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Physical Review Letters 2012年第19期109卷 198303-198303页

作者： Florian Libisch Chen Huang Peilin Liao Michele Pavone Emily A. Carter Departments of Mechanical and Aerospace Engineering and Chemistry Program in Applied and Computational Mathematics and Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544 USA Theoretical Division Los Alamos National Laboratory New Mexico 87544 USA

Dissociative adsorption of molecular oxygen on the Al(111) surface exhibits mechanistic complexity that remains surprisingly poorly understood in terms of the underlying physics. Experiments clearly indicate substantial energy barriers and a mysteriously large number of adsorbed single oxygen atoms instead of pairs. Conventional first principles quantum mechanics (density functional theory) predicts no energy barrier at all; instead, spin selection rules have been invoked to explain the barrier. In this Letter, we show that correct barriers arise naturally when embedded correlated electron wave functions are used to capture the physics of the interaction of O2 with the metal surface. The barrier originates from an abrupt charge transfer (from metal to oxygen), which is properly treated within correlated wave function theory but not within conventional density functional theory. Our potential energy surfaces also identify oxygen atom abstraction as the dominant reaction pathway at low incident energies, consistent with measurements, and show that charge transfer occurs in a stepwise fashion.

关键词： CHEMICAL reactions CHARGE transfer ADSORPTION SURFACE chemistry WAVE mechanics QUANTUM theory

Great expectations: The value of spatial diversity in wireless networks

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Great expectations: The value of spatial diversity in wirele...

作者： Diggavi, Suhas N. Al-Dhahir, Naofal Stamoulis, A. Calderbank, A.R. AT and T Shannon Labs Florham Park NJ 07932 United States Swiss Federal Institute of Technology Lausanne CH 1015 Switzerland University of Texas at Dallas Richardson TX 75083 United States Qualcomm San Diego CA 92121 United States Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States

In this paper, the effect of spatial diversity on the throughput and reliability of wireless networks is examined. Spatial diversity is realized through multiple independently fading transmit/receive antenna paths in single-user communication and through independently fading links in multiuser communication. Adopting spatial diversity as a central theme, we start by studying its information-theoretic foundations, then we illustrate its benefits across the physical (signal transmission/coding and receiver signal processing) and networking (resource allocation, routing, and applications) layers. Throughout the paper, we discuss engineering intuition and tradeoffs, emphasizing the strong interactions between the various network functionalities. © 2004 IEEE.

关键词： Wireless telecommunication systems

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

Convergence of deep fictitious play for stochastic differential games

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arXiv 2020年

作者： Han, Jiequn Hu, Ruimeng Long, Jihao Department of Mathematics Princeton University PrincetonNJ08544-1000 United States Department of Mathematics Department of Statistics and Applied Probability University of California Santa BarbaraCA93106-3080 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544-1000 United States

Stochastic differential games have been used extensively to model agents' competitions in Finance, for instance, in P2P lending platforms from the Fintech industry, the banking system for systemic risk, and insurance markets. The recently proposed machine learning algorithm, deep fictitious play, provides a novel efficient tool for finding Markovian Nash equilibrium of large N-player asymmetric stochastic differential games [J. Han and R. Hu, Mathematical and Scientific Machine Learning Conference, pages 221-245, PMLR, 2020]. By incorporating the idea of fictitious play, the algorithm decouples the game into N sub-optimization problems, and identifies each player's optimal strategy with the deep backward stochastic differential equation (BSDE) method parallelly and repeatedly. In this paper, we prove the convergence of deep fictitious play (DFP) to the true Nash equilibrium. We can also show that the strategy based on DFP forms an ϵ-Nash equilibrium. We generalize the algorithm by proposing a new approach to decouple the games, and present numerical results of large population games showing the empirical convergence of the algorithm beyond the technical assumptions in the theorems. Copyright © 2020, The Authors. All rights reserved.

关键词： Game theory

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

Extracting Kinetic and Stationary Distribution Information from Short MD Trajectories via a Collection of Surrogate Diffusion Models. (vol 5, pg 47, 2009)

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JOURNAL OF CHEMICAL THEORY AND COMPUTATION 2009年第8期5卷 2192-2192页

作者： Calderon, Christopher P. Arora, Karunesh Department of Computational and Applied Mathematics and Department of Statistics Rice University Houston Texas 77005-1892 and Department of Chemistry Biophysics Program University of Michigan 930 North University Avenue Ann Arbor Michigan 48109

Low-dimensional stochastic models can summarize dynamical information and make long time predictions associated with observables of complex atomistic systems. Maximum likelihood based techniques for estimating low-dimensional surrogate diffusion models from relatively short time series are presented. It is found that a heterogeneous population of slowly evolving conformational degrees of freedom modulates the dynamics. This underlying heterogeneity results in a collection of estimated low-dimensional diffusion models. Numerical techniques for exploiting this finding to approximate skewed histograms associated with the simulation are presented. In addition, statistical tests are used to assess the validity of the models and determine physically relevant sampling information, e.g. the maximum sampling frequency at which one can discretely sample from an atomistic time series and have a surrogate diffusion model pass goodness-of-fit tests. The information extracted from such analyses can possibly be used to assist umbrella sampling computations as well as help in approximating effective diffusion coefficients. The techniques are demonstrated on simulations of adenylate kinase.

