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which can be bounded by {{formula:689b249e-dc0e-40a1-84f6-608172ef6367}} . If we seek to bound the mean-squared error by {{formula:1e860a7f-2620-49b1-981b-e6cffe423b2c}} , then we can take {{formula:b38d0d6b-d2aa-4315-9e8e-68d630e357ce}} , {{formula:11b35efc-6aec-4191-b00b-a4b2924ab421}} , so the expected computational cost equals {{formula:a99fb483-ec80-4084-8d27-3af0a6d93677}} . This result is first stated in {{cite:b17d77b9e238eb083d44bed2956bfc49d2a951c3}}. In general, for high order schemes, the complexity of classical Monte Carlo method can be bounded as follows.
m
331fcc8ea58a7c5f94007a47f024cae0
Performance The performance of different models on Cifar-10 are reported in Table REF , and in Figure REF we display the radius-accuracy curves. Note that the area under a radius-accuracy curve is equal to the ACR of the model. First, the plots show that our proposed method consistently achieves significantly higher approximated certified test set accuracy than {{cite:155f06cbcd57f73cb7124b1ba03a823515f5bbc6}}. This shows that robust training via maximizing the certified radius is more effective than simply minimizing the cross entropy classification loss. Second, the performance of our model is different from that of {{cite:0c2febf7238a8e26b16504438cfa89a55d02cf9b}} for different {{formula:998f7d94-2549-4dcb-8a78-9cd7e60262ea}} . For example, for {{formula:caa57bfb-004f-46ad-8765-c5b858c99381}} , our model achieves higher accuracy than {{cite:0c2febf7238a8e26b16504438cfa89a55d02cf9b}}'s model when {{formula:ecebb549-19ca-4249-9a20-59d88164ad3a}} , but the performance of ours is worse when {{formula:c3691c6a-7c33-476a-b9e8-2deb97f9f5e5}} . For the average certified radius, our models are better than {{cite:0c2febf7238a8e26b16504438cfa89a55d02cf9b}}'s models{{cite:0c2febf7238a8e26b16504438cfa89a55d02cf9b}} releases hundreds of models, and we select the model with the largest average certified radius for each {{formula:bd172089-8803-49e8-b434-04e1f299f92b}} as our baseline. in all settings. For example, when {{formula:3f7f85ee-e81c-4e81-bd0a-8245b0b82e08}} , the ACR of our model is about 3% larger than that of {{cite:0c2febf7238a8e26b16504438cfa89a55d02cf9b}}'s. The gain of our model is relatively smaller when {{formula:a229234a-228c-4d95-bbe4-34828dde5511}} . This is because {{formula:400fd6f2-1ee3-441a-91cd-20d3a4dfe7a2}} is a very large noise level {{cite:155f06cbcd57f73cb7124b1ba03a823515f5bbc6}} and both models perform poorly. The ImageNet results are displayed in Table REF and Figure REF , and the observation is similar. All experimental results show that our proposed algorithm is more effective than previous ones.
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a2b6879bacc7e6082f5f04bc650f1ff4
Before applying our method to the entire sample set, it is necessary to validate this method using a spectrum subset equipped with reliable external stellar parameters. Therefore, we cross-match with APOGEE DR17 {{cite:afa92ee8761dc0d5b3d2c0438dfc3042719d2b4c}}, {{cite:655df0534c297bb5cb94f7a79b5fce9d1c1e3732}}, {{cite:dcfd6b748f7f64c5d997ab4a8fe1fe11449d53a6}} and 16 suitable papers from the literature, then compare the stellar parameters for the common stars.
m
6699789653cd8cc28c5dd47dd0ae74c4
One-stage approaches, such as DenseBox {{cite:85b79f2e2dcb7bd744f8e57539b382463064c63b}} and CenterNet {{cite:352d6f2b812c7369e9914c27ac7dce0042129d60}}, bypass the region proposal step and directly predict classification scores and bounding box regression offsets, aiming for real-time performance while maintaining high accuracy. There are some works that try to transplant the merits of two-stage methods to one-stage approaches. For example, RefineDet {{cite:68f33d912edd4f2a8fcd6018ec5a71a793b1774c}} uses a refinement module to mimic the second regression of two-stage approaches (see fig:abbr-arch (c)), and Consistent Optimization {{cite:134d3a7a053bfbaf9df32537176093264c9fa4f9}} reduces the gap between the training and testing phases by tying consecutive classification targets to the regressed anchors.
m
f67227775e2b947c39fe8cb06410f2c7
Like in case of HDNNPs, we cannot simply use Cartesian coordinates as input for the neural network, because the derived spins must be invariant with respect to translation and rotation of the system as well as to the permutation of chemically equivalent atoms. Therefore, the Cartesian coordinates are transformed to atom-centered symmetry functions (ACSFs) {{formula:8b70878f-c083-4ff1-ae2a-b8d65b9a15cc}} ,{{cite:909728477396f1869fde4d16aedb14aea103dcf5}} which meet all these requirements and describe the local chemical environments of each atom inside a cutoff radius {{formula:d844c3f4-d295-47c7-bf6d-de0b8c57d3c3}} . This cutoff has to be chosen sufficiently large to include all neighboring atoms, which are relevant for the value of the spin of the central atom. Due to their many-body nature, the number of ACSFs per atom is independent of the actual number of atoms inside the cutoff sphere, which is required for the use as input of a neural network with a fixed architecture.
m
f9e97081c07d84d5bbbf0c50073db04e
In Fig. REF , we present some qualitative examples of class-agnostic OD with DETReg {{cite:d8b98e52a333653270c193f40437affdcb873d3f}} trained using off-the-shelf proposals from Selective Search {{cite:32eb55268a48211e888fea4fbd2247989ee3ad28}} in comparison with DETReg trained using MDef-DETR proposals. Fig. REF shows some examples of improved Open-world detector (ORE) trained with MDef-DETR unknown pseudo labels. The images on the left of each example correspond to the ORE trained with unknown pseudo labels from RPN and on the right correspond to the ORE trained with unknown pseudo labels from MDef-DETR. The visualizations indicate that the improved model is better capable of detecting unknowns. Additionally, it reduces the miss-classifications of unknown categories with other known categories. For example, the second sample in Fig. REF (top row - right side), corresponds to a sample in task 3 where ‘laptop' belongs to the unknown categories set, was miss-classified as ‘TV', which is however correctly classified as an unknown with the improved model. This is advantageous as it can better aid continual learning, , the model can learn about the unknown categories when additional information about the unknowns are obtained via supervision. In Fig. REF , we present examples of qualitative results obtained for salient OD and camouflaged OD with specif queries, ‘all salient objects' and ‘all camouflaged objects' respectively, along with the bounding box annotations from the ground truth masks. {{figure:e22611e5-9d85-4d84-9290-6f80f0c4aaff}}{{figure:b3b50d20-d2f3-4c4e-9cd3-9e45f56fcd17}}{{figure:4ab073ef-9f8f-4a18-9e17-95a175c10860}}{{figure:961c81d5-fd62-49d2-9eb2-f328e7b0a1e5}}
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6ec4aeca484c492894f8033b3762fe05
In Figure REF a we select three individuals as exemplary career histories. Each line represents one individual, with circles denoting his/her publications, allowing us to observe his/her location. The size of the circle is proportional to citations the paper acquires in five years, approximating the impact of the work. By studying the whole corpus, we compute {{formula:a8fe750c-8735-4ace-a9ba-2fbadce82a90}} , the probability for a scientist to have visited {{formula:35f004c5-ea09-4fee-8ba5-376760dc22b5}} different institutions along his career (Fig. REF c), finding that career movements are common but infrequent: Only {{formula:98681245-3bf6-4ed3-8ac7-a058e61852c2}} of them never moved at all ({{formula:3a42b290-91ac-4416-a0cb-63647ecf5460}} ). For the ones that move, they mostly move once or twice, {{formula:9321967b-f534-4890-a2c7-57a68e0d2443}} decaying quickly as {{formula:d1844679-975c-4acc-a146-afd65a17ef74}} increases. We also compute {{formula:aaff068a-f2d4-468d-b2cf-0eede8fbe9e0}} , the probability to observe a movement at time {{formula:50030107-ecab-4a60-9286-10e5e0a433d2}} , where {{formula:ccc5891a-d019-4045-9933-709e0dc9e18f}} corresponds to the date of the scientist's first publication. We find that most movements occurred in the early stage of the career (Fig. REF b), supporting the hypothesis that changing affiliations is a rite of passage for young researchers {{cite:204f8c168e414fc109a9e76e18f4109e94fb4d25}}. This likely corresponds to the postdoc period where graduates broaden their horizons through mobility. This may also reflect the increasing cost of relocation and family constraints as family developed {{cite:58ba05fc43ca71b850c324b9b34835b0c54f8307}}, {{cite:62cc3deaa5e87037f9db20d321f75b33033a7e05}}. A third characteristic is the geographical distance of movements, {{formula:4f590214-4bc2-44ab-8caf-95b3724b54a4}} . Existing literature hints for somewhat competing hypothesis in the role geography plays in career movements. Indeed, research on human mobility suggests that regular human movements mostly cover short distances with occasional longer trips, characterized by a power law distance distribution {{cite:3c04c0bd06daf729814d99d1d8fba620d1e96f28}}, {{cite:a199ba2e0681eebb3bc06ae7109d6775ba9cbe67}}, {{cite:3fb01e33a3c70b97de82f5865b37b0290b41b979}}, {{cite:1e804e565006c5977860b02605169c7f4fb93583}}; in contrast, country-level surveys find increasing cross-country movements mostly due to cultural exposure and life quality concerns, indicating potential dominance in long distance moves in career choices comparing with typical human travels {{cite:99c3d92d4d9290d243405d35e38ab71c3f9d4de4}}, {{cite:4fef55702df8261d7089a2e2a97e7d9ec0cbcff3}}, {{cite:64cd93f6cff2a462239a415b2b0bd305276281b1}}, {{cite:3360d17df23953313d53f58bc13cf8b44d4a2f2f}}, {{cite:58ba05fc43ca71b850c324b9b34835b0c54f8307}}, {{cite:8ff0f783d6e07addc80f3f8a76c68a407bf1f711}}, {{cite:62cc3deaa5e87037f9db20d321f75b33033a7e05}}. We measure the distance distribution over all moves observed in our dataset, finding that our result is supported by a combination of both hypothesis. We find the probability to move to further locations decays as a power law {{cite:a76bc5a12b182ed80206fb6359c552ece4a8251c}}, {{cite:9c489e890d85ecedbcaf84e75b98c9d2345308ec}} , whereas the null model predicts this probability to be flat (Fig. REF d). This observation is consistent with studies on human mobility, that short distance moves dominate career choices. Yet, when comparing the power law exponents, we find the exponent characterizing career moves ({{formula:67d3a8e8-156b-4f79-8bb3-9eca29dbf1e1}} ) is much smaller than those observed in human travel ({{formula:f52e26e0-464d-4d53-86e7-f8e140ad819a}} ), corresponding to higher likelihood of observing long range movements. This observation might be explained by the influence that scientific collaborations can have on career movements as similar low exponents are observed for collaboration network between cities {{cite:7acf1ab4417a7996aecf54ad31bc91a6c2dcacb3}}. {{figure:5f0102cb-46a9-48b2-aa7f-9a25147a51c2}}
r
a36d8a367a2a62c46e065487f4803e57
Remark 2 We recall from Chapter 1 of {{cite:89d1d73117107398fe4723e7230edccb1dc36cdd}} that a closed subspace {{formula:86608b39-186e-4543-bb25-ebee47abd818}} is a {{formula:494e37d8-51a7-42c4-b883-7cb55a2a96a0}} -ideal, if there is a linear projection {{formula:6f70e051-663f-4b5f-9873-8ede573393e5}} such that {{formula:3c44e8ed-31c8-47f0-98a4-b6f52e425265}} and {{formula:bab3eaa2-8192-4959-8015-33be25bb8b3b}} for all {{formula:5183a434-67e2-4a01-b6c6-3c8b63765aea}} . Such a subspace is a proximinal subspace. Consequently if {{formula:7e2882f8-b6b9-4650-9daf-f01015ee66a9}} has the weakly Hahn-Banach smooth or Namioka-Phelps property, so does {{formula:5946e922-6e18-47a1-a45a-f8b209b8d40f}} .
r
a86ba761caa726300a706707555ae36a
Although the (simplified) Enskog-Vlasov equation has inherent kinetic advantages for accurate interfacial description, the macroscopic or simplified mesoscopic models (methods) are preferred by taking into account both the model complexity and computational costs. So far, the continuum methods are extensively used. Numerous computational fluid dynamics (CFD) methods have been proposed to solve the Navier-Stokes equation, which include the front-tracking method, the level set method, and the volume-of-fluid method {{cite:92c30cbe879fd8af512814a3634ed1321644c781}}, {{cite:e201d5efe830d3441dae12fe742c4b5e4a0140f5}}. The front-tracking method is usually not able to simulate interface coalescence and break-up phenomena. For the level set and volume-of-fluid methods, the interface reconstruction or reinitialization may introduce some non-physical numerical artifacts. Over the past few decades, the lattice Boltzmann method (LBM) has been developed as an efficient mesoscopic CFD method, which allows a direct mesoscopic modelling of many complex physical problems covering both the single-phase and multiphase flows {{cite:2780f4de8f7d029a65d2f499a3fb71fd547675d3}}, {{cite:95ddcd8e49c90eeb7ca3768c297e371b4e24c5bc}}. Prevalent multiphase LBM models include the colour-gradient model {{cite:e0833638baa6ee03fe2909845fc4faf2dd58d554}}, Shan-Chen model {{cite:f108f0d3a5026f563e9b318aa44778a7ef42d973}}, {{cite:2ac0d3d2f932405a094b338fb2a687c4b3ad657f}}, {{cite:0130baf91f80f0de98253e26af50fb125f2ce860}}, free-energy model {{cite:36f08d58559e77b49a9dd65ff8b72318552deccb}}, {{cite:ac598591397bf08620a50f8f401417c67c13ae88}}, and phase field model {{cite:a1e3ce781482c3c63ca4246bf3cc5aae37149d33}}, {{cite:d3d98dd5a59a4feaa4249ba301d88948e89be1a3}}, {{cite:cb2effd86cf0dd218aa1d83e4a305c6bbc7ffff9}}, which have been successfully applied to simulate a vast majority of multiphase flows at the continuum regime, with the superior advantage that the interfacial fluid dynamics can be automatically captured by incorporating a non-ideal equation of state and the intermolecular force during the particle collision and streaming processes.
m
155322af30b3f8956295f1036d60964f
Synchronization processes have attracted the interest of scientists for centuries and is in the focus of intense research today {{cite:0b424522d98372cea2f678b265297d5c00d213b6}}. This collective phenomena has been observed in biological, chemical, physical, and social systems {{cite:29c5a536e6b083032d854df364b7a6b2d3b4474d}}, {{cite:257058ce14c6351df515f74a7d570d80019b6e68}}. Many works have verified that the dynamics of synchronization depends on the connectivity pattern of networks {{cite:0b424522d98372cea2f678b265297d5c00d213b6}}. For instance, when the natural frequency distributions are unimodal and even, the critical coupling depends on the ratio between the first and second statistical moments of the degree distribution {{cite:035aa112306e32878b9be967104348bb2ba0c080}}, {{cite:b2629e00d677365803a61e8ec8c62148757e5473}}, {{cite:d89155f6def89638ded5a39973c3428aea87fe38}}. In addition, for networks in which there is a positive correlation between the network structure and dynamics, the critical coupling has an inverse dependence on the network average degre {{cite:c9ce60ac2918c775ba66cc8554f216f75dc466ae}}.
i
0a3e597cc87d78a0736175e2a4302ecd
{{cite:877843f990f12aec0666224a9f9e9f43d4fd48b6}} showed that current approaches {{cite:775d42ab0c289f95e683b50828d539eca5ca8817}}, {{cite:1f05d3cb1a6e7b40780e9f97179e22757b8f7f9d}}, which depend on gender direction for the definition of gender bias and directly target it for the mitigation process, end up hiding the bias rather than reduce it. The relative spatial distribution of word vectors before and after debiasing is similar, and bias-related information can still be recovered.
m
e45e1a2d6625e760ac6a6afa37ef7d48
In feature space, autoencoders show an interpolation property. The interpolation between two instances in the latent space produces a smooth semantic warping in data space {{cite:d91db5d0f27d17588da3b81e89de041351cf490f}}. In parameter space, non-linearities are captured as non-continuous attainment regions, e.g. a blob in feature-parameter space where the task fails, surrounded by an area where the task does succeed. Using a sequential importance sampling and re-sampling with attribution prior algorithm ({{cite:197685e9212938bfa2103fa3d3882a180a7b0b37}}, {{cite:4d1257353d4d5049c20473c1a24de41528dbeb0e}}), we can find the smallest possible change to {{formula:3d7ff554-e997-4b7d-b581-6f7bf90ea74a}} for a new trial to succeed with probability {{formula:e5017c0e-8de9-460b-896f-408d13dada91}} .
