检索结果-内蒙古大学图书馆

arXiv 2022年

作者： Huang, Xinmeng Yuan, Kun Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States Center for Machine Learning Research Peking University China

Decentralized optimization with time-varying networks is an emerging paradigm in machine learning. It saves remarkable communication overhead in large-scale deep training and is more robust in wireless scenarios especially when nodes are moving. Federated learning can also be regarded as decentralized optimization with time-varying communication patterns alternating between global averaging and local updates. While numerous studies exist to clarify its theoretical limits and develop efficient algorithms, it remains unclear what the optimal complexity is for non-convex decentralized stochastic optimization over time-varying networks. The main difficulties lie in how to gauge the effectiveness when transmitting messages between two nodes via time-varying communications, and how to establish the lower bound when the network size is fixed (which is a prerequisite in stochastic optimization). This paper resolves these challenges and establish the first lower bound complexity. We also develop a new decentralized algorithm to nearly attain the lower bound, showing the tightness of the lower bound and the optimality of our algorithm. Copyright © 2022, The Authors. All rights reserved.

关键词： Time varying networks

来源：评论

学校读者我要写书评

暂无评论

Ellipticity of the harmonic emission from graphene irradiated by a linearly polarized laser

引用

Physical Review A 2021年第3期104卷 033119-033119页

作者： Fulong Dong Qinzhi Xia Jie Liu Graduate School China Academy of Engineering Physics Beijing 100193 China National Laboratory of Science and Technology on Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China

We investigate the high-order harmonic generation in graphene irradiated by a linearly polarized intense laser, addressing the ellipticity or polarization properties of the harmonics. We exploit time-dependent density functional theory to calculate the harmonic spectra for a laser wavelength of 4770 nm and an intensity of 1.7 TW/cm2, and our numerical results can qualitatively reproduce recent experimental data. Our simulations also reveal that the harmonic ellipticity depends on both the harmonic order and the orientation angle between the graphene symmetric axis and the laser polarization direction. It can reach 0.68 for the ninth-order harmonic at the orientation angle of 20∘. To understand the mechanism of the high ellipticity, we develop a two-band model based on the tight-binding approximation. We may explain the ellipticity of high-order harmonic generation by investigating the transition dipole moments in the two-band model. Our theory further predicts a sensitive dependence of the harmonic ellipticity on the laser intensity for various laser wavelengths.

关键词： High-order harmonic generation Graphene Polarization Dipole approximation Tight-binding model Time-dependent DFT

来源：评论

学校读者我要写书评

暂无评论

Learning operators with coupled attention

The Journal of Machine Learning Research

引用

The Journal of Machine Learning Research 2022年第1期23卷 9636-9698页

作者： Georgios Kissas Jacob H. Seidman Leonardo Ferreira Guilhoto Victor M. Preciado George J. Pappas Paris Perdikaris Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia PA Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia PA Department of Electrical and Systems Engineering University of Pennsylvania Philadelphia PA

Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution of spatio-temporal dynamical systems and approximating general black-box relationships between functional data. We propose a novel operator learning method, LOCA (Learning Operators with Coupled Attention), motivated from the recent success of the attention mechanism. In our architecture, the input functions are mapped to a finite set of features which are then averaged with attention weights that depend on the output query locations. By coupling these attention weights together with an integral transform, LOCA is able to explicitly learn correlations in the target output functions, enabling us to approximate nonlinear operators even when the number of output function measurements in the training set is very small. Our formulation is accompanied by rigorous approximation theoretic guarantees on the universal expressiveness of the proposed model. Empirically, we evaluate the performance of LOCA on several operator learning scenarios involving systems governed by ordinary and partial differential equations, as well as a black-box climate prediction problem. Through these scenarios we demonstrate state of the art accuracy, robustness with respect to noisy input data, and a consistently small spread of errors over testing data sets, even for out-of-distribution prediction tasks.

