9ef3f415b99c5713cbe711ad48b82f28f}}, DETR {{cite:82ae3fdf7c3e90df45eb6691411755df178e888e}} and Flamingo{{cite:234b579b34fd0ecd65340241f30d2b4a8104d77a}}.
Our Glocal UniBlock is also motivated by the style of UniFormer {{cite:c95d8931cb36d5f728d2681dd3041ca4f63e8867}}.
But differently,
to decrease the global computation in UniFormer,
we change self-attention MHRA as cross-attention MHRA in our UniFormerV2.
Hence,
our Global UniBlock consists of Dynamic Position Embedding (DPE), cross MHRA and FFN.
On the contrary,
none of those works belong to such an operation combination,
without insight of UniFormer in video learning.
In fact,
these methods often use the standard cross-style transformer block including self MHRA, cross MHRA and FFN.
| d | 1c1bd72faa5181fb6881fef4cb1bf980 |
Information theory provides an ideal framework to study interdependencies in multivariate system, which establishes the notion of information as a common currency under which diverse systems can be measured and compared {{cite:4b076bcd7a65c4bb05958e348e6d870af3598e44}}.
A particularly promising approach for analysing the structure of interdependencies is the partial information decomposition (PID), which distinguishes different `modes' of information that multiple predictors convey about a target variable {{cite:57009ebc6f76a251b5f6835952c3fd641e8ac64b}}, {{cite:35828fb10d4165108fd2a9a505be5cb0898d2c97}}, {{cite:6f841cbaee9bc09fe0f89645383d302b7a968512}}. Two paradigmatic examples of such modes are synergy and redundancy {{cite:35b0013422a43a3d7871a08800a66aaf1901b21c}}, {{cite:22f4b9b556cb3ea9876b23d91a034506792f1751}}, {{cite:2a9ab79572e42366a757cca0222fcbf6e06a9c4d}}, {{cite:1206e36be419e496ccf006e3374f3c9e8dc406f3}}, {{cite:a7e40197b4a2e6023355b719e7f1f8121774a6d3}}: redundancy
corresponds to information which can be retrieved independently from more than one source, while synergy correspond to statistical relationships that exist in the whole but cannot be seen in the parts — this being rooted in the elementary fact that variables can be pairwise independent while being globally correlated.
| i | 0d289d3c0702ecb6dc2dee37583abbb1 |
The rapid evolution of neutron-star (NS) astronomy in recent years — in particular the recent NS radius measurements {{cite:40923280e845f9f9a059d06e8d487153065572ef}}, {{cite:ab190a9f526d605911014126dce9189df7371753}}, the discovery of massive NSs {{cite:7ca1557218299911537a480072de16844846fcd8}}, {{cite:c88f385752ff05e61c851ba96fd8bbc45406bc58}}, {{cite:8467dee096fc7ce5524410f11cc9d0b88038fb3f}}, and the advent of gravitational-wave and multi-messenger astronomy {{cite:eebd8aa81acbfcc296d9cbaadd11fea077e9daad}}, {{cite:b0737c01849536f4571240380fae41c7677a9df4}} — is for the first time giving us empirical access to the physics of the cores of NSs. Within the Standard Model and assuming general relativity, the internal structure of NSs is determined by the equation of state (EoS) of strongly interacting matter {{cite:57c4666b21ebcb4da5a90da351b6ed07123344aa}}, {{cite:499e0d5e41356431d194456c57bbcc8014db24c4}}.