m
a5508f4bdc50b0353c770d4af4bb80ba
In our paper we use Lifshitz theory {{cite:d69ac8e0aba954f976eec62728413f88bed7c0a3}}, {{cite:53f9f58c0716f9f0db158250538c2fde323ca207}}, {{cite:dd82184c4f2a973a3bf4acf004ed3e63164d3ecb}}, {{cite:67f2711e6d5330c261095c896b08a4a8a42c7b23}} to calculate vacuum forces. This is the theory that agrees best with experiments on the Casimir force {{cite:3b1ff5905203fa87da0b504469824013637a7d90}}, {{cite:d01de9dde3f55f0d089c1a82ec4027f5a0143d8d}}. Lifshitz theory uses the fluctuation–dissipation theorem {{cite:67f2711e6d5330c261095c896b08a4a8a42c7b23}} to relate the quantum stress of the vacuum to classical electromagnetic Green functions. The renormalization is carried out by subtracting from the total Green function the outgoing part such that only the scattered part remains. The physical picture behind this renormalization procedure is the idea that van der Waals or Casimir forces {{cite:d69ac8e0aba954f976eec62728413f88bed7c0a3}} are caused by the scattering of virtual electromagnetic waves at the boundaries or inhomogeneities of media. The outgoing Green function depends on the local dielectric environment, on {{formula:97b837d8-3d8d-4113-8174-96e2f71660ce}} and {{formula:140d9be6-7cda-48a4-b032-039a377eb369}} , and so renormalization is local.
i
bb894f5af9d82db0281a5ce7299194ab
Fig REF -(b-c) compares the PAVER results according to the score decompositions. Local-only and space-only saliency maps look alike in that they both assign higher scores on anomalous patches. However, unlike space-only saliency maps, local-only saliency maps tend to favor object-like patches for both supervised {{cite:13ec44f9d9cfadfa309714efa331570d7d2a9237}} and self-supervised pretraining {{cite:3de152606f15e4d124178b1d385bbaa61e9bb503}}. Time-only saliency focuses on subtle movement in the scene, which helps generate smooth transitions of saliency maps. We present more qualitative examples in Appendix. {{figure:d2339e9b-ea20-4083-900b-2df43081db6c}}
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117e184fecd3fa9681a6627ea005d187
The expression we obtain in the Heisenberg picure for the momentum diffusion constant is an ensemble average over random momentum kicks. We show that this momentum diffusion constant appears also in the rate of photon emission from two localized dipoles in blackbody radiation, and has the same form as the center-of-mass decoherence rate of a particle in a thermal photon environment. Such blackbody-induced decoherence was previously analyzed in a scattering-theory framework {{cite:5bfd6b052cdca9bbee5a3b2a684bccace297b03b}}, wherein which-path information carried by the thermal photons scattering off the particle causes the particle's center of mass to decohere and localize in the position basis. If the characteristic thermal wavelength {{formula:5fc8fd13-877e-4f8a-b4ca-391b0a4f4467}} of the electromagnetic environment is larger than the coherence length {{formula:a2869324-9cce-4379-b4b0-b54064499787}} , each scattered thermal photon only gains partial information about the particle's position (`long-wavelength limit'); for shorter wavelengths a single scatterer has sufficient information to resolve a coherent superposition (`short-wavelength limit'). It will be shown that the momentum diffusion constant is related specifically to the long-wavelength limit of the blackbody-induced center-of-mass decoherence rate.
i
2d3b51fc76078035d3e41c826b88feaa
We further visualized the Grad-CAM outputs for evaluating the explainability and generalizability of the models {{cite:316bdf63f58e931c7cc430566f8eb1b0505dcd0e}}. Our preliminary analysis suggests that the heatmaps from CheXViz models demonstrate higher and focused activations within the lungs, compared to the baseline models as shown in Appendix Figure REF . For future work, we intend to outline a methodology to quantify the generalizability of models for CXR classification using Grad-CAM heatmaps.
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aa648aa4d7cf84a502ead27bb324cae6
Finally, we evaluate the performances of the BSS algorithms (we refer to {{cite:1a948208e1443c7e9dba510f3c0b7e78182028fd}} for the evaluation of the performances of the deformations and spectra estimations). The Amari index {{cite:530f18312c9d66767cd9ec1b80f4ab56e291d98b}} is a measure of divergence between the matrix {{formula:d08a1f3c-c83a-4ddc-8318-e812b7ac3146}} and the identity matrix. The closer to zero the Amari index the better. On the bottom-right of figure REF , we display the evolution of the Amari index through time for each BSS algorithm. In table REF , we also compare the SIR, the SDR (Source to Distortion Ratio {{cite:161dad3dc6fb4c151754b4d59c72fb8c255247f6}}), and the time-averaged Amari index of the BSS algorithms. Those different criteria show that BSS-JEFAS performances are higher than those of SOBI and p-SOBI. Besides, in average, p-SOBI gives a better Amari index than SOBI, which is understandable because it takes into account the nonstationarity of the mixing matrix. Nonetheless, the SIR and SDR of p-SOBI are worse than those of SOBI. Indeed, because this method does not take into account the regularity of {{formula:ade6d8c1-dcd8-4420-9da2-d84008ef4217}} , the connections between slices are sensitive to discontinuities and create distortion in the estimated sources. {{figure:24a57784-9916-4c48-a79e-e5e3fe2791d7}}{{table:cf793c30-ccb2-4aee-9339-bbce1045d430}}
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f3e6a7e3ce4fceccb5b76b53ce4d654b
Another problem of the proposed model is decoupling the training data into disjoint French and English corpora. We would want to get more representative parallel data, which is closer to our data distribution. This can be done by tagging existing French corpus or translating the in-domain data to French, preferably with slots. We might also use OpenSubtitles ({{cite:5cf056b8aa3029309750016f171c6604dbd2b8dd}}, {{cite:5cf056b8aa3029309750016f171c6604dbd2b8dd}}) corpus, which might correlate much better with Alexa data, since it mostly consist of movie dialogues.
d
c7f5c1d998d3ff90be5a52394b1cd3d3
Recent approaches to understanding the black hole information problem using the AdS/CFT correspondence {{cite:4104085f2ea6942f94bc5ea2e3d3963097081907}}, {{cite:b38d23bddeef29c9acaac7f6831d2a4b454a1d62}} emphasize the role of entanglement islands in restoring the unitarity of the underlying dynamics. Models of entanglement islands in higher dimensions are most cleanly realized in the Karch-Randall (KR) braneworld {{cite:8378d212cce6265ffec66e39309a366241178d06}}, {{cite:2cab5e112455f49452fcda5d5272a2df41a9b3d8}}, later refined to the so-called AdS/BCFT correspondence {{cite:f4316009341aef066c4a7b07e9f7386fc203f069}}, {{cite:29ea2a027d24cae48039aa2a878bce88d21c03ce}}. In these models {{cite:9faae14adf765ba290403000da6d8fe4d16d5f61}}, {{cite:fec54f0a5c1a63f9aeddc850914d9fccc5120554}} (see also {{cite:2db3668069236399e69251c684ac84c2add39109}}, {{cite:f45d85cddd47e2691d9ffbf444f9c0a79dc137dd}}, {{cite:e1b9549dd3a95aa5d08153f6f5236ef0514faa62}}, {{cite:71db69e99f5962599094eed18a1e416cb736ce23}}, {{cite:01a169b7adfbd91d8ac984aced3738d2f43f7b18}}, {{cite:9c8e4c0c638a31bd71534247387830289f5cca35}}, {{cite:9f2b77176027b37c9f4eb3cf9cb2ad9aa4807cb6}}, {{cite:0cc03176835143eee6b868d5216aeeed1884aaf1}}, {{cite:043e1e7720e890a5291458d0c29b26aacbe4dea2}}, {{cite:9fbd56c8c68a08f5cd5dedd24041f5a0a49d1fab}}, {{cite:19cc516cdb2943cc93d214ec740c1ebd887a4c48}}, {{cite:8b1d5f2ab805874ecc025310974905fad4453a4d}}, {{cite:7d2dda73cc29212bf825440a259a9ca7c79143a6}}, {{cite:d6a7e0cfb6d59962db5b3daf0ade39a88f7a05b0}}, {{cite:1c64d4f8d30ae525ccaaaab7899f1bc723efaee2}}, {{cite:12f2fb7fae83a22f63d10f522cb74558e8405a3c}}, {{cite:a09c22260c58ec981a46088c47308ba719bda058}}, {{cite:60b41bedf8f5a2fc35472194d87a89799e6bbfe6}}, {{cite:ab7d6da21f86bb7541ff0a82178bd11d265dc7ed}}, {{cite:6e21391fcfb0bfb24b3c872ff2eb42d729c5668d}}, {{cite:eef2d9a737cda62862897272a252ba7bf6f82fdd}}, {{cite:331ff4dfc91c76c458c4977e733ab83e2d9024ba}}, {{cite:f7337cfbc8a89f4ea785fac444aaee8edf788c05}}, {{cite:6e9dde1446593c1be34fcce36b51068fd64dc13b}}, {{cite:11f0f0b2c8a7deeda367e47a1b3e421ba7e56de3}}, {{cite:98944aa1bc3c0cb0ea1e94697d8436e8d0a5880e}}, {{cite:dae85d23a607eff02f0a588020ab13b187e1aadb}}, {{cite:ba13520ada191483ba085d02a0e9109f7ab770e8}}, {{cite:153a89bf04295cb664602fe60e35868b4207900d}}, {{cite:b29cc1a596af76398f198b9c6ad4af322df1b9a4}}, {{cite:3779f9cafb289f985d294ad06b5754bc221f5e50}}, {{cite:4fd2a0f483102dd1c02cfbeb93e39b9377525785}}, {{cite:20bc014a34dafd74a968429712d65be3cc6ce938}} for related studies), the black hole is living on the KR brane and is coupled to a finite temperature bath modeled by a conformal field theory (CFT) on a manifold with a boundary. The bath absorbs the radiation from the black hole and the entanglement island of a subsystem of the bath is the component of its entanglement wedge disconnected from it. The entanglement island lives on the KR brane and contains the black hole interior.
i
5a595dc6b79a063cc8136cb781314dfe
Comparison of the nonlocal strength of different entangled states through their performance in some operational task is not new in literature. In fact, the seminal no-go theorem of John S Bell is one such well studied programme {{cite:14e8dbac0240269868504fa74100d7584ed947b9}}. Bell scenario can be thought as a game involving spatially separated multiple players. Success probability in these games with entangled resources introduces a hierarchy of nonlocal content of different states {{cite:14e8dbac0240269868504fa74100d7584ed947b9}}, {{cite:d5dcdad5a545f3a741b3f87ec92ac696f26699bb}}, {{cite:090db809c38fd571e1d0a977167dd6772edbf1f5}}, {{cite:fff6ce0155cff35b80a625238ac47e8363ec7214}} as well as classifies the type of nonlocality in multipartite states {{cite:7f7a6af0c1d0f93bfe1a19128a7c6d7962291873}}, {{cite:d96772d4eb60b9654e547150eaafa76e70b3a3b9}}. However, the crucial difference between Bell framework to the present one lies in the operational paradigm. Bell nonlocality is a resource under `wirings and classical communication prior to the inputs' {{cite:10619b776d3c0f1e8fef5be8140684116638d8a3}}. Post-input communication can enhance as well as change the type of nonlocality. Although Bell scenario captures some nonlocal aspects of multipartite quantum states (which finds useful applications in device-independent protocols {{cite:ce8aa02fb75340d3e71081cd2666033372f86959}}, {{cite:bc8c3267e2eb180f4a46d9871e630cf50cfc3d27}}, {{cite:7c085ed5e52ca83be570e3c807f6573b7a6951a0}}, {{cite:a63f70fb7a5530f469d57f1168be6fd0b7fbcfe0}}, {{cite:9a368d254f8357052a9bf0c209277bb76c020120}}), its entanglement characteristics are more naturally captured in the operational framework of LOCC, which has been adopted in the present work.
d
63101f1e761c5a73c89b8d88e2845aaa
Mathematical Logic can take many shapes and forms, but its most frequent uses, in Artificial Intelligence and elsewhere, involve a formalism called First Order Predicate Logic (FOPL). FOPL is also the logic most often taught (e.g., {{cite:179b493a3e441b56cc91d6a158401d0bf9554ba5}}, {{cite:b8598322f28151c3f8201d29a0f4f26e487c9827}}). When other logics are involved, these tend to be close variants of FOPL. Formalisation exercises require the student to have a thorough understanding of the meaning of FOPL. Formalisation is an interesting candidate for scrutiny because it taps into the students' understanding of various aspects of logic, and there are a number of studies dedicated to this problem (see REF ).
i
cb8e0f068ba2a4e2deb0f3c80fcaf3e2
Based on this observation, we propose to modify DeepSec accordingly to evaluate whether the optimisation problem and the relative solution proposed by {{cite:f4689883632c330e667338cee543f773dfd0595f}} can improve the robustness of deep learning models against adversarial attacks. In addition, we focus on the CIFAR-10 {{cite:d207503479468f7387e2aa80e4aa321663064e5b}} dataset because existing methods have already achieved a state-of-the-art accuracy near 100% on the MNIST {{cite:9d9bd86375878715c5d547f2a6440505ebbb6f03}} dataset.
m
cd45fab3625f5effa911dd71b3536114
As {{cite:49c12a55366bf4b282a404b1673146a3484928d6}} point out, the models of {{cite:2edc8073bc94aa439feaaf65eab0c2de912fa619}}, which are an application of those of {{cite:a8cf8addab11065d6a110bfd3cde2519f2fe93b1}} to the planetary regime, are premised on the assumption that, as for CTTSs, the H {{formula:3500dcb9-7118-4776-a43d-5fe8c8fcf5f7}} emission originates in the column(s) of gas accreting onto the planet. Because the heating mechanism of these columns is highly unknown {{cite:6837337f889560a3378662fcbaccb474870f1f9d}}, these models are parametrised by a maximal temperature {{formula:e5bf7186-0a12-4cdb-87da-e395f9d05a3e}} in the column. {{cite:2edc8073bc94aa439feaaf65eab0c2de912fa619}} do not consider emission from the post-shock region, which is appropriate for the stellar case. Thus in {{cite:41731e05a0eaa9fc424570ad88709ec8e908ca30}}, {{cite:49c12a55366bf4b282a404b1673146a3484928d6}}, {{cite:2f10bb7574d984d6bf9c826786fdc7a3c9098cba}}, and this work, we are exploring a complementary approach. Namely, we are calculating the emission of H {{formula:d931665e-675f-4a62-9357-642c8aca4f23}} and other lines by the postshock gas, showing that it can be a detectable source, and investigating here the absorption by the accreting material.
d
19d42bc2b4a74cde6e53d3ef0b0f6206
Control with learning has been considered in many application areas; see for example {{cite:fce0d1959f161760152c327ee21c15608dd6bde1}}, in which Dean et al. apply adaptive control techniques to learn and control linear systems on the fly; the related {{cite:e2d957704beb5d80efca07d73700a129574dd71e}}; as well as {{cite:ffc681829a36254922e3331d80b748766af8f6fc}}, in which Abeille and Lazaric use Thompson Sampling in the same setting. Online learning and control can further be expanded to other complementary problems including the study of tracking adversarial targets {{cite:b95087a0fccbe520d9fec60d833cea26bd607ad6}} and derivative-free optimisation for the linear quadratic problem {{cite:0f62a88d00b9a3eda9ad02270933cca823c10809}}.
i
008f847b25a042a091a81bef83fecaaa
Recent advances in adversarial machine learning {{cite:9c92ef279c36575e9a6e44e41313fb394fc6cdfa}}, {{cite:1defdbce0c113b4a83134251e208e093973b5bb3}} have investigated robustness to random initialization based perturbations, however, to our knowledge, no previous study investigates the effect of random-seeds and its connection on model interpretation. Our study analyzed the inherent lack of robustness in deep neural models for NLP. Recent studies cast doubt on the consistency and correlations of several types of interpretations {{cite:6abaab5c559761b4afcde1928ac8092a45f98504}}, {{cite:fc08c3473d7c9b3f604b44920ae5d5b70d60fb1b}}, {{cite:f96d2f4072ea047b3f3ce7dec72e4710768a8785}}. We hypothesise that some of these issues are due to the inherent instability of the deep neural models to random-seed base perturbations. Our analysis (in Section ) leads to the hypothesis that models with different instantiations may use completely different optimization paths. The issue of variance in all black-box interpretation methods over different seeds will continue to persist until the models are fully robust to random-seed based perturbations. Our work however, doesn't provide insights into instabilities of different layers of the models. We hypothesise that it might further uncover the reasons for the relatively lower correlation between different black-box interpretation methods as these are effectively based off on different layers and granularity.
d
43bb01a11b0efa5c60bdfae72b841add
This is a direct result of combining gravitation theory with uncertainty relation of quantum mechanics. It is immediately recognised that {{formula:1fdd3a2f-9de2-48ad-ad1d-8dc903e6fd4e}} is the Plank length, and the relation (REF ) implies that space-time at the Plank scale consists of what-so-called quantum foam {{cite:cba003e0e6a02a537a1574269bb6749f733c893d}}. First described by J. Wheeler and later studied in detail by S. Hawking {{cite:f70b6546968a7b77f39def49525347f71d236118}}, this quantum foam consists of a sea of virtual black holes, which Hawking described them as bubbles. These bubbles make the space-time posses a large second Betti number. Moreover, in his paper, Hawking argued that the space-time is simply connected and admits a topology {{formula:b36e74dc-121d-4190-90b9-a04fa24112b5}} or {{formula:656a3b31-2123-49a8-813d-98a82b50cce4}} ...etc.
