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Bayesian Estimation of the Log-linear Exponential Regression Model with Censorship and Collinearity

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2016年第1期45卷 152-164页

作者： Ariza-Hernandez, Francisco J. Godinez-Jaimes, Flaviano Reyes-Carreto, Ramon Univ Autonoma Guerrero Unidad Acad Matemat Chilpancingo Mexico

In this work, a simulation study is conducted to evaluate the performance of Bayesian estimators for the log-linear exponential regression model under different levels of censoring and degrees of collinearity for two covariates. The diffuse normal, independent Student-t and multivariate Student-t distributions are considered as prior distributions and to draw from the posterior distributions, the metropolis algorithm is implemented. Also, the results are compared with the maximum likelihood estimators in terms of the mean squared error, coverages and length of the credibility and confidence intervals.

关键词： Bayes' estimator Censorship Collinearity Coverages Log-linear regression metropolis algorithm Simulation study

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Machine learning of explicit order parameters: From the Ising model to SU(2) lattice gauge theory

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Physical Review B 2017年第18期96卷 184410-184410页

作者： Sebastian J. Wetzel Manuel Scherzer Institut für Theoretische Physik Universität Heidelberg Philosophenweg 16 69120 Heidelberg Germany

We present a solution to the problem of interpreting neural networks classifying phases of matter. We devise a procedure for reconstructing the decision function of an artificial neural network as a simple function of the input, provided the decision function is sufficiently symmetric. In this case one can easily deduce the quantity by which the neural network classifies the input. The method is applied to the Ising model and SU(2) lattice gauge theory. In both systems we deduce the explicit expressions of the order parameters from the decision functions of the neural networks. We assume no prior knowledge about the Hamiltonian or the order parameters except Monte Carlo–sampled configurations.

关键词： Classical statistical mechanics Gauge theories Machine learning Order parameters Phase transitions Heatbath algorithm Ising model Lattice gauge theory metropolis algorithm Monte Carlo methods Simulated annealing

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Reversal of Magnetisation in Ising Ferromagnet by the Field Having Gradient

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Communications in Theoretical Physics 2016年第11期65卷 563-570页

作者： Abyaya Dhar Muktish Acharyya Department of Physics Presidency University

We have studied the reversal of magnetisation in Ising ferromagnet by the field having gradient along a particular direction. We employed the Monte Carlo simulation with metropolis single spin nip algorithm. The average lifetime of the metastable state was observed to increase with the magnitude of the gradient of applied field. In the high gradient regime, the system was observed to show two distinct region of up and down spins. The interface or the domain wall was observed to move as one increases the gradient. The displacement of the mean position of the interface was observed to increase with the gradient as hyperbolic tangent function. The roughness of the interface was observed to decay exponentially as the gradient increases. The number of spin flip per site was observed to show a discontinuity in the vicinity of the domain wall. The amount of the discontinuity was found to diverge with the system size as a power law fashion with an exponent 5/3.

关键词： Ising ferromagnet metastable lifetime Monte Carlo simulation metropolis algorithm

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Polarizability of electrically induced magnetic vortex plasma

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Physical Review B 2017年第19期95卷 195136-195136页

作者： P. I. Karpov S. I. Mukhin Department of Theoretical Physics and Quantum Technologies National University of Science and Technology MISiS Leninski Avenue 4 119991 Moscow Russia

Electric field control of magnetic structures, particularly topological defects in magnetoelectric materials, has drawn a great deal of attention in recent years, which has led to experimental success in creation and manipulation by an electric field of single magnetic defects, such as domain walls and skyrmions. In this work we explore a scenario of electric field creation of another type of topological defect, magnetic vortices and antivortices, which are characteristic of materials with easy-plane (XY) symmetry. Each magnetic (anti)vortex in magnetoelectric materials (such as type-II multiferroics) possesses a quantized magnetic and an electric charge, where the former is responsible for interaction between vortices and the latter couples the vortices to an electric field. This property of magnetic vortices opens a peculiar possibility of creation of magnetic vortex plasma by nonuniform electric fields. We show that the electric field, created by a cantilever tip, produces a “magnetic atom” with a localized spatially ordered spot of vortices (“nucleus” of the atom) surrounded by antivortices (“electronic shells”). We analytically find the vortex density distribution profile and temperature dependence of polarizability of this structure and confirm it numerically. We show that electric polarizability of the “magnetic atom” depends on temperature as α∼1/T1−η (η>0), which is consistent with Euclidean random matrix theory prediction.

