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The synthesis results using GAN without the cycle constraint, CycleGAN {{cite:fb6f7dc12ef5ecff68f9a4da96b58ceaedc8556a}}, and our proposed method are shown in Fig. REF . We can see that the CycleGAN produced realistic images, while not being able to achieve structural consistency. By contrast, our method was able to keep the position and shape of the tongue consistent between the two modalities. The resulting images were expected to have realistic appearances and to be structurally consistent with its corresponding paired ground-truth {{formula:7177b200-fef3-41e5-b6d5-8454ad998ef1}} . For our quantitative evaluation, we used four evaluation metrics, including mean L1 error, structural similarity index measure (SSIM), peak signal-to-noise ratio (PSNR), and inception score (IS) {{cite:68aa84ef37af2ca4f7cad81bbfbc04febaaaef9f}}. Table REF lists numerical comparisons for the eight testing subjects. The proposed framework outperformed the other two comparison methods w.r.t. SSIM, PSNR, and IS. Of note, all of the compared methods do not have the L1 minimization objective as in {{cite:68aa84ef37af2ca4f7cad81bbfbc04febaaaef9f}}.
| r | aade2cf3af6be8456ff6819cd444c653 |
A useful consequence of the Representation Formula is the fact that if {{formula:d057f6a4-9894-455e-8177-d2fc9d6d7024}} is a holomorphic function with respect to the left multiplication by {{formula:27a3b54c-a37b-466c-8894-d6664869a86c}} , then there exists a unique slice-regular function {{formula:0b9f7792-4d0a-4e0f-8c2a-c191910bbb17}}
such that {{formula:d661412e-1f1d-4c01-802c-a6c18bfb678f}} . Such a function {{formula:0a28239c-68b7-46f3-acfe-eab20a83aeae}} will be called the regular extension of {{formula:5aefcd4c-5eb9-4111-9d91-fd2bd5ddbd9f}}, (see {{cite:ebddee9c8579c8df456d31d9c9617d9a7a4c1019}}). From now on if
{{formula:1fc14b68-1ee3-4a75-a524-655d68486e7f}} we denote by {{formula:ef7a39cf-e265-4bc7-bb30-985cade1aa94}} its restriction to {{formula:757a5103-4072-4f59-b79a-a2a92f31c7d1}} .
| r | 3c2950251c4f6161bc6bb5ec8b3602ef |
the resulting eigenvalue distributionWe only concern the eigenvalue distribution of a reduced density matrix as the observables of interest, such as entropies and capacity, are functions of the eigenvalues instead of eigenvectors. (entanglement spectrum) of the reduced density matrix (REF ) is known as the Hilbert-Schmidt ensemble {{cite:1e1cd75d5394f7d32f4b0643ebf62ffb74d841fe}}, {{cite:988151e04217dd1dc4146d21f05c0464b748738c}}
{{formula:111043f6-850c-4047-b876-44034f01c781}}
| r | 47d2d56607bd4af073435d4b0d8f8041 |
The goal of this work is to highlight difference between classification and retrieval robustness to label noise as well as to study retrieval-specific types of annotation errors. We choose ArcFace as one of the best-performing models for our experiments. Future work can extend presented results to a variety of training objectives {{cite:9702c3fe54c266bc215834986e8a5bb29f7224e6}}, {{cite:79ca6e179da4955ed5caadcd4397b7b08fcc92d3}} and model architectures {{cite:2ae664a7617d6b3e52b06f9cbbf4ede0f0805c7d}}, {{cite:e869df0e726df3a8b4765ae549e95c164cdf6304}}.
| d | 8dca8e57bd8cae4cf566d2a3945ea4e4 |
Motivated by applications to homogenization of particle systems {{cite:10aa9f7433cda33afdf2d0123024937a7e9a8585}},
Giunti, Gu, Mourrat, and Nitzschner recently addressed
a similar problem, and proved the Gevrey regularity of {{formula:864b7fc7-931f-4d19-acbb-e6ca357d4895}} in {{cite:cefcb4b7d90a1fcb8a7cebe3da2d7c7cce740cf4}} (a variant of {{formula:71a03ef8-b62a-4416-a5dc-4d169af3dde2}} , cf. Remark REF below). Their approach is based on Poisson calculus (cf. {{cite:0a41a2c5a55b1f0f69c1822deb3f585184778b2c}}), which they use both to derive formulas and to prove estimates. In the introduction of {{cite:cefcb4b7d90a1fcb8a7cebe3da2d7c7cce740cf4}}, the authors point out that their approach based on Poisson calculus could be used to prove the regularity of {{formula:2f9eae36-eb33-4c16-af36-a2bc3e19378f}} .
Besides that regularity was in fact already proved a few years ago in {{cite:627550d28d8c0b726c8e6ef91c450477a8762a4a}}, the approach of {{cite:cefcb4b7d90a1fcb8a7cebe3da2d7c7cce740cf4}} is mostly a specific reformulation of the general results and arguments of {{cite:7c521de9770fee061d1cfc98d05a14e0be302192}} (based on the original triad local approximation / cluster expansions / improved {{formula:3e527acb-d1f9-42c2-9e92-d2ca551c5c8a}} estimates) using Poisson calculus. The only new ingredient is a clever use of the independence of Poisson processes, which we have summarized in Lemma REF below.
Note that {{cite:627550d28d8c0b726c8e6ef91c450477a8762a4a}} is not cited in {{cite:cefcb4b7d90a1fcb8a7cebe3da2d7c7cce740cf4}} (it was announced in {{cite:7c521de9770fee061d1cfc98d05a14e0be302192}}), and that {{cite:7c521de9770fee061d1cfc98d05a14e0be302192}} is mentioned in {{cite:cefcb4b7d90a1fcb8a7cebe3da2d7c7cce740cf4}}
without detail and at the same level as {{cite:bbaa5576b1f34594daef1a86c7ba8a5103e3b8bd}} (which only treats first-order expansion in a discrete iid setting).
| i | 9d5beaf72b86fcb7898a4ae070594631 |
At last, another contribution of this paper is the Fair Tyler's M-estimator (Fair TME) model (REF ) we propose and solve in Section . The Tyler's M-estimator model {{cite:079bf9748b298de7f4fc883d4f04681db035bd65}} seeks to estimate a robust covariance matrix for a dataset which might contain outliers. This model and solution approaches for it have been studied recently and extensively {{cite:ab7c7bff4a002d1ca3d380c1d6ec759c23bbf962}}, {{cite:5e10fb3fa61e3e96c274a08b8b77a38dbcd46765}}, {{cite:5ef6fae23af0e7229b377c11bb682efa0d465163}}, {{cite:9db9d4967d4837b93251bcaeddef481bddc4b619}}, {{cite:04afc16c729bca37c8bb5762347eb6669c24f98d}}. Additionally, in recent years the discussion of fair models in data science and machine learning has increased {{cite:0a6a1975956d83684902ed2aa15da59d5f9ed98a}} leading to the development of models like fair PCA {{cite:419e03d520f772f466aa78dd89fde132ad18ac6b}}. The Fair TME model we develop seeks to find a robust covariance matrix that fairly represents different subgroups of a single dataset. We test our fair model on both synthetic and real datasets and demonstrate its superiority for fairness when compared to the standard TME model applied to an aggregation of the datasets.
| i | 4466480ee1b13a4e6267505676a3666d |
We note that, a similar approach could also be extended to the study of protoplanetary disks in dense environments under the effect of flyby stars, since in principle the disk hydrodynamics and the stellar dynamics have different time scales in a numerical simulation so the effect of passing stars could be simplified as a stochastic process (e.g. see {{cite:5f7436d6db1160d8e998d9126ae9204d33d15235}}).
| m | ac2b2e36fc40226c241d768a9867ed4c |
Before presenting the strong decays, we need to determine the quark pair creation strength {{formula:905b93c8-92b6-4fcd-8f5f-5ddfaf73cdd0}} firstly. As we discussed above, {{formula:f6a05106-a264-4862-9f63-fc2198818d24}} may be a mixing state, and the assignments of the {{formula:c165b71c-5bed-4ad5-8876-ed8efa6f9ef8}} and {{formula:7e76d9be-770c-41ce-aa8f-2926ede207d3}} are still in debate due to the unknown quantum numbers and poor decay information. In this work we take {{formula:1627e45b-6b07-48c5-bfc1-97e0945e321b}} by fitting to the experimental widths of {{formula:a041c303-76d7-477e-98ac-bcd63c05a956}} which is regarded as the {{formula:b19477ba-1efb-47b8-a639-042f1cb24306}} state in previous works {{cite:101d4fa2319e06c108aaf6595f5351c71b9ff362}}, {{cite:11d8341c342cc63dac12ee0e04d424e3fb13e5a7}}, {{cite:6298b8fe99c55cc18d64e162c74a346a97299022}}, {{cite:a945555b6fdab44cfb47c9ab118c4d9bb611d0a8}}, {{cite:ecc1375350379f7e36fdc332ffa57bf5335e3de7}}. The decay properties of the state {{formula:c2c5d80b-0de3-4aad-b08d-254a1c68bd6f}} with the assignment of {{formula:3ed3432f-5283-4977-ad61-7b2a29f2bbf7}} are shown in Table REF . The ratio of the decay modes are calculated as,
{{formula:20af3705-0ef4-4cae-8893-2dd8cdad5588}}
| r | 9b62e3c5c4f5bd9bba900036f6039878 |
Indeed, the proof of Theorem REF identifies a key yet unsurprising connection between the notion of true skewness, which is fundamentally a comparison of the rate of decay of the two sides of a distribution, and the hazard rate. It suggests that the notion of true skewness is an accurate reflection, and in a much more rigorous fashion than Pearson's coefficients of skewness, of the essence of what we imagine skewness to mean. More practically, the method by which we prove Theorem REF should work for a larger variety of distributions; a reasonable first direction would be skewed versions of other symmetric distributions, as introduced in, for example, Chapter 1 of {{cite:45863800d488a970b8acd4673bd4020c11ae50c5}}.
| d | 97819edae4c2725eac7e131bc56c98bd |
A well known variant of Newton's method is Levenberg-Marquardt algorithm {{cite:d7417a7cc7493b8359ab79283bf73cfd3b00640c}}{{cite:65213432192a1d69007b66f36847345a702a4c89}}, very popular for using in the least square fit problem where the cost function {{formula:948febe9-b9db-4097-b2a3-67c95b8d2f42}} is a sum of squares of real functions: {{formula:c6acdbd9-e8c1-4435-8fc8-413da86aafd6}} . Let {{formula:c5fe28df-5c6f-4abf-91f1-ac5a02bb40e0}} , and {{formula:341b8f0e-9cf9-4366-aa35-bbd644ae5e25}} the Jacobian of {{formula:7be51db1-c933-4ee0-a39c-11daebe7388b}} . Then the update rule for Levenberg-Marquardt algorithm is:
{{formula:a67aad51-eceb-4b84-8863-59cc3af37c1e}}
| i | cd6af84e2585fd890c0ddc9b146b8e65 |
We use the same architecture, hyper-parameters and training setup as in prior work {{cite:b6c1bc2f0f4c4a7594cf1fa779faa66685f89c65}}, which we report here for completeness.
The architecture is depicted in Table REF .
All models share the following hyper-parameters:
We used a batch size of 64, 10-dimensional latent space and Bernoulli decoders.
We trained the models for 300K steps using the Adam optimizer {{cite:b890dc77d4fc94a93dab0ef52007d345eda4c14b}} with {{formula:ce094cf9-65b7-4e9c-9d1f-99677e4708b2}} , {{formula:6fbc9b32-efb4-4daf-855b-2142351b1fe5}} , {{formula:d5f5ad2a-819a-48f4-9a92-ecb8924f2198}} and a learning rate of {{formula:a33ce60a-f257-4f58-b8bd-5cbda735dfbf}} .
| m | c925593dea80b3cd913d5ecd6fa84d90 |
Both the generator {{formula:89c39009-dbb0-4769-8125-bfae03ef8870}} and the discriminator {{formula:66af400c-7b3c-4bbb-97d8-3cc4f4ad3331}} are parameterized by neural networks. We train all discriminators models for {{formula:e6cb39d7-59e3-4040-ba9f-d8c9db3b7e5a}} k iterations. We use TensorFlow {{cite:d6300fc22ef831ad9a598799af36a7e1d1c2392c}} and Keras {{cite:a7b7039dcf76619743365bb05a5bbbbf1c34a1ad}} to implement the proposed models. Details are discussed in the Appendix.
| r | 59667723767b4a9c9544175eaefb088c |
Feed forward neural networks which are used in this present study, are the most used architectures because of their structural flexibility, good representational capabilities and a wide range of training algorithms available {{cite:5c26b2584a2c29254859aafb7604af7ef79278e3}}. All input signals are summed together as {{formula:ceb4162e-ac65-416f-8425-09997f183b31}} and the nonlinear activation function determines the output signal {{formula:4214fd77-aedb-4288-b947-f014574653e7}} . We use a sigmoid function
{{formula:7bb036da-18f5-48ba-af29-a395de1bb8fc}}
| m | 6cec528e7b31b71596386bd1f27a7e4f |
While our method works well in many practical scenarios, it still faces some limitations.
Particularly, the StyleGAN alignment process is prone to leaving portions of hair (e.g., pigtails) outside the cropped region. These `external' regions do not undergo any semantic manipulations, and may result in jarring transitions when attempting to modify attributes such as hair length or color.
A further limitation arises in the form of the `texture sticking' effect investigated in StyleGAN3 {{cite:f68fda1eabc30cb0e797de10d0ed7bb1b9d82f13}}. The use of per-frame optimizations, rather than latent-space interpolations, significantly reduces this effect. However, in some cases it is still visible. We hope that as inversion and editing tools for StyleGAN3 emerge, they could be joined with our approach in order to obtain sticking-free results.
| d | 8dcd63b9391eec15f91090095c27cb4d |
Even though point-based methods are easy to implement, it performs one instance one task and one has to resolve the optimization for other instances. This would sharply increase the cost time in reconstruction process. Therefore, this work proposes other computational modellings for learning of one class one task. Among these modellings, vector-based methods are the simplest.
As subsection REF shows, this class of methods learns the mapping between the temperature vector of monitoring points to that of PoIs.
This work selects the multi-layer perception (MLP) {{cite:603ec22482f656d523ffccbd784818c114ac16ae}}, Conditional Neural Processes (CNP) {{cite:e08b4252f8f5ba333e706b553956d928f4aa8b6f}}, and the Transformer {{cite:aab66ce43f8184a4bc9ee9eb3e78ecd37f0642f4}} as representatives.
| m | c762d6739765598105d6d669a9885096 |
FCGF {{cite:c9de91d36058c09da087f59c15d1448601ddd01d}} is one of the first U-Net methods that was applied to point cloud registration; thanks to the architecture and the sparse voxel convolutions, this method performs very well. It is also much faster than patch-based methods in inference. D3Feat {{cite:ced33c90e4eaf6e492f13879a42ff5ed03903a04}} uses Kernel Point convolutions {{cite:82020ee6540f9c7c276965e52b601995469443ee}} and jointly computes the detector and a descriptor.
