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SUBSPACE METHOD OF MOMENTS FOR AB INITIO 3-D SINGLE-PARTICLE CRYO-EM RECONSTRUCTION

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arXiv 2024年

作者： Hoskins, Jeremy Khoo, Yuehaw Mickelin, Oscar Singer, Amit Wang, Yuguan Departments of Statistics and CCAM University of Chicago Chicago IL 60637 USA Departments of Statistics and CCAM University of Chicago Chicago IL 60637 USA Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA Program in Applied and Computational Mathematics and Department of Mathematics Princeton University Princeton NJ 08544 USA Departments of Statistics University of Chicago Chicago IL 60637 USA

Cryo-electron microscopy (Cryo-EM) is a widely-used technique for recovering the 3-D structure of biological molecules from a large number of experimentally generated noisy 2-D tomographic projection images of the 3-D structure, taken from unknown viewing angles. Through computationally intensive algorithms, these observed images are processed to reconstruct the 3-D structures. Many popular computational methods rely on estimating the unknown angles as part of the reconstruction process, which becomes particularly challenging at low signal-to-noise ratio. The method of moments (MoM) offers an alternative approach that circumvents the estimation of viewing angles of individual projection images by instead estimating the underlying distribution of the viewing angles, and is robust to noise given sufficiently many images. However, the method of moments typically entails computing high-order moments of the projection images, incurring significant storage and computational costs. To mitigate this, we propose a new approach called the subspace method of moments (subspace MoM), which compresses the first three moments using data-driven low-rank tensor techniques as well as expansion into a suitable function basis. The compressed moments can be efficiently computed from the set of projection images using numerical quadrature and can be employed to jointly recover the 3-D structure and the distribution of viewing angles. We illustrate the practical applicability of the subspace MoM in numerical experiments using up to the third-order moment, which significantly improves the resolution of MoM reconstructions compared to previous approaches. Copyright © 2024, The Authors. All rights reserved.

关键词： Image reconstruction

Emergent spaces for coupled oscillators

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arXiv 2020年

作者： Thiem, Thomas N. Kooshkbaghi, Mahdi Bertalan, Tom Laing, Carlo R. Kevrekidis, Ioannis G. Department of Chemical and Biological Engineering Princeton University United States Program in Applied and Computational Mathematics Princeton University United States Department of Mechanical Engineering Massachusetts Institute of Technology United States School of Natural and Computational Sciences Massey University New Zealand Department of Applied Mathematics and Statistics Johns Hopkins University United States

Systems of coupled dynamical units (e.g. oscillators or neurons) are known to exhibit complex, emergent behaviors that may be simplified through coarse-graining: a process in which one discovers coarse variables and derives equations for their evolution. Such coarse-graining procedures often require extensive experience and/or a deep understanding of the system dynamics. In this paper we present a systematic, data-driven approach to discovering "bespoke" coarse variables based on manifold learning algorithms. We illustrate this methodology with the classic Kuramoto phase oscillator model, and demonstrate how our manifold learning technique can successfully identify a coarse variable that is one-to-one with the established Kuramoto order parameter. We then introduce an extension of our coarse-graining methodology which enables us to learn evolution equations for the discovered coarse variables via an artificial neural network architecture templated on numerical time integrators (initial value solvers). This approach allows us to learn accurate approximations of time derivatives of state variables from sparse flow data, and hence discover useful approximate differential equation descriptions of their dynamic behavior. We demonstrate this capability by learning ODEs that agree with the known analytical expression for the Kuramoto order parameter dynamics at the continuum limit. We then show how this approach can also be used to learn the dynamics of coarse variables discovered through our manifold learning methodology. In both of these examples, we compare the results of our neural network based method to typical finite differences complemented with geometric harmonics. Finally, we present a series of computational examples illustrating how a variation of our manifold learning methodology can be used to discover sets of "effective" parameters, reduced parameter combinations, for multi-parameter models with complex coupling. We conclude with a discussion of possible ext

关键词： Neural networks

Distributed nonlinear control of diffusion-reaction processes

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Distributed nonlinear control of diffusion-reaction processe...