i
abc9667611a025deb7cfd48dbcd712c1
Substantial efforts have been invested in promoting the progress of OS networks {{cite:41218ce4b41518fefa6f38b82b348b2af56709de}}. The Open-Air-Interface (OAI) community founded in Europe exploited a fully-fledged fourth generation (4G) protocol stack based on commercial off-the-shelf (COTS) hardware. As a further advance, the Open5G community founded in China developed the concepts, technologies and platforms of open-source fifth generation (5G). The O-RAN alliance {{cite:4f86c725c3b88c901fa452deabf78910f63c5d28}} founded by the global industry supported by academics has endeavoured to evolve RANs around the world. Additionally, the Linux Foundation (LF) launched the open network automation platform (ONAP) for orchestration. As for virtualization, the open platform of NFV (OPNFV) was conceived. Recently, there have also been a few open-source efforts on MEC {{cite:a1b26d02926f019f85e9ca470eb398f13f7d2e37}}. For example, the Akraino project built by LF offers a pair of blueprints, namely the 5G MEC/slice and the micro-MEC system, but unfortunately it remains focused on the virtualization layer of the MEC reference architecture. Based on all these efforts, we present a new paradigm for developing an all-encompassing open-source MEC (OS-MEC) scheme.
i
526a3570c5d9d476eba82af584c0857f
Intuitively, one would think that populating the memory with some reasonable criteria should be desirable. However, recent studies {{cite:f51b34366e371c0fc032c79bb8cb46daca9591aa}}, {{cite:f869b53de8ef2d3773d9cad0e561e235e1f38488}}, {{cite:30553b996a4687cab73c82a41d9276705c24c518}} show that when populating the memory by focusing solely on sample diversity or class balance, random selection of elements ends up performing nearly or just as well without adding an extra computation. How can we go about finding such criteria?
i
6ad2efb576169bfae9818d5d3aa73025
Another limitation of our approach is that its benefits are demonstrated empirically. It is an inevitable consequence of a lack of any theoretical guarantees for underlying AT frameworks. An interesting direction of future work is to explore whether any theoretical guarantees can be derived for anisotropic shaped noise distributions in SNAP by building upon the recent developments in randomized smoothing {{cite:2b9aa0bd795fe462b4ae82a37ca3a44290292b0f}}, {{cite:4b634f03a681ac36fa52c3ffe4fb1d44062ac1a6}}. This could be a potential avenue for bridging the gap between certification bounds and empirical adversarial accuracy.
d
84d77d7b9cf7f0bb6ccbb70fbcaca518
There are at least three advantages to consider conditional quantiles instead of the conditional mean in a regression setting. First, quantile regression, in particular median regression, provides an alternative and complement to mean regression while being resistant to outliers in responses; in addition, quantile regression is more efficient than mean regression when the error follows a distribution with heavy tails. Second, quantile regression is capable of dealing with heteroscedasticity, the situation in which variances depend on certain covariates. More importantly, quantile regression can give a more complete picture on how the responses are affected by covariates, particularly the tail behavior of the response conditional on covariates, for example in economic and actuaries. For more background on quantile regression, see the monograph by {{cite:a5136e527d1593d335ef4e9f392c1fff57b41f07}}.
i
03884d867b5fba3e05bc9c1ad2281885
The value of matter-antimatter asymmetry has been measured independently by BBN {{cite:d8ba281fa96f99a47b9385eb3f1a87c58eede695}} and the Planck {{cite:f4396f8ea34b42bf30071a48786f7f84004da2f1}} to {{formula:0da6e215-7fc1-4663-9251-f6d520fd829c}}
i
727aa33d6f23ca10dafd0449f8039aeb
For long timescales, the curves do not have the slope {{formula:93ba510d-6199-4dee-aa39-c23049aa2d65}} (corresponding to dimension {{formula:c1d5b4ff-d805-41b6-8078-7a6d61788ab6}} , the value for Gaussian random walks {{cite:ee12d6cea88cf047217d9d0633860a9147ff4ece}}), but are somewhat steeper. This is to be expected since the energy of an orbit changes through relaxation and this process is much slower; hence the angular momentum evolution is bounded unlike a true random walk, and cannot be described by simple diffusion, even for long timescales. There is a marked transition to a more coherent motion as indicated by a decrease in the slope. The point of this transition can be determined with reasonable accuracy for a given star, but it is not common for all stars. Even though the slope decreases, it never becomes zero; hence the evolution of angular momentum is never ballistic ({{formula:6ea4bb6a-6e95-46f7-9ecd-05f882276ce4}} ). This slope can also be determined with reasonable accuracy for a given star, but varies from star to star. Looking at the eccentricity evolution of the stars reveals that the transition point is later for the stars that moved into {{formula:24751607-ed2a-4f6f-b820-4794e4981304}} region where precession is slow. This is in harmony with the expectation that for more slowly precessing stars, the coherent torques last longer. The slope increases again for short timescales, but much before the period of the stars is reached. This randomization of the torques is a result of the stochastic nature of the processes that develop the torques and dominates the shorter timescale randomization that would result from orbital motion, at least down to the timescales we resolve.
r
0c1036b5d48c66519f69e93f222c24da
which aims at an approximate Lyapunov function {{formula:7c4ebff8-e27f-4269-a667-b60e1e50282e}} satisfying {{formula:ffe574e4-d8ad-41c2-946e-9dfc5e6148e7}} and {{formula:45025385-f8c3-47fa-8c0b-0cce20aac10f}} for all {{formula:d6b24bf9-f3ad-439c-9159-64dbc9ccab75}} . In {{cite:928a532e63e8e45f79d50b0d3382c362d4e9d21b}}, the following risk function is used: {{formula:c336d1e1-aeb7-4256-8c2c-0548d1cdf8c5}}
m
63ffa55ab914daa98e95c992cfc263cd
In this paper, we investigate the PEE aspects of the holographic BCFT setups in the context with entanglement islands, by combining two interesting dualities developed recently. The first duality is the triality of the AdS/BCFT setup inspired by the recent research of the black hole information paradox {{cite:749cea45d0f4c00822846637e0a751e2660a65f6}}, {{cite:1b40888a7db778f4c8969d86abdcae063f954de0}}, {{cite:93098e196b819ee7864a0bed412f7e531211cfb3}}, {{cite:c6e4c7776471de0b186a6e1eb3634fd59db9db0e}}, in which a {{formula:96e47cdc-2b12-404e-8349-62b529d63289}} dimensional BCFT can not only be described using an Einstein gravity on an asymptotically AdS{{formula:822fcce8-12c5-40ba-92b0-ed00f2b62f67}} space containing an ETW brane by the usual AdS/BCFT correspondence, but also can be viewed from the so-called brane perspective through braneworld holography, that is, described as a non-gravitational CFT{{formula:f6b761b1-eadf-4bae-a525-4adcab6f2b63}} glued to a gravity theory on the AdS{{formula:893e245a-e8f3-4c81-b6ba-9fe63608c6d8}} space. In particular, it is possible to design the holographic BCFT setup such that the effective theory on the brane is describing the black hole physics. Another duality is the “PEE=CFF” prescription proposed in {{cite:6eb0d717df6fbc167d3ee6322f809da5b6f0723b}}, where in the framework of holographic bit threads, the partial entanglement entropy (PEE) is explicitly identified as the component flow flux (CFF) in a locking bit thread configuration. Combining these two insights, we study the entanglement details between a set of specified subsystems in the presence of the entanglement island.
d
de6319393a30042397be23b7b719b366
To demonstrate the FQNGD algorithm for QFL, we perform the binary and ternary classification tasks on the standard MNIST dataset {{cite:d25f2f08d6e1825b8aec8d2f6ceb61e2ff1c5bdf}}, specifically digits {{formula:f7c99a42-f76f-4853-9e82-3ec9c6d7ebf4}} for the binary task and {{formula:b589eda8-5515-46e7-81f0-4420b8402c12}} for the ternary one. There are a total of 11379 training data and 1924 test data for the binary classification, and 19138 training data and 3173 test data are assigned for the ternary classification. As for the setup of QFL in our experiments, the QFL system consists of 6 identically local VQC participants, each of which owns the same amount of training data. The test data are stored in the global part and are used to evaluate the classification performance. {{figure:7cb703e1-1eff-459b-96fb-f63bc5b83de6}}
r
b9fdacc585a41b975990786183e0b024
For example, companies such as Apple, Google, and Waze offer GPS services make route recommendations to many drivers simultaneously. The time it takes a driver to reach its destination is in part a function of the other drivers on the road. It is established that certain network configurations can result in a prisoner's dilemma whereby individual drivers taking the fastest route makes all of the drivers worse off {{cite:fe69ddf00344657cd211d6ae78cbfb6210e870c6}}. There is evidence that this phenomenon is currently contributing to traffic congestion in the real world {{cite:54a3af42e0a2129db735018c1fc5b09ce8d040fb}}. A GPS application making recommendations in a traffic network may have to choose between making recommendations that are single agent optimal, social welfare efficient, or Pareto efficient. To the best of the authors' knowledge, no major GPS company has addressed this problem in the literature or otherwise. Our work can have an immediate impact on real world recourse problems such as this.
d
1fb1d4b44cefc85566a8fb1ce5a69ebf
We trained the ML-CRNN using the loss in Eq. (REF ) and the Adam optimizer {{cite:d98432e77ef77f1a3d74748d4375b6e8a74631dd}}, using a subset of the training data as the validation set. Training was stopped when the loss reached convergence on the validation set, and the epistemic covariance on the training set became negligible. The length of the temporal sequences that are fed to the NN during training is {{formula:7b2d6c64-d182-4469-add2-d1f62cb3ddc3}} ({{formula:c6a78de6-d14a-49d3-b598-63c4767facd8}}  s). During the evaluation, instead, the predictions are obtained by inputting a new radar frame in the ML-CRNN as soon as it becomes available. The ML-CRNN then uses the hidden state, {{formula:59e671ea-399e-4100-91be-ccbc7b11397f}} , and the current input to compute the prediction, similarly to how Bayesian filtering methods operate. The following metrics were used to evaluate the tracking error: (i) root mean square error (RMSE) and (ii) localization error outage, {{formula:f73b9566-1bea-4201-8efb-635f775b5fea}}.
r
da968bd5fbd7030dc6b96a1cd45e97b9
In this article we present a new approach to the measurement of jet quenching, based on the semi-inclusive distribution of charged jets recoiling from a high-{{formula:a869ab86-3f06-4b19-9d26-c4af25a1be70}} charged hadron trigger (“h-jet” coincidence) in central (0-10%) Pb–Pb collisions at {{formula:3591133b-4d30-4877-a0d9-12695dc78694}} = 2.76 TeV. Jets are reconstructed using charged particle tracks with the {{formula:0f050851-e31a-4408-9093-0af961bd4c27}} {{cite:a8ca35de3251e7b907c710140dc173eb9d3adf6c}} and anti-{{formula:25ca2878-4dda-412c-bbb6-cb3275e9f15b}} algorithms {{cite:cbc32172c8276e3e7720e0f9bd76a1d56dfad4e7}}, with infrared cutoff for tracks {{formula:d204d3a5-ecaa-47a2-9d6e-bd9f795e8c27}} {{formula:74a5defe-cc23-44ac-8d73-017319a8387d}} . Uncorrelated background to the recoil jet signal is corrected solely at the level of ensemble-averaged distributions, without event-by-event discrimination of jet signal from background, using a technique that exploits the phenomenology of jet production in QCD. The correction is carried out using an unfolding technique. This approach enables the collinear-safe measurement in heavy-ion collisions of reconstructed jets with low infrared cutoff over a wide range of jet energy and {{formula:8bce957d-30d6-41b0-a83f-36f7abed1fc7}} . Recoil jet distributions, which are differential in {{formula:5e72e850-9431-4edd-b255-bce7bfc81179}} and in azimuthal angle relative to the trigger axis, are reported for {{formula:dfad2537-e79b-46c7-a966-a4e6f03155a6}} = 0.2, 0.4 and 0.5, over the range {{formula:cb9e8f34-1b10-45fe-9801-7813ef78fb11}} {{formula:aebba207-9c85-4137-8ea3-bb7907233625}} .
i
1559561f30525d996bbbb533fbe3f6da
We remark that there are three orthogonal research directions towards the investigation of distributed VQAs. First, instead of employing the synchronization approach used in QUDIO, it is intrigued to design asynchronous distributed-VQAs schemes with convergence guarantees, which may further reduce the communication overhead and maximally utilize quantum processors with distinct qualities. Second, with the aim of reducing the runtime cost, it is important to integrate the effective measurement reduction algorithms with QUDIO and other distributed VQAs. Repressive examples contain grouping compatible operators {{cite:6242f42c9a4c7670efeba95dd71ea6a2894be931}}, {{cite:d43edd2369c0d87baf16e89b12864d6a9685eb68}} and classical-shadows based methods {{cite:4e2a402d9a9f0da80c8f3194b5ed9812294aceed}}, {{cite:fbba56725ebad7c56bd300af8ac154110d1b0b0a}}. Last, a promising direction is combining QUDIO with a recent work {{cite:6e761f398e9f7a7726eaa305a06443695630f59e}}, which splits the input quantum circuits into several individual quantum circuits with distributed optimization.
d
cac38d96c88c2383537374d2c4d5e7b2
Cross-Seasonal Relocalization. Finally, we show how Deja-Vu can be used to perform 6-DOF cross-seasonal relocalization. In practice this means that localization can be performed in previously unseen conditions without requiring additional training or fine-tuning. In order to demonstrate this, PoseNet {{cite:5b0dc86a1f04360d31b0b57604fb7a66a0dff4e1}} is trained on a subset of RobotCar sequences from one season and evaluated on a corresponding subset from a different season.
r
d0257c0ce8e6d260a6e3e7d02d17a47a
To tackle this issue, the reconfigurable intelligent surface (RIS) has emerged as a potential cost-efficient technique by creating favorable propagation conditions from BSs and users {{cite:af26ba6cb58a34305c760a29e1eae154175dfa8b}}, {{cite:d5bfd4d7c0e08420892f0b61b7ddaaae408cac9b}}. Benefited from a large number of RIS elements whose phase shifts are controlled by simple programmable PIN diodes, RISs can reflect signals and generate directional beams from BSs to users {{cite:9ddad0d1547dae2b419412888042627b47227b74}}. Unlike large-scale phased array antennas in the cell-free system enabled by phase shifters with inevitable power consumption, RIS requires no extra hardware implementation, such as complex digital phase shift circuits, thus greatly saving the energy consumption and complexity for signal processing {{cite:6541fb07cc1ca055b792f87aaa84d68f10910bdb}}. Hence, compared with the conventional cell-free systems, a lower level of power consumption is required to achieve the same quality-of-services (QoS). In other words, RIS provides a new dimension for cell-free systems to enhance the energy efficiency of the cell-free systems.
i
72f4fba3aec5e86a00325c6b3b8e8d6c
{{formula:37f39afc-568b-4dc4-8a29-4b4ec2d3cabb}} -LaYH{{formula:f2262a1b-7748-4802-ab3d-b1738569c6dc}} exhibits a higher {{formula:22c2a8a4-3fa6-4f78-9ccd-08f7e12b4681}}  (203 K at 180 GPa)  {{cite:9f176476b6b99baa17fa681b23f14fb542e06a3d}} However, for this structure, the imaginary phonon modes appeared as shown in Fig. REF , implying structural instability at least within the extent of the harmonic approximation. As shown in Fig. REF , another structure, {{formula:7bb2753a-8b85-4d27-8a6c-afdf61316ae9}} -LaYH{{formula:e9b55a1a-03f4-4d1f-9ab3-7462ba2c075d}} , is predicted to be more stable than {{formula:82768723-1b96-484a-be7c-0ac072b5da94}} . However, for both structures, the imaginary modes are found, without vanishing even on applying further pressure. {{figure:3056cdf2-03c0-4587-be75-aff439874827}}
d
60497ac991dd05231d6376f8da10a338
It will be very nice if this conjecture holds for {{formula:5f093fb9-5cb5-48b8-98c3-04bc893d889a}} . Recently Ichim, Katthän and Moyano-Fernández proved that Stanley's Conjecture holds for all factors {{formula:c8f68a21-b230-4993-89e2-114b2cdadf36}} as above if and only if it holds for their polarizations {{cite:d9dfd6d30b5450e15f08cacbc1d7b45fbf81de8d}}. Thus we may restrict to the case when {{formula:26bc9387-c31d-4c66-b7c7-4cd8bcec06db}} are squarefree monomial ideals. Unfortunately, there are few results in this case in spite of the many papers appeared on this subject (see {{cite:ed504dc9008b4b0130719926ab245412db140ce6}}, {{cite:592c456e571ea6da26f8ab5b5aabede28db0464a}}, {{cite:b531bc05b20fca2354fef6aec4477f74cf723c41}}, {{cite:e2bf80641b97bfe0fcf07b8921597cac2bf6862f}}, {{cite:9f78e1f9b694ab3794b0d5196a04e45d902286dd}}, {{cite:b3cbf56650f228f46651bdd623ec4362b5d8aae0}}, {{cite:de31dad5612b92ebe090a9dc02b398442c71d7d0}}). It is the purpose of our paper to study what these few results say in the non squarefree case using {{cite:d9dfd6d30b5450e15f08cacbc1d7b45fbf81de8d}}. We use here the lower bound given by Proposition REF (see Theorems REF , REF and Proposition REF ).