FCGF and D3Feat show poor generalization capabilities.
PREDATOR {{cite:fd9056d9e132c87aa5c93b843ea7ebffe28c3e27}} is composed of a Graph Neural Network and a cross attention module to compute meaningful descriptors, even if the overlap between two scenes is low.
These works reveal that U-Net-based methods are more flexible than patch-based methods. They can be coupled easily with a detector or with an end-to-end method {{cite:da831a8c1ef7582ea929425a9b90898c6a9cd981}}, and can also be used in multi-scene registration methods {{cite:5e2e6d9a08a8afeb5d81b395b88785506192ca64}}. The main problem with these methods is that they have poor generalization capabilities on unknown datasets.
The proposed method, which is mainly inspired by FCGF, maintains its advantages (speed, efficiency, modularity) while showing much better generalization capabilities than FCGF.
| m | 2ed4dd7da8841df73d0c23cdb99345c6 |
The camel-cow binary classification problem presents a typical example of the class-specific spurious correlations {{cite:61964b657c55a4e7c5dcde9125dbaa45c9f0d589}}. In the training dataset, camel images almost always exhibit sandy background, whereas cow images almost always exhibit green background. Extracting only the background color in this extreme case is sufficient for high accuracy on the training dataset. In test time, however, the networks then misclassify an image of a cow on a beige background. `Sandy/Beige background' is one type of a class-specific spurious correlation associated with the camel class, since this modality correlates with the camel class significantly more than the cow class.
This form of spurious correlation is well-studied in the binary classification setup {{cite:74f2e7c654d3fcc43db31e047a64deba1d3b92a6}}, {{cite:61964b657c55a4e7c5dcde9125dbaa45c9f0d589}}. In the multiclass classification setup, we additionally identify a new form of spurious correlations taking place:
| m | 8be98a560a9c660b2acb3de78a2945e2 |
The ODE system (REF ) is often stiff and it may be advantageous to solve it with an implicit method. A first order method is the backward Euler method {{cite:328f246751c0e45c85d0c9de32e1dd7ecf3c0e78}}
to compute {{formula:ec6009b5-e81a-4e75-885b-0aedc8a5709d}} :
{{formula:37db60b5-bb35-4f68-84b7-ccaff5b4ed1d}}
| m | 3a8819953dfdb41396828d5d3d67c44a |
Pre-trained extractor - Extractor-Abstractor framework [{{formula:e4b4ed9f-5ee6-4869-a1e5-a403a34502ae}} ]: The pre-trained extractor of the extractor-abstractor framework proposed by {{cite:2343f909ace1effe15c4aae657e257645e2458cd}} on ROUGE-L based exemplary-extracted sentences.
| m | 8405fccfa0e31255613ea93430558d8d |
In practice, the true number of clusters is typically unknown, and hence data are used to select a good value. In frequentist inference, model (REF ) is typically fitted with the EM algorithm for varying {{formula:cbf679a8-414a-4332-b5c2-62c56766baf7}} and then AIC, BIC or another criterion is used to choose {{formula:a2a688d8-8e70-4497-b81e-a7b6c3fc5c36}} . In the Bayesian literature, there are many approaches to account for uncertainty in {{formula:4e48557d-2ee9-48f1-8e8a-9bcdc11819bf}} and/or {{formula:b17e8c5d-6f20-4846-8d00-09711d342703}} . {{cite:dd26af155d1435379bf47e0cb7ea9bd41a53e3ee}} proposed to choose a prior on {{formula:919e0d70-22d3-44d2-9868-2c49c2358f29}} , and then update {{formula:b96b44e9-d8f2-4237-912d-b4373dd86af5}} along with the other parameters using reversible jump (RJ) Markov chain Monte Carlo (MCMC). Although RJ-MCMC can be very inefficient, {{cite:0595b7c789a8c3629870f9bc2e18a05f09b6d764}} proposed improved computational algorithms for inference under such mixture of finite mixture (MFM) models. {{cite:6e8956edefb0b24c54c0c01c306337aee89a562a}} extended the MFM class in several directions. Alternatively, a Bayesian nonparametric approach can be taken, letting {{formula:a6a82e3b-2ac5-4db6-ac0c-07362a829c57}} in (REF ) with {{formula:ef48ef42-1eaa-404c-b588-74fca457aab3}} increasing with {{formula:67c247eb-abb9-4d0c-b690-3be3b38f0669}} . Under a Dirichlet process (DP) {{cite:285407030bed09f740f398e137287244d6e43622}} {{formula:c262343a-8f34-494e-a330-3a6bab807b6f}} increases at a log rate in {{formula:99e50ff2-0191-4584-8997-f0242af14152}} , while for a Pitman-Yor process (PY) {{cite:b0b60e8434eae0a3e4ede450f339da9ca2d9f479}} the rate is a power law.
| i | 7506cd527b02c24f4348c96a3f3637ab |
The difficulty of knowing when the bubble crashes is a absence of any sort of fundamental value to measure price deviations. There is however a inherited risk of a crash that in Perepelitsa and Timofeev {{cite:7eec97af5612c19f1d86f8cb20e21b50601fba38}} we identified with the process of re-distribution of cash during an lifespan of ASPP in which a sizable group of traders run out of cash and become heavily invested in stock, while the other group accumulate most cash. Many trading processes in random environments, typically, have this property (Dragulescu and Yakovenko {{cite:ac7b449839952a221efcca5cddec0eb79d7fe32b}}, Basi et al. {{cite:30d00f7503c15af18e09fc47b7b19f04d05c4966}}, Cordier et al. {{cite:24bc0eaaf4eb9cce7072bf4980875d1f29d1ffd2}}).
| i | 6a0ad9741074c630e4901eb727a2efba |
Fine-tuning on other datasets.
We validate the effectiveness of Elodi when transferring to iNaturalist {{cite:3b9529b8897efcda2979e88cb0916c4510a30797}} following the protocol in {{cite:a93899a6cb8b3d9ae874e1c4d8c56ba9ee3e11fc}}.
Results of both full-data and data-growth setting are summarized in tab:iNaturalist.
{{table:76febaa5-58ce-40c7-a471-633b72fe98d0}} | r | b15a2b1613806448ce89a04d09436e60 |
ResPES at the Fe {{formula:8f575c2e-aca2-490b-9139-1b6c7c75e23d}} edge. The method of the resonant photoelectron spectroscopy for electronic correlated systems is a unique tool allowing to clearly assign the studied objects to one of the classes of insulating systems which are classified according to the discussed Zaanen-Sawatzky-Allen scheme {{cite:5644bfcf8020753dd854e90f3209fafcdbfd62b7}}. Figure REF presents the compilation of the respective results for FePX{{formula:f0619fda-c3f5-4b58-b2fc-a17e0a25234c}} crystals: (a) reference Fe {{formula:34b4bb64-b3cc-4787-b19b-1cb39510398a}} NEXAFS spectra and (b,c) a series of photoelectron emission spectra collected at the particular photon energies marked by the vertical lines in panel (a). For the ResPES measurements of {{formula:8d5920d1-790d-4e25-b9ae-b1dee2256180}} -derived valence band states at the Fe {{formula:ef4dc764-4d84-4a64-b186-941aadad1718}} absorption edge on FePX{{formula:7015a047-59a7-4e2a-be88-40f4aef7b3c0}} , the photoemission intensity is a result of the interference of two photoemission channels {{cite:bd3c3ab09d6d5bdb4e7a1e4e714bd7705ae62645}}, {{cite:278885753e3da45fecf12c94eef11d5f1761c427}}, {{cite:1d30ad353f3c55c0bb66bfa0e68d4b71a0536fdf}}: (i) a direct photoelectron emission from the valence band states {{formula:b9ff0fb3-ea7e-4243-9aac-4e78a902b99d}} and (ii) a photoabsorption process followed by a participator Coster-Kronig decay {{formula:e28b1b91-6e97-47ab-bdb5-cc9af110c5c3}} , where final states for these photoelectron emission channels are identical. The interference between these two photoemission channels leads to the Fano-type resonance for the states with the {{formula:1a9f3125-13a1-4f99-b23f-158f6bf389a8}} final-state character.
| r | a01cecfe1af817b56c73111fd89efc39 |
We propose two ideas to deal with the problem of implicit GNNs: one is to design a sophisticated network structure to better approximate the latently optimal weight distribution; the other is to change the loss function of the LTS. For the first idea, no model has the best performance on all datasets from Table REF and Table REF , which suggests that we could try to design a new LTS or network structure with better generalization capabilities. For the second idea, we can change the loss function of the LTS, making the weight of messages learn the structural information of graphs. Inspired by network embeddings {{cite:8baa3c500416a162eea8d9d32a072f231b6c1e28}}, {{cite:8d057e8f6e72409520f9a2b3c86712b8b445521a}}, {{cite:17581d9b4c9a0343a34608c41ea8200d1cbca36b}}, the loss function that retains the local or global topology structures may be added to the loss function of the LTS.
| d | f922fa8c06fe020ac003dd3906939420 |
Demand of large values of {{formula:b63c8e63-4884-4a07-abf9-34ac8e633d42}} as universality condition is rather natural from the following point of view. Consider the Solovay-Kitaev theorem {{cite:8ad0942acad007f87b9db761ae670a5db612cdca}}, {{cite:0a963df768e184cd7126bd5d96bce0c6902d5ab1}} that basically says that if one is able to approximate arbitrary unitary matrices with some zero-order accuracy (depending on its dimension), one also can approximate them with any desired accuracy. Moreover, the theorem provides a constructive algorithm for such an approximation {{cite:0a963df768e184cd7126bd5d96bce0c6902d5ab1}}. We intend to demonstrate the universality with the use of this theorem and find that it also requires the large values of {{formula:a91c3ca4-5eff-4c62-aaab-613a828c67f9}} .
| d | 5bff9f56f4adcb8e862dedc9613d079a |
The machine learning workflow {{cite:64c2619db1cf46a6443f32de547f738934c84aa8}} typically contains “data oriented” stages like data preprocessing, cleaning and exploratory data analysis. The use of relational databases for these stages come with a lot of limitations. Oftentimes, the data collected would not be well structured making it difficult to work with database queries {{cite:27ef939603d766387ceaa0f59ce7f8eaae18a679}}. Writing complex queries would require a strong familiarity with the schema which is not easy in case of wide tables with many columns {{cite:83f4088e893dc6aa3b210e3f9ce3697306a6f3c4}}. Dataframes have been introduced as an alternative to overcome some of these limitations. Dataframe is a data structure that organizes data into rows and columns like a spreadsheet. Over the years, the use of dataframes has become widely popular as they provide an intuitive way of storing and working with data {{cite:27ef939603d766387ceaa0f59ce7f8eaae18a679}}, {{cite:eaafd61f89345b1647545f2556a29f3b7e0fb7b5}}. They are convenient for use in REPL style imperative interfaces and data science notebooks {{cite:dfd774ac17feb47918ac7a3b63ab9fbb27a037b0}}. Several libraries {{cite:0698bcdb655ae8aa0c2c91473a93def0e7cdbd90}}, {{cite:433904ff721456efaa2b4c04c6d5dadfa0eb2b72}}, {{cite:416f5d7bd61ed4a43dda5a298249a1db764edc3b}} have been developed to enable the handling and manipulation of dataframes. These libraries provide a convenient interface to work with dataframes and are widely used for exploratory analysis, data ingest, data preparation and feature engineering. Dataframes offer several features including implicit ordering on both rows and columns by treating them symmetrically. The dataframe manipulation libraries offer data analysis modalities that include relational operators like filter, join, transpose and spreadsheet-like operators such as pivot.
| i | 9d978cfbe558e71fb748b7dabdcedf02 |
As indicated in the introductory section, next we shall provide a set-valued analogue of {{cite:89602ef1bfafe51095391e35fa573a727987a3c3}}.
| r | 40748e9e0f20d8dee72fba5cca18a96d |
With the exception of the UDR metric {{cite:bd78e5c8f76b08b59b0d2a5aae1f8cde1e9c9dd9}}, common techniques for evaluating representations for model selection rely on full knowledge of all the ground-truth factors of variation. We emphasize that the triplet score only requires knowledge of which observation is the odd-one-out. Furthermore, we aim to compare against the UDR metric in future work, however, we note that in comparison our proposed method requires far less computational resource.
In line with previous work {{cite:f9be2ab81ccd996633ea493746de193187cf3f5d}}, {{cite:03ec84edf34628f279b647e9959248abc1201f73}} we calculate this score by training a GBT classifier on 10,000 points and test on 5,000 points, however, we note that any classifier capable of implicitly comparing the distances is suitable (such as a MLP).
| m | c5d9bac1311647cedfc58c6155c57a9a |
In this section, we report on the experimental results obtained on KADID-10k {{cite:3862965b360fb6440f3f297bd7411b9402399a41}}
database. The rest of this section is organized as follows.
In Subsection REF , the evaluation metrics are defined.
Subsection REF describes the experimental setup.
In Subsection REF ,
the performance of the examined NR-IQA algorithms is reported on the entire
KADID-10k {{cite:3862965b360fb6440f3f297bd7411b9402399a41}}. Subsection REF reports the
performance
on individual distortion levels, while
Subsection REF presents the experimental
results with respect to the distortion types.
| r | 704bc4c5fc21ac09706c10d78efd7daa |
In {{cite:eaa79075a7a4e106bae6efbf4becde38baaa7ce1}}, {{cite:0d634431f02e9c87bc3d862588d1bf2d27e62c9d}}, {{cite:35138b658f8abe8603dd650bdddf56be6009e888}}, The error estimate about {{formula:cc0b971e-b424-47bc-8efb-93ced9fa428a}} was considered for consistent system or some inconsistent system. For any initial vector {{formula:20b1ce13-6743-4bfa-9d06-7f006c3529e3}} , Kunio Tanabe has proved that the limit of Kacmarz method is {{formula:50fd5c1e-1a60-45d4-8c12-d76d70cae38a}} for consistent linear system, where {{formula:27a5cd46-e039-44f6-b08d-5990f7e64c4c}} has been proved to be a Moore-Penrose generalized solution {{cite:52684567cd9e005ec17b260607dba412204c85ac}}, {{cite:414e4de99336e4a54845c9bbe5a339c8889cd267}}, {{cite:79e21d1b35d440a6a44e1a290f2eae591beaa759}}. Inspired by them, we will consider the theory analysis based on the error term {{formula:2d9576ae-6be4-4c1f-a89f-d1d247e8c85c}} rather than {{formula:1fb78ba6-fdf2-4723-986c-466c6bebdae0}} .
| m | 16126a2ae7cbd62c7660682918a54d83 |
In the denoising experiment on ImageNet, we use the Gaussian filter, bilateral filter, and median filter for denoising defense. The attack type is set similar to the experiment of adversarial noise attack. We only test in the scenario when the perturbation budget of {{formula:2641b133-3805-49a3-bc0e-dc898901ed05}} -norm attack {{formula:493cb667-f171-42f5-9ed7-f4120f8908bf}} is set to 0.0465.
