检索结果-内蒙古大学图书馆

HARADA’S CONJECTURE II FOR THE FINITE GENERAL LINEAR GROUPS AND UNITARY GROUPS

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Masahiro, Sugimoto Doctoral Program in Mathematics Degree Programs in Pure and Applied Sciences Graduate School of Science and Technology University of Tsukuba Japan

K. Harada conjectured for any finite group G, the product of sizes of all conjugacy classes is divisible by the product of degrees of all irreducible characters. We study this conjecture when G is the general linear group over a finite field. We show the conjecture holds if the order of the field is sufficiently *** Codes 20C15 Copyright © 2023, The Authors. All rights reserved.

关键词：

Artificial neural network approach for turbulence models: A local framework

学校读者我要写书评

暂无评论

Physical Review Fluids 2021年第8期6卷 084612-084612页

作者： Chenyue Xie Xiangming Xiong Jianchun Wang Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen 518055 People's Republic of China

A local artificial neural network (LANN) framework is developed for turbulence modeling. The Reynolds-averaged Navier-Stokes (RANS) unclosed terms are reconstructed by the artificial neural network based on the local coordinate system which is orthogonal to the curved walls. We verify the proposed model in the flows over periodic hills. The correlation coefficients of the RANS unclosed terms predicted by the LANN model can be made larger than 0.96 in an a priori analysis, and the relative error of the unclosed terms can be made smaller than 18%. In an a posteriori analysis, detailed comparisons are made on the results of RANS simulations using the LANN, global artificial neural network (GANN), Spalart-Allmaras (SA), and shear stress transport (SST) k−ω models. It is shown that the LANN model performs better than the GANN, SA, and SST k−ω models in the prediction of the average velocity, wall-shear stress, and average pressure, which gives the results that are essentially indistinguishable from the direct numerical simulation data. The LANN model trained at low Reynolds number, Re=2800, can be directly applied to the cases of high Reynolds numbers, Re=5600, 10 595, 19 000, and 37 000, with accurate predictions. Furthermore, the LANN model is verified for flows over periodic hills with varying slopes. These results suggest that the LANN framework has a great potential to be applied to complex turbulent flows with curved walls.

关键词： Compressible boundary layers Turbulence Artificial neural networks

Enhanced energy coupling for indirect-drive fast-ignition fusion targets (vol 17, pg 435, 2020)

学校读者我要写书评

暂无评论

NATURE PHYSICS 2020年第7期16卷 815-815页

作者： Zhang, F. Cai, H. B. Zhou, W. M. Dai, Z. S. Shan, L. Q. Xu, H. Chen, J. B. Ge, F. J. Tang, Q. Zhang, W. S. Wei, L. Liu, D. X. Gu, J. F. Du, H. B. Bi, B. Wu, S. Z. Li, J. Lu, F. Zhang, H. Zhang, B. He, M. Q. Yu, M. H. Yang, Z. H. Wang, W. W. Zhang, H. S. Cui, B. Yang, L. Wu, J. F. Qi, W. Cao, L. H. Li, Z. Liu, H. J. Yang, Y. M. Ren, G. L. Tian, C. Yuan, Z. Q. Zheng, W. D. Cao, L. F. Zhou, C. T. Zou, S. Y. Gu, Y. Q. Du, K. Ding, Y. K. Zhang, B. H. Zhu, S. P. Zhang, W. Y. He, X. T. Science and Technology on Plasma Physics Laboratory Laser Fusion Research Center CAEP Mianyang China (GRID:grid.249079.1) (ISNI:0000 0004 0369 4132) Institute of Applied Physics and Computational Mathematics Beijing China (GRID:grid.418809.c) (ISNI:0000 0000 9563 2481) HEDPS Center for Applied Physics and Technology Peking University Beijing China (GRID:grid.11135.37) (ISNI:0000 0001 2256 9319) Institute of Applied Physics and Computational Mathematics Beijing China (GRID:grid.418809.c) (ISNI:0000 0000 9563 2481) National University of Defense Technology College of Computing Science Changsha China (GRID:grid.412110.7) (ISNI:0000 0000 9548 2110) Shenzhen Technology University Center for Advanced Material Diagnostic Technology Shenzhen China (GRID:grid.499351.3) (ISNI:0000 0004 6353 6136) Science and Technology on Plasma Physics Laboratory Laser Fusion Research Center CAEP Mianyang China (GRID:grid.249079.1) (ISNI:0000 0004 0369 4132) Institute of Applied Physics and Computational Mathematics Beijing China (GRID:grid.418809.c) (ISNI:0000 0000 9563 2481) China Academy of Engineering Physics Graduate School Beijing China (GRID:grid.249079.1) (ISNI:0000 0004 0369 4132)

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

关键词： Energy science and technology Laser-produced plasmas

Simultaneous Estimation of Many Sparse Networks via Hierarchical Poisson Log-Normal Model

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Ge, Changhao Li, Hongzhe Graduate Group of Applied Mathematics and Computational Science University of Pennsylvania United States Department of Biostatistics Epidemiology and Informatics University of Pennsylvania United States

The advancement of single-cell RNA-sequencing (scRNA-seq) technologies allow us to study the individual level cell-type-specific gene expression networks by direct inference of genes’ conditional independence structures. scRNA-seq data facilitates the analysis of gene expression data across different conditions or samples, enabling simultaneous estimation of condition- or sample-specific gene networks. Since the scRNA-seq data are count data with many zeros, existing network inference methods based on Gaussian graphs cannot be applied to such single cell data directly. We propose a hierarchical Poisson Log-Normal model to simultaneously estimate many such networks to effectively incorporate the shared network structures. We develop an efficient simultaneous estimation method that uses the variational EM and alternating direction method of multipliers (ADMM) algorithms, optimized for parallel processing. Simulation studies show this method outperforms traditional methods in network structure recovery and parameter estimation across various network models. We apply the method to two single cell RNA-seq datasets, a yeast single-cell gene expression dataset measured under 11 different environmental conditions, and a single-cell gene expression data from 13 inflammatory bowel disease patients. We demonstrate that simultaneous estimation can uncover a wider range of conditional dependence networks among genes, offering deeper insights into gene expression mechanisms. © 2024, CC BY.