American Control Conference (ACC)

作者： S. Dubljevic P.D. Christofides I.G. Kevrekidis Department of Chemical Eagineering University of California Los Angeles CA USA Department of Chemical Engineering and the Program in Applied and Computational Mathematics Princeton University Princeton NJ USA

Deep density: Circumventing the kohn-sham equations via symmetry preserving neural networks

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arXiv 2019年

作者： Zepeda-Núñez, Leonardo Chen, Yixiao Zhang, Jiefu Zhang, Linfeng Jia, Weile Lin, Lin Department of Mathematics University of Wisconsin-Madison MadisonWI53706 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics University of California Berkeley BerkeleyCA94720 United States Department of Mathematics University of California Berkeley Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

The recently developed Deep Potential [Phys. Rev. Lett. 120, 143001, 2018] is a powerful method to represent general inter-atomic potentials using deep neural networks. The success of Deep Potential rests on the proper treatment of locality and symmetry properties of each component of the network. In this paper, we leverage its network structure to effectively represent the mapping from the atomic configuration to the electron density in Kohn-Sham density function theory (KS-DFT). By directly targeting at the self-consistent electron density, we demonstrate that the adapted network architecture, called the Deep Density, can effectively represent the electron density as the linear combination of contributions from many local clusters. The network is constructed to satisfy the translation, rotation, and permutation symmetries, and is designed to be transferable to different system sizes. We demonstrate that using a relatively small number of training snapshots, Deep Density achieves excellent performance for one-dimensional insulating and metallic systems, as well as systems with mixed insulating and metallic characters. We also demonstrate its performance for real three-dimensional systems, including small organic molecules, as well as extended systems such as water (up to 512 molecules) and aluminum (up to 256 atoms). Copyright © 2019, The Authors. All rights reserved.

关键词： Network architecture

Multilayer thin film growth on crystalline and quasicrystalline surfaces: A phase-field crystal study

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Physical Review B 2012年第24期85卷 245428-245428页

作者： Srevatsan Muralidharan Raika Khodadad Ethan Sullivan Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA and School of Mathematics Institute for Advanced Study Princeton New Jersey 08540 USA

In this paper, we explore the effects of misfit strain fields on both heterogeneous nucleation behavior and anisotropic growth of islands at submonolayer coverages and compositional patterning at complete monolayer coverage via simulations of a phase-field crystal model. In particular, deposition on top of a herringbone structure and quasicrystalline (QC) substrate are considered, the former representing a system with spatially periodic misfit strain fields arising from the presence of surface dislocations, and the latter representing a system which inherently possesses a wide range of local, aperiodic misfit patterns. In the case of single-component systems, we demonstrate that misfit strain fields lead to heterogeneous nucleation behavior and anisotropic island growth. In the case of QC substrate, a wide range of morphologies, such as coexistence of locally hexagonally ordered atomic clusters within a larger scale arrangement with overall QC symmetry and so-called “starfish” aggregates, is observed in a pure system at submonolayer coverages when the adlayer-substrate interaction strength and lattice mismatch are tuned. In the case of bulk-immiscible binary systems at complete monolayer coverage, strain-stabilized compositional domains emerge at low line tension values for both substrates. Interestingly, the compositional domains on the QC substrate inherit their symmetries at sufficiently low line tension values, while at larger line tension values, the domain structure begins to resemble the classical spinodal microstructure. Such domain structures should be readily observable in colloidal systems in which attractive interparticle and particle-substrate interactions can be tuned.

关键词： THIN films CRYSTALS NUCLEATION DISLOCATIONS in crystals MICROSTRUCTURE

Optimized Interactions for Targeted Self-Assembly: Application to a Honeycomb Lattice

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Physical Review Letters 2005年第22期95卷 228301-228301页

作者： Mikael C. Rechtsman Frank H. Stillinger Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics and PRISM Princeton University Princeton New Jersey 08544 USA

We devise an inverse statistical-mechanical methodology to find optimized interaction potentials that lead spontaneously to a target many-particle configuration. Target structures can possess varying degrees of disorder, thus extending the traditional idea of self-assembly to incorporate both amorphous and crystalline structures as well as quasicrystals. For illustration purposes, our computational technique is applied to yield an optimized isotropic (nondirectional) pair potential that spontaneously yields the three-coordinated honeycomb lattice as the ground state structure in two dimensions. This target choice is motivated by its three-dimensional analog, the diamond lattice, which is known to possess desirable photonic band gap properties.