The experiment result is showed in Fig. REF , in which we can obtain the coarse conclusion that denoising methods have no effect on the ImageNet dataset. It perhaps accords the hypothesis {{cite:59312fabfa452f47a42193600c2e324a8648ae80}}, {{cite:5afc716fdb9b29122997ad998be0da8efe7923b6}}, {{cite:894e0b484a1f0553cc04d20093998c57702afbd6}} that the neural network with large class numbers are inclined to be more vulnerable.
| m | 4e0b5334da1c28065095534d57a090b9 |
Next, our approach can be applied to other error correction codes and quantum algorithms that require a large number of gates. For example, most of the cost of a quantum circuit implementation of a discrete-time quantum walk algorithm {{cite:9b289503c350d7a2f4f4660c0b655d4f54f996ae}} is the unitary operator that walks a “quantum walker” in a certain space, called a Shift operator {{cite:5e0b7091ba33ea4b61f534d5d64faaae94e63a92}}. The circuit construction of the Shift operator depends on the space in which the quantum walk is performed (for instance, in a graph {{cite:14093a67a48f0d8a16d30bfc9f811d8ed4d49d71}}, one-dimensional space {{cite:50cf6deb647e3e5dbc809d2fc2422e26864823a5}}, or a hypercube {{cite:bcd86b8efc6282da520502d3337bccc83aeb29af}}), but in many cases, they consist of multiple controlled quantum gates {{cite:220876cf1ee57009cb0c42d8153221adc83dc28b}}. This is because the Shift operator depends on the state of the “quantum walker” at a certain time and transitions to the quantum state of the “quantum walker” at the next time step, and such dependence on the previous time is realized by control gates. A second example is Grover's search algorithm {{cite:564c0d70630ea68162ba83a193d40083ef0905b3}}. The practical cost of Grover's algorithm depends on the complexity of the unitary, called an “oracle”, which depends on the diffusion operator (inversion about the average). When the size of the search space is {{formula:c4a8f774-b329-4692-b998-e86807600170}} -qubits, it is common to use {{formula:50f0aa4e-281e-453b-b528-dab5dab4d4e9}} gates in the diffusion part {{cite:9db350ef2cad5016bd5185bb660c2e23440e80ed}}.
| d | b803659caaad0069273ac57156a9bf7e |
A natural representation of a scene is a graph {{cite:1bf71c976af6e13d48a4c8cbd2edb9eb8bf76f1b}}, {{cite:8b982997ef9472f0a7f32e79bf1d9a7c6b6230d1}}, {{cite:977f996178295a1eee5be4540ab85e7aeac370d2}}, where each object is a node, and an edge is a relation between objects such as `is next to` or `is on top of`. Features of the room such as walls, doors and windows can be represented as nodes of the graph {{cite:da8c893bd0da51fb048f423e160c556f3bed4953}}. This gives a simple method for conditioning – when the model is autoregressive on the graph and is able to generate one node at a time, the input is initialized with the required object nodes and then repeatedly expanded using the model. Such a representation lends itself well to processing with graph convolutional networks {{cite:a17a66413ac0071f36111cb175475ee761527a5f}}.
| m | d28e0749eb72e56bad48ecaf78715ef1 |
We also prove the first hardness of approximation results for {{formula:8b7f2dc2-5213-4478-9c19-e5588f25ab5f}} -{{formula:3628fb47-a00a-406c-91f5-4942a0c38670}} in {{formula:95659c91-79e6-49a2-97fb-dfcf2f27615a}} -metric (Theorem REF ) and {{formula:c9475b1b-4a53-4d51-99a3-ab4c9ca70472}} -{{formula:46f6580a-a2eb-4e34-b400-ac17c368974e}} in {{formula:20215d78-ad0f-42ff-9f97-4267c1e131bc}} -metric (Theorem REF ). Even though continuous {{formula:aed8769e-dade-4496-be92-deb5903702f2}} -{{formula:165086b9-9136-4c85-bbcd-dbf52742503e}} in {{formula:e9ed73c5-f5c4-40b6-9115-c1996bf33058}} has been actively studied for the bounded {{formula:ae964b5f-b5d1-463d-bd1d-36466b8897f2}} or {{formula:a63e4884-4e54-4135-8bad-170a8b8c0a7c}} {{cite:88bdccc4848d9e1b74bbd5dc9a41962759eb41b8}}, {{cite:5e749b813c96c46336a5eed55b57a64ca5cc4140}}, {{cite:02123004cd39a70d71cea9b71d9d3a09b35ce341}}, {{cite:33af86042f7dc129793a8eb1fc35b1d17e4a0f9d}}, and to the best of our knowledge, no hardness of approximation for the general case was known in the literature. We remark that independent to our work, in {{cite:6b13fe08bd3163c777bea9f04f7d7d87850f8521}}, the authors prove {{formula:727fb06f-f10c-4e80-a6b8-c960e950ef34}} -hardness of the Euclidean {{formula:a51b2f8d-5b48-44ec-8042-a51ef16159ff}} -{{formula:bd13987c-adc7-4edd-a437-358910458d93}} problem under {{formula:da429140-85a4-46f1-918d-5174ce7320a9}} .
| r | dc15f9960356ddf426f47f9c346f5054 |
It would be interesting to shed some light on the universality of the expression giving the gyromagnetic ratios in other examples such as flux compactifications and string theories on orbifolds breaking partially or totally space-time supersymmetry. A similar analysis can also be performed in principle in curved backgrounds like AdS or dS where one can use the consistency of the boundary correlators to constraint the gyromagnetic factor also in the context of Inflation. Furthermore, it would be interesting to study the connection of these results to fundamental properties like causality directly at the level of the observables focusing e.g. to the AdS and dS cases where causality can be mapped to concrete properties of the dual CFT correlators along similar lines as in {{cite:f5ab196f3c128df0c719d982899f1e4ef62d0fd7}}. We leave this as well as other interesting related questions for future work.
| d | 0b3738fa6280600b3ec57bc7dea4cacf |
The eikonal equation is a first-order non-linear partial differential equation (PDE) that is used in various applications: geometric optics, computer vision, image processing and others {{cite:21105dfe588450cec0d86af84a8b5d03b7df4f19}}. It is also used for computing the first-arrival traveltimes of seismic waves in many seismic applications: ray modeling {{cite:505c79caf9909a70b1c901b935c53bf4344a8a22}}; ray multipathing {{cite:e2b3b9a86e4d0bb25187a2b99dcff404e88ad4c2}}; traveltime tomography {{cite:d0d1c97bdf254f06a87276cc4c073855113d9d3c}}; Kirchhoff migration {{cite:be5428d97332e0869f902baee18c85bee9d411a2}}. There are well-known numerical techniques for solving the equation: Fast Marching Method {{cite:88656185e63725a63a2c1faa6c872ebeb3230410}}, {{cite:7bd7a45f7c39eeb262edc064ba7cef5d001f0cdc}} and Fast Sweeping Method {{cite:a2e3459a8966836efd30ac5cd99b26a58dc6a10d}}, {{cite:8981759a5eb7296cafea3c61b73bc1149236470e}}. Often, the seismic applications require massive computations of the traveltimes for many source-receiver pairs, demanding a high accuracy in complex velocity models.
| i | 962ee23f9b4faf9e16e9590960eeafd3 |
In addition, figures REF , REF and REF present the equivalent contour plot constraints for the sets 1, 2 and set 3, respectively, as well as the Bayesian most probable EoS together with their mass-radius curves and tidal deformabilities for the GW170817 case. While this paper was under revision in the refereeing process, the NICER experiment has published its results for the {{formula:58472755-ab90-4e18-b8db-1a5d1f008443}} measurement {{cite:4fcae99b9dfae20436ec072539fb15de809d0d97}}, shown in Fig. REF .
We have performed a BA using the NICER {{formula:cabf1ac2-aa2b-4730-9677-deca839d1f37}} measurements for
PSR J0740+6620 {{cite:4fcae99b9dfae20436ec072539fb15de809d0d97}} and PSR J0030+0451 {{cite:997f79b1d2b1dd8aa82da54aeb10f852c9765fd0}} as well as the LVC tidal deformability constraint from GW170817 {{cite:ecf31ae9ae0011e3e76e8cc8a5dbd68b768790fc}}.
The result is shown in Fig. REF .
A comparison with the three columns for fictitious radii in Fig. REF shows that the actual result of the NICER measurement is well compatible with the {{formula:6c7e5552-0e48-4608-9919-5d0604dfa1fc}} km case.
Therefore, the method of fictitious radii anticipation can be considered a reliable tool in predicting the implications of future {{formula:18a782eb-84c9-4018-bdae-fe88cc079da8}} measurements, e.g., by the NICER collaboration.
Moreover, for the most probable parameter set,
the corresponding EoS lead to the {{formula:b80a0654-0d3a-45b9-bdef-5ece375dfeaf}} sequences highlighted in Fig. REF which fulfill the {{formula:cff7419d-2b97-40dd-83db-3541a80873dd}} mass constraint but do not reach masses above {{formula:a866c626-a15a-4787-972a-314e91055fff}} which would be required if the lighter object in GW190814 was a (hybrid) neutron star.
{{figure:91c237de-ea43-4905-98fb-3ae4d7202bcd}} | r | 6841f9c702ebd9d362288dcb46e91fa7 |
Although the existing methods based the threshold-based framework in (REF ) with a classification-based loss or a Dice-approximating loss are widely used in segmentation prediction, and deliver encouraging performance in real applications, we show that the minimizer from (REF ) (based on the cross-entropy, the soft-Dice and the focal loss) is inconsistent (or sub-optimal) to the Dice metric, see Lemma REF . For Lovasz convex losses, it is still unclear if they are able to yield an optimal segmentation (convex closure is usually not enough to ensure the consistency {{cite:a8dea468841c0e96452519def15bb45d6de92121}}). Moreover, in practice, only a small number of pixel predictions are taken into account in one stochastic gradient step. Therefore, the Lovasz-softmax loss cannot directly optimize the segmentation metric (see Section 3.1 in {{cite:9cf85abf9ead5c3a87d92a134931749fb2667fdc}}).
Taken together, the currently dominant framework (REF ) with existing losses may yield a sub-optimal solution, demanding efforts to further improve the performance, robustness and sustainability of the existing segmentation framework.
| m | 88fd211439c89666c010847be7a1ee69 |
Heavy-ion collision experiments at the LHC, the RHIC, at GSI or the future FAIR, are expected to measure critical fluctuations in the event-by-event fluctuations of particle multiplicities related to conserved charges of QCD {{cite:d89e128404c60c858d6ce9e091f43299cc3040ee}}, such as net-proton number fluctuations {{cite:9691711077a6501f0fd99ccfd1e4869d0d924096}}, {{cite:ae5e04664f5f7db534af1e31822ee8ea0b554cd8}}. By varying the beam energy {{formula:56057773-0aad-459a-97fe-903cf6f4f7db}} regions with different baryo-chemical potential can be probed and coming close to the potential critical point the fluctuation observables should grow large. So far predictions have been formulated based on thermodynamic calculations {{cite:939ac61debd880fe8c2912204a52da9372ea121c}}, {{cite:1644e035517a2e7cd51b13a09c0355a78476642f}}.
| i | 4156bbfeed4d8c787e8e643838d7eb05 |
There are different methods to estimate the gradient {{formula:77debf6f-8c2e-49ab-86d8-17e17b6fb8e8}} , interested readers may refer to {{cite:fd4d2e11c7e73a0a0a397f891ecf5e330e00a56b}}.
Policy-based methods have the advantage of being effective in high dimensional or continuous action spaces and having better convergence properties.
| m | e309c751ea4500392cbe40c1df1bfc89 |
Our experiments demonstrate the quality of predicted depth and the importance of the scene flow network on two synthetic datasets and real-world videos. We first justify the design choice of the scene flow MLP against analytically deriving scene flow (Sec. REF ). We then evaluate our method on the synthetic Sintel {{cite:8328ce5d9fef7751464386c58939e585ef41e408}} dataset and show quantitative improvement over competing methods (Sec. REF ). To demonstrate the real-world capabilities of the method, we show qualitative examples on videos with significant camera and object motion (Sec. REF ). Finally, we show multiple video editing results based on our consistent depth estimates (Sec. REF ).
| r | 4ff7131a0f92a87dfa6d362868396f93 |
In conclusion, we have investigated the effect of receptor uniformity on the superselective binding of multivalent nano-particles, for which we devised a {{formula:a04ba459-3f37-45e2-bbc3-b7d9061ce28d}} -{{formula:7a7164a3-c399-4801-b14b-24946e78e60c}} MC simulation method to compare with analytical theory without any fitting parameter.
Our results show that more uniformly distributed receptors lead to higher superselective binding of multivalent particles. For receptors of SHU structures and square lattice, the maximum selectivity {{formula:b1567681-1de9-4e4a-b99c-c11173e1cabb}} can be significantly larger than {{formula:667df308-6e32-4e9e-bb94-46d5c648550c}} the valence of the nano-particle, which is the maximum superselectivity that receptors of the Poisson and Anti-HU distributions can reach. More intriguingly, the maximum {{formula:878eea45-9119-475e-bc2b-0f9f24e0a315}} exists at some intermediate strength of binding energy for receptors of SHU distributions and square lattice, which is due to an exponential dependence of bound fraction on the receptor concentration originating from the restriction of available receptors because of both the energy and combinatorial entropy. This is qualitatively different from the binding on receptors of the Poisson or Anti-HU distributions, in which weaker binding always enhances the superselectivity.
This suggests that for highly uniformly distributed receptors, one does not need to use nano-particles with very high valence to realize the ultra-selective nano-particle binding.
Although in principle, many receptors on cell membranes are mobile, the diffusion time scale of the receptor on cell membranes {{formula:bb65bd20-f052-43bb-a64b-68ec1a8f1335}} could be much larger than that of forming/breaking a bond with ligands on nano-particles {{formula:e36212dc-b522-4f04-bb70-16c922dc4492}} , and they can be seen as effectively immobile receptors.
Moreover, there are also many immobile receptors on cell membranes restricted and compartmentalized because of the interaction with the cytoskeleton {{cite:2beea34f9c3505b1618ba0031c0f7a8b949edee9}}. Therefore, our results highlight the importance of receptor distribution in biological systems. Although the purpose of our simulations is to capture the essential physics rather than seeking quantitative predictions for realistic multivalent nano-particle binding, it is possible to incorporate other effects, e.g., the geometrical constraints of substrates and nano-particles, the interactions among ligands and receptors, by changing the form of {{formula:3036a44d-1973-4bbc-9044-9475ac997dcf}} in Eq. REF and local activity {{cite:5d6c9a226a2bf3ed2ab3883818da0cd9f12d1897}} for more quantitative modelling of multivalent nano-particle binding.
| d | fa46853251a3aafd9ac01e82f8f4b086 |
The results of fine-tuning the SSL models are aligned with findings from computer vision {{cite:8d7a01c240b2a5aa6ad4fcc6820bbaa7eabc4d88}} and various speech tasks {{cite:b4d826e8f30e08e2c9c56e653e1f6d61c8600d81}}.
Even though fine-tuning the SSL models results in superior performance, we showed that the training set has a crucial role. We fine-tuned the wav2vec2_base model with natural speech and showed that the performance drops remarkably compared to all the other models.
