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computational Methods for Single-Particle Electron Cryomicroscopy

Biomedical Data Science 1000年第1期3卷 163-190页

作者： Amit Singer Fred J. Sigworth 1Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA email: amits@math.princeton.edu 2Departments of Cellular and Molecular Physiology Biomedical Engineering and Molecular Biophysics and Biochemistry Yale University New Haven Connecticut 06520 USA email: fred.sigworth@yale.edu

Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional (3D) structure of proteins and other biologically significant complexes at near-atomic resolution. It is an imaging method that does not require crystallization and can capture molecules in their native states. In single-particle cryo-EM, the 3D molecular structure needs to be determined from many noisy 2D tomographic projections of individual molecules, whose orientations and positions are unknown. The high level of noise and the unknown pose parameters are two key elements that make reconstruction a challenging computational problem. Even more challenging is the inference of structural variability and flexible motions when the individual molecules being imaged are in different conformational states. This review discusses computational methods for structure determination by single-particle cryo-EM and their guiding principles from statistical inference, machine learning, and signal processing, which also play a significant role in many other data science applications.

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Nucleation of Ordered Phases in Block Copolymers

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Physical Review Letters 2010年第14期104卷 148301-148301页

作者： Xiuyuan Cheng Ling Lin Weinan E Pingwen Zhang An-Chang Shi School of Mathematical Sciences and The Key Laboratory of Mathematics and Applied Mathematics Peking University Beijing 100871 China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544-1000 USA Department of Physics and Astronomy McMaster University Hamilton Ontario L8S 4M1 Canada

Nucleation of various ordered phases in block copolymers is studied by examining the free-energy landscape within the self-consistent field theory. The minimum energy path (MEP) connecting two ordered phases is computed using a recently developed string method. The shape, size, and free-energy barrier of critical nuclei are obtained from the MEP, providing information about the emergence of a stable ordered phase from a metastable phase. In particular, structural evolution of embryonic gyroid nucleus is predicted to follow two possible MEPs, revealing an interesting transition pathway with an intermediate perforated layered structure.

关键词： Nucleation

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Structure and dynamics of highly charged heavy ions studied with the electron beam ion trap in Tokyo

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Hyperfine Interactions 2011年第1期199卷 123-130页

作者： Nakamura, Nobuyuki Hu, Zhimin Watanabe, Hirofumi Li, Yueming Kato, Daiji Currell, Fred J. Tong, Xiao-Min Watanabe, Tsutomu Ohtani, Shunsuke Institute for Laser Science The University of Electro-Communications 1-5-1 Chofugaoka Chofu Tokyo 182-8585 Japan Chubu University 1200 Matsumoto-cho Kasugai-shi Aichi 487-8501 Japan Institute of Applied Physics and Computational Mathematics P.O.Box 8009 Beijing 100088 China National Institute for Fusion Science 322-6 Oroshi-cho Toki Gifu 509-5292 Japan Centre for Plasma Physics School of Mathematics and Physics Queen's University Belfast Belfast BT7 1NN United Kingdom Doctoral Program in Materials Science Graduate School of Pure and Applied Sciences University of Tsukuba Tsukuba Ibaraki 305-8573 Japan

In this paper, we present the structure and the dynamics of highly charged heavy ions studied through dielectronic recombination (DR) observations performed with the Tokyo electron beam ion trap. By measuring the energy dependence of the ion abundance ratio in the trap at equilibrium, we have observed DR processes for open shell systems very clearly. Remarkable relativistic effects due to the generalized Breit interaction have been clearly shown in DR for highly charged heavy ions. We also present the first result for the coincidence measurement of two photons emitted from a single DR event. © 2011 Springer Science+Business Media B.V.

