Statistical mechanics of warm and cold unfolding in proteins

We present a statistical mechanics treatment of the stability of globular proteins which takes explicitly into account the coupling between the protein and water degrees of freedom. This allows us to describe both the cold and the warm unfolding, thus qualitatively reproducing the known thermodynamics of proteins. Received: 19 March 1998 / Revised and Accepted: 25 May 1998     

动力系统简介

本文对动力系统这一学科的历史、理论、应用以及与其他学科的联系作一简介.     

Perfect information two-person zero-sum markov games with imprecise transition probabilities

Based on an extension of the controlled Markov set-chain model by Kurano et al. (in J Appl Prob 35:293–302, 1998) into competitive two-player game setting, we provide a model of perfect information two-person zero-sum Markov games with imprecise transition probabilities. We define an equilibrium value for the games formulated with the model in terms of a partial order and then establish the existence of an equilibrium policy pair that achieves the equilibrium value. We further analyze finite-approximation error bounds obtained from a value iteration-type algorithm and discuss some applications of the model.     

The property of being polynomial for Mal’tsev constraint satisfaction problems

A combinatorial constraint satisfaction problem aims at expressing in unified terms a wide spectrum of problems in various branches of mathematics, computer science, and AI. The generalized satisfiability problem is NP-complete, but many of its restricted versions can be solved in a polynomial time. It is known that the computational complexity of a restricted constraint satisfaction problem depends only on a set of polymorphisms of relations which are admitted to be used in the problem. For the case where a set of such relations is invariant under some Mal’tsev operation, we show that the corresponding constraint satisfaction problem can be solved in a polynomial time. __________ Translated from Algebra i Logika, Vol. 45, No. 6, pp. 655–686, November–December, 2006.     

Quadratically constrained minimum cross-entropy analysis

Quadratically constrained minimum cross-entropy problem has recently been studied by Zhang and Brockett through an elaborately constructed dual. In this paper, we take a geometric programming approach to analyze this problem. Unlike Zhang and Brockett, we separate the probability constraint from general quadratic constraints and use two simple geometric inequalities to derive its dual problem. Furthermore, by using the dual perturbation method, we directly prove the strong duality theorem and derive a dual-to-primal conversion formula. As a by-product, the perturbation proof gives us insights to develop a computation procedure that avoids dual non-differentiability and allows us to use a general purpose optimizer to find an-optimal solution for the quadratically constrained minimum cross-entropy analysis.     

A subjective Bayesian approach to the theory of queues II — Inference and information in M/M/1 queues

This is a sequel to Part I of A Subjective Bayesian Approach to the Theory of Queues. The focus here is on inference and a use of Shannon's measure of information for assessing the amount of information conveyed by the various types of data from queues. The notation and terminology used here is established in Part I.     

On the average length of lexicographic paths

A bound is given for the average length of a lexicographic path, a definition that is motivated by degeneracies encountered when using the randomized simplex method.     

A new approach for the derivation of bounds for the Jensen difference

There are many useful applications of Jensen's inequality in several fields of science, and due to this reason, a lot of results are devoted to this inequality in the literature. The main theme of this article is to present a new method of finding estimates of the Jensen difference for differentiable functions. By applying definition of convex function, and integral Jensen's inequality for concave function in the identity pertaining the Jensen difference, we derive bounds for the Jensen difference. We present integral version of the bounds in Riemann sense as well. The sharpness of the proposed bounds through examples are discussed, and we conclude that the proposed bounds are better than some existing bounds even with weaker conditions. Also, we present some new variants of the Hermite–Hadamard and Hölder inequalities and some new inequalities for geometric, quasi-arithmetic, and power means. Finally, we give some applications in information theory.     

基于主被动合作博弈的医患关系研究

针对我国医患关系日趋紧张,医患矛盾逐渐凸显这一问题,在对中国近五年医患事件进行分析的基础上,分别从信任程度、信息不对称程度、诊疗代价等多个视角出发,利用演化博弈理论和复制动态方程,构建了医患双方合作策略选择演化博弈模型,探究了影响医患关系演化的相关因素。研究表明:从长期来看,医患关系博弈系统存在两种演化路径:主动合作和被动合作;增大医患双方的信任程度,减小医患双方的信息不对称程度,降低医患双方合作成本,增大以政府为主导的仲裁机构对医患双方的奖励和惩罚都将会促使医患双方由被动合作转向主动合作。     

The Newton modified barrier method for QP problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues, to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a hot start. Starting at such a hot start, at mostO(In In ^-1) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, >0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that onlyO(In ^-1)O(In In ^-1) Newton steps are required to reach an -approximation to the solution from any hot start. In order to reach the hot start, one has to perform Newton steps, wherem characterizes the size of the problem andC>0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.Partially supported by NASA Grant NAG3-1397 and National Science Foundation Grant DMS-9403218.