An Euler–Monte Carlo algorithm assessing Moment Lyapunov Exponents for stochastic bridge flutter predictions

2013 ◽  
Vol 122 ◽  
pp. 65-77 ◽  
Author(s):  
Luca Caracoglia
Keyword(s):  
Monte Carlo ◽  
Lyapunov Exponents ◽  
Monte Carlo Algorithm ◽  
Moment Lyapunov Exponents

Monte Carlo Simulation of Moment Lyapunov Exponents

2005 ◽  
Vol 72 (2) ◽  
pp. 269-275 ◽  
Author(s):  
Wei-Chau Xie
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Lyapunov Exponents ◽  
Stochastic Systems ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
Two Dimensional ◽  
Bounded Noise ◽  
Moment Stability ◽  
Moment Lyapunov Exponents

A Monte Carlo simulation method for determining the pth moment Lyapunov exponents of stochastic systems, which governs the pth moment stability, is developed. Numerical results of two-dimensional systems under bounded noise and real noise excitations are presented to illustrate the approach.

Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

2020 ◽  
Vol 26 (3) ◽  
pp. 223-244
Author(s):  
W. John Thrasher ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Algorithm ◽  
Significant Bias ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy ◽  
Poisson Boltzmann Equation ◽  
The Stability ◽  
Potential Methods ◽  
The Individual

AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.

scholarly journals Bayesian cumulative shrinkage for infinite factorizations

Biometrika ◽  
2020 ◽  
Vol 107 (3) ◽  
pp. 745-752 ◽  
Author(s):  
Sirio Legramanti ◽  
Daniele Durante ◽  
David B Dunson
Keyword(s):  
Monte Carlo ◽  
Factor Analysis ◽  
Monte Carlo Algorithm ◽  
Model Complexity ◽  
Latent Factors ◽  
Shrinkage Process ◽  
Shrinkage Prior ◽  
Performance Gains ◽  
Shrinkage Priors ◽  
Model Dimension

Summary The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing shrinkage prior, called the cumulative shrinkage process, for the parameters that control the dimension in overcomplete formulations. Our construction has broad applicability and is based on an interpretable sequence of spike-and-slab distributions which assign increasing mass to the spike as the model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages relative to current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the performance gains are outlined in simulations and in an application to personality data.

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