{{table:ea7fc386-be29-4d8b-a3a0-ef21875153cb}} | d | ca5a860178c0d4a6432dc63e5b53ef65 |
S0 galaxies feature a large central bulge surrounded by a smooth disk with no spiral arms, consist mainly of old, red stellar populations and contain very little gas. They make up a significant fraction of all galaxies in the local Universe, particularly in high-density cluster environments {{cite:4c55d064f13c8214e121f47b8870b82cd1902de0}}. Yet despite their ubiquity, significant uncertainty remains as to how these galaxies formed.
| i | 28dc7a6871aef0d6de91a6292a6a5a2b |
The predominant algorithmic approach for learning to produce the answers conditioned on the question statements has been to train seq2seq models {{cite:4fe5d1ba8f993a01fbf1849ffeef9532c0447fd5}}{{cite:940bba293167fe58841b2b0a14d907dfc58e0e27}}{{cite:52934768924a10293dd17c191db6fc11250271e0}}. For some of the modules this approach yields very nearly 100% accuracy, however for other modules this does extremely poorly. For example, with this approach the best reported test accuracy for the module "numbers__list_prime_factors" is less than 25% {{cite:52934768924a10293dd17c191db6fc11250271e0}}.
| i | 85b61dc8755b0675090590560ad75eee |
What these models learn about speech, however, is not typically language-specific—at least, not in the same way that human perception is. Wav2vec 2.0 and HuBERT do not model language-specific differences in human speech perception, and can be seen as modelling a language-neutral or universal speech perception space. Indeed, they exhibit very few native language effect (see Figure REF and REF ). We note that the idea of self-supervised models learning universal speech features is consistent with the fact that models trained on one language, or multilingually, have proven useful for representing speech in unseen languages {{cite:8da60b2bd515d5c069cf3c6497c87248a292bc8b}}.
| d | c8f85eab1dc053e5bf4a18bb3e427f1c |
In this section, we present the results of numerical experiments to
evaluate the performance of the system under consideration. We consider
{{formula:8b768b07-6513-47bb-bb2f-1850aac6e21d}} PRs (unless stated otherwise), and the location of the ST,
SR, IRS and the four PRs in Cartesian coordinates are respectively
given by {{formula:7244cc8c-7a00-4406-9eb3-bfeaf31f566d}} , {{formula:9aae05c2-0cc9-4c0d-b030-56e30892f1df}} ,
{{formula:e8ce1179-92bb-459d-9afb-aef4a02e6554}} and {{formula:36c3229c-b286-4356-8a04-c71aaf6bbfce}} .
We assume that all small-scale fading is Rayleigh distributed, and
that the path loss between two nodes is modeled as {{formula:cf71a369-f3d3-448b-8656-08e143d261c3}}
dB, where {{formula:6e56b328-80e1-4c8a-9538-d49c95981d75}} is the path loss exponent, {{formula:e8c4d923-d93a-4330-92b4-d014d9c0a3a6}} is the distance between
the nodes, and {{formula:64c84a11-3db5-4bf5-b538-1f38bf6864c7}} {{formula:3bde15d0-f1d0-4a19-9379-275be9a540c8}} is the reference distance.
We assume that the path loss exponent for the ST-SR and ST-PR links
is 3.75, whereas that for the ST-IRS, IRS-SR and IRS-PR links is 2.2 {{cite:f7325d4191140e725d54c65dd0501b8a50d914ee}}.
Furthermore, we assume {{formula:5dc7d432-311c-4105-b7b7-b1fd3c66cef7}} , {{formula:23439547-a1b7-40f7-8bf7-a671a954a244}} , {{formula:4c762c10-b1c1-43cd-883b-1fcb28c50e11}} W
{{formula:0a1b11e8-0273-4a27-a930-c911f37d45fa}} , the noise power spectral density {{formula:86eb56aa-3bf7-4cfa-a1a2-97a5b3de0501}} dBm/Hz
and the system bandwidth is {{formula:6374426e-ed84-46e6-9d7b-1c7dca685bd1}} MHz. In Figs. REF -REF ,
the average achievable rate is computed over 100 channel realizations.
To run Algorithm REF, we start with
{{formula:7d6bd8d8-122f-4339-b83f-f0788b0b95d9}} and decrease it as {{formula:021e97a7-7148-4374-90a4-160bfd7e8252}} where {{formula:e4ec0ed5-7d2e-4459-9001-6466f4e87ff8}}
when the relative objective progress of {{formula:fba618f5-5255-481b-a25f-3a8497321852}}
{{cite:555a4bd6b243bb7f2617faf8d32250283cbc6471}} in Algorithm
is less than {{formula:09302a88-5602-4d99-9b55-3d8fb6ee9b4f}} . For Algorithm
we set {{formula:c3dcdec7-b039-4a50-9b28-e3e6a5fe9854}} in the backtracking line search. Algorithm REF
terminates when the difference between {{formula:aac523fc-367a-455c-a7d0-f260ec61c842}}
and {{formula:0d8dd348-d9ce-4505-b12b-1a6848d24ab2}}
is less than {{formula:0760405a-da0d-4bb6-8c3d-af1c7887bafd}} .
| r | 63f41282d09196d52c2f7c82c369dcbb |
For all {{formula:5f33801b-403b-4454-b9cb-b0c3f903c808}} , we denote by {{formula:a9059e61-77e4-475f-8776-60188271cff9}} the measure on
{{formula:91dde843-68ce-4694-8833-9f4ba526903b}} defined by {{formula:de04f684-a990-46d0-ae08-99330f0aef71}} . We let {{formula:65236749-359a-49b2-84c7-f999d1e1bec4}} be the
least upper bound of the measures {{formula:49941f75-88ea-402b-b697-c48d41837abe}} , with {{formula:92a780fa-405e-4e62-b83a-ae87639e7bba}} running over
{{formula:444c89b7-31b4-4f29-9125-6110e4a3ad69}} (see e.g. {{cite:50178e6fdc7bc99640010b1be663547e9d2030a0}}). The measure
space {{formula:255c81e2-019f-4e3e-a1fd-3ceaea5fc714}} is complete:
a set {{formula:32fd6fd4-005f-4eb2-8322-f622d00fcdb5}} is negligible iff {{formula:7dee3457-42bc-4380-9e27-e1e2626cd57c}}
is {{formula:9c675d9f-200e-41ce-a76a-0491cab71861}} -negligible for all {{formula:29fa3b40-938c-44f7-8c61-e05ec34dfb78}} .
| r | 70302a8755ad5077dbca1ed095f487e3 |
We fit the reflectivity (R) spectra with a Fano function{{cite:2bf9ec23567d69a0f70bc99c1ec0a47223d28b06}}:
{{formula:18946c02-5da2-4511-a0d7-5d60f3aefa05}}
| r | be4bf04ac862138a38f00cd168919dc1 |
On a smooth Riemannian manifold,
von Renesse-Sturm {{cite:ee0650e3547ab005f9c3b3cb0429b4fef532a742}} have characterized a lower Ricci curvature bound in terms of a gradient estimate for the heat semigroup, and a transportation inequality along the heat flow.
Münch-Wojciechowski {{cite:4af9e726ac367828dd32ea782290ff4761c1c704}} have studied its discrete analogue,
and produced a characterization of a lower bound of the Ricci curvature introduced by Lin-Lu-Yau {{cite:5902861c515a23fb9739978c98c0ebf74bcd55e1}} on (undirected) graphs (see also {{cite:bbed3d3522e3b3c5c1077c2b059a129a191b91ba}}).
| r | 329f048b037cb25d7a3de51e830b1914 |
For our goal, the renewed interest in statistical mechanics of closed quantum systems {{cite:26c96205e8846528139c67042a80727485bd1065}}, {{cite:dd40e2fb03051655fbffda241972a0417872c78a}}, {{cite:9dbcafa9ca335713c5c023dc777ae09d1e4da8ae}}, {{cite:55410372442466fd1d121ab6859a2f2d0e58f748}}, {{cite:23c36e2bb49ad13ff68d33b1fc9bdb9e8010d09f}}, {{cite:15e85c2d2705b308093f89fe0ebbc555510a02b1}}, {{cite:d82048cf5d77eebe4d32b9b481dac4ef4a4e2f76}}, {{cite:f65df776264c53935ca5fb9bd44e00e2c6ce859b}}, {{cite:5a454b8bf8fdd476744f8b60deecb34075687562}}, {{cite:1f2c5f91498f6eafd0fdded7a2abd262432a7c4e}}, {{cite:500ef26eb848fcf38ab815fce442664cc6c59c12}}, {{cite:5e4a0a418716f197a9d624bebd37ff0fc3253b85}}, {{cite:e9dd4278bee3726c522189c179a002cc84f5d4c8}}, {{cite:15d24202c14aad05623e0e6131a3018fa4620417}}, {{cite:2f7d23653133165fd27d11c44db9b9afcd40c47c}}, {{cite:d712cf5b5260c1b14bd4fa810b74487cda8eb266}} provides the perfect scenario. Such interest has been generated by the successful experimental ability to isolate and manipulate bosonic {{cite:2e54c5ca8b8034755bfc3c967accf9796c1595ae}}, {{cite:3184914b8c8fdd782ed02e7f0070e9b56e71c194}}, {{cite:308789f6b47610d5097d55d476beaaa53431e31f}}, {{cite:ba90424aff3c7c8e133e67bc2466ad04b69587f0}}, {{cite:4bd1e918d0d6e5672a61b0e428ba7fed545f1f9b}} and fermionic {{cite:af25c7c1b12836f551dafad4dffcfd268d0294aa}}, {{cite:e08f7abebfdda3dfbd63e2428c1787bd7d2fb545}}, {{cite:26f81a3abe76bb0335c9c2feb74586ce551635fe}}, {{cite:32e5a02201cbbd18506c2d6dd557e007f923f06e}}, {{cite:bcdb181b89e60994fe19e583cb520d8614df52e2}} many-body systems built on ultra-cold atomic gases subjected to optical lattices. Such quantum systems can be described by the many-particle Schrödinger equation; an arrow of time appears because, despite these systems being expected to present unitary evolution, some of their initial nonequilibrium nonthermalized properties may later thermalize.
| i | 75363fa01d64404a6a480087b690a37a |
In this work, we presented a new image analysis framework that utilises autoencoder (AE) and T-L networks as regularisers to train neural network (NN) models. With this new training objective, at testing time NNs make predictions that are in agreement with the learnt shape models of the underlying anatomy, which are referred as image priors. The experimental results show that the state-of-the-art NN models can benefit from the learnt priors in cases where the images are corrupted and contain artefacts. The proposed regulariser model can be seen as an application-specific training objective. In that regard, our model differentiates from the VGG-Net {{cite:9e3b847cebf6ad7833b9de1aa24168364a4b4c8a}} feature based training objectives {{cite:a4e96c66ac5ba0800a9c0ee2656a720e88faf8b4}}, {{cite:e8460e73b2cec9be0bbc4011957aa1af5bcbf3a0}}. VGG features tend to be more general purpose representations that are learnt from ImageNet dataset containing natural images of a large variety of objects. In contrast to this, our AE model is trained solely on cardiac segmentation masks and features are customised to identify anatomical variations observed in the heart chambers. For this reason, we would expect the AE features of the segmentations to be more distinctive and informative.
| d | f143dd8cad9e3188000deb001fc06c5b |
Section three contains a discussion of the effective Lagrangian.
This is followed by a brief discussion on the discrete symmetry transformation properties of the gauge potentials and the
terms of the equations of motion of the {{formula:0b17ba18-372b-4e2c-b152-5f3f611a44dc}} system obtained from the effective Lagrangian under consideration. In section four, we establish the unitary transformation matrix which diagonalises the mixing matrix.
In section five, using the same unitary matrix obtained in section four, we diagonalize the equations of motion and identify its similarity with Klein Gordon equation in the diagonal form. We take this equation and following the procedure of {{cite:5891157be3330153eb9b1229f3f543a1c4bbc449}}, we estimates the conversion probabilities of various modes into each other. In section six we discuss the physics of appropriate astrophysical environments where the mixing of the photons with scalar can take place.
We identify some possible signatures of this mixing from the EM signals coming out of these astrophysical environments. The implications of this modified system is discussed in section even. In section eight we provide possible implications of our work for some of the DM signatures existing in the literatures followed by an appendix where some technical details are elaborated.
| i | 1207e6fb95c7b0df97d16d400cb17fb3 |
We rely upon data from the analysis of Ref. {{cite:acf4893bffe44c0444afa3dfa5c4c7b0c896cc38}} that led to the claims of the {{formula:04cfd35d-f044-4a06-8ef2-c480718a0285}} and {{formula:f1d13392-97ba-4d77-b7e4-1bc7008bfd83}} resonances. We use these data to choose the parameters {{formula:78299294-dc43-46d9-aa2a-46a0b8ebbddb}} of the amplitude of Eq. (REF ). The parameter {{formula:701175e6-74cd-439c-96fc-4180c281ebfc}} which determines the strength of the {{formula:dd6bdf19-6a0d-48f1-953c-9274b0af3645}} state is chosen to be consistent with the data of {{cite:acf4893bffe44c0444afa3dfa5c4c7b0c896cc38}} and its not obvious observation in this experiment. With reasonable numbers for {{formula:990e0a06-e259-4a42-84e3-3cd9337968bc}} consistent with the experimental data we evaluate the magnitudes discussed in the former section.
{{figure:917c0adc-1d1e-4192-bba6-00df6f9967e9}} | r | dc1a81fff2120532a051c369daef236c |
Related works. Stochastic submodular maximization has been extensively studied in the literature {{cite:7001e65347c9899ff0aca1de7fa2434d34e71ccd}}, {{cite:960408ac7e3393147a27a13019f31cc4feaf834b}}, {{cite:ebb4973be313cfa40976694dcabba04d04e5426d}}. While most of existing works assume that the cost of each item is deterministic and pre-known, we consider state-dependent item costs. Our problem reduces to the stochastic knapsack problem {{cite:2729cc67cfa6b3f2a4fcd67c20255314eb1784c3}} when considering linear objective function. Recently, {{cite:924d0538e3a39af89b0fc705b357d2aa7747666b}}, {{cite:c36ec3a9fd7065366da84fc84667b4dc5cf46e18}} extended the previous study to the stochastic submodular maximization problem, however, their model does not incorporate outer constraints. Hence, our study can be considered as an extension of {{cite:924d0538e3a39af89b0fc705b357d2aa7747666b}}. Our work is also closely related to submodular probing problem {{cite:3267863aadce7004e0168dbe678d3d00b4241d9b}} where they assume each item has binary states, our model allows each item to have multiple states.
| i | 75b9e1053adc7735c80aa0ddfaae788c |
For crosslingual clustering, as shown in Table REF , our system achieves state-of-the-art performance on BCubed F1 {{cite:a15807885b9ddc62706dbb7dfb206173a1685ac2}} (+8.04) and on the standard F1 (+11.33) despite producing a larger amount of clusters. Furthermore, we perform an ablation study that shows the relative importance of the system components. 4-F Rank+Acc. refers to the clustering system with a 4-feature ranking and acceptance model, which used only {{formula:5307c7f4-26fd-433c-b1d5-af636ddbdfbf}} and the timestamp features. Adding the other features (8-F Rank+Acc.) improved both standard (+1.42) and BCubed F1 (+1.22). Finally, the cluster merge model was added to our system (8-F Rank+Acc.+M.), resulting in gains for both standard (+3.35) and BCubed F1 (+0.86).