关键词： Heavy ions

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Multiple time scale numerical methods for the inverted pendulum problem

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Lecture Notes in computational Science and Engineering 2005年 44卷 241-261页

作者： Sharp, Richard Tsai, Yen-Hsi Engquist, Björn Program in Applied and Computational Mathematics Princeton University NJ 08544 United States Department of Mathematics University of Texas at Austin 1 University Station C1200 Austin TX 78712 United States

ISBN: (纸本)9783540253358

In this article, we study a class of numerical ODE schemes that use a time filtering strategy and operate in two time scales. The algorithms follow the framework of the heterogeneous multiscale methods (HMM) [1]. We apply the methods to compute the averaged path of the inverted pendulum under a highly oscillatory vertical forcing on the pivot. The averaged equation for related problems has been studied analytically in [9]. We prove and show numerically that the proposed methods approximate the averaged equation and thus compute the average path of the inverted pendulum.

关键词： Inverted pendulum

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Optimal estimation of Eddy viscosity and friction coefficients for a Quasi‐three‐dimensional numerical tidal model

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Atmosphere 1995年第3期33卷 581-611页

作者： R.W. Lardner[a] & Y. Song[a][b]* [a] Applied and Computational Mathematics Program Simon Fraser University Burnaby B.C. V5A 1S6 Canada [b] Institute of Marine and Coastal Sciences Rutgers University New Brunswick NJ

It is shown that the parameters in a quasi‐three‐dimensional numerical tidal model can be estimated accurately by assimilation of data from current meters and tide gauges. The tidal model considered is a semi‐linearized one in which advective nonlinearities are neglected but nonlinear bottom friction is included. The parameters estimated are the eddy viscosity, bottom friction coefficient, water depth and wind drag coefficient, the first three of which are allowed to be position‐dependent. The adjoint method is used to construct the gradient of a cost function defined as a certain norm of the difference between computed and observed current and surface elevations. On the basis of a number of tests, it is shown that very effective estimation of the nodal values of the parameters can be achieved using the current data either alone or in combination with elevation data. When random errors are introduced into the data, the estimated parameters are quite sensitive to the magnitude of the errors, and in particular the eddy viscosity is unstably sensitive. The sensitivity of the viscosity can be stabilized by incorporating an appropriate penalty term in the cost function or alternatively by reducing the number of estimated viscosity values via a finite element approximation. Once stabilized, the sensitivity of the estimates to data errors is significantly reduced by assimilating a longer data record.RésuméOn montre que les paramètres d'un modèle numérique quasi trois dimensions de la marée peuvent être estimés avec exactitude en assimilant les données de courantomètres et de marégraphes. Le modèle de la marée examiné est semi linéarisé et les non linéarités advectives y sont négligées mais la friction de fond non linéaire est incluse. On a estimé les coeffecients de viscosité, de friction de fond, de la profondeur de l'eau et de traînée du vent, allouant les trois premiers d'être translatables. La méthode adjointe est utilisée pour construire le gradient d'une fonction de

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Density-based and transport-based core-periphery structures in networks

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Physical Review E 2014年第3期89卷 032810-032810页

作者： Sang Hoon Lee Mihai Cucuringu Mason A. Porter Oxford Centre for Industrial and Applied Mathematics Mathematical Institute University of Oxford Oxford OX2 6GG United Kingdom Program in Applied and Computational Mathematics (PACM) Princeton University Fine Hall Washington Road Princeton New Jersey 08544-1000 USA Department of Mathematics University of California Los Angeles Los Angeles California 90095 USA CABDyN Complexity Centre University of Oxford Oxford OX1 1HP United Kingdom

Networks often possess mesoscale structures, and studying them can yield insights into both structure and function. It is most common to study community structure, but numerous other types of mesoscale structures also exist. In this paper, we examine core-periphery structures based on both density and transport. In such structures, core network components are well-connected both among themselves and to peripheral components, which are not well-connected to anything. We examine core-periphery structures in a wide range of examples of transportation, social, and financial networks—including road networks in large urban areas, a rabbit warren, a dolphin social network, a European interbank network, and a migration network between counties in the United States. We illustrate that a recently developed transport-based notion of node coreness is very useful for characterizing transportation networks. We also generalize this notion to examine core versus peripheral edges, and we show that the resulting diagnostic is also useful for transportation networks. To examine the properties of transportation networks further, we develop a family of generative models of roadlike networks. We illustrate the effect of the dimensionality of the embedding space on transportation networks, and we demonstrate that the correlations between different measures of coreness can be very different for different types of networks.

