检索结果-内蒙古大学图书馆

Critical dynamics in multicomponent lipid membranes

学校读者我要写书评

暂无评论

Physical Review E 2009年第2期80卷 020902(R)-020902(R)页

作者： Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) and Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

The formation and dynamics of spatially extended compositional domains in multicomponent lipid membranes both in vivo and in vitro lie at the heart of many important biological and biophysical phenomena. While the thermodynamic basis for domain formation has been explored extensively in the past, the roles of membrane and exterior fluid hydrodynamics on domain formation kinetics have received less attention. A case in point is the impact of hydrodynamics on the dynamics of compositional heterogeneities in lipid membranes in the vicinity of a critical point. In this Rapid Communication it is argued that the asymptotic dynamic behavior of a lipid membrane system in the vicinity of a critical point is strongly influenced by hydrodynamic interactions. More specifically, a mode-coupling argument is developed which predicts a scaling behavior of lipid transport coefficients near the critical point for both symmetric and asymmetric bilayers immersed in a bulk fluid.

关键词： Hydrodynamics

Deterministic guarantees for Burer–Monteiro factorizations of smooth semidefinite programs

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Boumal, Nicolas Voroninski, Vladislav Bandeira, Afonso S. Mathematics Department Program in Applied and Computational Mathematics Princeton University Department of Mathematics Center for Data Science Courant Institute of Mathematical Sciences New York University

We consider semidefinite programs (SDPs) with equality constraints. The variable to be optimized is a positive semidefinite matrix X of size n. Following the Burer–Monteiro approach, we optimize a factor Y of size n× p instead, such that X = YY. This ensures positive semidefiniteness at no cost and can reduce the dimension of the problem if p is small, but results in a non-convex optimization problem with a quadratic cost function and quadratic equality constraints in Y. In this paper, we show that if the set of constraints on Y regularly defines a smooth manifold, then, despite non-convexity, first- and second-order necessary optimality conditions are also sufficient, provided p is large enough. For smaller values of p, we show a similar result holds for almost all (linear) cost functions. Under those conditions, a global optimum Y maps to a global optimum X = YY of the SDP. We deduce old and new consequences for SDP relaxations of the generalized eigenvector problem, the trust-region subproblem and quadratic optimization over several spheres, as well as for the Max-Cut and Orthogonal-Cut SDPs which are common relaxations in stochastic block modeling and synchronization of rotations. Copyright © 2018, The Authors. All rights reserved.

关键词： Stochastic systems

Convergence acceleration of ensemble Kalman inversion in nonlinear settings

学校读者我要写书评

暂无评论

arXiv 2019年

作者： Chada, Neil K. Tong, Xin T. Applied Mathematics and Computational Science Program King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia Department of Mathematics National University of Singapore 119077 Singapore

Many data-science problems can be formulated as an inverse problem, where the parameters are estimated by minimizing a proper loss function. When complicated black-box models are involved, derivative-free optimization tools are often needed. The ensemble Kalman filter (EnKF) is a particle-based derivative-free Bayesian algorithm originally designed for data assimilation. Recently, it has been applied to inverse problems for computational efficiency. The resulting algorithm, known as ensemble Kalman inversion (EKI), involves running an ensemble of particles with EnKF update rules so they can converge to a minimizer. In this article, we investigate EKI convergence in general nonlinear settings. To improve convergence speed and stability, we consider applying EKI with non-constant step-sizes and covariance inflation. We prove that EKI can hit critical points with finite steps in non-convex settings. We further prove that EKI converges to the global minimizer polynomially fast if the loss function is strongly convex. We verify the analysis presented with numerical experiments on two inverse problems. Copyright © 2019, The Authors. All rights reserved.

关键词： Inverse problems

Executive Summary of Dagstuhl Seminar on Structured Decompositions and Efficient Algorithms (08492)

学校读者我要写书评

暂无评论

Executive Summary of Dagstuhl Seminar on Structured Decompos...

Structured Decompositions and Efficient Algorithms 2008

作者： Dahlke, Stephan Daubechies, Ingrid Elad, M. Kutyniok, Gitta Teschke, Gerd Philipps-Universität Marburg FB12 Mathematik und Informatik Hans-Meerwein Straße Lahnberge Marburg35032 Germany Princeton University Program in Applied and Computational Mathematics Fine Hall Washington Road PrincetonNJ08544-1000 United States Technion Computer Science Department Haifa Technion City32000 Israel Universität Osnabrück Institute of Mathematics Osnabrück49069 Germany Hochschule Neubrandenburg University of Applied Sciences Institute for Computational Mathematics in Science and Technology Brodaer Str. 2 Neubrandenburg17033 Germany

New emerging technologies such as high-precision sensors or new MRI machines drive us towards a challenging quest for new, more effective, and more daring mathematical models and algorithms. Therefore, in the last few years researchers have started to investigate different methods to efficiently represent or extract relevant information from complex, high dimensional and/or multimodal data. Efficiently in this context means a representation that is linked to the features or characteristics of interest, thereby typically providing a sparse expansion of such. Besides the construction of new and advanced ansatz systems the central question is how to design algorithms that are able to treat complex and high dimensional data and that efficiently perform a suitable approximation of the signal. One of the main challenges is to design new sparse approximation algorithms that would ideally combine, with an adjustable tradeoff, two properties: a provably good 'quality' of the resulting decomposition under mild assumptions on the analyzed sparse signal, and numerically efficient design. The topic is driven by applications as well as by theoretical questions. Therefore, the aim of this seminar was to bring together a good mixture of scientists with different backgrounds in order to discuss recent progress as well as new challenging perspectives. In particular, it was intended to strengthen the interaction of mathematicians and computer scientists. © 2009 Dagstuhl Seminar Proceedings. All Rights Reserved.