{{table:db1c3706-dbaa-4ab7-9364-0afb56db1640}} | r | 0bf774c130ba8bcfd5247224f6a83dfd |
In this work we propose a model, the BC-PF model, that couples in a very natural way Antal et al's {{cite:0563b87256029955c815565020c8a03bf31d0d1c}} dynamics of structural balance and Hegselman and
Krause's {{cite:65c30fc37294a00e31ce8290f875e3a43b3ec3be}} model of opinions formation under bounded confidence. We rely on two basic ideas: (i) Social relationships change according to a
preferential “opininion-based” rule, and (ii) individuals' opinions evolve over time taking into account only the opinions
of their friends in the social network. Because we build on two literatures, the BC{{formula:2d0c1fe8-7692-4abc-a658-cdf3e94076ae}} PF model yields a number of results that contribute
to the literature of both structural balance and opinion/beliefs formation. Additionally, the BC{{formula:4e3e55ed-ce86-4a7e-94e2-b2b5c6ce09df}} PF model produces results that can be related to real-world phenomena.
| d | 4cd0e9d6878c471071bacce1c824d0ac |
1)
Multimodal Affordance Detection
{{formula:0e9f5643-126a-485b-8fe2-c3a6fb9dec41}} RGB-D Affordance Detection: Depth information provides rich spatial structure and layout information, which facilitate extracting geometric clues to improve the performance of affordance detection. Many previous works consider depth information for affordance detection {{cite:6fb34959335840406f44b8f923878b20ffe8afec}}, {{cite:fca7298b494b7bf0d26499ee2ff40743d0943722}}, {{cite:baa585053c31cbc13a3b32d9070c0ba84170a98f}}, {{cite:4d9be37a7d082cb83aaaaa3a847c57daec1ffac6}}. Our PADv2 dataset also provides depth information annotations, which can be exploited in future work to estimate human action purpose and capture the intra-class commonality of objects belonging to the same affordance category.
{{formula:6d5be035-840c-49a7-8b6b-a03f4391ebd4}} Vision-Language Affordance Detection: In this paper, the task of affordance detection is accomplished by mining human action purposes from support images. While in real life, human intentions may also be described by language, e.g., “want to drink water”, which conveys the information to find objects that can be filled from the scene {{cite:0a776000f10da17daecd3a930129b38953e44267}}, {{cite:fbe81ff1c633e089fd6a12de57359b1ec8ca9451}}, {{cite:be2930d0072f5154a66366c2a779e9a421a43780}}. In the future, it is also promising to consider the marriage of vision and language for the affordance detection task.
2)
Affordance Detection from Machine Learning Perspectives
{{formula:2ae309a6-f491-49a5-a726-5dc7a13984cc}} Weakly Supervised, Semi-Supervised, and Unsupervised Affordance Detection: Affordance detection based on supervised learning usually requires large-scale labeled data with pixel-level accurate annotations for training, which are labor-intensive to collect and annotate. Alternatively, weakly supervised, semi-supervised, and unsupervised learning methods are also worth further study for affordance detection
{{cite:011aac5af28ab53c436605ed05486af1e7f44f6c}}, {{cite:b9097d2fe9a7768d35f1b28b4835cb494c4efd34}}, {{cite:fe4f185f23abf451b0af777444473597639c80fa}}, {{cite:77c7d00516522060c6187336eb5e6817d04532d6}}, {{cite:727882f7aeff8e7f238689af0129ce0a8185ff7a}}.
{{formula:5c500a00-09f6-450c-bd43-7cb5e6dda498}} Affordance Detection from Imbalanced Data: Most of the existing affordance datasets have imbalanced data distribution from real-world scenes, e.g., some long-tailed categories only have a small number of samples. Data imbalance poses a significant challenge to the task of affordance detection, since the model has to learn a fast adapting ability as well as overcoming the forgetting problem due to the insufficient amount of training data of long-tailed affordance categories. Nevertheless, it is of great practical significance and worth more research efforts {{cite:781ed474e6b7fbc1799b500994316a02db58290a}}, {{cite:0a280f8bb754989fe5f02741ca1fe3d9c9cbb1e9}}, {{cite:c3e3e7e2b30c6ec685ca6acfb59cbbe00304f407}}, {{cite:123bf627e8e061dcbcfc1b1ab97fdc597fcaf77d}}.
3)
Real-world Applications and Systems
Some potential applications (CBIR {{cite:4e2e95098c7ba30eb1ef86cfbe1ea9d6e19c35d8}}, learning from demonstration {{cite:a5ac12965d1bc82b314fda15a7f66964f8403163}}, {{cite:b9097d2fe9a7768d35f1b28b4835cb494c4efd34}}, and self-exploration of agents {{cite:eb98b6d1dfd3bad89e3f1ea2e8067f90b25991c1}}) have already been discussed in the previous section. It is interesting to explore how practical systems can be enhanced by incorporating the affordance detection model. Moreover, developing an embodied agent that can continuously learn to perceive object afforance in real-world environment and interact with them to accomplish specific tasks could also be a promising research topic.
| d | 24a26ea72f60b334141005bb27841cfa |
From the results in tab:vocresults and tab:aderesults we see that our method based on implicit modeling of the background performs better than most methods using explicit background modeling and without additional data.The results for ADE20k show that we perform on par with the state-of-the-art on the two simpler scenarios and clearly surpass the results by SDR {{cite:1f32f0c9370d2f9d477fab50a20548461e8e61f9}} and MiB {{cite:05cc5f8ca9115508882523f70ee5abd74dd9991d}} when using multiple increments.
| r | 0b9c95e5052cde296eb0129418dee1bb |
Let us make a remark on higher-dimension irrelevant operators not included in (REF ). The higher level descendants
of {{formula:61af9674-b4f6-44a1-8e6c-a469cbded3de}} potentially appearing in (REF ) are {{formula:0565f371-8c02-492e-acf1-57e4ffda8520}} , {{formula:184bf6a6-0414-4f36-b20d-ff5f15f83067}}
and {{formula:2e18fb52-aa45-4230-bdb0-df9494b48403}} , which fill the slots {{formula:a7dda72f-ce87-47c5-b616-06e734c320e8}} and 10 in Table REF . These are all representatives of an infinite series of operators {{formula:8dc1f80c-b714-421d-8e0d-214ab3977fae}} , {{formula:d7d6e93f-6a61-4911-9da9-50fa33f2bc0a}} (odd integers not divisible by 3) introduced in Ref.{{cite:d82dff1ec631e507c7a043ab6ee2b619eea0a80d}}. These operators generate an infinite-dimensional "generalized {{formula:024cdfcb-5a20-4427-a030-9c8b32dab83e}} deformations" which preserve integrability. Although for the generalized deformations there is no formula describing the dependence of the finite-size energies on the deformation parameters {{formula:c561da99-a4f0-4cf8-9b8d-d3e82d011600}} as simple and efficient as (REF ), the special properties of the operators {{formula:f0389c5e-87aa-4fab-8ac3-12c12e0d2c86}} give at least some control over the effect of these operators in the effective action (REF ). In particular, the corresponding deformation of the S-matrix is known, and can be used to take account for the contributions of the operators {{formula:595911c3-8da6-41de-8b66-d1154f085983}} through the TBA technique.
Including the contributions of these operators may significantly improve the power of the effective action (REF ), especially for the higher energy levels. We hope to return to this question in the future.
| d | 7036f141128197a6dc0105248729d461 |
Additionally, as discussed in Remark REF , we can use our bias formula results (in particular, (REF )) to devise schemes for sensitivity analyses of proximal inference studies. While (REF ) was derived under the strong assumptions that the data generating process is a LSEM and {{formula:4df0a1b1-7d6c-46e6-995a-2de8a98ba5ab}} is not an effect modifier, an analyst might reasonably conduct a sensitivity analysis using (REF ) as we described even if they did not believe their data were generated by a LSEM (and did not construct their proximal inference estimators under that assumption), and even if they did not believe that {{formula:296f9f1b-47c5-40f9-bbf4-1ba521d1faea}} is not an effect modifier. There is a long history of unrealistic simplifying assumptions in sensitivity analysis. For example, {{cite:41bf94411a9c94520d1c6f5c29b607fab7c685cc}} and {{cite:01ab08fd46fcae8fa069e778959ac93d4f3de9d4}} both assume a one-dimensional binary confounder for tractable sensitivity analysis of no unobserved confounding. Later, {{cite:76593ec31a31879ca7487c84bc0fb9beb9e5a225}} developed an approach that made far fewer restrictions. We are in the early stages of proximal inference, so we currently need to settle for sensitivity analyses that make strong simplifying assumptions.
| d | 6638cf7fb45c7d8ca147e92bbbc62b91 |
There are at least two known proofs of this. The standard one uses the concept of extremal length (see {{cite:d5dbbae1fb4488dd68501e7d3695ba849cb98eff}}, {{cite:c28a7ddf7002eb4906a76c6d966253d6e0c608e9}}, or {{cite:82721055c3c27dc006b022143d9ccb5b5c17a02d}}). The second, which is not as widely known, is to repeatedly apply Schwarz's reflection principle in order to extend {{formula:a7968631-4634-4350-81f3-f584e30b4538}} to a conformal self-map of {{formula:26ee14a8-8638-4474-ac55-2e76d244aded}} . We present here a third, using the conformal invariance of Brownian motion.
| r | 307ebd34ebd4f9f66e2e9363cac27ce2 |
In other words, The Hubble rate problem concerns about the discrepancy between the Hubble rate inferred from the CMB data and the one obtained from local measurements. In particular, Planck collaboration fits the CMB data using a 6 parameters model based on the {{formula:466adea8-7097-43ab-b14c-2147fdae4e91}} CDM cosmology, and from this fit infered (model-dependent) Hubble constant to be {{formula:bf157d0f-3513-4c06-b28a-9da633427db9}} {{cite:43ebe929ecd4d5f2e13336c5015125632c1ce15d}}, whereas local measurements favor larger values that range from {{formula:04ab645e-4726-4870-814b-79a86e81d463}} up to {{formula:4344609e-c0a8-45f3-8682-75b2b76d4eb9}} , depending on the dataset used {{cite:eec6d0f7d4c9223fcf0588330dc138c712794c7a}}. We will adopt a more conservative value {{formula:11c8f8ed-d796-4b50-968b-7ba5cf002b66}} {{cite:52dcf0eee4c36a577bb19dd666ae69d3efc87f16}} as a reference.
| i | 8516523d9a54d962dac6c1cf0d59df29 |
Differential privacy (DP) {{cite:5b1064a45eb50ae6bfe668e28e04353f4e5f2e9f}} provides means to accurately bound the compound privacy loss of multiple accesses to a database.
Common differential privacy composition accounting techniques such as
Rényi differential privacy (RDP) based techniques {{cite:81ef39774a1c9b0829982191c8978031af67f316}}, {{cite:487e9e4d3e86da380a7226c140361db35df852e7}}, {{cite:6d821bbb5189a8419c09eedbb31011c2264ed307}}, {{cite:14c45663a0d52734c7a713c5c31cc2447ef573b3}}
or so called optimal accounting techniques {{cite:4633a9f4403563f18a46bc74e64d81def558f146}}, {{cite:53aebe54367541a2b6a46055c801d161464d5c55}}, {{cite:f58e8b3a788231e73690559ea922241a87cbe714}}
require that the privacy parameters of all algorithms are fixed beforehand.
{{cite:e8de7a2165dfab89592b710b0d473cd0cdb17b98}} were the first to analyse fully adaptive
compositions, wherein the mechanisms are allowed to be selected adaptively.
{{cite:e8de7a2165dfab89592b710b0d473cd0cdb17b98}} introduced two objects for measuring privacy in fully adaptive compositions:
privacy filters, which halt the algorithms when a given budget is exceeded, and privacy
odometers, which output bounds on the privacy loss incurred so far.
{{cite:7eee2d6ae13abe87d23ab59a68da87d6e0407b91}} have tightened these composition bounds using filters to match the tightness of the so called advanced composition theorem {{cite:60162c5ae5b77dfaa660eb3a2b9fe2c5592ceeed}}. {{cite:68250998dfb2cf8c5f38c9c8f7dc80d47f1be029}} obtain similar {{formula:c585bdc4-2df3-4ecf-829c-244487d57589}} -asymptotics via RDP analysis.
| i | c1fb931d720e7bfe168d9f27390f0d23 |
We experiment on PhysioNet MIT-BIH Arrhythmia dataset {{cite:970eb61537d16248a05ac7a113c784d4d5282b99}} for heartbeat classification and PTB Diagnostic ECG dataset {{cite:408e10fd8b08db72a046802dece04ba246eb4ce8}} for MI classification. For our experiments, we used ECG lead-II re-sampled to the sampling frequency of 125Hz as the input.
| r | 3c9f52107c13c86555874371835af913 |
Consider now a minimal TT-representation of a tensor {{formula:21bb5c41-98d7-414d-9985-4cbcc22f35b6}} whose TT-cores {{formula:91083af3-87ca-40ce-97f2-4c3365f4f10a}} are random with standard normal distribution. The TT-cores of its left-orthogonal TT-representation {{formula:24f07c30-518d-4661-93dd-b70c379439ab}} then have left unfoldings {{formula:038c1a0f-9d8e-409d-95dc-93c1fbe37e69}} that are distributed uniformly on {{formula:d79e53d9-a289-4060-bd3a-47b4bec762b6}} . What can be said about the distribution of their subblocks {{formula:c16ee3a4-c926-422a-ab0c-b423fbd3f386}} ? It is known that if we take a random orthogonal matrix {{formula:9615218c-89f4-4180-aa6a-4c30b695fbdf}} , pick any of its subblocks {{formula:2ed727c6-fbef-4ad6-a9e8-1a1e3fb0aa81}} , and let {{formula:542f83ea-e102-42bd-805b-c58db2f158c0}} then the matrix {{formula:d15dcb3f-726e-4cc6-a1df-55ddb1e22896}} converges in distribution to a standard normal random matrix {{cite:8ce0c7a2f05714eb48300afa96b6db01ec74cc3a}}, {{cite:fd5e32fa01d412b88f17d964d91ec36add5c8dc6}}. As a consequence, we can, informally, treat the blocks {{formula:547030be-1bee-438c-bbe5-e7b0d85ff93e}} as random matrices sampled from the standard normal distribution. Random matrix theory provides probabilistic estimates on the largest singular value of standard normal random matrices {{cite:d1d78fabf33d4d3d891066c94b6586cbbc5f6113}}. With probability at least {{formula:7ab7f72d-ed0f-4cf3-80f8-ddc8f00d8d76}} we have
{{formula:346947cc-f3c3-4527-ac8b-2d5348274f6a}}
| d | 90042fc3310439f752103184d959eeb0 |
The Integral Field Unit (IFU) spectroscopy measurements of the galaxy NGC 628 were carried out within the PPAK Integral Field Spectroscopy Nearby Galaxies Survey, PINGS,
{{cite:4056692b549028d1dba1b3c8e6ff352ea12cf95e}}, {{cite:97d026b70a327ced6cb84460f8e795ff124df65f}}. The 382 fibre bundle has a field of view (FoV) of a hexagonal shape of 74 arcsec × 64 arcsec. Each fibre projects to 2{{formula:a65e07d5-5c1d-454c-a8bd-52070e7aea42}} 7 in diameter
on the sky, and the fibre-to-fibre distance is 3{{formula:a196c2bc-6fc8-4442-b363-4f56712bfae5}} 2, which yields a total filling factor of 0.6. A dithering scheme with three pointings has been used to cover the
complete FoV of the bundle. The spatial resolution of full width at half maximum (FWHM) is {{formula:68bc498b-83b4-4ba6-a8f9-1e0098e1bfe0}} 2.5 arcsec. The catalog of H ii regions in NGC 628 is generated,
and the spectra of detected H ii regions are extracted {{cite:97d026b70a327ced6cb84460f8e795ff124df65f}}. The angular size of a nearby galaxy usually exceeds the diameter of the field of
view of the spectrograph. Therefore a number of pointings are observed to form a mosaic, for instance, {{cite:4056692b549028d1dba1b3c8e6ff352ea12cf95e}} obtained 34 pointings for the NGC 628.
