Inequalities for entropy-based measures of network information content

This paper presents a method for establishing relations between entropy-based measures applied to graphs. A special class of relations called implicit information inequalities or implicit entropy bounds is developed. A number of entropy-based measures of the structural information content of a graph have been developed over the past several decades, but little attention has been paid to relations among these measures. The research reported here aims to remedy this deficiency.     

The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center

We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one-dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C¹ map on any compact manifold.     

Quasi-potentials of the entropy functionals for scalar conservation laws

We investigate the quasi-potential problem for the entropy cost functionals of non-entropic solutions to scalar conservation laws with smooth fluxes. We prove that the quasi-potentials coincide with the integral of a suitable Einstein entropy.     

Minimization of Energy Functionals Applied to Some Inverse Problems

We consider a general class of problems of the minimization of convex integral functionals subject to linear constraints. Using Fenchel duality, we prove the equality of the values of the minimization problem and its associated dual problem. This equality is a variational criterion for the existence of a solution to a large class of inverse problems entering the class of generalized Fredholm integral equations. In particular, our abstract results are applied to marginal problems for stochastic processes. Such problems naturally arise from the probabilistic approaches to quantum mechanics. Accepted 26 March 2001. Online publication 19 July 2001.     

信息熵的收敛性与收敛速度

本讨论了连续时间,状态空间有限的马氏过程的信息熵的收敛性质,给出了可测转移矩阵的极限形式,得出具有可测转移矩阵的马氏过程的信息熵在时间趋于无穷大时存在且有限,对于具有强遍历转移函数的马氏过程的信息熵按多项式一致收敛。     

On solving convex quadratic semi-infinite programming probelms

In this paper we study a from of convex quadratic semi-infinite programming problems with finitely many variables and infinitely many constraints over a compact metric space. An entropic path-following algorithum is introduced with a convergence proof. Some practical implementations and numerical experiments are also included     

Benchmark Estimation for Markov chain Monte Carlo Samples

While studying various features of the posterior distribution of a vector-valued parameter using an MCMC sample, a subsample is often all that is available for analysis. The goal of benchmark estimation is to use the best available information, that is, the full MCMC sample, to improve future estimates made on the basis of the subsample. We discuss a simple approach to do this and provide a theoretical basis for the method. The methodology and benefits of benchmark estimation are illustrated using a well-known example from the literature. We obtain nearly a 90% reduction in MSE with the technique based on a 1-in-10 subsample and show that greater benefits accrue with the thinner subsamples that are often used in practice.     

具随机生成元的受控随机发展方程的Pontryagin型最大值原理

本文研究当控制区域是凸集时带有随机生成元的受控正向随机发展方程的Pontryagin型最大值原理.运用Malliavin分析方法,本文给出了当p>=2时控制系统温和解的存在唯一性,运用转置方法获得了当1相似文献   

Nonisothermal immiscible compressible thermodynamically consistent two-phase flow in porous media

In this paper, we introduce a new model of the nonisothermal immiscible compressible thermodynamically consistent two-phase flow in a porous domain Ω. This model includes the term describing the skeleton and interphase boundary energies. In the framework of the model, we derive the equation for the entropy function in the whole Ω and then obtain the estimate of the maximal entropy of the system.     

一种图论方法在电力系统故障恢复中的应用

引述了图论理论中的一个最大流问题的解法一标号法，并将其应用到电力系统的故障恢复策略的生成当中。文章首先介绍了有关标号法的基本内容；之后列出了标号法所用的临界约束和参量，讨论了电力系统故障恢复策略生成的具体部分，对在容量限制下故障系统的恢复，提出了一种数值研究方法。最后，给出了一个实际故障系统的恢复策略生成例子。