关键词： Clustering algorithms

The knowledge gradient for sequential decision making with stochastic binary feedbacks 33

学校读者我要写书评

暂无评论

The knowledge gradient for sequential decision making with s...

33rd International Conference on Machine Learning, ICML 2016

作者： Wang, Yingfei Wang, Chu Powell, Warren Department of Computer Science Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Operations Research and Financial Engineering Princeton University PrincetonNJ08544 United States

ISBN: (纸本)9781510829008

We consider the problem of sequentially making decisions that are rewarded by "successes" and "failures" which can be predicted through an unknown relationship that depends on a partially controllable vector of attributes for each instance. The learner takes an active role in selecting samples from the instance pool. The goal is to maximize the probability of success, either after the offline training phase or minimizing regret in online learning. Our problem is motivated by real-world applications where observations are time consuming and/or expensive. With the adaptation of an online Bayesian linear classifier, we develop a knowledge-gradient type policy to guide the experiment by maximizing the expected value of information of labeling each alternative, in order to reduce the number of expensive physical experiments. We provide a finite-time analysis of the estimated error and demonstrate the performance of the proposed algorithm on both synthetic problems and benchmark UCI datasets.

关键词： Benchmarking

Beyond trees: classification with sparse pairwise dependencies

学校读者我要写书评

暂无评论

The Journal of Machine Learning Research

The Journal of Machine Learning Research 2020年第1期21卷 7728-7760页

作者： Yaniv Tenzer Amit Moscovich Mary Frances Dorn Boaz Nadler Clifford Spiegelman Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel Program in Applied and Computational Mathematics Princeton University Princeton NJ Los Alamos National Laboratory Los Alamos NM Department of Statistics Texas A&M University College Station TX

Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attaining low classification errors. In this setting, the optimal classifier is linear in the log-transformed univariate and bivariate densities that correspond to the tree edges. In practice, observed data may not be well approximated by trees. Yet, motivated by the importance of pairwise dependencies for accurate classification, here we propose to approximate the optimal decision boundary by a sparse linear combination of the univariate and bivariate log-transformed densities. Our proposed approach is semi-parametric in nature: we non-parametrically estimate the univariate and bivariate densities, remove pairs of variables that are nearly independent using the Hilbert-Schmidt independence criterion, and finally construct a linear SVM using the retained log-transformed densities. We demonstrate on synthetic and real data sets, that our classifier, named SLB (sparse log-bivariate density), is competitive with other popular classification methods.

关键词： binary classification graphical model Bayesian network sparsity semi-parametric

Machine learning based non-Newtonian fluid model with molecular fidelity

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Lei, Huan Wu, Lei Weinan, E. Department of Computational Mathematics Science & Engineering Department of Statistics & Probability Michigan State University MI48824 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We introduce a machine-learning-based framework for constructing continuum non-Newtonian fluid dynamics model directly from a micro-scale description. Polymer solution is used as an example to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the micro-scale polymer configurations and their macro-scale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the micro-scale model and the relevant terms can be parametrized using machine learning. The final model, named the deep non-Newtonian model (DeePN2), takes the form of conventional non-Newtonian fluid dynamics models, with a new form of the objective tensor derivative. Numerical results demonstrate the accuracy of DeePN2. Copyright © 2020, The Authors. All rights reserved.

关键词： Viscous flow

Hyperuniformity of quasicrystals

学校读者我要写书评

暂无评论

Physical Review B 2017年第5期95卷 054119-054119页

作者： Erdal C. Oğuz Joshua E. S. Socolar Paul J. Steinhardt Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA

Hyperuniform systems, which include crystals, quasicrystals, and special disordered systems, have attracted considerable recent attention, but rigorous analyses of the hyperuniformity of quasicrystals have been lacking because the support of the spectral intensity is dense and discontinuous. We employ the integrated spectral intensity Z(k) to quantitatively characterize the hyperuniformity of quasicrystalline point sets generated by projection methods. The scaling of Z(k) as k tends to zero is computed for one-dimensional quasicrystals and shown to be consistent with independent calculations of the variance, σ2(R), in the number of points contained in an interval of length 2R. We find that one-dimensional quasicrystals produced by projection from a two-dimensional lattice onto a line of slope 1/τ fall into distinct classes determined by the width of the projection window. For a countable dense set of widths, Z(k)∼k4; for all others, Z(k)∼k2. This distinction suggests that measures of hyperuniformity define new classes of quasicrystals in higher dimensions as well.

关键词： Microstructure Structural properties

Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Weinan, E. Han, Jiequn Jentzen, Arnulf Department of Mathematics Princeton University United States Program in Applied and Computational Mathematics Princeton University United States Faculty of Mathematics and Computer Science University of Münster Germany

In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning. They are potentially free of the curse of dimensionality for many different applications and have been proven to be so in the case of some nonlinear Monte Carlo methods for nonlinear parabolic PDEs. In this paper, we review these numerical and theoretical advances. In addition to algorithms based on stochastic reformulations of the original problem, such as the multilevel Picard iteration and the Deep BSDE method, we also discuss algorithms based on the more traditional Ritz, Galerkin, and least square formulations. We hope to demonstrate to the reader that studying PDEs as well as control and variational problems in very high dimensions might very well be among the most promising new directions in mathematics and scientific computing in the near *** Codes 65C05, 65K10, 65M75, 90C06 Copyright © 2020, The Authors. All rights reserved.

关键词： Monte Carlo methods