| i | 6ff7e56d476d5a2639755f6eea12aa29 |
The task of identifying a parameter set yielding the “best fit” model for a given data set (or representation of data) is well-known. In fact, the Kullback-Leibler divergence was invented (Kullback and Leibler (1951) {{cite:868e25c9726934df47e1893fdd662d977c6f1aa3}}) to address just such a challenge.
| m | a9df3e379f00f50e79c9c2da61fc0d52 |
Table REF presents average Friedman test ranks {{cite:7568341a82d03f9d3b9d4110ef498989a602d26c}} for each classifier on each tested metric (the lower the rank the better). Setting a significance level {{formula:560d2589-aff8-4eee-af7b-b97caf938f53}} , we can reject the null hypothesis of the Friedman test stating that the performances of the classifiers are equivalent only for the number of selected features, their standard deviation, and processing time. This means that the final predictive performance of classifiers was comparable when using any of the tested feature selectors, yet some them were significantly faster and chose less features than others. The critical distance plots for the Nemenyi post-hoc test {{cite:7568341a82d03f9d3b9d4110ef498989a602d26c}} (Figures REF and REF ) indicate that FRFE is significantly faster than all the other selectors except RFE{{formula:92ca67ac-2818-492b-bce1-a3a69a318e0a}} (which was forced to use the same number of evaluations). Moreover, {{formula:56e26d43-af12-44f7-8de2-c5c1cfc8a118}} -SRFE selectors tend to choose smaller feature subsets than their RFE counterparts.
{{figure:c9f53673-0d6c-4c80-a093-1294593b0d58}}{{figure:e8c31b4c-940f-4096-b633-d53a23772de1}} | r | 10da9f1fdf9a63beedfbfe1ee680c3b9 |
Specifically, in {{formula:72836534-a3b0-440d-b474-5d8df524593e}} , the set of feature vectors obtained from the training video {{formula:69d99b71-18e8-4f0d-9b4a-b125d9fee79e}} , the feature vectors are ordered by default as {{formula:22cc3d81-8fdd-4259-9558-cb2da5655542}} , but we randomly rearranged this order to create a new dataset and used it for training.
The results of the experiments using the UCF-Crime dataset {{cite:ddc9447aa181d78aa6f44d218ef34b96d5b8652f}} are shown in TableREF . In both methods {{cite:ddc9447aa181d78aa6f44d218ef34b96d5b8652f}}, {{cite:b8f4dbed27eac75ed5b93992fd9cc71dcc89a443}}, there was no degradation in accuracy due to random reordering of feature vectors.
{{table:3d63f6e1-193c-43ee-8fa4-4dc1d7392bd2}} | m | 86ea0651dc7f13b6a457517f0d02ce5b |
which is the famous Camassa-Holm (CH) equation.
There are many properties of the CH equation. For example, it is completely integrable {{cite:71c935230238281acbb38cca1f5f82ea3e9c49dd}}, {{cite:a43f0b9616d9d9540deb9ccc58cf2d4b165ca051}}, {{cite:b6f4726ea0abc81715a5c434c17d8688a0a67d5b}} and has a Hamiltonian structure {{cite:4a5782c27c0635846bfdf445c1e24ce074252943}}. Its solitary waves solutions and peakon solutions of the form {{formula:025cfca2-cb70-431d-818b-9c247fa0f89e}} were studied in {{cite:52d255577a9a6ed9361981ebdf569ba8774e45d5}}, {{cite:d217a2d872a1d14c24c020e1afb781337bdadac8}}, {{cite:006fb7fd3b80781d8e20c0a8a8b978babd7ffa59}}, {{cite:75fd16056cd8f8245b427d77c37195740250be85}}. The local well-posedness and ill-posedness global strong solutions, blow-up strong solutions of the CH equation were investigated in {{cite:f37cc8be6b6dc6bd7a76987b8dc7069fbe26caa2}}, {{cite:61478f0b0a353a5060b403eca2e515b2223bd744}}, {{cite:7e1fcfd37008c675dcec77ae2b4f26ffc548e41f}}, {{cite:677f9ae4219a397235ade9820b7bab3167044805}}, {{cite:2b94a75da8347c04e24c15d354c623a341585085}}, {{cite:6e352ef67e21b809e556fe83d7657a1e7134c5d6}}, {{cite:d8bb67a5e5508e26d80ccb84e985155478833370}}, {{cite:faab5c9a270f127fa3bc90551339049400c7567c}}, {{cite:ef8db98bbf609737fccdae2e90f4dd5b3db3e284}}, {{cite:230b1f4197f617c23550c736d08637e9f3268fa6}}, {{cite:263ad1a04bc30f786f371d14cabdf7602980bea1}}, {{cite:797b4f3e42b77275429f3fd45d038e28dbdea9fe}}, {{cite:e55bcad5f6b3c455cd99f37e772cf63ee9fffd28}}, {{cite:b85e60159a57d6c5245d3b1256b91efc0a894e83}}, {{cite:75fd16056cd8f8245b427d77c37195740250be85}}, {{cite:aaf8625a27bd8ab03c24a01bfa07323f4819a9c2}}. The global weak solutions, global conservative solutions and dissipative solutions f the CH equation also were studied in {{cite:d20c6a36d52b5d65e25b57a48c0ac3dddd707859}}, {{cite:38ab98e4fedef61e667f1095d4af63e103f6aaae}}, {{cite:ffc692a5da24ba4dbbf9010e40a51814b2ab7386}}, {{cite:bd01882f92e9d53847755ca5b0ffc9df20abf6bc}}, {{cite:f7dd5eccaca08f043853de2009e2530b82530a64}}, {{cite:bf405f34a281dbddfc6a32467ca37e8864956480}}.
| i | 7c29140be5397734d9e6da58c7a49c58 |
Phase retrieval, under various names and methods, has been explored in many different contexts. Classically defined "phase retrieval" as pioneered in the above cited studies by Gerchberg, Saxton, Fienup and Gonslaves began with the challenge of reconstructing a signal from the modulus of its Fourier transform, but has recently expanded to include analysis of more general quadratic forms {{cite:2b529d45298daad7dfeed9f3823c7c4ca8115037}}. From another perspective, wavefront estimation from shearing interferometry {{cite:8b52c5cfda8e1d39b812b11626bbbe67f6f58407}}, {{cite:85be236b83f7ffc074e0e80030fe6a422dd4599a}} has long been used in adaptive optics and astronomy. Phase estimation also lies at the center of two mode interferometry, as explored extensively in gravity wave detection and quantum state analysis {{cite:259070ad463388821328ed4aec6ac75f824bea96}}. This paper applies algorithms from conventional phase retrieval to physical measurements related to shearing and two mode interferometry. The advantage of this approach is that low rank measurements reduce the physical and computational complexity of phase retrieval while enabling near quantum limited field estimation. The main contributions of this paper are:
| i | 625e4b50c5ef6998b3968028b32f4aef |
The simulation parameters are set as follows:
the measurement model is the target position plus Gaussian noise of zero mean and standard deviation {{formula:d79369c0-cf07-4dd8-91b9-84ba6f248816}} .
The clutter model assumes that the clutter returns originate from points that are uniformly distributed over the surveillance region,
while the number of clutter returns is assumed to follow the Poisson distribution with a known mean {{formula:59624cf0-aa13-45b7-a711-20c826308352}} during each scan (see Fig. REF ).
The target space is set to 1000m.
For each track, the two-point method {{cite:d27d6acac4684722675108cbf45e6208e5b7a29e}} is applied for track initialization and the tracking gate is performed with a threshold such that the probability of excluding the target-derived measurement is {{formula:2375048c-0250-4661-92d7-a4085dcf2fcf}} {{cite:0d2e0194bb5592864d526e1ca2cca784f0f732e2}}.
{{formula:dd438ca7-a1f3-4e1a-ad55-c671d7367f93}}
| r | 08d374dc588fc3cc05834c54f962a788 |
We also investigate the spectral properties on the pre-trained model, BERT from {{cite:751aea3c2afd61a89bfe5f08ac37536f5e2aac08}}, with fine-tuning on Sentiment140 dataset of tweetshttps://www.kaggle.com/datasets/kazanova/sentiment140 from {{cite:0667675487afbee0955a27dc05f84627ad396448}}. We fine-tune BERT model to train a binary classifier on Sentiment140 and capture the evolution of CK spectra, rather than the NTK due to the size of BERT, in Figure REF (see also Figure REF in Appendix REF ). A heavy-tailed CK spectrum with several spikes already exists in this pre-trained model. Unlike Figure REF (and every other randomly initialized NN) where the first spike of NTK becomes larger than at random initialization after training, in Figure REF (a), the leading eigenvalue first decreases and then increases. Moreover, similarly with Figure REF (d), Figure REF (b) shows that the alignment of the first eigenvector of the CK and training labels becomes more apparent through fine-tuning with the highest increase correlating with the leading eigenvalue decrease. Heuristically, this process seems to unlearn the features in the pre-trained model and, remarkably, learn new features on the new dataset in only a few epochs of fine-tuning (For more details of these two experiments, we refer to Appendix REF ). We believe that the evolutions of the kernel matrices and some spectral metrics are crucial for understanding feature learning through fine-tuning {{cite:17ba7f3e20b19012cd3d32841020997d445266aa}}. A more comprehensive exploration of the evolutionary spectral properties of “foundation models” may help shed further light on these phenomena.
{{figure:03e7b459-c379-42c3-baa7-be2844710b8d}} | d | b4ed941288f0c3b01271cb70a6a70707 |
It is important to note that the brute-force search algorithms underlying all of
our tractability results are not immediately usable in real-world software engineering
because (1) the problems solved by these algorithms are simplified versions of
real-world problems and (2) the running times of these algorithms are (to be blunt,
ludicrously) exorbitant. The first difficulty is a consequence of our complexity
analysis methodology described in Section and cannot be avoided.
This is not so bad, as algorithms for simplified problems may still be useful guides in
developing algorithms for more complex and realistic versions of those problems. The
second difficulty is also not as bad as it initially seems because it is well known within
the parameterized complexity research community that once fp-tractability is
proven relative to a parameter-set, surprisingly effective fp-algorithms can often be
subsequently developed {{cite:5edf622f883a722d7e2880164a1b4ec9b2f42ddd}}, {{cite:4a09365955d96e11c864980dbdb285769e95c4dd}}. This may involve
adding additional parameters to “minimal” parameter-sets that imply the greatest
possible number of fp-tractability results. Such algorithms typically have runtimes
with greatly diminished non-polynomial terms and polynomial terms that are are additive
rather than multiplicative and linear in the input size.
| d | 523f8570241f8fc1c65cba8caa5ed854 |
As contrastive loss, we choose the state-of-the-art SupConLoss {{cite:01fb78d1680737bfd0863353335e836a8ccce383}}. It outperforms other losses like SimCLR {{cite:7b28f788b0ad72508268ea6b1088f91c08c9ceff}}, only has one hyperparameter, the temperature, and does not require hard negative mining like the triplet loss. However, our framework is more general and also works with other contrastive losses.
| m | 23df687a5793011b50ee27d92202950f |
where {{formula:afee5cdd-88eb-4a81-9bdc-615337204d30}} MeV and {{formula:9eed9fdf-bc66-40bf-9a89-9015bcd20818}} .
The above expression is compared to the data points
from {{cite:aed84bb6e7375e075c478c34f2a9c9c6220159a0}} in Fig. REF . We emphasize that Eq. (REF )
is not the result of a global best {{formula:0bc6faa3-914c-42c3-9c85-c32d1c77e740}} fit. We try to get a better
description of the higher energy data points, which will be relevant for the study
of the {{formula:a3742029-6b46-486c-8f86-515bd48c03a9}} ratio measured at the LHC. The STAR points are shown just for
comparison.
{{figure:3c32522a-27f9-49e8-a774-e438dd05b9d5}} | r | 3a20b6a79d3035d6d6bd756be3524ce9 |
In the process of light propagation, the photon number may not be conserved due to the scattering and absorption of some opaque sources. Therefore, considering an opaque universe, the photon flux received by the observer will be reduced by {{formula:8296e6c9-0f2f-4efe-98ea-7297296a54e1}} . If {{formula:93937972-4171-4f64-b639-39019f95e5f5}} , it indicates the deviation of CDDR. The main difference between the CDDR and the cosmic opacity is that they choose different parameterized forms for {{formula:9afd7bfb-ad1f-4583-a564-694e9691d6c2}} . Holanda et al. {{cite:38f177c8a3f62063b0216de1c28e820d94a3c01e}} proposed two parameterized forms of {{formula:d80bcd50-28fa-448a-a546-efc32498cf3e}} , {{formula:f429f1a2-a47b-4ae8-bfe3-7e163b964b44}} and {{formula:78554710-0af1-4195-a31f-685ffc7096b5}} to test the CDDR. They consider these expressions have several advantages such as a manageable one-dimensional phase space and a good sensitivity to observational data. For cosmic opacity, it is studied from the parameterization of optical depth {{formula:403ae359-8573-4f57-a7ca-2de4c2011762}} , {{formula:fa302a5c-ee60-4a6e-9174-fab6fd540a54}} as described earlier. One of the effective methods to test the CDDR is to verify the conservation of photon numbers. Therefore, in this paper, we use optical depth parameterization considering photon number conservation to verify the effectiveness of the CDDR.
| m | 9741ae86e8fba693ea67f01b31528026 |
Limitations and future directions.
