A methodology for analyzing decision networks, based on information theory

This paper assumes the organization as a distributed decision network. It proposes an approach based on application and extension of information theory concepts, in order to analyze informational complexity in a decision network, due to interdependence between decision centers.Based on this approach, new quantitative concepts and definitions are proposed in order to measure the information in a decision center, based on Shannon entropy and its complement in possibility theory, U uncertainty. This approach also measures the quantity of interdependence between decision centers and informational complexity of decision networks.The paper presents an agent-based model of organization as a graph composed of decision centers. The application of the proposed approach is in analyzing and assessing a measure to the organization structure efficiency, based on informational communication view. The structure improvement, analysis of information flow in organization and grouping algorithms are investigated in this paper. The results obtained from this model in different systems as distributed decision networks, clarifies the importance of structure and information distribution sources effect’s on network efficiency.     

效用信息熵在射击目标选择数学模型中的应用初探

针对装甲兵射击目标选择的特点,建立射击目标选择的数学模型,结合层次分析法,运用效用信息熵理论,通过实例不仅给出了射击目标的合理排序,还得到了影响射击目标选择的主、次要因素,可为装甲兵作战指挥自动化系统辅助决策提供一种新的方法.     

Some properties of frost deformations

Some properties of polymers used for the thermoplastic recording of information are discussed and experimental data on the region of non-Newtonian and Newtonian flow in a polymer are presented. A Bingham body can thus be selected as a mathematical model and can be used to offer an explanation for the variations in the informational properties of the support material during the process of recording visualization.     

The Scenery Flow for Hyperbolic Julia Sets

We define the scenery flow space at a point z in the Julia setJ of a hyperbolic rational map T : C C with degree at least2, and more generally for T a conformal mixing repellor. We prove that, for hyperbolic rational maps, except for a fewexceptional cases listed below, the scenery flow is ergodic.We also prove ergodicity for almost all conformal mixing repellors;here the statement is that the scenery flow is ergodic for therepellors which are not linear nor contained in a finite unionof real-analytic curves, and furthermore that for the collectionof such maps based on a fixed open set U, the ergodic casesform a dense open subset of that collection. Scenery flow ergodicityimplies that one generates the same scenery flow by zoomingdown towards almost every z with respect to the Hausdorff measureH^d, where d is the dimension of J, and that the flow has a uniquemeasure of maximal entropy. For all conformal mixing repellors, the flow is loosely Bernoulliand has topological entropy at most d. Moreover the flow atalmost every point is the same up to a rotation, and so as acorollary, one has an analogue of the Lebesgue density theoremfor the fractal set, giving a different proof of a theorem ofFalconer. 2000 Mathematical Subject Classification: 37F15, 37F35, 37D20.     

电渗流中传热传质过程与熵的分析

在壁面存在恒定热通量条件下,分析微通道内电渗流中传热传质过程与熵的生成.建立数值计算模型,分别采用Poisson-Boltzmann方程、Navier-Stokes方程、Nernst-Planck方程和能量方程来描述微通道内双电层电势、流场、离子浓度和温度的分布情况.引入熵产生,进一步研究不同流动参数对流体传热过程的作用,讨论不同流动参数下各热效应的变化规律,并具体分析热效应参数对流体总熵增加及各部分热效应对总熵比重的影响.结果表明,动电参数与Joule(焦耳)热系数的增大会使得传热性能减弱,动电参数对传热性能影响更为明显;流体的总熵为动电参数、传质系数和质量弥散系数的增函数.     

An entropic economic order quantity (EnEOQ) for items with imperfect quality

This paper presents an entropic version of an EOQ model with imperfect quality items. The approach adopted herein models the commodity flow (demand rate) as a heat flow in a thermodynamic system. As a result, an entropy cost term is added to the classical inventory cost to form an entropic total inventory cost function. This provides an estimation of the hidden or difficult to estimate cost inventory systems that usually are the result of disorder (or entropy). A mathematical model is developed with numerical results presented and discussed.     

On entropy stable schemes for degenerate parabolic multispecies kinematic flow models

Entropy stable schemes for the numerical solution of initial value problems of nonlinear, possibly strongly degenerate systems of convection–diffusion equations were recently proposed in Jerez and Parés's study. These schemes extend the theoretical framework of Tadmor's study to convection–diffusion systems. They arise from entropy conservative schemes by adding a small amount of viscosity to avoid spurious oscillations. The main condition for feasibility of entropy conservative or stable schemes for a given model is that the corresponding first‐order system of conservation laws possesses a convex entropy function and corresponding entropy flux, and that the diffusion matrix multiplied by the inverse of the Hessian of the entropy is positive semidefinite. As a new contribution, it is demonstrated in the present work, first, that these schemes can naturally be extended to initial‐boundary value problems with zero‐flux boundary conditions in one space dimension, including an explicit bound on the growth of the total entropy. Second, it is shown that these assumptions are satisfied by certain diffusively corrected multiclass kinematic flow models of arbitrary size that describe traffic flow or the settling of dispersions and emulsions, where the latter application gives rise to zero‐flux boundary conditions. Numerical examples illustrate the behavior and accuracy of entropy stable schemes for these applications.     

Stationary measures and hydrodynamics of zero range processes with several species of particles

We study general zero range processes with different types of particles on a d-dimensional lattice with periodic boundary conditions. A necessary and sufficient condition on the jump rates for the existence of stationary product measures is established. For translation invariant jump rates we prove the hydrodynamic limit on the Euler scale using Yaus relative entropy method. The limit equation is a system of conservation laws, which is hyperbolic and has a globally convex entropy. We analyze this system in terms of entropy variables. In addition we obtain stationary density profiles for open boundaries.     