关键词： Dzyaloshinskii-Moriya interaction Helicoidal magnetic texture Magnetic vortices Magnetoelectric effect XY model Helimagnets Multiferroics Multilayer thin films metropolis algorithm Micromagnetic modeling Simulated annealing

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Near-optimal protocols in complex nonequilibrium transformations

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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 2016年第37期113卷 10263-10268页

作者： Gingrich, Todd R. Rotskoff, Grant M. Crooks, Gavin E. Geissler, Phillip L. MIT Dept Phys Phys Living Syst Grp Cambridge MA 02139 USA Univ Calif Berkeley Dept Chem Berkeley CA 94720 USA Univ Calif Berkeley Biophys Grad Grp Berkeley CA 94720 USA Lawrence Berkeley Natl Lab Phys Biosci Div Berkeley CA 94720 USA Kavli Energy NanoSci Inst Berkeley CA 94720 USA Lawrence Berkeley Natl Lab Div Chem Sci Berkeley CA 94720 USA

The development of sophisticated experimental means to control nanoscale systems has motivated efforts to design driving protocols that minimize the energy dissipated to the environment. Computational models are a crucial tool in this practical challenge. We describe a general method for sampling an ensemble of finite-time, nonequilibrium protocols biased toward a low average dissipation. We show that this scheme can be carried out very efficiently in several limiting cases. As an application, we sample the ensemble of low-dissipation protocols that invert the magnetization of a 2D Ising model and explore how the diversity of the protocols varies in response to constraints on the average dissipation. In this example, we find that there is a large set of protocols with average dissipation close to the optimal value, which we argue is a general phenomenon.

关键词： nonequilibrium irreversible thermodynamics entropic sampling methods metropolis algorithm Ising model

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Robust inference for mixed censored and binary response models with missing covariates

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STATISTICAL METHODS IN MEDICAL RESEARCH 2016年第5期25卷 1836-1853页

作者： Sarkar, Angshuman Das, Kalyan Sinha, Sanjoy K. Novartis Healthcare Pvt Ltd Hyderabad Andhra Pradesh India Univ Calcutta Dept Stat Kolkata W Bengal India Carleton Univ Sch Math & Stat Ottawa ON K1S 5B6 Canada

In biomedical and epidemiological studies, often outcomes obtained are of mixed discrete and continuous in nature. Furthermore, due to some technical inconvenience or else, continuous responses are censored and also a few covariates cease to be observed completely. In this paper, we develop a model to tackle these complex situations. Our methodology is developed in a more general framework and provides a full-scale robust analysis of such complex models. The proposed robust maximum likelihood estimators of the model parameters are resistant to potential outliers in the data. We discuss the asymptotic properties of the robust estimators. To avoid computational difficulties involving irreducibly high-dimensional integrals, we propose a Monte Carlo method based on the metropolis algorithm for approximating the robust maximum likelihood estimators. We study the empirical properties of these estimators in simulations. We also illustrate the proposed robust method using clustered data on blood sugar content from a clinical trial of individuals who were investigated for diabetes.

关键词： binary model censored regression model expectation maximization algorithm metropolis algorithm missing data robust estimation

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When Non-Elitism Outperforms Elitism for Crossing Fitness Valleys 16

When Non-Elitism Outperforms Elitism for Crossing Fitness Va...

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Genetic and Evolutionary Computation Conference (GECCO)

作者： Oliveto, Pietro S. Paixao, Tiago Heredia, Jorge Perez Sudholt, Dirk Trubenova, Barbora Univ Sheffield Sheffield S1 4DP S Yorkshire England IST Austria Campus 1 A-3400 Klosterneuburg Austria

ISBN: (纸本)9781450342063

Crossing fitness valleys is one of the major obstacles to function optimization. In this paper we investigate how the structure of the fitness valley, namely its depth d and length l, influence the runtime of different strategies for crossing these valleys. We present a runtime comparison between the (1+1) EA and two non-elitist nature-inspired algorithms, Strong Selection Weak Mutation (SSWM) and the metropolis algorithm. While the (1+1) EA has to jump across the valley to a point of higher fitness because it does not accept decreasing moves, the non-elitist algorithms may cross the valley by accepting worsening moves. We show that while the runtime of the (1+1) EA algorithm depends critically on the length of the valley, the runtimes of the non-elitist algorithms depend crucially only on the depth of the valley. In particular, the expected runtime of both SSWM and metropolis is polynomial in l and exponential in d while the (1+1) EA is efficient only for valleys of small length. Moreover, we show that both SSWM and metropolis can also efficiently optimize a rugged function consisting of consecutive valleys.