Our method inherits some limitations from prior video and view generation methods. For example, although our method produces globally consistent background sky, it does not ensure global consistency of foreground content. Addressing this issue potentially requires generating an entire 3D world model, which is an exciting future direction to explore. In addition, as with Infinite Nature, our method can generate unrealistic views if the desired camera trajectory is not seen during training (e.g., in-place rotation). Alternative generative methods such as VQ-VAE {{cite:0e1af631d54857943c9f0452124be5e87b66545d}} and diffusion models {{cite:a60b87f9826b6fed6a53ac95271ebc58741a4fc7}} may provide promising paths towards addressing this limitation.
| d | 29e67cebd7f659d049afacb9e43074c3 |
Our method also generalizes to the image domain as shown in Table REF . CLASTER outperforms previous work in five out of eight tasks and obtains comparable results in the remaining three tasks. We compare our approach to several state-of-the-art methods: Region Graph Embedding Network with the Parts Relation Reasoning branch (RGEN) and without the branch (R-PRR) {{cite:7297fa8b91e3e08a7f28bd9be3a6bcfb0c644ede}}, the evaluation of output embeddings(SJE) {{cite:b4eb4c6e9224fd69b5117d42273f607993fe4d3f}}, the feature generating networks (WGAN) {{cite:e54a98db783c8f40f8d2ea9940f0ecdb48b69641}}, the feature generating framework (VAEGAN) {{cite:1e4ee273e8e037e168472be70292906de6b6c822}} and the latent embedding feedback method (LEF) {{cite:bb6c22c911da7dfb5e61400c90228a444929463f}}. {{cite:7297fa8b91e3e08a7f28bd9be3a6bcfb0c644ede}}).
{{table:33a6e7cd-9bdb-4965-925c-31205db72c42}} | r | 8e1c00abd2541f0f84475fc42f2dffab |
We have presented the first sensitive X-ray view of the reddened, strongly lensed quasar
2MASS J1042+1641 ({{formula:27b8612a-b09d-4b14-8a5a-70390c6a1df6}} ), combining data from the Chandra, XMM-Newton and NuSTAR observatories.
This is a quadruply lensed system, based on optical/IR imaging ({{cite:ee6540544ed5876110ca208fb04f843ceb2c7bd1}}), and
the Chandra data show clear X-ray emission from each of the four quasar images (see
Figure REF ). The flux ratios are consistent with those seen at longer
wavelengths, and, within the limitations of the available data, we do not see any evidence
for large differences in their X-ray spectra (which can occur if some of the intervening
absorption occurs in the lensing galaxy, e.g. the cases of B1152+199 and
GraL J234330.6+043557.9; {{cite:9340f5062e71203684c385d96ab376709b3a96d0}}, {{cite:757eb9e4b76e8e77fcf5a08332d18795386cd8fd}}, {{cite:e3c270ebd721863302f1d205b74f001fb65bbf96}}). This is consistent
with the absorption being intrinsic to the background quasar, as concluded by
{{cite:ee6540544ed5876110ca208fb04f843ceb2c7bd1}} and assumed throughout this work. The X-ray flux ratios show that the
flux anomaly seen at longer wavelengths, in which image A dominates the total flux, is
also clearly seen in the X-ray data. {{cite:ee6540544ed5876110ca208fb04f843ceb2c7bd1}} suggest that this may be due to
substructure (as predicted by {{formula:9df2f320-7b17-4f7b-8dc9-42bc5762a205}} CDM) surrounding the main lensing galaxy
(e.g. {{cite:e69fe953ddebf6f3de53add2fe04f638ea94192d}}), as opposed to the microlensing alternative, as they argue that the
flux anomaly is still seen at longer wavelengths where microlensing should be less of an
issue. The fact that the image flux ratios seem to be similar in both the X-ray and the IR
bands would be consistent with this interpretation, although the reasonably large
uncertainties (Table REF ) mean that strong conclusions cannot be drawn
from the X-ray data here. It is also worth noting, though, that the long-term X-ray
lightcurve (which formally shows the integrated flux, but in reality is likely dominated by
image A) appears to be relatively stable over a baseline of {{formula:e8316a22-a629-4ffd-ab9b-2050a9fcced5}} 8–9 years (in the
observed frame; see Fig. REF ); there is a hint of a variability event in the XRT data
just prior to MJD 58800, but the uncertainties on the most elevated data points are
extremely large.
{{figure:d3c734f8-3f7b-4ee3-abdb-a92d7c2245cf}} | d | d929249090695bd1e753dec11d8c2999 |
Reinforcement Learning (RL) has achieved remarkable success in solving various complex tasks in games {{cite:d803d2f530ceb9d2dec3cd550ed59716d6d2f570}}, autonomous driving {{cite:72a257439cfd37032228f3abcc8f27bbcfeed781}}, and robot manipulation {{cite:d215bf424d91e7b33940cd1ecc25f89ba0aa6c00}}, among other fields. In RL setting, an agent tries to learn the best actions by interacting with the environment and evaluating its performance based on reward signals. More specifically, in Markov Decision Processes (MDPs), the mathematical formalism for RL, after taking an action, the state changes according to a transition probability model and a reward signal is received based on the action taken and the current state. The main goal of the learner is to find a policy that maps the state space to the action space, maximizing the expected cumulative rewards as the objective function.
| i | 13a9a336734e8af8accfd1b186e7fb70 |
On the other hand, contact binaries are taken as distance tracers because of the period-color correlation first discovered by {{cite:40664674ec6fa4cad5b6f4ef8efad919286f4f17}}. The absolute-magnitude calibration of contact binaries was developed by {{cite:30a5674d3bbf7321ac4d4f27c32f8bdb6a5c1d74}}, {{cite:3d2315367a0088b9a7214d631a45909ecf7574e3}}, {{cite:71dad30beb39618ba0a02b6784fafc338ace21db}}, via the parallax data of the {{formula:4f6f8639-ae82-4094-9be1-7446eca6c191}} Mission {{cite:61b93bffaf49f36ee2c2959e19dd27c39476e8e7}} and the contact binaries in the open or globular clusters. By using the first {{formula:4c67f3e6-decd-402a-a938-d211d34d1034}} satellite Data Release {{cite:7f55f958e9d938337e9d648546d632fbc77af9c0}}, {{cite:ac81e1d6b76d575d104d6d079a1f4003419fecbf}}, {{cite:01c5a26bb8c5db821fdde945aafcf805c353a6c3}} improved this calibration. According to their formula
{{formula:d78a2c15-8ddd-41d9-b7eb-d2fc0f9e7db5}}
| d | ad2bb4365fc5f31582a64f8695b2dd88 |
where {{formula:7b492aed-55e0-43a8-9778-9b51dacb4370}} is the number of edges running from group {{formula:6df4a690-d540-4b0c-a3aa-54da8492a072}} to group {{formula:1a7a9538-d67b-4bf8-8b65-eb805749d86b}} , {{formula:6da42317-2b1b-4ac0-b238-77104a13d41e}} ({{formula:44f68620-c001-4ad9-ab83-9456f97efabe}} ) the number of vertices in {{formula:8cb42772-8aa0-4aa5-9c73-56ee97b59878}} ({{formula:d231a5e6-7e6c-42fb-9cdd-b23d3d2e4aab}} ) and the sum runs over
all pairs of groups (including when {{formula:635a3f29-6d72-481c-abb4-739dfe9df90e}} ). This version of the model, however, does not account for the degree heterogeneity of most real networks,
so it does a poor job at describing the group structure of many of them. Therefore, Karrer and Newman proposed the degree-corrected stochastic block model (DCSBM) {{cite:08044938a7734a2ab7bd2a5ad15ead3f37088b50}},
in which the degrees of the vertices are kept constant, on average, via the introduction of additional suitable parametersThe authors were inspired by modularity maximisation,
which gives far better results when the null model consists of rewiring edges by preserving the degree sequence of the network (on average), than
by preserving only the total number of edges..
The unnormalised maximum log-likelihood for the DCSBM is
{{formula:6df0cfa3-152d-498f-a0fc-cfeeff26b1be}}
| m | b9ced6322e2f91627ab44fc5e82f0928 |
This investigation has demonstrated that the metabolic networks of
microorganisms are more accurately modelled with a network growth
model in which network size is a modifying factor, a concept which
has surprisingly not previously been considered. This model, as well
as fitting the graphical measures examined, also demonstrates a one
possible mechanism which may be significant in the network
evolution. This suggests that when the metabolic networks are
growing (or evolving) the size of the network causes it to be
increasingly unlikely for a new metabolite to join the network and
participate in the reactions. Due to the size dependent growth
networks having a densely connected cluster, these networks will
have an increased resilience to targeted attacks than that of the BA
model, which are known to be devastated by targeted attacks
{{cite:5eb86fbcadf01bcc5b7bb891371bc2af59cf2fb8}}. This suggests that the structure of
metabolic pathways gives them a greater resilience to targeted
attacks than if they were examples of scale-free networks, modelled
by preferential attachment.
| d | ff8855b7f0bf7cb3ae4aeb6556ab046c |
Three potential improvements related to the technical results in our work are: Firstly, a major challenge would be to tie the hardness of simulating approximate standard-resolution energy measurements to well-known complexity-theoretic conjectures beyond BPP{{formula:dcdbe526-0872-43f0-b518-a674c9ec53aa}} BQP. This program would require techniques beyond the Stockmeyer-method and
Polynomial-Hierarchy collapses{{cite:15162e48c4ce965fc1ae6c04a623cbceca6b139e}}, {{cite:eb21e632b0128064e0577e9ef4800bcc9a4f33c8}}; Secondly, in this manuscript we have not investigated the verifiability of the standard resolution proposals. However, due to the small size of the energy output space, classical verification methods similar to those in Refs. {{cite:ad0411e5893f073d8eb339a629041bae0900adee}}, {{cite:a0cadb39634de23bc559e35f2a1a676d72a3ab42}}, {{cite:3fba3db8ce32e535cb69edb5bcea869804cc1246}} could be developed; Thirdly, it would be interesting to improve the locality of our Hamiltonians. The locality of the examples based on 5-local Hamiltonians on 2D lattices could, in principle, be improved using the general techniques presented in Ref. {{cite:f4a6b8b529a869e1c98e01068ed9fcd08ba0a359}}, which show that there exist simple 2-local universal Hamiltonians that can reproduce the physics of other Hamiltonians, including the energy spectrum and measurement statistics. The examples based on circuit-to-Hamiltonian constructions could be improved using techniques such as, e.g., perturbation gadgets or space-time circuit-to-Hamiltonian constructions {{cite:52580504ae0ac619b0d66ea0c03745ab4ac9b3eb}}, {{cite:f035d64a78344d644a7eb55c84e11baea56ae665}}.
| d | 92c1edf8e003ce5df96fbd07fcaee8ec |
Models for traffic on a single lane predict the occurrence of
interesting collective phenomena in the kinetics of relaxation to
stationary state and in some physically observable quantities in the
stationary state when passing is not allowed{{cite:47d07c36560ba1d05dea2f98c5d5f73c4bcb657e}}, {{cite:0ed26f28fad9deeef88c6797d186549d0d6b0e81}}, {{cite:27aee0360ac82006511c6f4650941a98d1f76202}}, {{cite:0e97a6384c96f65dd6f37e9d268fa458984e4d90}}, {{cite:93db3c343ee763b708e897739146f531bf29ada9}}, {{cite:a5e070f800024f5c992bfb5dbc5fbccb606b3175}}, {{cite:a2fd7436af9c9910ba057e11a60bcf45500e58df}}, {{cite:405d33f85c5961189114effa13a9bbd44c2f725f}}, {{cite:46fa1d7f2b00da05ff3caf91997e56b172e6e322}}.
The main reason for the
emergence of the collective phenomena is heterogeneity in traffic (namely, differences in driving characteristics from vehicle to vehicle), typically modeled as quenched disorders in the parameters of the
models{{cite:47d07c36560ba1d05dea2f98c5d5f73c4bcb657e}}, {{cite:27aee0360ac82006511c6f4650941a98d1f76202}}, {{cite:2181169778218bcdc4d6f2954ba4365d980d8bae}}, {{cite:aae697d8c7f451776741ffa68023ef6c112abcb0}}. For instance, an interesting phenomenon occurs
when the desired speeds of the drivers/vehicles in the traffic
are heterogeneous and if passing is not allowed. Faster vehicles in the system form platoons behind the slower vehicles
and the average platoon size grows with time
as a power-law {{formula:787b3002-8556-40ca-aa02-f8231f21cd47}} until all the platoons coalesce
and form a single giant platoon. {{formula:f7dcea84-28cf-4471-bf39-b64a51417449}} is the exponent of the quenched disorder
distribution in desired speeds of vehicles in the low-speed limit.
The collective phenomena on a single lane are have been studied
using various kinds of approaches of cellular-automata,
car-following models{{cite:93db3c343ee763b708e897739146f531bf29ada9}}, {{cite:a6f0eea79b24d5617dc703b92e0675410aea08d9}}, {{cite:f7655b92775b56a66c490409fcf0438d79f82980}}. New approaches are still being developed
to efficiently model the complex phenomena. A particularly
interesting development is the application of evolutionary games
to traffic{{cite:364ebdbc2d89d85e33ff41f2aa4c5f3ef7b4fc61}}, {{cite:fb739e3430a38cd5473b24acb80627d84348c2f1}}.
Nevertheless, the question of what happens in a two lane system,
when lane changing is allowed, is not fully understood.
| i | e115d629d1f67e51def2b3e7018704a0 |
to transfer the target style,
where {{formula:81f88a8b-c24f-4f47-b807-34d8503d5c33}} , {{formula:ba27d45c-4140-4662-9380-6a9ca127ea4a}} and {{formula:bd1c8f0f-2a28-4fef-868f-76d69b0af25a}} are the content, the style and the generated signals, respectively;
{{formula:3ce82c4a-f9c5-4939-aa0e-dbab5c44b2dd}}
and {{formula:9138901c-081f-4a02-aefd-580b33a6b7be}}
are the content and style loss, respectively;
{{formula:61448553-1045-4550-a9f1-5ae1b4d10bc5}} controls how much penalty will be exercised over the deviation of the generated audio from the content loss,
{{formula:0aa2d4bc-1331-4f07-9f1f-d5d9d981a9d7}} and {{formula:82131f60-3d1e-45ca-ae9b-ba96aa401acb}} are the indices for content and style layers.
The size of {{formula:d5656313-9e27-49f6-a00b-e0da9bd430e8}} varies between different neural network architectures.
For example, {{formula:49820a96-45c0-47e9-b83e-6a394352f229}} in VGG-16, {{formula:86fd9af7-9baa-4b65-99ac-f50428a8d0f5}} in SoundNet{{cite:46eb9ba60906028e21cff8bce352bc95f31f17df}} and
{{formula:5bf914bd-7209-466a-bf95-3af54cc26bdf}} in the wide-shallow-random network by Ulyanov and Lebedev{{cite:5a2c8defa6973a71ca7dfeb9303db53dce8c4121}}.