关键词： .honeycomb inverse PRL week ending pair potential spontaneously diamond lattice

Bayesian Spectral Graph Denoising with Smoothness Prior

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Bayesian Spectral Graph Denoising with Smoothness Prior

Annual Conference on Information Sciences and Systems (CISS)

作者： Sam Leone Xingzhi Sun Michael Perlmutter Smita Krishnaswamy Program for Applied Mathematics Yale University Department of Computer Science Yale University Department of Mathematics Boise State University Department of Genetics Yale School of Medicine Wu Tsai Institute Yale University FAIR Meta AI Computational Biology and Bioinformatics Program Yale University

Here we consider the problem of denoising features associated to complex data, modeled as signals on a graph, via a smoothness prior. This is motivated in part by settings such as single-cell RNA where the data is very high-dimensional, but its structure can be captured via an affinity graph. This allows us to utilize ideas from graph signal processing. In particular, we present algorithms for the cases where the signal is perturbed by Gaussian noise, dropout, and uniformly distributed noise. The signals are assumed to follow a prior distribution defined in the frequency domain which favors signals which are smooth across the edges of the graph. By pairing this prior distribution with our three models of noise generation, we propose Maximum A Posteriori (M.A.P.) estimates of the true signal in the presence of noisy data and provide algorithms for computing the M.A.P. Finally, we demonstrate the algorithms’ ability to effectively restore signals from white noise on image data and from severe dropout in single-cell RNA sequence data.

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Structural Effects and Aggregation in a Social-Network Model of Natural Resource Consumption

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IFAC-PapersOnLine 2017年第1期50卷 7675-7680页

作者： Manzoor T. Rovenskaya E. Muhammad A. Department of Electrical Engineering Lahore University of Management Sciences (LUMS) Lahore Pakistan Center for Water Informatics & Technology (WIT) Lahore University of Management Sciences (LUMS) Pakistan Advanced Systems Analysis Program International Institute for Applied Systems Analysis (IIASA) Laxenburg Austria Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State University Moscow Russian Federation

In this paper we consider a networked system of natural-resource consumption, where the agents are governed by a recently reported model of consumer psychology Dynamics of the consumption for each agent are influenced by the state of the resource and consumption of her neighbors. The process is parameterized by the psychological characteristics of each agent. This study extends the original model to incorporate the underlying network topology and explores the effects of aggregation via densely-connected communities present in the network. The exercise yields new interpretations of the predictions made by the original model in context of the influence network. We present aggregation mechanisms first for certain canonical structures of the consuming population and later on for a class of non-canonically structured populations. In the end we present an approximate aggregation scheme for populations where only some inaccurate information of the consumer characteristics is available. © 2017

关键词： Control in economics identification of environmental systems Modeling Multi-agent systems Natural resources management Social Networks

Image recovery from rotational and translational invariants

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arXiv 2019年

作者： Marshall, Nicholas F. Lan, Ti-Yen Bendory, Tamir Singer, Amit Department of Mathematics Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States School of Electrical Engineering Tel Aviv University Tel Aviv Israel

We introduce a framework for recovering an image from its rotationally and translationally invariant features based on autocorrelation analysis. This work is an instance of the multi-target detection statistical model, which is mainly used to study the mathematical and computational properties of single-particle reconstruction using cryo-electron microscopy (cryo-EM) at low signal-to-noise ratios. We demonstrate with synthetic numerical experiments that an image can be reconstructed from rotationally and translationally invariant features and show that the reconstruction is robust to noise. These results constitute an important step towards the goal of structure determination of small biomolecules using cryo-EM. Copyright © 2019, The Authors. All rights reserved.

关键词： Electron microscopes