i
dc80a3decffb4f2981ecbab924b8f7e9
where {{formula:70be3b13-b504-4a6a-bad8-4da4d4a6a7d8}} represent Cartesian indices, {{formula:c2999aab-07ff-466a-94cd-cfe9976cf4ae}} , and {{formula:026e758f-0499-4cd0-9425-f7456a40e8c5}} is the linear conductivity tensor. In the multiscale Maxwell-TDDFT method, we use TDDFT {{cite:806a145ec1bbd0a709385c7ef74c5f84736ebd99}} in the time-domain calculation {{cite:8f758c409fac3807a190d2e9323b635df5f00316}}, {{cite:b06103467e30162ed2312dcd253c307f0bc3c97e}} to relate {{formula:1dded5eb-1d68-4c2c-8d62-3c96e384d9e5}} with {{formula:08ee0fad-9871-44f8-abf6-6f016b6e4085}} . We retain the locality in the relation, assuming that the electric current density at {{formula:2034d99d-512d-4533-b32f-f658576fd7d7}} , {{formula:70681c39-4157-4b49-aa93-a7e2b09f89b6}} , is determined by the vector potential at the same position, {{formula:1dfe0108-d5b0-459b-8fd0-d1b85b3a8517}} . We also assume that the macroscopic field {{formula:d51784d0-9f32-461b-90eb-a442abbbdd94}} is sufficiently smooth at the atomic scale so that the microscopic electronic motion can be treated in the dipole approximation. Namely, at each position {{formula:3c5f35cc-318e-4910-a62a-529cd076c0d3}} , we consider a microscopic electronic system that is infinitely periodic and is subject to the spatially uniform electric field given by {{formula:0d5a7b19-5d40-49a6-a297-5852f1b4506c}} .
m
615a82fee5a4e5ea9a4224bc69e1f7a0
Grad-CAM++ (G+) {{cite:0590977f35fa52c6c5b931b7259128c003d015f8}} is an extension of Grad-CAM combining the positive partial derivatives of feature maps of a convolutional layer with a weighted special class score. The weights {{formula:5783e57b-3f78-4666-9b68-02d7391fc6d9}} associated to each feature map is computed as follow : {{formula:c25f592b-d12e-4b0d-860f-72b65bca5439}}
m
29baa79d9aac0a03fb5c9f88e7706a89
Lemma 37 (LCU Lemma {{cite:97db056ae6946426890c78000260d07f66896ad9}}, {{cite:c83b61d2ce1d7dd3bf13f91158b80ea16ac135e7}}, {{cite:6b020c29d811123fafc2caaeb85d25af84e715de}}) Let {{formula:3cdcb156-bcf3-42a0-af84-77cd239578f2}} be unitaries on a Hilbert space {{formula:774cd894-b6da-4187-a81c-18ad91b98813}} , and {{formula:15158053-8d6f-4169-a63f-12f145363690}} , where {{formula:47c2b0e7-220d-400b-9ee1-31e05fe94649}} . Let {{formula:ced170dc-75e1-4578-95bb-6aa22dd08ef7}} and {{formula:4ae909cb-08d1-4665-b135-f469415b9501}} be a unitary such that {{formula:d8ef9e31-d5d0-4f45-8f30-c352c2fcff7f}} . Then {{formula:4e197f85-bee7-4171-ad01-15ee741cd8d4}} , i.e., for every {{formula:48afdeda-a158-4fe3-ad86-7b494006d980}} we have {{formula:df5d0917-0b01-4c19-b3de-c212e5b7483b}} , where {{formula:85dfd0cc-ab52-4680-bdc4-27a561322d96}} . {{formula:c6a335fe-05a4-4344-9374-60c6e6fcbe1b}}
r
73c2b4b9d0899af87db2362a8ec7c975
Learning to reweight training samples are widely used in Curriculum learning {{cite:ea1fbb3a9b49d70d8c64510feb5fcd6eec7a32e0}}, hard-sample Mining {{cite:777919b6d087cf310c04b02b51e60870d99fff93}}, domain generalization {{cite:1326775f9d997a26cc9a234a48498adef0b47aa1}}, {{cite:db3a83928ab5f38e80444319bdec0d3bf5d3e181}}, {{cite:04aca44b2a7b51102fd3d7da0048ffba64bb99ff}}, debiasing {{cite:4326142786f982d7ae93503008d067884bec3b66}}, model calibration {{cite:9c441e1e9986e1f197274d273a05b52929534f05}}, adversarial defense {{cite:d562a565f40cbee8a4475321391d253adf66af7d}}, etc. Our method is closely related to Focal Loss {{cite:777919b6d087cf310c04b02b51e60870d99fff93}} and worst case optimization {{cite:1326775f9d997a26cc9a234a48498adef0b47aa1}}. {{cite:9c441e1e9986e1f197274d273a05b52929534f05}} points out that focal loss could prevent model from over-confidence prediction. {{cite:1326775f9d997a26cc9a234a48498adef0b47aa1}} improves the model generalization ability by assigning more weights for groups with worst performance. By focusing on the uncertain samples identified by local and global models, FLIT makes the local training more consistent across clients, and eventually leads to better federated learning performance.
m
b4b7f9a8dc16d59784906662038aa60c
In this work we address the aforementioned challenges using an interactive theorem prover (ITP). In particular, we use the ITP Isabelle/HOL {{cite:cc5db4b364535190d004dbf2f45d51ce52d31117}}, which implements a formal mathematical system combining higher-order logic (HOL) and simple type theory. Our first contribution is that we formally specify an abstract syntax for the temporal fragment of PDDL 2.1 in Isabelle/HOL and, based on that, formalise its semantics. Compared to a pen-and-paper semantics, this has the advantage that it removes any room for ambiguity. Furthermore, during formalising this fragment of PDDL, we found that certain parts of the semantics as specified by {{cite:c1ae2912be03e8b367ba92e50ccd854c63c592d3}} could be simplified. As our second contribution, we implement an executable plan validator for the temporal part of PDDL2.1 and we formally verify, using Isabelle/HOL, that it correctly implements the semantics which we formalised. Our validator checks
i
696186afc4d3bc09f97866c40f296392
This work was supported by the Italian Space Agency ASI under contract 2018-24-HH.0 in support of the Italian participation to the Gaia mission, and by the grant Astrometric Science and Technology Roadmap for Astrophysics (ASTRA) from the Italian Ministry of Foreign Affairs and International Cooperation (MAECI). The numerical simulations were executed at the CINECA supercomputing centre. A.G.B. is thankful to the Astrophysical Observatory of Torino for their warm hospitality during his short-term visits. A.G.B. is also grateful to Lennart Lindegren (Lund Observatory) for kind permission to use his drawing software. This research made use of NASA's Astrophysics Data System. Diagrams were produced using the astronomy data visualisation software TOPCAT {{cite:208e81b5f360d694c5797d97a5480057eb887f9a}}.
d
343bc1c257ca9a3f9b37d2873e188065
where {{formula:0715e2ab-1aba-41a9-81a3-4f74e53cf14d}} and {{formula:d9e497de-7d28-4092-a44c-8210409fcf0b}} being the decay constant of {{formula:19805e82-554c-4f1c-a15f-b94206092c85}} meson {{cite:0811acd649e754cba45f97294811b0627912c711}}. Considering the heavy quark limit and chiral symmetry, the coupling constants between the light meson and charmed meson pair have the following relationship {{cite:a230fafb8acb969b904fa3a260fef248032c990e}}, {{cite:dc8d67b6eceee8b6318a4c629372f0764f4edd87}}, {{cite:41957c0ac604764bd2399ce6f156c52f52ee6564}}, {{cite:bb6436fd67fbbfb3f7394224b45e0a85f7993948}} {{formula:354b3d4e-a9eb-4ba4-93a5-000939ad0a4e}}
r
5468718b3c84e1134b7bfda5464ff958
We first compare performances of three single-hand methods, i.e. Boukhayma et al.  {{cite:ce7bf71f5585057dad7c47437671c2400afe1013}}, Pose2Mesh {{cite:49971e1041d53bfea65dbc92962e02db3dd0f844}} and BiHand {{cite:09eec82bda1c0e13f437dc26aa4026f01be7a29a}}. Our approach significantly outperforms all the state-of-the-art single-hand approaches. On the “IH26M-ALL” split, compared with BiHand {{cite:09eec82bda1c0e13f437dc26aa4026f01be7a29a}}, our model reduces MPJPE from {{formula:bd66d163-37a9-41d4-a03a-41dc6a72ffea}} mm to {{formula:fbb6da1e-4289-493d-8f95-bd3458ef9425}} mm, resulting in as much as {{formula:b4302b0a-4f30-4d75-a357-63640d75e11f}} error reduction. And in the more challenging “IH26M-Inter” split, our approach obtains about {{formula:52310bc5-5622-4106-9508-a34afea65773}} accuracy improvement. This shows existing single-hand pose estimators do not handle heavy hand-hand occlusions and are easily confused by the other distracting hand.
m
faed5e04a08711d3b1cc2c0ea08a1496
Additionally, comparing the difference of nuclear modification effect between {{formula:930bc93b-d05b-4241-a5a6-af59811362a1}} -jet and {{formula:591c660a-2fbf-44be-968a-faf6b09c52c8}} -jet is of importance to study the mass hierarchy of jet quenching. The comparisons of the {{formula:65f81311-b813-435e-ae16-3008ca5e708e}} distributions between {{formula:9dc83f4e-ab32-4f76-ae87-7b4ee30be0c1}} -jet and {{formula:f0aa502d-6775-4211-aeb0-b93e7c9d6bc9}} -jet are presented in Fig. REF . In p+p collisions, we can see that the {{formula:60488629-aeee-4bf4-9071-e627b5bbc189}} distributions of {{formula:ec3fdd54-2754-47ec-81b4-01de561414b5}} -jet have a visible peak near {{formula:953e81cb-2bb8-41f7-b543-dde8f7e39e5f}} in both of the two {{formula:abc9d4db-4e4e-4bd2-8031-890b363b9f99}} intervals {{formula:287101c5-5a6b-44c1-8ffb-5ea8527d9643}} GeV/c and {{formula:d73bd139-99e4-4c4b-a846-c88e762f1902}} GeV/c, which are much higher than the peak of {{formula:52c7df55-3ac3-4421-9b26-01637835a361}} -jet for the same {{formula:9c68938a-c461-489f-87b3-96f60016874f}} interval. Especially, the peak of {{formula:6833b41d-128b-46c1-bca6-500a3d376c64}} -jet near {{formula:1a864a8d-0f97-4d98-9510-accca724e65d}} in the {{formula:5bd76af8-10f5-4aee-a8eb-7899daf233ca}} interval {{formula:9e187e38-9cea-4923-a83d-36f3ef724850}} GeV/c in p+p collisions is disappeared. These results indicate that the bottom quark jet may have harder fragmentation function compared to that of charm jet, which is consistent with the previous theoretical studies on the fragmentation function of heavy quarks {{cite:9c01a0e15739567095be8fd19b837292e636eae4}}, {{cite:d311cd7c6e9340d0e12436bd869ddd3a4c46800e}}. Since {{formula:c0beea48-2283-47d9-b0ba-bbe3a9245798}} represent the momentum fraction of heavy quarks in jets, the centralized distribution near {{formula:260e5331-a11c-4788-b8ef-fa7269233200}} means that less radiation of bottom quark during the vacuum parton shower compared to charm. Hence we argue that the comparison of {{formula:1783dd16-8c1b-4633-97fc-37e0a25164b6}} distributions of charm and bottom jets within the same kinematic region may provide a complementary test of the dead-cone effect to the recent ALICE measurements {{cite:ea7bcc4091b10c6e6dcebe3e1f7de6e4ed825557}}. As for the {{formula:122831a8-71be-4c0a-a5f6-9d35abb7db6d}} distributions in Pb+Pb collisions, we find an overall shift from larger to smaller {{formula:484e13d1-39d3-4b8a-b418-5982d5996cac}} values compared to their p+p baseline both for {{formula:37feaa75-c231-4451-b9cd-0614d1d24719}} -jet and {{formula:6232e853-3dbc-4cd6-983d-1c44170306f9}} -jet. In addition, we can observe significantly larger values of the ratio PbPb/pp of {{formula:d04b6a0b-0358-4dea-9731-5a33a5821645}} -jet compared to {{formula:e0877469-68df-465d-afdb-3f1591f5a9db}} -jet in both the two {{formula:f734eecd-5790-48a5-af31-8b8f91dca670}} intervals. Due to the larger mass, the bottom quarks should loss less energy than charm when passing through the QGP medium, {{formula:14d02cc7-78bf-4c5d-a649-a42465978ed2}} -jet may have weaker shift of {{formula:cfa77d28-9357-45ba-a558-b6c270a5cf7c}} compared to {{formula:83ebf9ff-0b39-4d78-bf01-3421f4e743b2}} -jet. Nevertheless, we observe that the initial {{formula:7be264b0-ac87-4aa2-95a3-6b47aff8be5d}} distributions of {{formula:56b0ab57-6fac-4fc9-9299-8a869fa04dc1}} -jet seems much steeper than the one of {{formula:5878bc51-adb7-4fe5-83eb-1f47fdc7c5b2}} -jet in both the two {{formula:ef415ddb-d661-44b1-b5d1-3ac8b424cffd}} intervals, which lead to much less {{formula:78a79107-2281-4a96-90d8-f67bce3d96e4}} -jet events distributed at the region of {{formula:47d52ebf-e430-4672-8b0c-a7a0913d1fc5}} compared to {{formula:5390b737-f87e-4539-929b-efae4a5e6942}} -jet. In this way, the ratio of PbPb/pp at {{formula:148dd17a-ae13-44a6-904a-1af2295e4dac}} may be more sensitive to the shift of {{formula:76787ee3-5bb8-4019-b9e2-99e5d7b312ce}} from larger values. Therefore, eventually we can observe that the ratio of PbPb/pp of {{formula:51e3df93-4df9-4f12-8aa0-46819aa4c05a}} distribution of {{formula:8d21eb16-f109-4d16-bfd5-d03ea615590f}} -jet is more evident compared to that of {{formula:215d8101-f4a9-4d8a-aa33-c544ac75390b}} -jet. Note that similar results have also been obtained in the previous studies, such as the medium modification of the splitting functions {{cite:ab3d513fbaa163ca55a545e31f35cf4c8a764717}} and radial profiles {{cite:7f576bd2e94334344396c25d93c2d158af163988}} of heavy quark jets. No doubt that may be of interest to test these predictions in the upcoming experimental measurements at the LHC energy. {{figure:ab64cdcb-f953-4902-935f-629c03498647}}
r
6a5a69461047ff04fddb91113c86435a
In survey {{cite:45b5b56d11d2966650678591f99d710a16790c9a}}, it is pointed out that we can consider this hybrid query strategy in either implicit or explicit way. BADGE {{cite:648b0bb3640dd62155c65c4e6bc569ef20a41782}} considers the hybrid query scheme in an implicit way. Since both the prediction uncertainty of the model and the diversity of the samples in a batch are considered simultaneously, BADGE {{cite:648b0bb3640dd62155c65c4e6bc569ef20a41782}} can automatically balance the forecast uncertainty and sample diversity without manual hyperparameter adjustments. Wasserstein Adversarial Active Learning (WAAL) {{cite:32d5139e7ec7eacc1db388054b4c20371b88a105}} proposes a hybrid query strategy that explicitly balances uncertainty and diversity {{cite:45b5b56d11d2966650678591f99d710a16790c9a}}. In addition, WAAL {{cite:32d5139e7ec7eacc1db388054b4c20371b88a105}} models the interactive procedure in AL as a distribution matching problem by using Wasserstein distance.
m
cce23e6409232bfc7d7168d62d9d2b4f
Self-supervised learning is another recent paradigm but for unsupervised learning where the supervisory signal for feature learning is automatically generated from the data itself. Seminal works {{cite:2e95626205da96de4091c4b0abf83ba06a7b3273}}, {{cite:32037cf2bdab1ad01c85e2f2da479973f2690af7}}, {{cite:1b892838dd1802e4e0a522d4d273019f0aa7350b}}, {{cite:be42f17fb968c889bcc8d56441fa75e3f60c2da4}} have relied on heuristics to design pretext learning tasks such that high-level image understanding must be captured to solve them. Discriminative approaches based on contrastive learning in the latent space {{cite:aef26cf8a10ff016b117d6f1013dd034f29b3570}}, {{cite:99e9dc65362fb69b82f01d091092cc08ae1491ee}}, {{cite:dafc4ac6c414642fa1bdcdfc89b4276942560f17}}, {{cite:f836b3e7163966e8f5b86e3013a3d8ff9ad7a960}}, {{cite:416bb084b11a674b89689f81be02c06f7ea5be4e}}, {{cite:d84c60fd41c96cbdd0e2d7ccd583e5eb29b5b515}}, {{cite:95d791038bc04163da69a417a3456a93a1e2b5db}}, {{cite:d63045036429677b0b46a44bee7dcaa6c1c83e99}}, {{cite:04bf9cc2a963566989c724a50e219f9b5612588e}}, {{cite:eb0b4029c672023f9a4831b12ccc7160b255b260}} have shown recently that self-supervised learning is especially useful with the large availability of unlabeled data, effectively closing the gap with supervised learning when leveraging models with large capacity. These methods are trained by reducing the distance between different augmented views of the same image (positive pairs), and increasing the distance between augmented views of different images (negative pairs). More recently, BYOL {{cite:304e2b4d9c9e8256389a9344b114f519cd3a2402}} showed that one can also learn transferable visual representations via bootstrapping representations and without negative pairs.