关键词： Transport properties Diffusion Approximation computational chemistry Computer simulations

Cosserat elasticity as the weak-field limit of Einstein-Cartan relativity

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Physical Review D 2024年第10期109卷 104052-104052页

作者： Matthew Maitra Jeroen Tromp Institut für Geophysik ETH Zürich Sonneggstrasse 5 Zürich 8092 Switzerland Department of Geosciences Program in Applied and Computational Mathematics Princeton University Princeton 08540 NJ United States

The weak-field limit of Einstein-Cartan (EC) relativity is studied. The equations of EC theory are rewritten such that they formally resemble those of Einstein general relativity (EGR); this allows ideas from post-Newtonian theory to be imported without essential change. The equations of motion are then written both at first post-Newtonian (1PN) order and at 1.5PN order. EC theory’s 1PN equations of motion are found to be those of a micropolar/Cosserat elastic medium, along with a decoupled evolution equation for nonclassical, spin-related fields. It seems that a necessary condition for these results to hold is that one chooses the nonclassical fields to scale with the speed of light in a certain empirically reasonable way. Finally, the 1.5PN equations give greater insight into the coupling between energy-momentum and spin within slowly moving, weakly gravitating matter. Specifically, the weakly relativistic modifications to Cosserat theory involve a gravitational torque and an augmentation of the gravitational force due to a dynamic mass moment density with an accompanying dynamic mass moment density flux, and new forms of linear momentum density captured by a dynamic mass density flux and a dynamic momentum density.

关键词： Alternative gravity theories Solar system & its planets

Stable super-resolution of images: A theoretical study

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arXiv 2018年

作者： Eftekhari, Armin Bendory, Tamir Tang, Gongguo Institute of Electrical Engineering École Polytechnique Fédérale de Lausanne Program in Applied and Computational Mathematics Princeton University Department of Electrical Engineering Colorado School of Mines

We study the ubiquitous super-resolution problem, in which one aims at localizing positive point sources in an image, blurred by the point spread function of the imaging device. To recover the point sources, we propose to solve a convex feasibility program, which simply finds a nonnegative Borel measure that agrees with the observations collected by the imaging device. In the absence of imaging noise, we show that solving this convex program uniquely retrieves the point sources, provided that the imaging device collects enough observations. This result holds true if the point spread function of the imaging device can be decomposed into horizontal and vertical components, and if the translations of these components form a Chebyshev system, namely, a system of continuous functions that loosely behave like algebraic polynomials. Building upon recent results for one-dimensional signals [1], we prove that this super-resolution algorithm is stable (in the generalized Wasserstein metric) to model mismatch (namely, when the image is not sparse) and to additive imaging noise. In particular, the recovery error depends on the noise level and how well the image can be approximated with well-separated point sources. As an example, we verify these claims for the important case of a Gaussian point spread function. The proofs rely on the construction of novel interpolating polynomials, which are the main technical contribution of this paper, and partially resolve the question raised in [2] about the extension of the standard machinery to higher dimensions. Copyright © 2018, The Authors. All rights reserved.

关键词： Optical transfer function

Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons

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arXiv 2018年

作者： Davison, Elizabeth N. Aminzare, Zahra Leonard, Naomi Ehrich Dey, Biswadip Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We study the dynamics of a low-dimensional system of coupled model neurons as a step towards understanding the vastly complex network of neurons in the brain. We analyze the bifurcation structure of a system of two model neurons with unidirectional coupling as a function of two physiologically relevant parameters: the external current input only to the first neuron and the strength of the coupling from the first to the second neuron. Leveraging a timescale separation, we prove necessary conditions for multiple timescale phenomena observed in the coupled system, including canard solutions and mixed mode oscillations. For a larger network of model neurons, we present a sufficient condition for phase locking when external inputs are heterogeneous. Finally, we generalize our results to directed trees of model neurons with heterogeneous inputs.34A26, 34C15, 34C60, 34D15, 34E17, 37G05, 37G10, 92B20, 92C20 Copyright © 2018, The Authors. All rights reserved.

关键词： Bifurcation (mathematics)

Robust group synchronization via cycle-edge message passing

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arXiv 2019年

作者： Lerman, Gilad Shi, Yunpeng School of Mathematics University of Minnesota 127 Vincent Hall 206 Church Street SE MinneapolisMN55455 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We propose a general framework for solving the group synchronization problem, where we focus on the setting of adversarial or uniform corruption and sufficiently small noise. Specifically, we apply a novel message passing procedure that uses cycle consistency information in order to estimate the corruption levels of group ratios and consequently solve the synchronization problem in our setting. We first explain why the group cycle consistency information is essential for effectively solving group synchronization problems. We then establish exact recovery and linear convergence guarantees for the proposed message passing procedure under a deterministic setting with adversarial corruption. These guarantees hold as long as the ratio of corrupted cycles per edge is bounded by a reasonable constant. We also establish the stability of the proposed procedure to sub-Gaussian noise. We further establish exact recovery with high probability under a common uniform corruption *** Codes 90-08, 62G35, 68Q25, 68W40, 68Q87, 93E10 Copyright © 2019, The Authors. All rights reserved.

关键词： Crime