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Critical dynamics in multicomponent lipid membranes

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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

Radiative transport for two-photon light

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Physical Review A 2014年第3期90卷 033815-033815页

作者： Vadim A. Markel John C. Schotland Department of Radiology Department of Bioengineering and Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia Pennsylvania 19104 USA Department of Mathematics and Department of Physics University of Michigan Ann Arbor Michigan 48109 USA

We consider the propagation of two-photon light in a random medium. We show that the Wigner transform of the two-photon amplitude obeys an equation that is analogous to the radiative transport equation for classical l... 详细信息

关键词： LIGHT propagation PHOTONS WIGNER distribution RANDOM measures CONVECTION-diffusion equations RADIATION

Deterministic guarantees for Burer–Monteiro factorizations of smooth semidefinite programs

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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

Parsimonious reconstruction of network evolution

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Parsimonious reconstruction of network evolution

Lecture Notes in Computer science

作者： Patro, Rob Sefer, Emre Malin, Justin Marçais, Guillaume Navlakha, Saket Kingsford, Carl Center for Bioinformatics and Computational Biology University of Maryland College Park MD 20742 United States Department of Computer Science University of Maryland College Park MD 20742 United States Computational Biology Bioinformatics and Genomics Concentration Biological Sciences Graduate Program University of Maryland College Park MD 20742 United States Program in Applied Mathematics Statistics and Scientific Computation University of Maryland College Park MD 20742 United States School of Computer Science Carnegie Mellon University Pittsburgh PA 15213 United States

ISBN: (纸本)9783642230370

We consider the problem of reconstructing a maximally parsimonious history of network evolution under models that support gene duplication and loss and independent interaction gain and loss. We introduce a combinatorial framework for encoding network histories, and we give a fast procedure that, given a set of duplication histories, in practice finds network histories with close to the minimum number of interaction gain or loss events. In contrast to previous studies, our method does not require knowing the relative ordering of unrelated duplication events. Results on simulated histories suggest that common ancestral networks can be accurately reconstructed using this parsimony approach. © 2011 Springer-Verlag.

关键词： Genes

Convergence acceleration of ensemble Kalman inversion in nonlinear settings

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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

Multiple Imputation with Neural Network Gaussian Process for High-dimensional Incomplete Data

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arXiv 2022年

作者： Dai, Zongyu Bu, Zhiqi Long, Qi Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States Division of Biostatistics University of Pennsylvania United States

Missing data are ubiquitous in real world applications and, if not adequately handled, may lead to the loss of information and biased findings in downstream analysis. Particularly, high-dimensional incomplete data with a moderate sample size, such as analysis of multi-omics data, present daunting challenges. Imputation is arguably the most popular method for handling missing data, though existing imputation methods have a number of limitations. Single imputation methods such as matrix completion methods do not adequately account for imputation uncertainty and hence would yield improper statistical inference. In contrast, multiple imputation (MI) methods allow for proper inference but existing methods do not perform well in high-dimensional settings. Our work aims to address these significant methodological gaps, leveraging recent advances in neural network Gaussian process (NNGP) from a Bayesian viewpoint. We propose two NNGP-based MI methods, namely MI-NNGP, that can apply multiple imputations for missing values from a joint (posterior predictive) distribution. The MI-NNGP methods are shown to significantly outperform existing state-of-the-art methods on synthetic and real datasets, in terms of imputation error, statistical inference, robustness to missing rates, and computation costs, under three missing data mechanisms, MCAR, MAR, and MNAR. Code is available in the GitHub repository https://***/bestadcarry/MI-NNGP. Copyright © 2022, The Authors. All rights reserved.

关键词： Gaussian noise (electronic)

An improved model of damage depth of shock-melted metal in microspall under triangular wave loading

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Chinese Physics B 2021年第9期30卷 412-418页

作者： Wen-Bin Liu An-Min He Kun Wang Jian-Ting Xin Jian-Li Shao Nan-Sheng Liu Pei Wang Department of Modern Mechanics University of Science and Technology of ChinaHefei 230027China Institute of Applied Physics and Computational Mathematics Beijing 100094China Graduate School of China Academy of Engineering Physics Beijing 100088China College of Materials Science and Engineering Hunan UniversityChangsha 410082China Science and Technology on Plasma Physics Laboratory Research Center of Laser FusionChina Academy of Engineering PhysicsMianyang 621900China State Key Laboratory of Explosion Science and Technology Beijing Institute of TechnologyBeijing 100081China Center for Applied Physics and Technology Peking UniversityBeijing 100871China

Damage depth is an important dynamic parameter for describing the degree of material damage and is also a key fundamental issue in the field of impact compression *** present work is dedicated to the damage depth of shock-melted metal in microspall under triangular wave loading,and an improved model of damage depth considering the material's compressibility and relative movement is *** damage depth obtained from the proposed model is in good agreement with the laser-driven shock loading *** with the previous model,the proposed model can predict the damage depth of shock-melted metal in microspall more ***,two-groups of the smoothed particle hydrodynamics(SPH)simulations are carried out to investigate the effects of peak stress and decay length of the incident triangular wave on the damage depth,*** the decay length increases,the damage depth increases *** the peak stress increases,the damage depth increases nonlinearly,and the increase in damage depth gradually slows *** results of the SPH simulations adequately reproduce the results of the proposed model in terms of the damage ***,it is found that the threshold stress criterion can reflect the macroscopic characteristics of microspall of melted metal.

关键词： damage depth theoretical modeling microspall triangular wave

Distributed linear regression by averaging

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arXiv 2018年

作者： Dobriban, Edgar Sheng, Yue Wharton Statistics Department University of Pennsylvania United States Graduate Group in Applied Mathematics and Computational Science Department of Mathematics University of Pennsylvania United States

Distributed statistical learning problems arise commonly when dealing with large datasets. In this setup, datasets are partitioned over machines, which compute locally, and communicate short messages. Communication is often the bottleneck. In this paper, we study one-step and iterative weighted parameter averaging in statistical linear models under data parallelism. We do linear regression on each machine, send the results to a central server, and take a weighted average of the parameters. Optionally, we iterate, sending back the weighted average and doing local ridge regressions centered at it. How does this work compared to doing linear regression on the full data? Here we study the performance loss in estimation, test error, and confidence interval length in high dimensions, where the number of parameters is comparable to the training data size. We find the performance loss in one-step weighted averaging, and also give results for iterative averaging. We also find that different problems are affected differently by the distributed framework. Estimation error and confidence interval length increase a lot, while prediction error increases much less. We rely on recent results from random matrix theory, where we develop a new calculus of deterministic equivalents as a tool of broader interest. Copyright © 2018, The Authors. All rights reserved.

关键词： Linear regression

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

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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