相关论文: New Algorithm for Mixmaster Dynamics

We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for…

We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture…

The Mixmaster or Bianchi IX cosmological model has become one of the archetypal settings for studying gravitational dynamics. The past decade has seen a vigourous debate about whether or not the Mixmaster's dynamics is chaotic. In this talk…

The performance of space-time adaptive processing (STAP) is often degraded by factors such as limited sample size and moving targets. Traditional clutter covariance matrix (CCM) estimation relies on Euclidean metrics, which fail to capture…

In this note, we propose a symplectic algorithm for the stable manifolds of the Hamilton-Jacobi equations combined with an iterative procedure in [Sakamoto-van~der Schaft, IEEE Transactions on Automatic Control, 2008]. Our algorithm…

The widespread popularity of replica exchange and expanded ensemble algorithms for simulating complex molecular systems in chemistry and biophysics has generated much interest in enhancing phase space mixing of these protocols, thus…

We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…

In this article, we propose an accuracy-assuring technique for finding a solution for unsymmetric linear systems. Such problems are related to different areas such as image processing, computer vision, and computational fluid dynamics.…

We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence,…

The Bianchi IX cosmological model is analyzed in a generalized uncertainty principle framework. The Arnowitt-Deser-Misner reduction of the dynamics is performed and a time-coordinate, namely the volume of the Universe, naturally arises.…

In this work we prove sufficient conditions for the Glauber dynamics corresponding to a sequence of (non-product) measures on finite product spaces to be rapidly mixing, i.e. that the mixing time with respect to the total variation distance…

Studying Yang-Mills field and gravitational field in class A Bianchi spacetimes, we find that chaotic behavior appears in the late phase (the asymptotic future). In this phase, the Yang-Mills field behaves as that in Minkowski spacetime, in…

We provide a Hamiltonian analysis of the Mixmaster Universe dynamics on the base of a standard Arnowitt-Deser-Misner Hamiltonian approach, showing the covariant nature of its chaotic behaviour with respect to the choice of any time…

We study in this paper a forward-backward-forward dynamical system for solving a mixed variational inequality problem in a real Hilbert space. For the convergence analysis of our proposed system, we apply the Lyapunov analysis to obtain the…

Hidden Markov models have successfully been applied as models of discrete time series in many fields. Often, when applied in practice, the parameters of these models have to be estimated. The currently predominating identification methods,…

We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev…

An important paradigm in the understanding of mixing times of Glauber dynamics for spin systems is the correspondence between spatial mixing properties of the models and bounds on the mixing time of the dynamics. This includes, in…

The goal of this paper is to provide a new analysis of the classical dynamics of Bianchi type I, II and IX models by applying conventional Hamiltonian methods in the language of Ashtekhar variables. We show that Bianchi type II models can…

A fast algorithm for B-splines in mixed models is presented. B-splines have local support and are computational attractive, because the corresponding matrices are sparse. A key element of the new algorithm is that the local character of…