关键词： deep learning reproducing kernel Hilbert spaces wavelet scattering networks functional data analysis universal approximation

来源：评论

学校读者我要写书评

暂无评论

The attractor of the stochastic generalized Ginzburg-Landau equation

引用

science China mathematics 2008年第5期51卷 955-964页

作者： GUO BoLing~1 WANG GuoLian~(2+) Li DongLong~3 1 Institute of applied Physics and computational mathematics,P.O.Box 8009,Beijing 100088,China 2 The graduate School of China Academy of Engineering Physics,P.O.Box 2101,Beijing 100088,China 3 Department of Information and Computer science,Guangxi University of Technology,Liuzhou 545006,China Institute of Applied Physics Computational Mathematics P. O. Box 8009 Beijing 100088 China The Graduate School of China Academy of Engineering Physics P. O. Box 2101 Beijing 100088 China Department of Information Computer Science Guangxi University of Technology Liuzhou 545006 China

The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system. Then we prove the random system possesses a global random attractor in ... 详细信息

关键词： generalized Ginzburg-Landau equation random dynamical systems random attractor 35K05

来源：评论

学校读者我要写书评

暂无评论

T-Cal: an optimal test for the calibration of predictive models

The Journal of Machine Learning Research

引用

The Journal of Machine Learning Research 2023年第1期24卷 15959-16030页

作者： Donghwan Lee Xinmeng Huang Hamed Hassani Edgar Dobriban Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia PA Department of Electrical and Systems Engineering University of Pennsylvania Philadelphia PA Department of Statistics and Data Science University of Pennsylvania Philadelphia PA

The prediction accuracy of machine learning methods is steadily increasing, but the calibration of their uncertainty predictions poses a significant challenge. Numerous works focus on obtaining well-calibrated predictive models, but less is known about reliably assessing model calibration. This limits our ability to know when algorithms for improving calibration have a real effect, and when their improvements are merely artifacts due to random noise in finite datasets. In this work, we consider detecting mis-calibration of predictive models using a finite validation dataset as a hypothesis testing problem. The null hypothesis is that the predictive model is calibrated, while the alternative hypothesis is that the deviation from calibration is sufficiently *** find that detecting mis-calibration is only possible when the conditional probabilities of the classes are sufficiently smooth functions of the predictions. When the conditional class probabilities are Hölder continuous, we propose T-Cal, a minimax optimal test for calibration based on a debiased plug-in estimator of the ℓ2-Expected Calibration Error (ECE). We further propose adaptive T-Cal, a version that is adaptive to unknown smoothness. We verify our theoretical findings with a broad range of experiments, including with several popular deep neural net architectures and several standard post-hoc calibration methods. T-Cal is a practical general-purpose tool, which--combined with classical tests for discrete-valued predictors--can be used to test the calibration of virtually any probabilistic classification method. T-Cal is available at https://***/dh7401/T-Cal.

关键词： uncertainty quantification calibration nonparametric statistics hypothesis testing minimax optimality

来源：评论

学校读者我要写书评

暂无评论

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

arXiv

引用

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

来源：评论

学校读者我要写书评

暂无评论

Method for measuring promptγ-rays generated by D-T neutrons bombarding a depleted uranium spherical shell

引用

Chinese Physics C 2016年第1期40卷 37-46页

作者：秦建国赖财锋蒋励刘荣张信威叶邦角朱通华 Department of Modern Physics University of Science and Technology of ChinaHefei 230026China Institute of Nuclear Physics and Chemistry CAEPP.O.Box 213Mianyang 621900China Graduate School China Academy of Engineering PhysicsMianyang 621900China Institute of Applied Physics and Computational Mathematics P.O.Box 8009Beijing 100088China

The prompt T-ray spectrum from depleted uranium （DU） spherical shells induced by 14 MeV D-T neutrons is measured. Monte Carlo （MC） simulation gives the largest prompt 2/ flux with the optimal thickness of the DU spherical shells 3-5 cm and the optimal frequency of neutron pulse 1 MHz. The method of time of flight and pulse shape coincidence with energy （DC-TOF） is proposed, and the subtraction of the background y-rays discussed in detail. The electron recoil spectrum and time spectrum of the prompt γ-rays are obtained based on a 2＇＇ × 2＇＇ BC501A liquid scintillator detector. The energy spectrum and time spectrum of prompt γ-rays are obtained based on an iterative unfolding method that can remove the influence of γ-rays response matrix and pulsed neutron shape. The measured time spectrum and the calculated results are roughly consistent with each other. Experimental prompt γ-ray spectrum in the 0.4-3 MeV energy region agrees well with MC simulation based on the ENDF/BVI.5 library, and the discrepancies for the integral quantities ofγ-rays of energy 0.4-1 MeV and 1 3 MeV are 9.2% and 1.1%, respectively.