i
4004b1e33b7de47bdfad4b5805d4397c
Multi-view human pose estimation methods benefit from the complementary information from different camera views, e.g. multi-view geometric constraints to resolve the depth ambiguity, different views of the depicted person to deal with the occlusion problem. Many existing multi-view based methods  {{cite:001d4b5077bf805347e372c5b82f70961ef866eb}}, {{cite:22ee005df2c1cf27058ff9b7360cbc5315952ef9}}, {{cite:18e3eb90b0045b2c952c36a32a2426701852d8a4}} follow a pipeline that first takes multi-view images as input to predict 2D detection heatmaps and then projects them to 3D poses through volumetric convolutional networks or Pictorial Structure Model (PSM)  {{cite:3522962792eb8611edd1c56911707a5c2c8c0fc2}}, {{cite:552fdf5f0b597e49d316638dcda0cf104f3f4a76}}, as shown in Figure REF (a). However, using the convolutional neural network to perform 2D-3D lifting requires quantities of labeled 3D data as supervision, which is difficult and costly to collect. PSM discretizes the space around the root joint by an {{formula:357ec814-973d-45b6-a72b-963633ee648e}} grid and assigns each joint to one of the {{formula:db52b78c-bbe4-4df6-b1cc-51f8c131611a}} bins (hypotheses), therefore requiring no 3D ground truth. However, the 2D-3D lifting accuracy of PSM based method is subject to the number of grids, and the computation complexity is of the order of {{formula:6e511072-53a6-4286-894b-5e00d6169a8d}} which is computationally expensive.
i
35340154ed0151b0714b73b5246b8ed0
In the last few decades, the topological theory of distributed computing has been successful in giving a range of fundamental insights and results, most notably the simplicial complex model of distributed tasks, protocols as simplicial subdivisions, and the impossibility results on a significant family of distributed tasks {{cite:d56371a85ba5ee3e4898b5e3445405e0ec477d14}}, {{cite:bdcebb7a3cd269fcab075e0fabe69a1b005113c8}}. Though it has been recognized since the earliest work by Saks and Zaharoglou {{cite:0b56d20c9dc10a775b4ffd4edee980e7a351fb40}} that the topological model is an interpretation of epistemic knowledge held by distributed processes, the rigorous connection was established only very recently by Goubault, Ledent, and Rajsbaum in {{cite:c11701ac442c7c9b207d18e117d0bc4f50ccd018}}. They defined the task solvability in terms of a multi-agent dynamic epistemic logic (DEL) {{cite:4b109bfe3d0ff56e2ea7a1a883276bce62544d11}}, establishing the isomorphism between the topological models and an appropriate class of logical models of epistemic knowledge.
i
7ecd925a6a0b6b0a49212772aa8116ce
Augmentation: Recoloring. Since MultiPIE {{cite:c39ecaf96c119499d7f2a8cc20074f14e5874395}} was acquired in a controlled setting, it has more or less uniform hue and saturation across all images. To artificially inject some diversity in the overall image color, and prevent visual overfitting, we build an image colorization model. Inspired by {{cite:80ec40667d3cd990e976c42d308ec9e1383716a5}}, we train two separate pix2pix {{cite:0374ec0a5771c56bea1da2c03f6176c18876cace}} style GAN models where the input is a grayscale image and the target is set as its colored counterpart (original image). To manipulate the color style of the same grayscale image differently, we train these two models with randomly sampled 10K images from the UMDFaces {{cite:99450be3a049620131e31bd8636486cf0efee10f}} and FFHQ {{cite:264c0fd0e4d34356c9d67381459ef17910fbc1d4}} datasets respectively. The trained generators are used to augment the color style of the MultiPIE training set.
r
19d2bfd4a36908382bb0d6ca3c884db9
The separation of rotations and internal motions is also an important step in the analysis of the {{formula:adbb3018-d9cc-414e-abca-6d77ef2d08bf}} -body problem, as discussed, for example, in {{cite:acb91b1430efa0f23c3392b6bdfb0da3be25607f}}. There, an appropriate choice of the reference frame makes it possible to write the Lagrangian as a sum of rotational and deformational components. Further local decompositions seek to isolate rotational velocity components based on the velocity gradient. Examples include the deformation-rotation decomposition of {{cite:2a299dc457d6534e9d8b822157d2f6cda490d37d}} and the procedures of {{cite:a65dbbbfef106d9062c9186c30bef99937f85eb7}}, {{cite:d3e161abeac20234a0c10421e5fccf720d32dea5}}, {{cite:335bb92dd5034189b57a731cc3b1195fdf319bcc}} and {{cite:5ebcb2d1240e40c8ad0782da37d9fbb3c6f7e964}}. In the Lagrangian frame, only infinitesimal decompositions of the flow have been obtained. The closest of these in spirit to the present study is the polar decomposition, which yields a polar rotation tensor that is pointwise the closest rigid-body rotation to the deformation gradient ({{cite:f7d9ef5fea7c68c3bb29308646ba447f7c5a1903}}).
i
d626b0989e327621f921b68fcfa00c66
We performed XRD measurements to characterize the crystal structures of the as-synthesized {{formula:7de654b9-3435-4179-b980-2584fc18e656}} NiO{{formula:ad01b376-7582-45af-aa7b-941c4fd7e246}} samples. The corresponding data are shown in Figure REF , together with refinements via the Rietveld method and the calculated Bragg peaks. As illustrated in Figure REF (a), after extracting the apical oxygen in {{formula:d4869e87-45aa-46ea-90a6-12a9b38a24f1}} NiO{{formula:af2d72ea-a019-42c2-b617-6af659914989}} , the NiO{{formula:238a533e-dbaf-4a31-8704-ceb1484ff42f}} -planes in {{formula:531c6279-c85e-4b75-bbd0-2bcee648e0fb}} NiO{{formula:e02130d0-ec87-4d66-a002-8dc18520a7f3}} are separated by rare-earth metal ions layer by layer. The reduction might in principle be incomplete or introduce crystalline disorder or even destroy the NiO{{formula:9e75c7d1-6455-4c74-b685-dd93a4b07205}} -planes into elemental Ni. However, the calculated curves fit well with the experimental ones, and all {{formula:b8c00129-c544-46d7-81bc-803603c1b406}} NiO{{formula:0b35e0a5-c8a6-497c-9b87-eac966a23761}} compounds can be successfully refined as tetragonal phases with the same space group {{formula:6da14734-33bf-433b-a618-1e0a22285ea2}} . These XRD results indicate that no significant distortions were introduced in the NiO{{formula:f89e8226-d12a-4407-b204-f1731a88deb3}} -plane by the reduction, and the compounds can indeed be considered as the infinite-layer phase. The crystal parameters obtained from the Rietveld refinements are presented in Table1. The {{formula:ea728654-0ea3-4531-987c-62ea2aee7c8f}} -axis parameters of LaNiO{{formula:a515d784-1841-4a3e-8afd-c142fa921ed8}} , PrNiO{{formula:a7338a81-5de5-487c-9205-db6f2d8502be}} and NdNiO{{formula:364572f4-aaee-478d-b9c4-2080b6095f1a}} are 3.363 {{formula:b6a4f04d-c069-4db5-88a6-442999d63ab9}} , 3.285 {{formula:9a4468b9-f30a-4aac-8cae-f777992f74a7}} and 3.279 {{formula:1414b188-086b-476c-8bb3-e51f27ce5b40}} , respectively. They are close to the reported values for bulk samples{{cite:dd7a01159755fcbdd7ab349005fd249fa2470c81}}, {{cite:b107d07fbe1fbc0a4d7b78a2800b6cf82cbf50f4}}, {{cite:3ada241324cea55ec519566ec663380fe3786699}}, {{cite:2e3f3564f82a5466a8049d2057f12e79f4154362}}, {{cite:ca8d41781184f6f4d44ce8a9e3a49b5c3a6ad137}}, but 3{{formula:d2a76edc-9312-469f-950d-d29c0c820ef6}} smaller than in thin films{{cite:a9b0a1cd3d1fcf0d0aef161725dad892df6edbd2}}, {{cite:1100d17159d672014a957e8bc1acab6cebf931dc}}. The different {{formula:6fd800ea-26dc-49a5-ba46-922070514e99}} values in our samples can be simply attributed to the different radii of rare-earth metal ion for coordination number {{formula:46b5d41e-c969-4f72-92e5-69a61be9aa52}} = 8 that {{formula:5ccbf7e8-86d8-42e6-bd1f-bcfede4dd20c}} (La{{formula:452827fd-e860-4d7e-ad74-711a18fc475f}} ) = 1.15 {{formula:d046fcf2-b69c-4af8-8b6c-7d0e44669f52}} , {{formula:cc924044-d24e-49eb-aa6e-41a8df932a0a}} (Pr{{formula:e661ba54-66d7-4a24-a195-349385549aa0}} ) = 1.11 {{formula:61c0bd28-41fb-49b1-9add-8b069ab28bd2}} and {{formula:f5baf87d-1464-4735-b1b9-56d829dfb108}} (Nd{{formula:cacc9bce-3eed-483e-a00a-6f075355cc33}} ) = 1.10 {{formula:df1d654f-9c52-4461-9bbd-10db38181ba9}}{{cite:1090dd8447fbc5840de71e6bb0a893e7be897446}}.
r
f3e91042a092dd4fd33c964153b54615
The 95% CL interval for the observables considered in the fit are also shown in table REF . We can see that the agreement with the experimental values are excellent. Moreover, our result for {{formula:02f808b7-4d57-4f03-b5e8-54815c530094}} is compatible with {{formula:1ae62f23-ab44-4bd2-9f0c-6943947b7eef}} of Ref. {{cite:4cb76a95862e8e20ba1bae67f90fee2081b0856d}} as well as with {{formula:cb935846-6115-42b1-974f-175767482583}} from the fit in Ref. {{cite:94f275caba9ae3bc06f9dfb45c1ff0552c59074e}}. Our intervals for {{formula:3e67fa99-2b1e-49df-a8bc-9f9159f83804}} and {{formula:2591694f-a857-4418-a343-2d3568fda983}} are also compatible with Refs. {{cite:94f275caba9ae3bc06f9dfb45c1ff0552c59074e}}, {{cite:1f22ce06af1452ba4d443102bdf35f3a3e19c123}}. The value of {{formula:d9fb4187-c782-4df3-be69-49a1fed6d75f}} agrees with {{cite:8a62b651687f1ee5309bb141fee0597ab59d8183}}.
m
cc016cb605cd32aa4e8bed5946621a85
Consensus dynamics in systems composed by multiple agents is a fundamental aspect in many areas of social and biological sciences {{cite:384f21e15417c25b3e0979baae6799a4f4e521e6}}, {{cite:ca3d7dca8185daf4faebe18742b35ba49d6b8629}}. Understanding the structural and dynamical conditions that allow consensus to be established has both theoretical {{cite:ac63d1b59aa2851f25793c0f29d49a0cffb0b0bd}}, {{cite:0c2510e29a73593cb766b22cf06feb0a7371496f}}, {{cite:ad78678a448298071d3c52edd41563900558cf26}} and applied implications {{cite:0c7d7abb6caaa9e1b108a4c2ebd8472563a2bb22}}. Interest in the subject covers several important phenomena, such as dynamics of cultural elements {{cite:c0b0cb349c0dac90ae79baea42fa4818f35d9e70}} and flow of information in society {{cite:483925ad655332f1c11c0814bad5d5a3eeab8b8e}}, epidemic spreading {{cite:b2f161bfb9c3d262773dfa67ac2ef65a532c48a7}}, {{cite:5ecfccd2fe9c8161cd65b63be61e6bb5bf2dc670}}, and animal collective behavior {{cite:7c8ae774195a8d39ae56b361c8bfb0ae251c992b}}, {{cite:5b62b76de2871ad8c741eed33fb76af6eeb054e8}}. In particular, the problems of allelic drift in population genetics {{cite:2b749ca34788b55903ece2830929bf1146fa7582}} and opinion dynamics in human societies may be treated under this framework and have classically been described with two theoretical foundations: the Moran model and the Voter model.
i
fb9848eec7d15de291c7466ce9a9b830
The extension of integrable systems to noncommutative space-time is not our aim in this paper, but it is still a potentially interesting topic. (For reviews see, e.g. {{cite:ed78f0f73861ef822d82c372798f15197cd5364b}}, {{cite:9fbb9b3afc6e9fe89b90418bacb56aa02b63a9b3}}, {{cite:71ae3dc8e47edf92c7d15b4b266859478b88f9eb}}.) In the previous work {{cite:c48a240a03ee6a154d7e02973f6f73e859c1b46a}}, we showed that on the Euclidean space {{formula:b98958e3-bb05-4c60-a36e-474e9ebfba27}} , noncommutative multi-soliton solutions of anti-self-dual Yang-Mills equations is equivalent to the commutative ones in the asymptotic region. By quite similar arguments, we can make the same conclusion on the Ultrahyperbolic space {{formula:f1d8901a-0a00-47c0-8f38-07262a9c8e21}} . This means that on {{formula:e90af868-c789-4c2a-92f5-7b48a3da3e56}} , the behavior of three-dimensional branes (soliton walls) in the asymptotic region are not affected by the background {{formula:cc100757-c8bc-4a9e-8d86-4605d575e092}} -field. On the other hand, the soliton equations of lower-dimensional integrable systems can be derived from the anti-self-dual Yang-Mills equations by suitable reduction procedure even when the space-time coordinates are noncommutative {{cite:b49290c5718e3e0a62c57dfc6a094132586e65c5}}. Therefore, the techniques presented in this paper could be applied to the lower-dimensional soliton equations even in noncommutative space-time because quasideterminants are especially suitable for the description of noncommutative integrable systems. (e.g. {{cite:a959b6230b7158f268d5146e66f75fe9e022d5a6}}, {{cite:5b10b56d267c778863cdc0e0f6200211eb0ee3a8}}, {{cite:2ca77e54b32bcf6fde25d556054f4873b689afb1}}, {{cite:c16134dfe7185f6845dc3945aafc165ab7e7d7cc}}). Furthermore, the asymptotic behaviors of noncommutative multi-soliton solutions are proved to be the same as the commutative ones in lower-dimensional integrable systems (e.g. {{cite:7e83a3034e86b548e49774d1925c51d85419cd44}}, {{cite:199687993f48bcb0ce15acf7ae2e16b686982a57}}, {{cite:dcb85beb697a192aa27d3296f96d3795e01c627d}}, {{cite:7a68ef4983aa5deaed4bf67086e2327a749350bd}}), but the physical interpretation are still uncertain.
d
186217e47507bcf206e3b50593c3660e
which agrees with our result (REF ) within the errors. Note that our result (REF ) agrees with the latest estimate {{formula:1eda6462-76e7-40ed-90ba-5e7d775711f4}} , recently updated by the PDG{{cite:e5971a8e9e792728b6ba5e9bb82aa6b896541181}}.
r
a28e31122aa7f36aab4d0a232fb84c1d
Heavy-quarkonium production in {{formula:6b444fc2-1651-454c-b78f-15aa904ec5a5}} boson decay, which has attracted much attention on both theoretical and experimental sides in the past decades {{cite:d1c0bf9473cd6a7abdb493c6ab10d36602c02036}}, {{cite:0b44587a4f55a18915e74d54e6fb8c22dcca9c26}}, {{cite:fd7f0e757777dd88df4063f795208959fe7af202}}, {{cite:227eb53913b739a45072315fd823ff26ce30a80c}}, {{cite:523dd76c4e8c7c68e4df3ad823b2fd91f65d2d7b}}, {{cite:e4840d1edf87c17e3b0d64cfeb4174462efa3976}}, {{cite:516217476c3833a244dd1201cb15d6dc6fa05b34}}, {{cite:e426d5690677d860890096b1358644cf40f1b273}}, {{cite:e5f5e4100e75dd2ca36c4ab3a4bf529f6cb8dedb}}, {{cite:3da4143911579bfe9f7fbfbfa032d0a96c61cedd}}, {{cite:d6115e3d34793060aa63690e0cf4314aa6b72a81}}, {{cite:7e0b80e481d4e3c515325cfad7f850e4dc3976aa}}, {{cite:f4b5c271f7b96c369170687badbba2dbb87d48de}}, {{cite:3e54c758a419b23ac334516439db5d3140d29a44}}, {{cite:9b4f5530ad426d8219d16efe314e531146d38ee4}}, {{cite:d1c843b295bb260df1d75af586a8a3f66bf43456}}, {{cite:5171e81029bca6f61b7611e02cc4b902d6eb72a0}}, {{cite:1e96cdc99d7fd6e9df2325ac319bd638ef8e7ffd}}, {{cite:17cb77d8666f13dfe1127ae2918e4887966f79fa}}, {{cite:2236bfa991c2fa3c2e3bd769479b90938c442aac}}, {{cite:d3d080e3aec8fc11d048ca610e0f1d3154a80095}}, {{cite:63fd4a0c0cbdef401c6efa9613c0ac3449103725}}, {{cite:d5fabc707df46712caa1018476566ee47fddb796}}, {{cite:9e1d3f30eaf9f9e6949a984f50d4d956f041cb03}}, {{cite:a031770ed4838f49d4981811a244738f87e60dc5}}, {{cite:fe95cb1b5b8c287e7ecd2d59213e68cd4cde7f9c}}, {{cite:6d829e3dd6671ae99a5b11ffd1cc577eac335b0a}}, {{cite:a8fb22fc535ca59b041fb6cc5e5bbcef74d67551}}, {{cite:b0eff80ecde15721bf6971f279929c1f8daa6b3a}}, {{cite:80d57bb8fdeb3e45fd697dde522631cf26bc5aad}}, {{cite:fb2e5467c7c4f1ac551783f4a18012da2646eec6}}, {{cite:ff2beb216741894adfe21eadcc80f6327b5d0e2e}}, {{cite:80345025c65fc8661e1d0f807779edc82a772fb4}}, can offer independent test of the quarkonium-production mechanism and provide references to distinguish different models. A well-known example is that the measurements of {{formula:50d3fe98-0158-44fc-97f7-13086e374477}} inclusive production in {{formula:64fbc043-2a93-41c2-b6cc-bd20a498e087}} decay apparently exceed the predictions given by the color-singlet (CS) mechanism but coincide with that built on the non-relativistic QCD (NRQCD) framework {{cite:7e0b80e481d4e3c515325cfad7f850e4dc3976aa}}, {{cite:f4b5c271f7b96c369170687badbba2dbb87d48de}}, {{cite:3e54c758a419b23ac334516439db5d3140d29a44}}, {{cite:be6c93bcd43757b949dbc71406a2893b93f70001}}, which is regarded as a solid evidence to favor the NRQCD factorization.