关键词： MESOSCALE convective complexes -- Computer simulation COMMUNITY organization TRANSPORTATION SOCIAL networks DENSITY MARKOV processes DEPENDENCY (Imperialism)

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Particle swarm optimization with local search for height-map surface reconstruction from point clouds in reverse engineering

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Neural Computing and Applications 2024年 1-20页

作者： Gálvez, Akemi Fister, Iztok Deb, Suash Fister, Iztok Iglesias, Andrés Dept. of Applied Mathematics and Computational Sciences E.T.S.I. Caminos Canales y Puertos University of Cantabria Avda. de los Castros s/n Santander39005 Spain Faculty of Pharmaceutical Sciences Toho University 2-2-1 Miyama Funabashi274-8510 Japan Faculty of Electrical Engineering and Computer Science University of Maribor Koroska cesta 34 Maribor2000 Slovenia IT & Educational Consultant Ranchi India Distinguished Professorial Associate Decision Sciences and Modeling Program Victoria University Melbourne Australia

Surface reconstruction is a classical process in industrial engineering and manufacturing, particularly in reverse engineering, where the goal is to obtain a digital model from a physical object. For that purpose, the real object is typically scanned or digitized and the resulting point cloud is then fitted to mathematical surfaces through numerical optimization. The choice of the approximating functions is crucial for the accuracy of the process. Real-world objects such as manufactured workpieces often require complex nonlinear approximating functions, which are not well suited for standard numerical methods. In a previous paper presented at the ISMSI 2023 conference, we addressed this issue by using manually selected approximation functions via optimization through the cuckoo search algorithm with Lévy flights. Building upon that work, this paper presents an enhanced and extended method for surface reconstruction by using height-map surfaces obtained through a combination of exponential, polynomial and logarithmic functions. A feasible approach for this goal is to consider continuous bivariate distribution functions, which ensures consistent models along with good mathematical properties for the output shapes, such as smoothness and integrability. However, this approach leads to a difficult multivariate, constrained, multimodal continuous nonlinear optimization problem. To tackle this issue, we apply particle swarm optimization, a popular swarm intelligence technique for continuous optimization. The method is hybridized with a local search procedure for further improvement of the solutions and applied to a benchmark of 15 illustrative examples of point clouds fitted to different surface models. The performance of the method is analyzed through several computational experiments. The numerical and graphical results show that the method is able to recover the shape of the point clouds accurately and automatically. Furthermore, our approach outperforms other alternati

关键词： Particle swarm optimization (PSO)

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Parallel block-preconditioned monolithic solvers for fluid-structure-interaction problems

arXiv

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arXiv 2018年

作者： Jodlbauer, D. Langer, U. Wick, T. Doctoral Program on Computational Mathematics Johannes Kepler University Altenbergerstr. 69 LinzA-4040 Austria Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergerstr. 69 LinzA-4040 Austria Institut für Angewandte Mathematik Leibniz Universität Hannover Welfengarten 1 Hannover30167 Germany

In this work, we consider the solution of fluid-structure interaction problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary Lagrangian-Eulerian framework and a nonlinear harmonic mesh motion model. Monolithic approaches require the solution of large, ill-conditioned linear systems of algebraic equations at every Newton step. Direct solvers tend to use too much memory even for a relatively small number of degrees of freedom, and, in addition, exhibit superlinear grow in arithmetic complexity. Thus, iterative solvers are the only viable option. To ensure convergence of iterative methods within a reasonable amount of iterations, good and, at the same time, cheap preconditioners have to be developed. We study physics-based block preconditioners, which are derived from the block LDU-factorization of the FSI Jacobian, and their performance on distributed memory parallel computers in terms of two- and three-dimensional test cases permitting large deformations.65N30, 65M60, 49M15, 35Q74 Copyright © 2018, The Authors. All rights reserved.