With these assumptions, NS observations can be used to empirically determine the EoS {{cite:7d4461b20e776bf92a78c4b7b212ef06a5ba4d50}}, {{cite:f66bbfdde45bfbc8b247b0c0f714c47de529e084}}, {{cite:5fe502106abe2c9b1a0a94e7c5b886f6b3bc223d}}, {{cite:366f72c2ab7a70342bb3f53c8a56e6646cdf59dd}}, {{cite:cb05ab81f00d64211f791223edb421ab1e848299}}, {{cite:f62ce1c454fe0ce32c9d05f0dc55dc5c8b65c837}}, {{cite:219815f4c2c087819e63bc16495b26b22719d975}}, {{cite:ee1e0cfb9ae9e3d207a4734fd53e1dee21e46ba6}}, {{cite:32785d837859d36944444a9d474eb2b07503191a}}, {{cite:7833aa4b5b4a313ce46d1ad3c1631c450fac6048}}, {{cite:485f448d45281f6e86ee34dd5b3c419b7e739ac8}}, {{cite:119ac77336d87e1fabe17f5c4c378ca53eba7c2f}}, {{cite:420776bdc65b46a246857d2e757ddda36115169f}}, {{cite:9fb455829959fd3bfbf84499f0ef78ba8ec1b876}}, {{cite:0f488ce75c8e15d1569b40debe60c59f98ef3ea7}}, {{cite:92f127991c81c0aa4c3a307c0d791fe7884ff513}}, {{cite:fa581a053f95e8c1765c8caa2b70b84145f4d533}}, {{cite:7a3b46be2296cc9d5528db6e7588e5fee9586944}}, {{cite:828a59871c88e2bbb7e565260abd31c026ac6e3e}}, {{cite:e3c6023f84eb8be3979c959226bd503630c89189}}, {{cite:eed9f29f56fde6639a9f5e074f33748239e700a9}} (for reviews, see {{cite:bb49a2380f5077ef789103340129cc7769ab7d0b}}, {{cite:5e35c4e408bed3f67881d0659c8fff0b5bcb13c6}}, {{cite:d3947e522e8800bbac9ca03a8aa61f6dc3ce333f}}, {{cite:0fcb2c80b935c763357dcf81ea0e4c3d466c4b5d}}, {{cite:abb5d58e28d479b51d39a9115e3d912bf7a64eb8}}, {{cite:ff8cf02cc2e7655ee0de41f35089e2995467be0f}}, {{cite:0542c149496e61005b5f1492ddc8441ba28770da}}). And if the EoS can be determined theoretically to a sufficient accuracy, comparison with NS observations allows to use these extreme objects as laboratory for physics beyond standard model (see, e.g., {{cite:bda6b3e2ecbb7e8deb69e84b647b097af02b9146}}, {{cite:2254786ea098d93a0221c7f89860426f381dc4fd}}, {{cite:ba22d099ea1625a2885cf93d856b1622bfadf1d8}}, {{cite:b0875c5f959c00a2c880dd7d0a46fcacd1922844}}, {{cite:7d141c90296b8586cbf112f63b8b2f48d7070521}}, {{cite:e51680f4897b7d40c53e1916a8745b198e440fe7}}, {{cite:b52a7530a43d061da957bb81ee2fb64117d36916}}, {{cite:b548cf32d27f078675edde290ac3e9051cd22bb7}}, {{cite:bf0b23cad914e04b804bc4b0eb880d392a6ada71}}) and/or general relativity (e.g., {{cite:70f70b0ca08242aa4759c3f3c8426b93de37622b}}, {{cite:0e0fba525ed722c75ba092f5064f17897c00d93b}}, {{cite:156b7010fa316ebe3cc0c6c015faccb35b2f375f}}, {{cite:872e80c67416b43cb173b4af3c0c5712641cc3b3}}, {{cite:1956e8c8c6793dcbdfcd10713fc1f3548393e907}}).
| i | dceaba9f9a688cd1e028d13eb8a46c05 |
In this work we have reviewed and extended the model for spinning extended objects introduced in {{cite:4cd99184ea4a6182c4e2881c0dfa653978ae781c}}, which is derived using the tools of EFT known as the coset construction {{cite:b6ba598e70a419bafcaf21b113c6831bd8ff2aba}}, {{cite:0847b75e121e4cc719a9d47ecd0e2d5db1aefec7}}, a very powerful method that allows us to derive the effective theory based on symmetry principles only. In {{cite:4cd99184ea4a6182c4e2881c0dfa653978ae781c}}, a spinning extended object whose ground state breaks spacetime symmetries, is coupled to a gravitational theory formulated as a gauge theory with local Poincaré symmetry and translations being nonlinearly realized. We have extended it by including the internal structure {{cite:5beea1b1acfc23dd1bb62467560074d2d88f12a5}}, {{cite:365402096b321964793f698b0491bbc343c56c69}} and electromagnetic charge {{cite:365402096b321964793f698b0491bbc343c56c69}}, {{cite:b5fbaebcb670da12fb0f6cb9653645ac8ae541c5}}, such that we describe charged spinning compact objects, the most general compact object allowed in a theory of gravity such as general relativity, that includes a classical theory of electromagnetism as well. Within the approach of the coset construction, the coefficients of the effective theory are to be matched from the full known theory, and ultimately, from observations.