i
e0bc7508f9c484762765998710490f44
We use a neural volumetric representation to represent objects, i.e., an MLP network encodes the 3D coordinates and regresses the density and radiance values of the 3D volume {{cite:0e5105f3550b748b45f508d78fc539d14dd4b5a5}}. The output volume can be rendered from a virtual camera using volumetric integration to produce the final image. The network is trained in an adversarial manner using monocular images as the training data.
m
afe971079715788a06ceb83b2d1df655
The data are well described by the hadronic cocktail within the statistical and systematic uncertainties. The contribution from {{formula:a95e0d71-7be6-4be1-aff5-fbb053aef2fc}} dominates the dielectron yield at low {{formula:317cce36-51b3-4f2e-a0c5-07823ab43840}} and relatively small {{formula:7ec63727-b6a6-40b2-a18f-0745748b3c4d}} , whereas the {{formula:2804b6a5-1e08-4556-9e49-1993fe2290bb}} becomes relevant at high {{formula:df8f87ce-dd10-4007-b5f6-1cf475445437}} and large {{formula:c1e2917c-f729-4595-8753-f00a7357779e}} . To investigate the processes of heavy-quark production we changed the generator from PYTHIA to POWHEG, switching from leading order in the HF quark generation to next-to-leading order. To quantify the differences the total {{formula:32f5662e-2c00-426a-a12e-6a784ae7ab3d}} and {{formula:c7e9b3d8-00f7-4f2d-8f62-300b59491559}} cross sections are extracted from the data by fitting the results two-dimensionally as a function of {{formula:2ba1e245-ae25-49b5-aa0d-6da3103ae193}} and {{formula:035515ac-f832-4071-8af7-1c94374dda60}} and one-dimensionally as a function of {{formula:c1268fab-e945-4a83-987f-04f94dd0b1bf}}  in the IMR allowing the contributions of the two HF components to vary. The results are shown in the left and right panels of Fig. 5 for PYTHIA and POWHEG{{cite:0c60c523eb4cacb31b609a67223d30c63c9dd07c}}, respectively. Both fits give consistent results for a given MC event generator. The uncertainties are fully correlated between the cross sections extracted with PYTHIA and POWHEG. Significant model dependences are observed which reflect the different rapidity distribution of charm quarks and different {{formula:9d7e0968-b9d5-4f23-a063-bce1325aa7c1}} spectra of the {{formula:e58644ea-0d41-49ca-b5cc-ef793483cf72}} and {{formula:a691992d-7b93-4553-8b45-6701b0c644b8}} contributions predicted by the two models. {{figure:db5fe680-e0b3-4b66-9856-e3cddc6013bd}}
r
5221e6860cad6b93496a42b3287c2c13
where {{formula:76e6db30-e726-457d-aae8-6c94d574efa7}} and {{formula:b7393c69-358a-4faa-996d-5ebf6c5d2b75}} are two positive proximal regularization parameters serving as step sizes for updating. In the literature, such a method is also reemphasized as primal-dual hybrid gradient (PDHG) method, which has been widely used in image processing {{cite:778c377ddcfbd1bfef4329dadd72b28c74140b74}}, {{cite:2ce8f07955d42ba4f511d528c16e6dffb00b1994}}, {{cite:7c248a545b11a264e87cbeaefa92a49f6f2c9bd1}}, {{cite:4f7a2f3e4ea24fb07bb99beff0e4cc9161358e11}}. Although some convergence properties have been established under additional conditions {{cite:2ce8f07955d42ba4f511d528c16e6dffb00b1994}}, {{cite:c99854b20415b2830d3397af2cfe9e7bb525d0bf}}, {{cite:fc15e7678af698a90d9473e45b082f399d6ea587}}, the most recent work {{cite:9213bce15d00d27d2f7e597555fb4764163b7c2b}} showed that the AHPD method with any constant step size is not necessarily convergent for solving generic convex-concave saddle point problems. In 2011, Chambolle and Pock {{cite:f3143cc9e78fc5559edd00f82d31e7d7e0344205}} judiciously introduced a First-Order Primal-Dual Algorithm (FOPDA) by absorbing an extrapolation step for algorithmic acceleration. Specifically, for given the {{formula:e9e8882a-5e42-481c-94cc-99f8568f8fd1}} -th iterate {{formula:3759f33f-6fac-4391-82b8-665cb7addc71}} , the iterative scheme of FOPDA reads as xk+1 = xX{ f(x) + Ax, yk+ 2 x-xk 2 },
i
db4d801dd23b621c84e0886edd35798c
In terms of limitations and directions for future work, one important limitation is that we only consider one type of adversarial loss to enforce fairness. While this adversarial loss is theoretically motivated and known to perform well, there are other recent variations in the literature (e.g., {{cite:ad5a255c0590076442f946d3d5e24f6cbd00b692}})—as well as related non-adversarial regularizers (e.g., {{cite:4dfbe63770d9f17b59028f9df3afe025391c850f}}). Also, while we considered imposing fairness over sets of attributes, we did not explicitly model subgroup-level fairness {{cite:530a015d590109bd9ecc86f782d34d84dbc5e1d7}}. Extending and testing our framework with these alternatives is a natural direction for future work.
d
7eae109bb29ec661bc0983b6fb8b6ba9
In the case of electromagnetic systems, where electromagnetic forces might be prevailing, the standard formulas for energy-momentum of the electromagnetic fields already contain the contributions of the electromagnetic forces to the energy-momentum of the system. However, there has been a persistent opinion that the energy and momentum in the electromagnetic field of a moving charge should behave as components of a 4-vector under a Lorentz transformation. With this in mind, modifications in definitions of energy and momentum have been proposed, in the case of “bound fields” {{cite:36a5e31fda9959f89ca20bb5f51f4d60c15cedc4}}; these modified definitions have made their appearance even in the standard textbooks {{cite:ca6211ac80bd39a5079695b05f22c2a43e5e327a}}, {{cite:5834cc4042703db277deb96e88d7e7c9ae786c80}}. However, as was recently demonstrated {{cite:471468acc24808ed64efb96a92b34daa503332e3}}, there is no need for separate definitions for energy-momentum of bound fields (fields associated with charges) and free fields (electromagnetic waves no longer tied to the charges, responsible for their generation). All we need to remember in the case of systems involving charges is that there might be contributions of the stabilizing forces (Poincaré stresses {{cite:de9a60f7650e0593ea71bbe6b15bc25b86a5409c}}) too, to the energy and momentum of the total system, which would neutralize those “unwanted” terms. It has been demonstrated that the stabilizing forces, responsible for retaining the charges on individual capacitor plates in spite of the forces of repulsion between charges along the plate surfaces and also for keeping the plates apart against the perpendicular force of attraction between them, do explain successfully {{cite:dc8b81631c430089fc5d7496b10e9ca832513ef1}} the null results of the famous Trouton-Noble experiment {{cite:800cceb51860208a6e31bc1c1b0091a1cbfbfad2}}.
d
9345ad0b11854c9da6cf830f7ab98b44
The magnetization of solids comes from two parts: spin magnetization and orbital magnetization (OM). For the OM, the relevant theory had been confined to calculating the change of OM as a bulk quantity{{cite:597ac7d3f534fe9012d8b92c45c589b52c5f79bf}}, {{cite:ee1ebf0e37739780ccbe7d732a9a988d83dbcf7c}}, {{cite:5693ba31eae10f90b021d9fc466845511b419b4d}}, {{cite:5009142ba649593a9dee488e984d2a9835a7be5d}}. Until 2005, the modern theory of OM in solids was developed{{cite:4616590eed0880ca27a53a7cf98bf91d015b84ec}}. The OM is then found to be closely related to topological properties of solids{{cite:ddb138b41825ab332e8526e55e59ce8a1d916e87}}, {{cite:c7dcda6513a1d956a0dfdaf8261a4ffef4f21fc4}}, {{cite:776e83d367e1f034a5332438654096063bb314a8}}, {{cite:beb25d25e877a386b515b1cfe3098d5e30b0815d}}, {{cite:ae995efc4f38b69029f94fa8d46559f1ef52ae92}}, {{cite:0cd9e081c3348fff0dde21a58aeda4ecd51eb29f}}, {{cite:602201be5c0e009d34ddd73b0255b2eb639a07c1}}, {{cite:600bca84009bd72c546bd695406dd1b411be52c5}}. Recently it is proposed as the central quantity of a topological memory device{{cite:00910d2969db09d1e1014d3080ac89af463e2b60}}. How to tune the OM in solids is an important objective of orbitronics{{cite:abdfc1c5d4b72d68e4d8d0b345776e344e41ad6d}}, {{cite:2992856e1636ac63104ff4a61048cf9ffa2288c5}}, {{cite:379f6f340b86dd904ee66c010f2817134fd77c6a}}. Besides the induction of OM from external fields{{cite:18fc4bda092a048b8d9f5874cd3f28b7b50d1311}}, {{cite:7a8a9dd96fbd9539528bad9753802516693ee50f}}, {{cite:a2ee6670e7a04845bb412795c7c13f8722f62b58}}, {{cite:13058f9dc924c4c2d7282a7f7e54d53236be619f}}, {{cite:1f8b89050d3bc2bee0b239a941b4c9c3972b3239}}, {{cite:b94a376a4d9ee75ba647c4c9117dbb78c2667f25}}, {{cite:d0a7109e30cc13953061d8d8318727020005ca2c}}, {{cite:322f9cf22efe1fc8994bf9794d8f4cb78fdbc9c0}}, another method is to produce a spontaneous OM, such as, by engineering material structures{{cite:a03cf98f31566465d6925ee64b81d557fbea7f28}}. These potential applications raise demands of predicting materials' OM based on a deeper understanding of calculation methods.
i
d782a776083a00f790a6b9699c1260e9
DIAYN {{cite:e95cdd5feaa99244fb73aecbe5bdc20fb08caab2}} To avoid learning a homogeneous set of skills, we consider applying an information-theoretic diversity objective to the fixed-length skills framework. Such approaches typically learn task-agnostic skills in a reward-free setting to improve exploration. Instead, we explore whether promoting skill diversity in our domains can aid in learning more meaningful high-level actions. We linearly combine task rewards with the DIAYN objective when training the low-level policy: {{formula:896bea51-b904-4183-9b3f-1ae1479699e2}} , where {{formula:3a85470f-6476-4c11-998d-385e08a99da2}} is a hyperparameter, {{formula:86163352-d84f-48e3-9103-b547f41f8cee}} the environment reward, {{formula:4646b3e7-86e6-4e0d-90b3-f82baa7e07c9}} the current discrete skill, {{formula:eedc691d-2b6a-4fd5-9129-6bfeddd3d0a3}} a neural network trained to predict the skill distribution given the next state, and {{formula:9c4ee9ac-2bcf-4726-94b1-279a3f40610a}} a neural network trained to predict the prior skill distribution. The high-level policy was trained to maximize undiscounted environment rewards (without the diversity objective).
m
2760df5b93e12e42bd0f17b0e52f239f
In order to derive these synthetic images, we divided our study into four different steps: we start by simulating the gaseous disk containing the different giant planets using 2D isothermal hydro-simulations with the FARGO2D1D code {{cite:4088e9e3425f8b1e965ea4aaa6d42bac5d2b02ad}}. These simulations allow us to derive a detailed radial gas profile that is used as input for a dust evolution model, derived in the TWO-POP-PY code {{cite:3b0a631951ad0224faf22cb1fe9135b1d7f51f18}}. This radial dust model takes growth, fragmentation, and drift into account. The resulting dust size distributions are then extended in three dimensions and used in a radiative transfer code, RADMC3D {{cite:2a2392c6db19248c9c610f7aa7583941ddf3f85a}}, to derive the synthetic images at different wavelengths; these images are finally convolved with different beam sizes in order to represent more realistic observations.
i
587349472ec4e9cc447a2cacbc6f6672
Similar to other fields, augmentation plays an important role in GCL. Common approaches include randomly adding or dropping node and edges {{cite:a815f31f22fe41dba1299b56f25abdfe59a967e6}}, {{cite:8797f450e4c35afb3b687f519d5c7e3a8f90c28a}}, {{cite:d862787482bcf700af96205c761c94d75ac3ad59}}, feature shuffling {{cite:ef1f7926d06b6bf8af0995fe5c2376f7fa383fb2}} and diffusion method {{cite:5df69ad27d4cbb0aaa1ccc3466593d4dd04e2afb}}. However, random augmentations from these methods often change the graph structure and hence lead to meaningless graph views {{cite:460ea306d8631d830442562249f0f86345f50028}}. To address this issue, latest research begins to use adaptive augmentations such as GCA {{cite:578eed4c807ee1b68980a2e90d23bd255d57f80e}}, or automated augmentation methods such as JOAO {{cite:fe108d184ee253a49f0af0cd80f3441ee04f4c6e}} and AutoGCL {{cite:4d08530627023a97f50f53dc62a3748b941039c5}}. While these works utilize augmentations explicitly, our iGCL takes an implicit way to apply latent augmentations with graph semantic meanings. Unlike existing latent augmentation methods in computer vision {{cite:b46c4fddd44d985d6b5f6f5fac4cf7c3c82943b8}}, {{cite:6cfdf99d61e11c7177e72daf63b388fcbc265ddd}}, the proposed method generates latent augmentations in an unsupervised manner, and are optimized by a novel expected contrastive loss with a computationally efficient upper bound.
m
6b983ccab527b064e75d77ab6bddbfa9
A pitfall of such heuristics, noticed by the authors themselves, is that style and content-bearing words are treated as equal candidates for the change. Some neural methods bypassed the issue with a similar 3-steps procedure. That is the case of {{cite:7b022356cab6bc0f93579e9345eccf95dff92c19}}, who proposed a variation of the pipeline in {{cite:54e2854af49f349c99e03d11d563b9577404e181}}. There, (1) only style-bearing words are deleted, upon decision of a Bert-based transformer, where an attention head encoded the stylistic importance of each token in a sentence. Next, (2) candidate substitutes are retrieved: the sentence from a target style corpus are extracted to minimize the distance between the content words of the input and those in the retrieved sentence. Lastly, (3) the final output is generated with a decoder-only transformer based on Gpt that, having learned a representation of both the content source words and the retrieved attribute words, finally generates the new text. It should be noted that this method was not specifically designed to transfer genre-related attributes, and indeed, it achieves different results when dealing with other styles. Similarly, the work of {{cite:4000e32c20756938cfc48a1c3f8c4de526ab4185}} address gender as an ancillary task and use a same methodology that first identifies the style at a word-level and changes those in the output (they are discussed further in Section REF under Politeness).
m
06002947a4d0275e7b45f5ce580ebe89
In this section, we conduct numerical experiments to verify our theoretical results using logistic regression on the MNIST dataset {{cite:85ea2c0f5ce51cfb22dcf2f7604b58abf9a45355}}. Following the same procedure as in existing works {{cite:218841d12c2c7a6e4b3aaae41a4cd3d6f86741be}}, {{cite:d5a49542c08109af916d3e6dab493e7249ed5197}}, {{cite:b5ae729ccda2e465712b4300b70774a2a2fd12e8}}, we distribute the data evenly to {{formula:3f0969c3-a3f1-4ac0-9541-11dfe24ae62c}} clients in a label-based partition to impose data heterogeneity across the clients, where the heterogeneity level can be characterized by a parameter {{formula:90232383-0efc-4840-9ff4-5e0979fc02a3}} . As the MNIST dataset contains 10 classes of labels in total, {{formula:8c9bf000-a82a-4cfe-ba3d-dc942c44a90b}} represents the i.i.d. case. The smaller the {{formula:710451ca-f5b8-4286-9e7d-dbb2d98dcef4}} -value, the more heterogeneous the data across clients. We simulate Gaussian MAC with signal-to-noise ratios (SNRs) of [{{formula:31d70115-2094-4db5-b81b-b234342dce05}} ]dB, [10]dB and [20]dB. {{table:0e4f80a6-a68b-4bca-b6c5-6f352fd3624c}}
r
5f27e4c513e8b52f84ff2843d8a18c59
The Label Propagation algorithm (LPA) detects communities using network structure alone {{cite:2156665de84e60dba3f98580c020d52cd842fce3}}. The algorithm doesn’t require a pre-defined objective function or prior information about the communities. It works as follows:
m
84e2abf58c01c7bb4055d9ae5b32c29e
The two-stage detector, such as Faster R-CNN {{cite:6e81952c9882ad06d22dfb2cf477242f1d8ad3a9}}, is a paradigm of object detection algorithm that first generates a set of region proposals and then classifies the objects within those proposals (see fig:abbr-arch (a)). These algorithms can be conceptualized as cascades, where the first stage removes a significant number of background samples and the second stage classifies the remaining regions. In addition, Cascade R-CNN {{cite:d73cd51570e23c249dd6c92e6ce48a2cb155a470}} extends the two-stage paradigm by using multiple sub-networks to progressively improve the quality of the region proposals (see fig:abbr-arch (b)). Our OSCAR follows the idea of a cascade refinement, but it differs in two important aspects: (1) Instead of using a sparse set of candidate object boxes for the next stage, OSCAR performs soft region proposal on dense predictions by down-weighting easy background samples; (2) Although it performs progressive refinement on the predicted results, OSCAR remains a one-stage detector, not a two-stage method, avoiding the additional computational overhead of general cascading pipelines.