关键词： Expectation maximization algorithm

Active learning of uniformly accurate inter-atomic potentials for materials simulation

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Zhang, Linfeng Lin, De-Ye Wang, Han Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China CAEP Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing100088 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Beijing Institute of Big Data Research Beijing100871 China

An active learning procedure called Deep Potential Generator (DP-GEN) is proposed for the construction of accurate and transferable machine learning-based models of the potential energy surface (PES) for the molecular modeling of materials. This procedure consists of three main components: exploration, generation of accurate reference data, and training. Application to the sample systems of Al, Mg and Al-Mg alloys demonstrates that DP-GEN can produce uniformly accurate PES models with a minimal number of reference data. Copyright © 2018, The Authors. All rights reserved.

关键词： Potential energy

Unbiased Estimation of the Vanilla and Deterministic Ensemble Kalman–Bucy Filters

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Álvarez Ballesteros, Miguel Ángel Chada, Neil K. Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this article we consider the development of an unbiased estimator for the ensemble Kalman–Bucy filter (EnKBF). The EnKBF is a continuous-time filtering methodology which can be viewed as a continuous-time analogue of the famous discrete-time ensemble Kalman filter. Our unbiased estimators will be motivated from recent work [Rhee & Glynn 2010, [31]] which introduces randomization as a means to produce unbiased and finite variance estimators. The randomization enters through both the level of discretization, and through the number of samples at each level. Our estimator will be specific to linear and Gaussian settings, where we know that the EnKBF is consistent, in the particle limit N → ∞, with the KBF. We highlight this for two particular variants of the EnKBF, i.e. the deterministic and vanilla variants, and demonstrate this on a linear Ornstein–Uhlenbeck process. We compare this with the EnKBF and the multilevel (MLEnKBF), for experiments with varying dimension size. We also provide a proof of the multilevel deterministic EnKBF, which provides a guideline for some of the unbiased methods. © 2022, CC BY-NC-SA.

关键词： Continuous time systems

Berry phase and Hannay angle of an interacting boson system

学校读者我要写书评

暂无评论

Physical Review A 2011年第4期83卷 042107-042107页

作者： S. C. Li J. Liu L. B. Fu Science and Technology Computation Physics Laboratory Institute of Applied Physics and Computational Mathematics Beijing 100088 China Graduate School China Academy of Engineering Physics Beijing 100088 China Center for Applied Physics and Technology Peking University Beijing 100084 China

In the present paper, we investigate the Berry phase and the Hannay angle of an interacting two-mode boson system and obtain their analytic expressions in explicit forms. The relation between the Berry phase and the Hannay angle is discussed. We find that, in the large-particle-number limit, the classical Hannay angle equals the particle number derivative of the quantum Berry phase except for a sign. This relationship is applicable to other many-body boson systems where the coherent-state description is available and the total particle number is conserved. The measurement of the classical Hannay angle in the many-body systems is briefly discussed as well.

关键词： GEOMETRIC quantum phases ANGLE modulation INTERACTING boson models MANY-body problem COHERENT states QUANTUM interference HARMONIC oscillators

Unbiased and Multilevel Methods for a Class of Diffusions Partially Observed via Marked Point Processes

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Alvarez, Miguel Jasra, Ajay Ruzayqat, Hamza Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this article we consider the filtering problem associated to partially observed diffusions, with observations following a marked point process. In the model, the data form a point process with observation times that have its intensity driven by a diffusion, with the associated marks also depending upon the diffusion process. We assume that one must resort to time-discretizing the diffusion process and develop particle and multilevel particle filters to recursively approximate the filter. In particular, we prove that our multilevel particle filter can achieve a mean square error (MSE) of O(∈2) (∈ > 0 and arbitrary) with a cost of O(∈-2.5) versus using a particle filter which has a cost of O(∈-3) to achieve the same MSE. We then show how this methodology can be extended to give unbiased (that is with no time-discretization error) estimators of the filter, which are proved to have finite variance and with high-probability have finite cost. Finally, we extend our methodology to the problem of online static-parameter estimation. Key words: Unbiased Methods, Multilevel Monte Carlo, Non-Linear Filtering, Point Processes, Parameter *** Codes 60G55, 60G35, 62M20, 62F30 © 2023, CC BY.

关键词： Diffusion

Regularized matrix data clustering and its application to image analysis

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Gao, Xu Shen, Weining Ombao, Hernando Department of Statistics University of California IrvineCA United States Program on Applied Mathematics & Computational Science King Abdullah University of Science and Technology Saudi Arabia

In this paper, we propose a regularized mixture probabilistic model to cluster matrix data and apply it to brain signals. The approach is able to capture the sparsity (low rank, small/zero values) of the original signals by introducing regularization terms into the likelihood function. Through a modified EM algorithm, our method achieves the optimal solution with low computational cost. Theoretical results are also provided to establish the consistency of the proposed estimators. Simulations show the advantages of the proposed method over other existing methods. We also apply the approach to two real datasets from different experiments. Promising results imply that the proposed method successfully characterizes signals with different patterns while yielding insightful scientific interpretation. Copyright © 2018, The Authors. All rights reserved.

关键词： Matrix algebra