Free Entropy

Free entropy is the analogue of entropy in free probabilitytheory. The paper is a survey of free entropy, its applicationsto von Neumann algebras and its connections to random matrixtheory, as well as a discussion of open problems and of a basicvariational problem, connected to random multimatrix models.     

Entropy for semigroup actions on general topological spaces

This paper introduces both notions of topological entropy and invariance entropy for semigroup actions on general topological spaces. We use the concept of admissible family of open coverings to extending and studying the notions of Adler–Konheim–McAndrew topological entropy, Bowen topological entropy, and invariance entropy to the general theory of topological dynamics.     

Deng entropy

Dempster Shafer evidence theory has been widely used in many applications due to its advantages to handle uncertainty. However, how to measure uncertainty in evidence theory is still an open issue. The main contribution of this paper is that a new entropy, named as Deng entropy, is presented to measure the uncertainty of a basic probability assignment (BPA). Deng entropy is the generalization of Shannon entropy since the value of Deng entropy is identical to that of Shannon entropy when the BPA defines a probability measure. Numerical examples are illustrated to show the efficiency of Deng entropy.     

Combinatorial lemmas and applications to dynamics

The well-known combinatorial lemma of Karpovsky, Milman and Alon and a very recent one of Kerr and Li are extended. The obtained lemmas are applied to study the maximal pattern entropy introduced in the paper. It turns out that the maximal pattern entropy is equal to the supremum of sequence entropies over all sequences both in topological and measure-theoretical settings. Moreover, it is shown the maximal pattern entropy of any topological system is logk for some with k the maximal length of intrinsic sequence entropy tuples; and a zero-dimensional system has zero sequence entropy for any sequence if and only if the maximal pattern with respect to any open cover is of polynomial order.     

Numerical modeling of a non-linear viscous flow in order to determine how parameters in constitutive relations influence the entropy production

Some rheological materials, such as melting polymers, cosmetic creams, ketchup, toothpaste, can be modeled as non-NEWTONian fluids by using a non-linear constitutive relation. An incompressible flow of this kind of amorphous matter can be considered as a thermodynamic process, and a solution for the pressure, velocity and temperature fields describe it fully. Since such flow processes are generally irreversible, entropy is produced leading to dissipation in the system. This energy loss can be measured indirectly in a cone/plate viscometer which is used to determine viscosity of a BINGHAM fluid. While dissipation is an observable quantity we also want to be able to calculate it. Thus the goal of this work is to explain briefly how to compute a transient flow of a viscous fluid in two-dimensional channel under a sinusoidal traction and calculate the dissipated energy for non-NEWTONian fluids. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global optimization of expensive-to-evaluate functions: an empirical comparison of two sampling criteria

In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each of these evaluations usefully contributes to the localization of good candidates for the role of global minimizer, a stochastic model of the function can be built to conduct a sequential choice of evaluation points. Based on Gaussian processes and Kriging, the authors have recently introduced the informational approach to global optimization (IAGO) which provides a one-step optimal choice of evaluation points in terms of reduction of uncertainty on the location of the minimizers. To do so, the probability density of the minimizers is approximated using conditional simulations of the Gaussian process model behind Kriging. In this paper, an empirical comparison between the underlying sampling criterion called conditional minimizer entropy (CME) and the standard expected improvement sampling criterion (EI) is presented. Classical test functions are used as well as sample paths of the Gaussian model and an industrial application. They show the interest of the CME sampling criterion in terms of evaluation savings.     

Analysis on linear stability of oblique shock waves in steady supersonic flow

An attached oblique shock wave is generated when a sharp solid projectile flies supersonically in the air. We study the linear stability of oblique shock waves in steady supersonic flow under three dimensional perturbation in the incoming flow. Euler system of equations for isentropic gas model is used. The linear stability is established for shock front with supersonic downstream flow, in addition to the usual entropy condition.     

不含混沌真子系统的Li-Yorke混沌

研究了一类Li-Yorke混沌系统,该系统没有真子系统是Li-Yorke混沌的,我们称之为混沌极小系统.本文证明混沌极小系统是拓扑传递的,而且该系统每个非空开集都包含一个不可数混乱集.混沌极小系统不一定是极小的,本文构造了一个这样的反例.特别地,我们考察了线段连续自映射,指出该类系统都不是混沌极小的,线段上混沌极小子系统的存在性和该系统有正熵是等价的.     

Richardson数对后台阶流动熵产的影响

后台阶流动是研究伴随有传热现象的分离流动的常用模型．虽然Richardson数的改变会明显影响分离流动的流动和传热特性,但是迄今为止关于Richardson数对后台阶流动熵产影响的研究依然很少．基于求解熵产方程,第一次系统研究Richardson数对后台阶流动熵产的影响．对于求解熵产方程所需的速度和温度等变量,通过格子Boltzmann方法来得到．通过上述工作可以发现,后台阶流动中熵产和Bejan数的分布随Richardson数变化显著．总熵产数是Richardson数的单调减函数而平均Bejan数是Richardson数的单调增函数．     

Local entropy theory for a countable discrete amenable group action

The local properties of entropy for a countable discrete amenable group action are studied. For such an action, a local variational principle for a given finite open cover is established, from which the variational relation between the topological and measure-theoretic entropy tuples is deduced. While doing this it is shown that two kinds of measure-theoretic entropy for finite Borel covers coincide. Moreover, two special classes of such an action: systems with uniformly positive entropy and completely positive entropy are investigated.