关键词： Iterative methods

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Multigoal-oriented error estimates for non-linear problems

arXiv

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arXiv 2018年

作者： Endtmayer, B. Langer, U. Wick, T. Doctoral Program on Computational Mathematics Johannes Kepler University Altenbergerstr. 69 LinzA-4040 Austria Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergerstr. 69 LinzA-4040 Austria Institut für Angewandte Mathematik Leibniz Universität Hannover Welfengarten 1 Hannover30167 Germany

In this work, we further develop multigoal-oriented a posteriori error estimation with two objectives in mind. First, we formulate goal-oriented mesh adaptivity for multiple functionals of interest for nonlinear problems in which both the Partial Differential Equation (PDE) and the goal functionals may be nonlinear. Our method is based on a posteriori error estimates in which the adjoint problem is used and a partition-of-unity is employed for the error localization that allows us to formulate the error estimator in the weak form. We provide a careful derivation of the primal and adjoint parts of the error estimator. The second objective is concerned with balancing the nonlinear iteration error with the discretization error yielding adaptive stopping rules for Newton's method. Our techniques are substantiated with several numerical examples including scalar PDEs and PDE systems, geometric singularities, and both nonlinear PDEs and nonlinear goal functionals. In these tests, up to six goal functionals are simultaneously controlled. Copyright © 2018, The Authors. All rights reserved.

关键词： Newton-Raphson method

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Precise determination of pair interactions from pair statistics of many-body systems in and out of equilibrium

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Physical Review E 2022年第4期106卷 044122-044122页

作者： Salvatore Torquato Haina Wang Department of Chemistry Department of Physics Princeton Institute of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study 1 Einstein Drive Princeton New Jersey 08540 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA

The determination of the pair potential v(r) that accurately yields an equilibrium state at positive temperature T with a prescribed pair correlation function g2(r) or corresponding structure factor S(k) in d-dimensional Euclidean space Rd is an outstanding inverse statistical mechanics problem with far-reaching implications. Recently, Zhang and Torquato [Phys. Rev. E 101, 032124 (2020)] conjectured that any realizable g2(r) or S(k) corresponding to a translationally invariant nonequilibrium system can be attained by a classical equilibrium ensemble involving only (up to) effective pair interactions. Testing this conjecture for nonequilibrium systems as well as for nontrivial equilibrium states requires improved inverse methodologies. We have devised an optimization algorithm to precisely determine effective pair potentials that correspond to pair statistics of general translationally invariant disordered many-body equilibrium or nonequilibrium systems at positive temperatures. This methodology utilizes a parameterized family of pointwise basis functions for the potential function whose initial form is informed by small-, intermediate- and large-distance behaviors dictated by statistical-mechanical theory. Subsequently, a nonlinear optimization technique is utilized to minimize an objective function that incorporates both the target pair correlation function g2(r) and structure factor S(k) so that the small intermediate- and large-distance correlations are very accurately captured. To illustrate the versatility and power of our methodology, we accurately determine the effective pair interactions of the following four diverse target systems: (1) Lennard-Jones system in the vicinity of its critical point, (2) liquid under the Dzugutov potential, (3) nonequilibrium random sequential addition packing, and (4) a nonequilibrium hyperuniform “cloaked” uniformly randomized lattice. We found that the optimized pair potentials generate corresponding pair statistics that accur

关键词： Nonequilibrium statistical mechanics Optimization problems Structural properties Complex materials

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