| d | 9644f017bdd911b7d46025a45cd079b8 |
As observed in the Fig. 1,
the structures are mostly
clathrate structures formed
by units with
La@H{{formula:c948df98-bdc4-4447-9889-32c6a984808a}} and Y@H{{formula:33f36655-3814-4ad7-9fb1-5536c602e44f}} cage structures.
Several other clathrate superconductors
have been identified,
{{cite:49ba82fbb0de5ff51cbb3c076464195ca90f8cfb}}, {{cite:064b75ef922e2aeae723898e77c26fb98fb994f4}}, {{cite:19d1198c2de2e010ab27874369df13f49d8cb305}}, {{cite:caabbe50879e8ca027897f453baf89ecc402d5ef}}, {{cite:c9c8a06230c1b7969cb9b1227e384964a5b0845a}}, {{cite:02513c2f779df6b3862fdd9a6d402870f314ebc3}}, {{cite:a82bafe64646427700df9718cfc0652daef9bca3}}
and hence it would be plausible
for this structure to exhibit superconductivity.
Different periodicities
of the La- and Y-layers along the {{formula:1daa740a-3ffb-41be-886b-39160a639653}} -direction
correspond to LaYH{{formula:70d90223-bc0d-4387-b81d-2c751c14a774}}
[(La/Y)(La/Y){{formula:e1c25afb-5f1b-4e73-98a8-cd78d0ebd235}} ]
and LaY{{formula:22247e32-2294-4e23-aebe-0831e5273ece}} H{{formula:39c5e381-9824-4232-bdfa-b7056651613c}}
[(La/Y/Y/Y)(La/Y/Y/Y){{formula:de169a63-ff75-4998-a1c8-c507a2a30a58}} ], respectively.
| r | be6a3c41466b2e47a974e23d50c6cc68 |
In this section, we systematically evaluate the performances of proposed tp-training and ml-training algorithms in expanding the set of labeled nodes in the context of the node classification problem.
We start our discussion by describing the datasets and our experimental setting.
Next, we analyze the performance of the algorithms as a function of the key parameters.
We also compare the performance of our proposed methods against the only
other existing method for label expansion, co-training {{cite:7783a9b622d2d399b45329807ff83d95504809f6}}.
We then investigate the performance of each algorithm as a function of the available number of labeled nodes.
| r | 0dfa30dd3ea17a59ad6ebbe3bba39630 |
Numerical experiments are performed on the DARP instances presented in {{cite:a11180c4860a562f7934856c08d98d76ce1d1b05}} and on the e-ADARP instances presented in {{cite:7ab4fa5a76aa5ff7b1d9e2289c1ce403187d3cf5}}. Specifically, we extract routing solutions by employing the adaptive large neighborhood search in {{cite:0ac8e09453ce697c630dd53033844560bb482324}}, with 1,000 iterations. At every iteration of the large neighborhood search, we solve the scheduling problem through a linear program and compare its results to the route evaluation procedures by {{cite:a11180c4860a562f7934856c08d98d76ce1d1b05}} and {{cite:82cefcdaca41bf4de0422f9e04a007944f275e12}}, as well as this paper. This results in a thorough comparison of the scheduling algorithms on about 15,000,000 feasible DARP solutions and about 2,500,000 feasible e-ADARP solutions. As explained in Section , for the e-ADARP, the linear program is obtained by supplementing (LP1) with charging and battery management constraints/decision variables as proposed in {{cite:7ab4fa5a76aa5ff7b1d9e2289c1ce403187d3cf5}}. The numerical experiments are implemented in Julia v1.8.2 and run on 2 x AMD Rome 7532 @ 2.40 GHz 256M cache L3 CPU clusters. Each instance is run on two of such CPUs with 8 Gb of RAM. The LP is implemented in the JuMP modeling language {{cite:2785a955c4402cfe256152619b258a3daec083db}} v1.3.1 and solved with Gurobi v0.11.3.