In our simulation, we have {{formula:12777067-5f4e-443a-8365-eb77dc27e5b2}} .
| m | 5c53a1a4159218ff23f037ebb9af56c0 |
Note that the linear span of {{formula:1cd8b6a4-1ff3-43d4-b23b-dbe2230d900a}} and {{formula:f724b3a2-638d-4468-a932-1fc012145cce}} is same as {{formula:6dc2f5f1-502e-458e-930e-065f25a8b160}} because {{formula:767be1e8-eeb3-4005-a05a-e9f5e9a53b0c}} and {{formula:4a26ae47-41fb-4d90-92de-5ac75d10f5fb}} only differs by a scaling constant. Hence Theorem remains unaltered even if we use the scaled B-spline basis {{formula:eb2431fa-c0da-4e78-b2ac-eb22c7d6e080}} .
Another result which is due of {{cite:47c0417f06e2abc2e84eadcee31facf0635c4158}}, is used in this paper to bound the minimum eigenvalue (e.g. the operator norm of the inverse) of the sample covariance matrix formed by {{formula:7dbb8115-cd84-4792-8822-eaa864879334}} in terms of the population covariance matrix {{formula:247daeef-2456-4720-9ead-7b32f78db6fb}} is the following (see Lemma 6.2 of {{cite:48772b59846ef25ad51fb742b3ee593b6e897ac7}}):
Let {{formula:4a02cf43-7ef4-4986-b1ea-7e88eee69ef7}} be independent symmetric non-negative {{formula:6d08f104-e91c-4697-8472-c62a8faa9a8f}} matrix-valued random variable. Let {{formula:9e99db7d-f18f-4b4c-81b1-6bb41cb9b5a1}} and {{formula:5f3714d9-c5e1-43f0-981d-13d286c29014}} . If {{formula:2e58df3d-9edc-4de8-bcd8-777de85c888a}} a.s. then we have:
{{formula:ff6bec16-af7c-4385-a789-ffe748ead23e}}
| d | 470f9304b89195414830793e79304aeb |
In this paper we propose MetaPG (see Figure REF ), an evolutionary method that evolves a population of Policy Gradient RL algorithms {{cite:c8fd21d3855085bbd296d93c9a2989ff5fc5da10}}; algorithms are represented in the form of directed acyclic graphs, using multiple fitness scores encoding independent RL objectives that are taken into account by means of NSGA-II algorithm {{cite:ae9ec845432c4c79e6bde31535f640a763eacfa7}}. Compared to manual design, this strategy allows us to explore the algorithm space more efficiently by automating search operations. Then, given this multi-objective perspective, we are able to obtain a Pareto-optimal set of RL algorithms that lay on the plane that jointly maximizes fitness with respect to each objective, approximating the underlying tradeoff among them.
{{figure:dfeb3f1e-b926-4f9d-9455-549484a196fe}} | i | b9191a2ab9e0165a6949696de61a5b2c |
Unfortunately, our estimate of the most probable orbital geometry (Table REF ) is not very distinctive.
The Bayes factor {{formula:cd03733e-a2a4-4977-8cff-ef1b8455ae0b}} as given by {{cite:db0e1c82a96d96e2d584022b964aa0c81fbc3854}}, calculated for our case 4 leads only to a “barely worth mentioning” rating, which means it is not significant.
However, future investigations of this geometry might show different results.
In this context, it will be particularly interesting to find out whether or not larger planets lead to more significant results.
We carried out basic simulations for larger Kepler-20 planets by increasing {{formula:ccfa4b97-d2a9-4a86-958b-3455e7c75e09}} by constant factors in our models and also simply scaling the transit depth of the real data by the same amount.
For this setup, we find a maximum probability of about {{formula:b8d0f4ac-440f-4284-b7fb-b58e2f9627fc}} for planets enlarged {{formula:c0265574-df49-4fb3-8265-5ba2821d6216}} times their real size.
Planets of even greater size do not increase the probability of this geometry.
Artificial PPOs which are then larger than the photometric noise would have been detected in the first place, and information hidden in the noise, such as photometric activity, becomes less important in the determination of the posterior.
This is the case for a planet radius {{formula:37bfa072-d2c8-4606-b927-3fa80cf10cf0}} of the smaller component.
In addition, simulated Kepler-20 data with noise lower than a PPO signature, that is {{formula:437c4ba7-0a4b-4c4b-8599-304e701dc721}} if the original planet radii are considered, do show a similar behavior.
Here the mentioned probability decreases for lower noise until the data no longer show the tendency of the geometry.
This is not surprising because, due to the symmetry, the method described in Sect. REF is only valid if there is at least something in the data, or real significant PPOs.
In the latter case, this will lead to significant results, while in cases like Kepler-20 this can only serve as a hint.
Despite these limitations, our obliquity sampling is still useful for excluding individual angles {{formula:c1b3f484-96e5-4854-bcaa-816e5bcdfba1}} Also, for larger planets, the peaks and dips become wider covering a larger fraction of angles {{formula:b80da5c3-8fb2-44cd-875b-94803e725f27}} , leaving only a small fraction of allowed angles.
This approach also benefits from longer observations covering additional multi-transits at different phase angles.
| r | a5abf4b97813111c0a0c66151d6b8b23 |
In this section, we discuss the optimized set of residue pair distances obtained from our GA-based approach. As described in the method part, the unbiased and extensive MD simulation data (>100{{formula:5dbb6062-82dc-4aa8-b14d-cd635204c515}} ) simulating the folding process of the proteins is taken from literature{{cite:b36c8f98449bf7ba962aac5ab931e6f5eafd5354}}. Preliminary sets of residue pair distance are randomly selected from the set of all the possible residue pairs as the starting point of the genetic algorithms. These sets go through selection, mutation and crossover steps to provide a new generation of residue pair distances. In the setting of GA, we choose a population size of 10%, mutation percentage of 50% and crossover percentage of 20%. Next, the newly generated residue pair distances are used to build MSMs and assign new GMRQ scores (fitness scores) for evaluation. The next iteration will then go back to the selection step and select according to the newly assigned fitness scores. As the process goes through more iterations, the GMRQ scores will converge and a best GMRQ score can be found.
{{figure:27dfa67f-f766-40d3-a7f2-cb9727bf0cb3}}{{figure:318b8ec2-9501-42ee-a01a-045ed3b28b2c}} | r | ce79054bf629805690d69fc6a07996df |
Recent work on canonical correlation analysis {{cite:6886b3d05df8b5f05d41b448ce8354be4ad20140}}, {{cite:b030bac37c5cf3062ffc348483edd781936182b8}}, {{cite:4857ae39e63c7f561ca7ab653d0221a1e4a57734}}, slow feature analysis {{cite:4d9b6d5991b55f7b0fe2e24abedebf84a3a3a00b}}, and ICA-like algorithms have led to biologically plausible NNs {{cite:b1fbfa257b0ec88f9227b2e6bdc53124cf5e0e3b}}, {{cite:8ec85e64479781f93c3b7eeb00d75ee9fc04707a}}, {{cite:77425428defc9cea9ccf6c8b52f56476fafeaea2}}, {{cite:8a2b16093f402d13dba6256e327a16a37f5fec7d}}, some of which rely on two-compartment neurons {{cite:25db7b7310c3691c2bc2525a2e81493154f9f9ae}}, {{cite:30e84357ee30e644a14c28c359dea5ccaf76ef15}}. These NNs could, in principle, be used for popular BSS tasks known as second-order blind identification {{cite:4426c067ea1a3c06c49cd6c2eb19cbf932a9a59c}}, {{cite:24ec080624e37c5ddc90869970cd592059d69346}}, {{cite:e9805dff09951976289b2072db1990a47eef87ef}}, {{cite:0d34061a8875e63411d2d31a4e2362ae1c3c9ddc}} or in the context of kernel ICA {{cite:1293fb4006ebdae0f095738a0907f93e587f5a9e}}, {{cite:97100978fe9a57e4bd3f28becd159fb40461e3b7}}. This suggests the existence of a single model of two-compartment neurons and non-trivial local learning rules for BS. In future work, we aim at proposing such a model, including high-order statistics, temporal correlation, and diversity of views.
| d | 0aea793a14973645c890af9a25e326bd |
It is a fact of life that neutrino oscillation data support large mixing angles and at least two neutrinos having tiny masses {{cite:c42c7220a4a2acff916391779a9d83a70dfebf53}}, {{cite:89c39bd3077e7b3dca705389df9c6c4140225c44}}, whereas the Standard Model of particle physics (SM) postulates that all three neutrinos are massless Weyl fermions.
As the SM is an otherwise successful description of data across many scales, one is inclined to extend the model in order to reconcile this discrepancy and reproduce the well-established {{cite:762b2d4839920a5996f6680df1f0eb75a4c3a094}}, {{cite:b6e84be10ec0c58a4f2759e885d6be406da4ea3f}} Pontecorvo-Maki-Nakagawa-Sakata (PMNS) paradigm {{cite:a7e9209c74dbc4862ab65596b562366cdb94094a}}, {{cite:a1e3ba3b903a04b6b40da4eb015b68350a4506a0}}, {{cite:fcfdbbae3c2ecfce4959a17c2a66667f05df7328}} from more fundamental principles.
What is less clear, is which, if any, of the many neutrino mass models throughout the literature are at least partially correct.
| i | 500655a215b0066f19541b38d518fc24 |
Figure REF shows the optimal level of precision {{formula:14ad39bd-6c28-4333-8b21-a5ce8b1c16f7}} when varying the number of local iterations {{formula:c063dc74-7f4c-4e2b-8f14-a05edede1c1b}} . We use the same CNN architecture in Fig. REF . We can observe that {{formula:a1f1eb83-ce89-4b98-be7f-738768e6c082}} increases with {{formula:10081037-7f64-46c2-bcc0-3d64ff65b5e4}} . This is because, as {{formula:f4c0178b-b0cd-4e3f-b221-6ff38b4f8b81}} increases, the local models converge to the local optimal faster as SGD averages out the effect of quantization error {{cite:32d0442b16eaa514ce108ff360996e0d8b5ebaf1}}. Hence, a lower {{formula:7bbeb861-3771-47e9-87ef-64f2a8a001c1}} can be chosen by leveraging the increased {{formula:bbe9d97f-9875-4bd4-a977-9d243fd28e29}} to minimize the total energy consumption. We can observe that only {{formula:c724ddf0-ef45-4f99-a5cf-b9b115579499}} is required at {{formula:c859a52d-be3d-4954-b6b5-53728a7c5f74}} while we need {{formula:406c57cb-0df5-4d2a-92b3-1e417405f8fa}} at {{formula:be1c5105-a70a-45d5-bfb8-9e579bd364ce}} .
{{figure:8bbd6397-5b20-484f-ac2d-df68b17f9988}} | r | 6901bec61e4a51fe72a5cc8253062e7d |
Two of the meshless techniques are the Moving Particle Semi-implicit method (MPS) {{cite:1c7b37796b48460af9d5914d2e4d95cf408fcba8}} and the Smoothed Particle Hydrodynamics (SPH) {{cite:3d7cb7c941ac41dc8a763870f50673631af8fdc7}} {{cite:836ad3e8aef7ef33927539864dee96a655404ec5}}, the latter initially intended to astrophysics applications and then adapted to fluid simulation. The MPS authors idealized it to simulate the flows of incompressible fluids, which refers to a fluid whose material density is constant within a fluid parcel, a property found in liquids. Its main difference from the original SPH, which can be considered an advantage for the MPS regarding numerical precision, is that the calculations adopt a semi-implicit predictor-corrector model {{cite:1c7b37796b48460af9d5914d2e4d95cf408fcba8}}. However, the SPH is more prevalent in CG and VR applications due to the high computational load occasioned by the MPS calculations, including solving the Poisson Pressure Equation (PPE).
| i | ce94b56462577f0ae2c8b0c46b72e61d |
We compare our GPVTF model with the following baseline methods.
We first employ standard spectral clustering methods on the modality-specific features, i.e., visual features {{formula:d2ad473d-6a42-4bf3-8dd0-b41239c0e89f}} and tactile features {{formula:0dfb79be-59e3-471e-b115-1cc9ca040a11}} , which are termed as SC1 and SC2.
ConcatPCA concatenates feature vectors of different modalities via PCA and then performs standard spectral clustering.
GLMSC {{cite:ffe7a9d8af5b35946c649d2740354465908b0e16}} proposes a subspace multi-view clustering model under the assumption that each single feature view originates from one comprehensive latent representations.
VTFC {{cite:47a4db09976d25e9862b8f3aaf171deb0b6cfc29}} is a pioneering work to incorporate visual modality with tactile modality in the object clustering tasks based on auto-encoders and NMF.
IMG {{cite:2cfd4d5f42068311e3d2fcdbea57a3f13e45ec45}} does the incomplete multi-view clustering by transforming the original partial data to complete representations.
GRMF {{cite:beb1b5e47f59dec77b040819cfd9a163cf990f25}} exploits the complementary and local information among all views and samples based on graph regularized matrix factorization.
UEAF {{cite:4de5f6652cc1fff7e7f2609fb374953da5beaadd}} performs missing data inference with locality-preserved constraint.
| m | bf3c7dd9594dbee75a72ad7ff12fdacb |
In Table REF , we evaluate the performance of Img2Prompt on various open-sourced LLMs other than OPT, including GPT-J {{cite:af78dbf33756a3166cb128072391b7555238657b}}, GPT-Neo {{cite:b7f3a93a86f8ff4709cacf37057ae6e3dd74db34}} and BLOOM {{cite:e25841e64a5970222c2daee4fb53271933e25b8e}}.
The experimental results show that Img2Prompt enables various LLMs to perform zero-shot VQA tasks, and that all of them achieve superior performance to zero-shot PICa {{cite:f0cf99381044926d97fd503c90e0739ec25c083d}} and Frozen {{cite:b7d6a09764f4e16bd3bff393daf4e1f30e69e75e}}. This is a strong evidence for showing our method’s generalization ability with different LLMs.
| r | ea9112a8f50b0795213126a0d7db06c5 |
If {{formula:f7bf63c6-20e7-44bc-be88-ded7e117209e}} and {{formula:90af94b1-c376-462d-ba2e-d64dd6313073}} are not commutative, it is very difficult to calculate the matrix exponential {{formula:6bf0af18-e87a-4606-9c1f-9f98975b9369}} . Thus, we propose another discrete model motivated by the Lie-Trotter product formula {{cite:dedf12c624adffe210dc565c43339a1ebeb642a3}}:
{{formula:6ff45c9c-92e2-40fc-a125-f8c7763013bf}}
| m | 0e6a1a1a5c911d03c053167b37c5d472 |
An interesting observation is that there is an almost one-to-one correspondence for n steps of APE and n steps of Stout smearing when {{formula:cdcc9e9d-b5ec-4763-99f2-3ccb01610678}} . As seen in the plot on the lhs. of fig. REF , {{formula:1dd8cf4c-235c-4e88-8630-ebfb043363e9}} for a large number of smearing steps. This is consistent with results by Capitani et al. {{cite:64e0f87748cf08e781377b9f7fed85653a760352}}, where such a relation has been derived from perturbation theory. While they have focused on global observables with up to 3 smearing steps, our nonperturbative result reflects the local similarity of both methods and their strongly correlated topological charge densities up to 50 steps.
{{figure:cd8be1d0-3f3e-4253-8dfb-33b813264bf8}} | m | f30ee5e286b9c8f69826a233966a1e13 |
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