m
fbb08a191a3fbfe918f2d6f76699d49a
The ConferencingSpeech 2022 challenge aims to stimulate research in the above-mentioned areas. We provided comprehensive training and test datasets that contain at least 200 hours of speech samples with subjective test scores. We hope this challenge helps facilitate idea exchanges and discussions in this special session. Meanwhile, this challenge has the following features: 1) We aim for non-intrusive models for evaluating the speech quality (i.e., without reference speech signals), which is more practical in online conferencing applications. 2) With the continuous expansion of bandwidth in voice communication systems, the existing standardized non-intrusive objective speech quality assessment method for narrowband speech such as defined in ITU-T P.563 is no longer applicable. Therefore, this challenge aims to effectively evaluate the speech quality for signals with broader bandwidth. 3) To truly reflect subjective opinion on speech quality, the training and test datasets contain the mean opinion score (MOS), which is obtained through subjective absolute category rating tests in crowdsourcing and in accordance with the ITU-T Rec P.808 {{cite:b7fc8002c02cb5d92148956a85827f4eb45204cb}} using its open-sourced implementation {{cite:9b7910e6f50f29b688222671057d54560abadf3f}}. 4) As far as we know, this is the first challenge on non-intrusive objective speech quality assessment in online conferencing. We provide a training speech corpus of more than 200 hours of speech samples with corresponding subjective MOS which are covering most of the impairment scenarios users might face in on-line speech communication. It is believed that this will also promote the development of non-intrusive objective speech quality assessment methods. {{table:ddf9f95d-c5e3-48cd-9df6-2ee42a914f6b}}
i
26c432d0b1e3afdbbe64741103a92cbf
We compare our M2MRF with four tiny lesion segmentation methods (VRT, PATech, iFLYTEK {{cite:c5e84e29e21fec9826c280daf47aaf91c757bc3d}} and L-seg {{cite:81e27548727f743e03be985ac625c89ad31c1246}}), six state-of-the-art CNN-based methods and two recent transformer-based methods (Swin-base {{cite:b44c3103063c84437fdc47b4daf9a524840f97dc}} and Twins-SVT-B {{cite:90213c28cb806863deb89f3c9045c3585fe616d6}}). Among four tiny lesion segmentation methods, performance of L-Seg {{cite:81e27548727f743e03be985ac625c89ad31c1246}} is directly borrowed from original paper and the rest are top three methods borrowed from the 2018 ISBI grand challenge. Results of six CNN-based segmentation methods and Twins-SVT-B {{cite:90213c28cb806863deb89f3c9045c3585fe616d6}} are obtained via fine-tuning pre-trained model on ImageNet1K {{cite:99019fefe257819989899a7777fbdf3d0032aae9}} with IDRiD {{cite:c5e84e29e21fec9826c280daf47aaf91c757bc3d}} training set while Swin-base {{cite:b44c3103063c84437fdc47b4daf9a524840f97dc}} is ImageNet-22K.
m
aa2bbb4bcefea8b43cb0b080466834cf
Fig.REF -(c) shows the results, which were dominated by {{formula:6394df09-3967-40bd-8107-78b7719d93ef}} . The realistic left side swinging with forward drifting should be distributed in {{formula:b5623a48-9695-4825-a916-5960c73e8af5}} , which could not be resolved from {{formula:b857a15e-79d8-4b1b-bf05-7312cc057383}} in this resolution. As shown by “shoulder,” a slight asymmetry with respect to {{formula:b25b32a6-9709-4565-9417-1d2fbe083ea9}} can be noticed, indicating that {{formula:1fe116a5-7e6e-4196-8ee7-77817a9fbeca}} was preferred to {{formula:7f9ade17-f3bc-492b-b363-eee77c30fa58}} for both the gear-on and -off phases. This result indicated that {{formula:3ac2274b-7cb7-4d34-928b-9bdeb5520d04}} , which is naively acceptable but may lead to cause opposite curling. Therefore, this effect should suppress the major curling, providing another possible reason for the weak dependence of the total curl on {{formula:82946789-cd2f-4a7b-bef8-a236aeecedd2}} . We found no evidence for the unnaturally large asymmetry {{formula:bd9d1301-5f19-4dc0-964e-80a11c459cd1}} requested by the previously proposed forward-backward asymmetry models {{cite:fe245942e2c7b9abe9fc8de14cf04d41e31d339f}}, {{cite:687d1c3402c8004f87d4ff7e3f6fe3cb1eabbd18}}, {{cite:5ce4faf476bca5c5c8df03fe11f2661c409120e3}}, {{cite:b107c7c103b2463dcb933debed515219cf252198}}, {{cite:ce006b688330e8aae9375b0b8566f31469fce87b}}, {{cite:49957622342ac6d81186e5b864c64eb73e6b52ee}}, {{cite:9759f999a03ad42189c6d0050c43c46e46185e5a}}, {{cite:5c56f064535a44e44ecfa14654699557dbaccfa8}}, {{cite:5423eb8fee8e3572d7cd3d4f8eb8dee10cd30bb3}}, {{cite:cfe3c3a9ef679017f3a8edc8a4e539aef2078094}}, {{cite:5887a9bf57d324b6c157d02bc92efe51c8abd3f9}}.
d
e863b4ee71aadab981ecad8d4a950059
In parallel, enabling OOD generalization on Euclidean data has received surging attention and several solutions were proposed {{cite:87a9fd21493f096c5ff16aa6c942129da6a91c8d}}, {{cite:9e5969520445287097133ffad3781e3bcf8fc3be}}, {{cite:c9b5aa7c0e4a6e4b524fec0a922163a24f514ba5}}, {{cite:9df62e18926e39539ca1f43e1f7604e81db73a12}}, {{cite:862781524389f559c547a7a804caa529c3d56e32}}, {{cite:ab7adeb33083a2a528946075745eed0eb2b4b327}}, {{cite:76ea51a0d1801f297e7cc2e7a6c55e4ecd11e15e}}, {{cite:26fd202f08066472c7c97fed1601a20fb4eaabce}}. In particular, the invariance principle from causality is at the heart of those works {{cite:ac5b052f7e36f5c356bd0cacfd8757ce722e9f63}}, {{cite:650788165e7b262b68a25b88b5d014dbe7c073e9}}. The principle generically assumes that there exists a subset of inputs that carry most of the information about the underlying causes of the label. Predictions that merely focus on this part are invariant to a large class of distribution shifts in the sense of Independent Causal Mechanism (ICM) assumption {{cite:650788165e7b262b68a25b88b5d014dbe7c073e9}}, {{cite:948d8058386f9804d287c33f0efa5b2179eed76b}}, {{cite:af7e33847d2fe20fbad9284f89ca5f8528bb6ced}}, {{cite:26fd202f08066472c7c97fed1601a20fb4eaabce}}.
i
205a78d82a6500f8032d32bd962a20a8
Compact stars provide perfect places for investigating the nature of particle interactions at very high densities in a natural way {{cite:b123277f88a7947a7b8b34107b7a5bcc1b0bc03c}}. Neutron stars (NS) are compact objects of very high energy density having approximate masses {{formula:57277600-4293-4945-928a-af4b91c51c38}} and radii {{formula:858c853e-25ac-446d-b80d-a80c05a8b0ea}} times smaller than the Sun's radius. Therefore, they are perfect natural systems to study nuclear matter properties at high densities. In fact, density inside the core of a NS can be as high as several times the density that is reached inside a heavy atomic nuclei {{cite:45ce8e84039d38f2ba936c598792d5c98e85052a}}. Despite attempts of many decades, we still lack a proper understanding of the thermodynamical behaviour inside a compact star. The extreme conditions at the interior of a compact star comprising matter of uncertain composition have prompted many investigators to study its gross macroscopic properties within the framework of General Relativity. In order to understand the microscopic properties, the macroscopic properties such as NS masses and radii have been used as important tools to constrain its EOS.
i
41e01e2ae04011b1126c913f41d8862b
We use YouTube-8M dataset for our experiments which provides us with frame-wise video and audio features extracted at a rate of 1Hz using Inception v3 and VGGish respectively for 3862 classes {{cite:93e1ef9aae4051b14a24da809f20aab558c5d793}}. We use binary cross-entropy loss to train our models. We evaluate our models using the metrics mentioned in  {{cite:cb9aa9e371d5ed6dc18436228a690a343f28cbaa}}: (i) Global Average Precision (GAP), (ii) Mean Average Precision (MAP), (iii) Precision at Equal Recall Rate and (iv) Hit@1. Our training set consists of approximately 4 million videos. We use 32000 videos from the official development set for validation and use the rest as test set. We used Adam optimizer, with an initial learning rate of 0.0002 and batch size of 64. We compute validation set GAP every 10000 iterations and perform early-stopping with patience of 5. Based on that, the learning-rate scheduler decreases the learning rate by a factor of 0.1 with patience of 3. We compare the following models with baseline:
r
d740570a18c4b306aa562296533354de
Algebraic Complexity theory is the study of the complexity of those computational problems that can be phrased as computing a multivariate polynomial {{formula:b3549c73-e759-4424-8fba-d71126a07100}} over elements {{formula:fe9ef538-8376-4aa3-9ae0-dda14cda2e56}} Many central algorithmic problems such as the Determinant, Permanent, Matrix product etc. can be cast in this framework. The natural computational models that we consider in this setting are models such as Algebraic circuits, Algebraic Branching Programs (ABPs), and Algebraic formulas (or just formulas), all of which use the natural algebraic operations of {{formula:3c85627e-b996-4cd2-9353-0327c620ac47}} to compute the polynomial {{formula:de7f4214-fd7f-4926-b650-d9e494783dd2}} . These models have by now been the subject of a large body of work with many interesting upper bounds (i.e. circuit constructions) as well as lower bounds (i.e. impossibility results). (See, e.g. the surveys {{cite:294ac7b08dc5a9091c139e820e1b8115db05aa68}}, {{cite:74038236b6d5feb9c725d6e4ee9de35b23f9ccf5}} for an overview of many of these results.)
i
c577e1e7f25669b1cd24adb94985dfad
A few notes follow our construction of the lower-upper-level problems. First, the lower-level optimization is still a convex problem: a quadratic program with equality constraints only. The insight here is to significantly reduce the computation time of the quadratic program by keeping the equality constraints only: a QP can be reduced to an equivalent unconstrained problem by eliminating the equality constraints {{cite:fe6971969eb5fb4349547bad6d6f344720c2831b}}. Second, the upper-level problem, despite different forms than in {{cite:6af3a315a17be58b4c429ae415ceb620d1037bea}}, {{cite:9637845f1ed1e8054cdadb3d830252cd8e4fddc0}}, {{cite:b42807a625e86bce4e25322f270b5a6c61cfa54e}}, is generally hard to solve due to its non-convexity. Coordinate-descent may be applied to successively solve (REF ) and (REF ) in a row despite the fact that the computation time can be forbidden for real-time planning. Instead, we use gradient-descent on (REF ) to only update on {{formula:ef5157a5-721d-424a-8cb0-9a081bf70c82}} and {{formula:247b0579-4424-443e-a2ed-fde85ce10241}} once (REF ) is solved. Consequently, the updated values of {{formula:094a0cf3-8b1a-4e87-bd5b-5ef058d4b8dd}} and {{formula:6ba2329f-a04c-4eac-a2c8-14f2f00d9a55}} are plugged into (REF ) as parameters. In order to update {{formula:23a24537-63c7-4f45-997f-f6aed6950d63}} and {{formula:5445bf0c-e451-4bc8-b9ab-aabe0378edc3}} , we need {{formula:75f85de4-9bba-488b-b21d-15fef70e597d}} and {{formula:913f471d-5e21-4f3a-933e-ba51b3a21fb7}} to update {{formula:3aa387d9-ae7b-4164-9656-d10ac62aff6f}} and {{formula:70320591-dfee-4a2f-b7a5-d8d728eb09af}} by {{formula:b50f0cc0-fa4c-48f4-bc82-cfff89cc9e44}}
m
bee73d32aa1a506f8273d6bc9deddb35
As a crosscheck, we also compare our constraint results with the results in the literature {{cite:5de8f20e12c6b4ab24e3ed54a14786a78bfde57b}}, {{cite:17db673f6190af6400d8b7d233848c516c6c6af0}}, {{cite:d491dbf8b85e39b75caef863152d5ce11786d7c9}} and find that they are statistically consistent. For example, in the {{formula:89727c09-fd82-427f-8973-0e8b9b3871dd}} CDM model, we obtain {{formula:10d535b8-ae7d-44dd-8dee-524ab22614e0}} km s{{formula:0833d632-af7d-4044-8672-311a0a441463}} Mpc{{formula:0c85871e-3af8-46f1-a95d-8cafdd9e1a70}} using the CBS data as shown in Table REF , and Ref. {{cite:5de8f20e12c6b4ab24e3ed54a14786a78bfde57b}} gives {{formula:12f6a916-c356-4184-82cc-4cf6ed8d7301}} km s{{formula:312a4546-34fd-4461-9861-37678f6fdde1}} Mpc{{formula:e4b5eb50-218a-4b0a-892a-4a3d54959e66}} using the Planck 2018 TT,TE,EE+lowE+lensing+BAO+Pantheon data. Moreover, in the {{formula:3d8c91d5-d5e7-45d9-a24d-5bd5a7bc565a}} (t)CDM model, we obtain {{formula:f15b9a07-72cc-4184-8088-d013e1a3f776}} using the CBSH data as shown in Table REF , and Ref. {{cite:17db673f6190af6400d8b7d233848c516c6c6af0}} gives {{formula:c88d4d66-5299-4794-900b-f0bb263dd675}} using also the CBSH data, but in which the Planck 2015 data and an earlier local {{formula:e018e616-4b5c-43d7-bbce-a41b8cb2e8ab}} measurement are used. Through all these tests of the robustness of the results, we further confirm that our models are helpful to relieve the {{formula:0719c284-7ce7-48eb-ac3d-07513ed3e7a5}} tension. {{table:39b443bc-fb8f-41d2-87f5-97401c6a3a5e}}
r
fe6bf98ee50c5f29811dff88b98d0f37
For self-supervised learning, pretext tasks {{cite:22f6d4efc7f487d21bb5fd81d7f89a5e40ea103e}} are pre-designed for networks to solve, and some characteristics of the data set are utilized to generate the pretext task goals (i.e., ground truth for pretext tasks) computing the loss function. In other words, visual features are learned by learning objective functions of pretext tasks. The commonly used pretext task includes generation-based methods such as image colorization {{cite:d095051d74e0c17c663ca73c9f739edc2e6412e9}}, image super-resolution {{cite:efc85b72d3abce58cceb1cfb6c3c231b25b0ef55}}, image inpainting {{cite:1bff269ba9ec272f96f6a2d662ca222afb6f01dc}}, image generation by Generative Adversarial Networks (GANs) {{cite:6e51717e8a18e22acb1ed330e7195d8d121428a1}}, {{cite:cd2f2b819ddaee840f9c6c5996862d32893a8252}}. Some pretext tasks hidden spatial information and let the CNN correctly restore it, includes image jigsaw puzzle {{cite:b4c9dac8090f1cb380feaeb20e1bc4a1331c4ec0}}, {{cite:b14d5099c2aed114f9078f1e8074ef94987ad7d2}}, {{cite:6a155784f702a457391c48b821567e41148e4c82}}, {{cite:84a9797a48dc31b2df8bad453282c0b9507f3c8a}}, context prediction {{cite:7003f43506a33151d7b5cba4b5eb4505feceb490}}, and geometric transformation recognition {{cite:381e24ee0d4bd4a16810e399855d8e41dfad4dca}}, {{cite:cd2f2b819ddaee840f9c6c5996862d32893a8252}}. Some pretext tasks are designed to learn visual features from videos providing rich temporal information. These tasks disorder the video frames first and force a CNN to predict if the input frame sequence is correct {{cite:66d2cf730811e40b8a67f8a3fd40ac97db7c2316}}, {{cite:b90636bcc9cf11b95b00e3aba76b1847a7202aee}} or the correct order of frame sequence {{cite:49a155a602687e4da04dbd2b1c5b472912e66a6d}}, {{cite:80cf2870e5ef128a314bd84a3173b84d9de3a9e7}}. Although pretext-based methods can learn discriminative features, those approaches usually require experts that have the domain knowledge to carefully design. Therefore, it is not easy to transfer these approaches to other domains.