| r | a3967f64db740b09973a25838eace49f |
An important implication of our results is that the dominant heating
mechanism in active regions cannot be both highly concentrated low
in the corona and steady or quasi-steady (slowly varying or
impulsive with a rapid cadence). Active regions would look much
different if this were the case. Loops resembling our models—and
therefore unlike those observed—would be common. This claim must
be qualified with some caveats. It is acceptable for the heating to
decrease with height as long as the scale length is greater than
about 20% of the loop half length. Only shorter scale lengths
produce thermal nonequilibrium. Even these short lengths might be
allowed if only one leg of the loop is heated, because then a steady
flow equilibrium can be established. It is unclear, however, whether
these steady equilibria can reproduce the excess densities,
intensity scale heights, and temperature profiles that are observed
{{cite:7f2717a715c36a3816d4a186f93c4c9d88a1040e}}, {{cite:4c960f01c530b3ac992c9a6ad3feb776c2c0d215}}.
| d | a013c8bcd74d890d1822ca1c8e688c7c |
As shown in Table REF and Table REF , we provide more quantitative results on SPair-71k {{cite:a0b06d5bbbb5deb7cbd38cbd596fe7a034fba0fb}}, PF-PASCAL {{cite:e8481382941710272b474d410f4d4852c2713868}}, and PF-WILLOW {{cite:4e8483ef4ace861380bc5c0035bc9cb19b625fa4}} in comparison to other semantic correspondence methods, including CNNGeo {{cite:b35be37215b214e65bedb04bd09ab6ea874407b3}}, WeakAlign {{cite:a656f2da3d42e9697b9bd851dd1cbf16a427aeeb}}, NC-Net {{cite:7d9af5336be1817fd2ee54e99320e53928309905}}, HPF {{cite:0489d57ee9e0ac7516bf07e6aa17b4df4df63a27}}, SFNet {{cite:28aba9b4473c795eb0ef19e44b4abc513965c9bd}}, DCC-Net {{cite:f37eca3f51658ab06305e38ba3dee01a4bf7ddb8}}, GSF {{cite:0a5a7a4d0d2d7ef7ff90c75575c2a6d1024bf379}}, SCOT {{cite:c21b8dc63861783966c6e6fa5a64cb21fee12332}}, DHPF {{cite:9483ea4d271203c5b5b1a2cab4097ac7d76b7f00}}, CHM {{cite:52fd6e3d253eb1fe3cddf8b325436efbcb8731b6}}, MMNet {{cite:26ae063e288bb9f037b4db35003ee23bd2f8ce22}}, PMNC {{cite:a9be4e6e03f96cdb5e3f9db52db80f1d6aafcc5f}} and CATs {{cite:ff1253bf9efe0046055558a3c2805888d91bc1f1}}.
| r | de86173d7fafc819294f5e570c1f1425 |
(R1). Here we analyze the forecasting results on the different datasets at horizons 3, 6, and 12, respectively. For reference, we also add a vanilla LSTM {{cite:1f803f06c1279687a4ac61968f14d53c005b1b84}} baseline that jointly forecasts all timeseries, as well LSTM-U, which consists of {{formula:0489667e-d602-40b1-bb89-55d135cec929}} univariate LSTMs. Essentially, the LSTM uses information from all timeseries, though lacks typical GNN properties such as permutation equivariance and does not leverage sparsity. LSTM-U is on the other end of the spectrum and simply views all timeseries as completely independent. In Table REF (appendix) we present the results.
| r | 571940dacd126eb32bbe06f03576c9d8 |
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