关键词： fitness valley valley path non-elitism runtime analysis natural evolution theory strong selection weak mutation regime metropolis algorithm simulated annealing

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Scattering and radiation computation with spectral methods

Scattering and radiation computation with spectral methods

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作者： Zhang, Jianing Texas A&M University

学位级别：Ph.D.

Surface roughness, a fundamental characteristic of atmospheric ice particles, is essential for defining an appropriate particle morphology model to simulate optical properties of atmospheric particles. This dissertation presents a dynamic stochastic parameterization approach based on combining the discrete differential geometry and stochastic partial differential equations to generate particle overall shapes and the degree of surface roughness. The scattering of light by particles modeled as Gaussian spheroids with size parameters up to 300 is simulated with the Invariant Imbedding T-Matrix (II-TM) method to investigate the effect of particle surface roughness on the single-scattering properties, including the phase matrix, single-scattering albedo, and extinction efficiency. It is shown that high-frequency oscillations of the phase matrix with respect to scattering angle are gradually suppressed as the degree of roughness increases. The dissertation presents a more thorough method of roughened particles in light scattering computation than various ad hoc methods reported in the literature. We discuss how surface roughness influences the Muller matrix patterns of ice particles. These results also enable better understanding of microphysics on ice surface and more accurate parameterization of atmospheric ice particles. We show that surface irregularity changes the phase matrix elements dramatically. An analysis of optical modeling of mineral dust aerosols as Gaussian spheroids is presented. The modeling results are compared with experimental measurements of feldspar to validate the applicability of roughened model particles. The Gaussian spheroids shows better data fitting than smooth spheroids. Furthermore, we analyze population density and shape distributions of Gaussian spheroid for different mineral dust species. In addition to the scattering study, we propose a new Monte Carlo method for radiative transfer based on the metropolis algorithm.

关键词： Spectral method T-Matrix Surface roughness Random field metropolis algorithm Thesis

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Stiffer double-stranded DNA in two-dimensional confinement due to bending anisotropy

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Physical Review E 2016年第6期94卷 062407-062407页

作者： H. Salari B. Eslami-Mossallam H. F. Ranjbar M. R. Ejtehadi Department of Physics Sharif University of Technology P.O. Box 11155-9161 Tehran Iran and School of Nano Science Institute for Research in Fundamental Sciences (IPM) Tehran 19395-5531 Iran

Using analytical approach and Monte Carlo (MC) simulations, we study the elastic behavior of the intrinsically twisted elastic ribbons with bending anisotropy, such as double-stranded DNA (dsDNA), in two-dimensional (2D) confinement. We show that, due to the bending anisotropy, the persistence length of dsDNA in 2D conformations is always greater than three-dimensional (3D) conformations. This result is in consistence with the measured values for DNA persistence length in 2D and 3D in equal biological conditions. We also show that in two dimensions, an anisotropic, intrinsically twisted polymer exhibits an implicit twist-bend coupling, which leads to the transient curvature increasing with a half helical turn periodicity along the bent polymer.

关键词： Chain stiffness Persistence length Polymer behavior Polymer conformation & topology DNA Ideal-chain models metropolis algorithm Monte Carlo methods Worm-like chain model

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MIXING TIME OF metropolis CHAIN BASED ON RANDOM TRANSPOSITION WALK CONVERGING TO MULTIVARIATE EWENS DISTRIBUTION

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ANNALS OF APPLIED PROBABILITY 2015年第3期25卷 1581-1615页

作者： Jiang, Yunjiang Stanford Univ Dept Math Stanford CA 94305 USA

We prove sharp rates of convergence to the Ewens equilibrium distribution for a family of metropolis algorithms based on the random transposition shuffle on the symmetric group, with starting point at the identity. The proofs rely heavily on the theory of symmetric Jack polynomials, developed initially by Jack [Proc. Roy. Soc. Edinburgh Sect. A 69 (1970/1971) 1-18], Macdonald [Symmetric Functions and Hall Polynomials (1995) New York] and Stanley [Adv. Math. 77 (1989) 76-115]. This completes the analysis started by Diaconis and Hanlon in [Contemp. Math. 138 (1992) 99-117]. In the end we also explore other integrable Markov chains that can be obtained from symmetric function theory.

关键词： Jack polynomials metropolis algorithm mixing time random transposition

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