m
4bdf7c543d34621a709666e40843d458
Based on their very high radio and {{formula:800cea45-b7ab-42d4-921d-24fde2445f72}} -ray powers we estimate that similar sources make up only 2.1 per cent of the total IBL and HBL populationThis is the fraction of sources with radio and {{formula:b325fec8-05a1-4f32-b125-e4aeee1d7cf1}} -ray powers larger than those of TXS 0506+056 in the IBL/HBL sample put together by {{cite:5ada692b910480f8b85bbfab0757b20f2c3f18fa}}. GB6 J1542+6129 has {{formula:02ba81da-58a8-42e9-8c9b-84d2abace860}} W Hz{{formula:9b7870ed-feac-439a-a8e0-157b1498318f}} and {{formula:1366e7b0-4ed7-448f-af56-7c4befa016aa}} erg s{{formula:032711c0-7f35-4e7d-ab31-2e109b9ed36c}} .. Since IBLs plus HBLs comprise {{formula:16cf38dc-73ec-4299-82fb-c35f607075be}} per cent of the Fermi-4LAC (clean sample) blazars with SED classification {{cite:659f415aaf6332e0621132c333cef4809b60b41a}}, {{cite:42f6f06c7cd8ed0798ef1a29e47af7edddd61ccc}}, blazars of the type IceCube has associated with neutrinos constitute at most 1 per cent of the {{formula:b72527f0-c32d-4f6a-bdc0-59f48d7eda2f}} -ray selected population ({{formula:318fd4a7-0aad-4a44-8e99-1896739d0a90}} sources), since we have not included in our calculation their other peculiar properties.
d
bcb1d1401d959c1591a6e347dc4a9d22
Here, we focus on fourth-order differential equations in one dimension with Dirichlet and Neumann boundary conditions, approximating functions by the cubic Hermite element {{cite:0d4742de85172930ba470ad18cb48c0a34bfa272}}.
m
e6a5920016e58ab64424581f53476bf5
Integrated gradients {{cite:bf759ed1e061e381658d7cf10f1bdbeeeee320c4}} is another method of analysing the gradient of the prediction output with respect to features of the input. It is defined as the integral of the gradients along the straight line path from a given baseline to the input image. A series of images are interpolated between the baseline (e.g. matrix of 0s) and the original image, and the integrated gradients are given by the integration of the computed gradients for all the images in the series.
m
252c20e0fd85519a416038cf5500632b
Though the definition of an optimal algorithm is usually tailored to an average number of tests, when choosing between several algorithms, it is desirable to evaluate their performance taking into account multiple aspects. For example, an algorithm A1 may perform slightly better than A2 in terms of an average number of tests. However, A1 may have considerably larger variance than A2 and, therefore, the previously mentioned slight gain of A1 could be gladly traded by the practitioner in favour of A2. We have already mentioned that the importance of PTA remained unrecognized in the literature and there is more to say on that. Many GT algorithms described in the literature (including pioneering Dorfman's algorithm of {{cite:90ee670a141aa5d9402c5278f6a10132784f6a25}}) have limited applicability due to the dilution effect. To be more precise, for a typical algorithm of this kind to perform optimally for a given {{formula:2a75a384-ba68-4378-9949-373706f3b08e}} , one has to test items by grouping them into pools of size {{formula:44612951-0ae1-4649-b59a-5a59ebe37321}} . If this {{formula:f1eaf0f8-20f9-4493-8408-c8c28c9441ab}} is large (say 64 items or even more), the operating characteristics (sensitivity and specificity) of the test kit at hand may become unacceptably low (aka dilute) making this way the algorithm unsuitable for that particular applicationin theory, BTA3 stated in the Introduction prevents from this; however, in practice, it may be a serious obstacle. With respect to this property, PTA is a very favourable option: it requires only pools of size {{formula:5f5617f6-30de-4ebb-b9f5-284cfb37b5c8}} , and this holds true for all {{formula:41b539e1-05fe-4048-8029-3a43de89491c}} 's in the region of its optimality {{formula:4a831091-2f32-400e-8275-b9b8168e1e0e}} . The region {{formula:5028b9ef-ac95-457e-9883-fe775aefb54a}} where PTA performs optimally is bounded away from 0 in contrast to many other GT algorithms which do better for {{formula:6b01cec0-1862-4da6-9591-b3bcc0d28e37}} 's close to 0. In certain applications this property may be of significant importance. For example, consider a screening for a quite widespread infectious disease. Yao and Hwang {{cite:b1df6d5fdb8718e146780735b4a909849aca574c}} conjectured that there exists such {{formula:9dc268e1-a849-401b-b48d-ed62b468f267}} that for {{formula:6d224b70-7fc8-4877-8206-84689f735905}} PTA is optimal over all (not necessarily nested) algorithms satisfying BTA. Our Prop. REF demonstrates that, despite apparently simple recurrence governing evolution of {{formula:22e083ef-48cf-4a74-821d-a0bd036251b0}} (see Eq. (REF )), the resulting dependence structure is not so simple. At least we were not able to analyze its behaviour neither by making use of Markov chains theory, nor by making use of martingale theory. A well developed apparatus of weakly dependent sequences also did not promise easy deduction of Corollary REF . More than that, even direct moment calculation exercise, though accomplishable for {{formula:2e888dde-9da4-441a-98aa-44d40671af17}} at a reasonable price (see Lemma in Section 4 of {{cite:b1df6d5fdb8718e146780735b4a909849aca574c}}), becomes much more involved when it comes to {{formula:21b822e3-6f22-468c-9df0-94e58fef3968}} and higher order moments. This way, {{formula:4b84f147-da37-4cf2-947b-911306dcc6e6}} yields an example of a sequence of positive integer valued random variables having an interesting probabilistic structure encountered in practical application and not designed artificially for learning or other purposes.
d
bf3ff02819820f96f3a95eb04ba64d3a
While such equivalency tools can produce compact surrogate models, standard MOR has significant drawbacks in certain applications. For example, the majority of MOR techniques used in power systems are only applicable for linear systems (e.g., prony analysis and matrix pencil methods {{cite:f007c5de6778de69bb30088e76b2e00f68937676}}, {{cite:e00cbe0aa5c909338143c8744abfbc1a9f475da7}}; Autoregressive models {{cite:0837baba3c2be14dcf78fc8fdf79bb37a2caeb14}}; Gramiam-based approaches {{cite:2aa34be8fb8d25aef612b56c9d7948d1ba729b82}}). Second, most MOR methods are projection based, and the resulting dynamical model must still be directly simulated by an ODE solver. Finally, most classical MOR tools which are applicable to power systems cannot efficiently compress any given nonlinear function with an arbitrary degree of accuracy. For example, the Koopman Mode Decomposition requires infinite terms to approximate a logistic map {{cite:4add933bdd59be010014116726f9252590a8446e}}, and Sparse Identification of Nonlinear Dynamics (SINDY) {{cite:bd7fd43874731d3cc19ce0a44d82a29c053d7cea}} may fail if the nonlinear basis functions are poorly chosen.
i
cdb235a3130f5ca1ee3b5b3cf703ee2b
We compare all methods on the Completion3D benchmark {{cite:fd10edd57e2a17592db03529eb73c34482619668}}, an evaluation platform designed for 3D point cloud completion, and replace the original dataset with our generated synthetic one outlined above. In our setting, TopNet {{cite:fd10edd57e2a17592db03529eb73c34482619668}}, PCN {{cite:cb58a4278f46a086feda200fb6e793bcdaae652a}}, FoldingNet {{cite:39b85244978c11f970a40b9874950ab95d88c99d}} and AtlasNet {{cite:d59b5dbd13670a28c33375e36b2c4a08a45776b9}} directly predict a complete point cloud containing 2048 points, whereas our SA-Net outputs a 1D array with 2048 values from which we further decode the sparse point cloud. According to the analysis in {{cite:cb58a4278f46a086feda200fb6e793bcdaae652a}}, we use the PCN encoder for all methods.
m
3f282dd39a7787a4e27ead5cd6daadde
Existing saliency-based WSSS {{cite:376e1b4781ab333eccafbce0653e305bf4884041}}, {{cite:c946c1f57741ba482e8bec1d33508af2ddf918fc}}, {{cite:e2d56b88f434e95f144620e6fada830151cfa1d0}}, {{cite:f1e304a59037267f8199d8c6f090c237bfd5ec41}}, {{cite:a2f3d41328d2eced6e4726b50f866802397c3a32}}, {{cite:8fb52ead854bec6aad03e41af0464aaacc3510e2}}, {{cite:d9695bc41a1f577e0c2f8efa6e0f51ca631d793a}} and SSSS {{cite:e2d56b88f434e95f144620e6fada830151cfa1d0}} methods utilize both saliency detectors (trained on the DUT-S {{cite:e5231def7490f7bc76df49468c61236e5c5bdba5}} or MSRA-B {{cite:720dd716a660497e96128e0e10eb7152a883f387}} datasets which have pixel-level binary segmentation ground-truth for a large number of overlapping instances in the VOC12 dataset) and a portion of semantic segmentation GT, respectively. Following this line of work, we choose the objectness-based dataset to introduce a better proposal model which addresses the severe center bias issue of saliency detectors (see Fig. REF (a, b)) for WSSS (e.g., saliency inherently ignores objects near the border). We compare with both WSSS and SSSS techniques since we do not fall neatly within either category of supervision (i.e., comparing against methods which use only CAM is unfair but we also do not use any semantic segmentation GT). Moreover, in contrast to the previous methods {{cite:6ea470f335b932eba1d9d00a7cd8ce3883021ce9}}, {{cite:e0ed02d4fe94f75a37551e38362f65c66fe97e30}}, {{cite:a2d22485bdc765f7cf90e4cbff138197cb5c4753}}, {{cite:e92edcf37b80a6edb3e885afbffbb003d9b72d0e}}, our framework does not require multiple stages of label inference and training for pseudo-label generation, but instead operates in a single stage. Additionally, the objectness branch improves the performance of the segmentation network by propagating boundary and semantic information back through the network. We believe the objectness branch helps with semantics because it forces the model to treat objects more uniformly (since the objectness label is binary). This can guide the segmentation model to treat nearby pixels as the same semantic object class and promote more spatially uniform predictions, which is correct in many cases.
d
8bab39bc6cb9797046798bd11cc1f17f
are the (generalized) Laguerre polynomials (see {{cite:1b822bae245f2f39ed98b95ee6a4e212d6122070}}). In particular, {{formula:4eb4930c-e3cb-4891-a27e-bd338357766c}} {{formula:8f8f9545-23dd-452a-9cb2-7bb2c9b15f73}}
r
2e2f7ab90e97d5dac8e70a89b8a64d49
We start from the model for a three-dimensional (3D) magnetic-doped TI thin film along the {{formula:1d83a9b2-d6cb-4fbb-a496-3bcda940c0ac}} axis {{cite:c5c783aa69adb351920280a4cd7b29f21695d146}}, {{cite:f59c4705d1694d496766d56a3cd004b83c38566b}}. The low-energy excitations around the {{formula:767a3420-140b-4ede-9753-14c364ab02df}} point consist of a bonding and antibonding state of the {{formula:004e08f9-15cc-4678-a316-465b0045c81e}} orbitals, labeled by {{formula:d3edf725-dba0-4dcd-8751-54e4c73f183f}} and {{formula:94614b9a-0650-49b9-8048-de1ab47f328b}} , with {{formula:459afb2e-9b99-4ed0-b195-b0c1dfa4a372}} being the even and odd parity, and {{formula:12d6baf9-fb0a-48b2-8240-138d17c193d2}} , {{formula:ed85518f-67b4-411f-969d-1fdd7310b747}} denoting the upspin and downspin. In the four-component basis {{formula:fd1277d5-7003-4729-8e8c-2acd55a96ee1}} , the Hamiltonian is written as {{cite:c5c783aa69adb351920280a4cd7b29f21695d146}}, {{cite:f59c4705d1694d496766d56a3cd004b83c38566b}} {{formula:03d7d694-43c5-4fa4-bb3a-05e10c269ce4}}
m
36f739226db095d0a70a8269f2c35f6f
There are few small adaptations on some methods to provide as output positive, negative and neutral decisions. For this, we have used the codes shared by the authors of {{cite:450add519eaeef91e31027a289bcf18de1b21a24}}. More details about these implementations can be found there. The considered methods include: VADER {{cite:bcb79ef6b0196fea727d805f880662429f4b7fb3}}, AFINN{{cite:f5772d45e9c21e37a8d078b9cbee9819cda1a314}}, OpinionLexicon {{cite:b1c0510a06ed2201a92af6d3e01f2c7b55360ceb}}, Umigon {{cite:3ae99876931ae1c2377875976a051f15474dcad6}}, SO-CAL {{cite:bed909cef60fb4e781056128eb297085a041a8ff}}, Pattern.en {{cite:47187eae28c647c1fb017f3aff81965a53563040}}, Sentiment140 {{cite:7b705046683936bfceff67fa7721ddf979987a65}}, EmoLex {{cite:d120707da85c8e450fef90640ade2aa850f5d0a7}}, Opinion Finder{{cite:f5d954b6409162e3a14b6e26df0c113a67b94b6b}}, and SentiStrength {{cite:f5e9704dd8d01b991a102e0761e0153c26987e26}}. A brief description of these methods can also in found in {{cite:450add519eaeef91e31027a289bcf18de1b21a24}}.
m
03819a5afd3270b028c6c25a3bab11f6
We focus on the production-destruction equations (REF ) and derive MP MS scheme in this subsection. In {{cite:cc4a00d9554d8cc8c54cfb3f3e787b14de685658}}, the explicit SSP MS methods for the nonlinear ODE {{formula:303502c5-04db-4605-8d25-dbdfb27b57e7}}
m
66bb9ad29ccb4519ff86a1674ccf5a46
Our major contribution is to exploit the existing motion history in the scene. With the explicit modeling of the motion history, our model predicts the motion between consecutive frames and predicts the future frames in the motion space. Besides in motion space, SLAMP predicts the future frames in pixel space. With these two predictions, SLAMP achieves a decomposition of the scene by attending pixel predictions for the static or occluded parts of the scene and motion predictions for the dynamic parts of the scene. SLAMP achieves state-of-the-art results on challenging real-world datasets with a dynamic background while performing on par with the previous methods on generic video prediction datasets such as KTH {{cite:bed5c44488f3a5de337545d937d7e0550e5d0134}} and BAIR {{cite:e7bbc923795569e5b3279b24a5886a806fe31c5d}}.
m
8d18d21ba8d8485f777d05a55ec74bed
The flexibility and range of action of ML and QML techniques is typically specified by the so-called universality approximation theorems. A universal approximation property takes place when a proposed restricted family of functions can approximate any function in a much larger class with arbitrary precision. There are many results of this type that are part of classical analysis dealing with, for instance, polynomials and Fourier series, and others that were added in the early days of ML like, for example, feed-forward neural networks {{cite:b6e43fb168f26071c956d579600f453ced5fea42}}, {{cite:4aacd1bd2c37037d5f08e801fafd8ff1a945adb5}}, {{cite:35f088a2f4dc3d400d8778a754e00af7a9901871}}. Further results of this type have been proved for various ML paradigms like recurrent neural networks {{cite:dbcb4446c60ee90b7546b44a9224fe67e9215e40}}, support vector machines {{cite:d5c8b24ee53910bffd69b10a11f29709b2b327d2}}, extreme learning machines {{cite:a04932bd7f80e66eabd50a921eabc54a0f0dc635}}, {{cite:e2be7970213e2c79211eec4dda2ab942ac287d76}}, or kernel methods {{cite:3594c2728c1d9d197c7b531c349ac831343be3c5}}, {{cite:0ee84d5155ce60ce93cc391f7e6ad0ef303e5378}}, {{cite:c6ff574660c7ed52c78eb6db0ad65edf859d3c6d}}. Universality results have also been obtained in the QML context, such as for one qubit algorithms {{cite:792102fae3004b04a1e728b6669c9694cfe225d7}}, {{cite:ca72cbc0a397906f4bdd2b66a1319857a99f551f}}, and general quantum circuits {{cite:817ed52e24033d750266b61e93439f50272d1549}}, {{cite:de2765db8c7f246f967da7c78b42efbea68af901}}. A framework in which we are particularly interested is quantum reservoir computing (QRC). As in classical reservoir computing (RC) {{cite:2904de6d28a4cf0e54e3865f265e2b866ad45a43}}, {{cite:a4ae05d94c4ea979ab117a0b9988ef7e57363973}}, {{cite:4c8b1342e0e2a9dd0a6b61f9ed1b2610d4f29449}}, QRC harnesses the rich dynamics of (quantum) dynamical systems to solve tasks where memory and prediction capabilities are required. Since the first work on QRC {{cite:af34640031790008e5f28e9cea321c29bcd4d15a}} many have followed (see {{cite:446f6af3b902d98cdfbaee8002b5987913e3e315}}, {{cite:e1988d058e42d50708e9df6daf7541105bcf33c9}} for reviews). This includes both experimental implementations {{cite:ebe896d751732b244ad239db245fcfda8c2eb509}}, {{cite:4a68b8585429ade9a86deb60d68a7281fcc56dd8}}, {{cite:f41ca6416fc66c07245299f6d5dd49b7f1a34b0a}}, {{cite:efb34fec2db096824ddc99bf74acfa3205139583}}, {{cite:09c11aef4edafc1f98b69fd4bb765aefa5d1c422}} as well as theoretical contributions on the universal approximation question {{cite:49c09f50834a55a8b86ca92621dc83771707b04c}}, {{cite:ebe896d751732b244ad239db245fcfda8c2eb509}}, {{cite:305740f2d4db3904e0a4c580703d7ba6cd35c1b4}}. The latter was inspired by the works in the classical framework {{cite:bf210770d3c7b1b3c3b8ba66deaf86e19b10ebed}}, {{cite:66fe20d0fe839de8c8ad2ef17bccba4be1645925}}, {{cite:4aa8d360eb8e0fe492d5d42281642ee12e442374}}, {{cite:fc5cbaf7e77201b0c0a3a843a991f010de8add7f}}, where the discrete-time setting of RC theory fits well within the quantum dynamical map description.
i
1339ad57fca31a1f45f55a49192b8ede