关键词： D-T neutron depleted uranium prompt γ-ray delayed γ-ray time of flight

来源：评论

学校读者我要写书评

暂无评论

Median variant of fuzzy c-means

Median variant of fuzzy c-means

引用

17th European Symposium on Artificial Neural Networks - Advances in computational Intelligence and Learning, ESANN 2009

作者： Geweniger, Tina Zühlke, Dietlind Hammer, Barbara Villmann, Thomas University of Leipzig - Med. Dep Computational Intelligence Group Semmelweisstrasse 10 04103 Leipzig Germany Fraunhofer Institute for Applied Information Technology Life Science Informatics Schloss Birlinghoven 53229 Sankt Augustin Germany Clausthal University of Technology Institute of Computer Science Clausthal-Zellerfeld Germany University of Applied Sciences Mittweida Department of Mathematics/Physics/Informatics Computational Intelligence Group Technikumplatz 17 09648 Mittweida Germany

In this paper we introduce Median Fuzzy C-Means (MFCM). This algorithm extends the Median C-Means (MCM) algorithm by allowing fuzzy values for the cluster assignments. To evaluate the performance of M-FCM, we compare ... 详细信息

ISBN: (纸本)2930307099

关键词： Fuzzy systems

来源：评论

学校读者我要写书评

暂无评论

Efficient numerical methods in air pollution transport modelling: Operator splitting and richardon extrapolation 17

Efficient numerical methods in air pollution transport model...

引用

17th International Conference on Harmonisation within Atmospheric Dispersion Modelling for Regulatory Purposes, HARMO 2016

作者： Havasi, Ágnes Faragó, István Zlatev, Zahari Department of Applied Analysis and Computational Mathematics Eötvös Loránd University MTA-ELTE Numerical Analysis and Large Networks Research Group Budapest Hungary Department of Environmental Science Aarhus University Roskilde Denmark

ISBN: (纸本)9789639931107

The mathematical modelling of air pollution processes is usually based on a system of nonlinear partial differential equations called transport-chemistry system. The numerical integration of this system is a rather difficult computational task, especially in large-scale and global models, where the number of grid-points can range from a few thousand to a few hundred thousand, and the number of chemical species is typically between 20 and 200. We present two robust techniques that can significantly enhance the efficiency of the numerical solution and the computer realization. During operator splitting the different sub-processes of the described phenomenon are treated separately, by coupling the corresponding mathematical problems through their initial conditions. Richardson extrapolation is based on a combination of two numerical solutions obtained by different discretization parameters. We present the basics of these methods and illustrate their benefits in different environmental models. © 2018 Hungarian Meteorological Service. All Rights Reserved.

关键词： Air pollution

来源：评论

学校读者我要写书评

暂无评论

Understanding the Influence of Digraphs on Decentralized Optimization: Effective Metrics, Lower Bound, and Optimal Algorithm

arXiv

引用

arXiv 2023年

作者： Liang, Liyuan Huang, Xinmeng Xin, Ran Yuan, Kun School of Mathematics Science Peking University China Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States ByteDance Applied Machine Learning China Center for Machine Learning Research Peking University China

This paper investigates the influence of directed networks on decentralized stochastic non-convex optimization associated with column-stochastic mixing matrices. Surprisingly, we find that the canonical spectral gap, a widely used metric in undirected networks, is insufficient to characterize the impact of directed topology on decentralized algorithms. To overcome this limitation, we introduce a novel metric termed equilibrium skewness. This metric, together with the spectral gap, accurately and comprehensively captures the influence of column-stochastic mixing matrices on decentralized stochastic algorithms. With these two metrics, we clarify, for the first time, how the directed network topology influences the performance of prevalent algorithms such as Push-Sum and Push-DIGing. Furthermore, we establish the first lower bound of the convergence rate for decentralized stochastic non-convex algorithms over directed networks. Since existing algorithms cannot match our lower bound, we further propose the MG-Push-DIGing algorithm, which integrates Push-DIGing with a multi-round gossip technique. MG-Push-DIGing attains our lower bound up to logarithmic factors, demonstrating its near-optimal performance and the tightness of the lower bound. Numerical experiments verify our theoretical results. Copyright © 2023, The Authors. All rights reserved.

关键词： Topology

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：