6元素集合上T0拓扑总数的计算

文中证明了有限预序集与有限偏序集的一些性质,并基于有限集上的拓扑和其上预序的一一对应关系,利用这些性质通过对极小元和极大元个数进行分类讨论,以一种有别于计算机算法而又容易理解的计算方法得出6元素集合上的T₀拓扑总数为130023.     

ON THE PROJECTION OF THE EFFICIENT SET AND POTENTIAL APPLICATIONS

Abstract

We study the efficient set X _E for a multiple objective linear program by using its projection into the linear space L spanned by the independent criteria. We show that in the orthogonally complementary space of L, the efficient points form a polyhedron, while in L an efficiency-equivalent polyhedron for the projection P(X _E ) of X _E can be constructed by algorithms of outer and inner approximation types. These algorithms can be also used for generating all extreme points of P(X _E ). Application to optimization over the efficient set for a multiple objective linear program is considered.     

Stability analysis of the Pareto optimal solutions for some vector boolean optimization problem

In this article we consider the boolean optimization problem of finding the set of Pareto optimal solutions. The vector objectives are the positive cuts of linear functions to the non-negative semi-axis. Initial data are subject to perturbations, measured by the l ₁-norm in the parameter space of the problem. We present the formula expressing the extreme level (stability radius) of such perturbations, for which a particular solution remains Pareto optimal.     

Magnetic Resonance Imaging Segmentation via Weighted Level Set Model Based on Local Kernel Metric and Spatial Constraint

Magnetic resonance imaging (MRI) segmentation is a fundamental and significant task since it can guide subsequent clinic diagnosis and treatment. However, images are often corrupted by defects such as low-contrast, noise, intensity inhomogeneity, and so on. Therefore, a weighted level set model (WLSM) is proposed in this study to segment inhomogeneous intensity MRI destroyed by noise and weak boundaries. First, in order to segment the intertwined regions of brain tissue accurately, a weighted neighborhood information measure scheme based on local multi information and kernel function is designed. Then, the membership function of fuzzy c-means clustering is used as the spatial constraint of level set model to overcome the sensitivity of level set to initialization, and the evolution of level set function can be adaptively changed according to different tissue information. Finally, the distance regularization term in level set function is replaced by a double potential function to ensure the stability of the energy function in the evolution process. Both real and synthetic MRI images can show the effectiveness and performance of WLSM. In addition, compared with several state-of-the-art models, segmentation accuracy and Jaccard similarity coefficient obtained by WLSM are increased by 0.0586, 0.0362 and 0.1087, 0.0703, respectively.     

On α-Limit Sets in Lorenz Maps

The aim of this paper is to show that α-limit sets in Lorenz maps do not have to be completely invariant. This highlights unexpected dynamical behavior in these maps, showing gaps existing in the literature. Similar result is obtained for unimodal maps on [0,1]. On the basis of provided examples, we also present how the performed study on the structure of α-limit sets is closely connected with the calculation of the topological entropy.     

HL-2M 装置供电系统研制

为满足 HL-2M 装置的供电需求,须配套建设相应的供电系统。通过仿真计算 HL-2M 装置的总体供 电需求,考虑到 HL-2A 装置现有的供电系统设备,提出了兼顾 HL-2A 和 HL-2M 装置供电需求的总体配置方案。介绍了国内首台 300MVA 立式交流脉冲发电机组、磁体电源、高压电源和电源控制系统的研制情况。     

Collective Strategy Condensation: When Envy Splits Societies

Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait—the propensity to compare one’s own success with that of others—expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.     

Active Inference: Applicability to Different Types of Social Organization Explained through Reference to Industrial Engineering and Quality Management

Active inference is a physics of life process theory of perception, action and learning that is applicable to natural and artificial agents. In this paper, active inference theory is related to different types of practice in social organization. Here, the term social organization is used to clarify that this paper does not encompass organization in biological systems. Rather, the paper addresses active inference in social organization that utilizes industrial engineering, quality management, and artificial intelligence alongside human intelligence. Social organization referred to in this paper can be in private companies, public institutions, other for-profit or not-for-profit organizations, and any combination of them. The relevance of active inference theory is explained in terms of variational free energy, prediction errors, generative models, and Markov blankets. Active inference theory is most relevant to the social organization of work that is highly repetitive. By contrast, there are more challenges involved in applying active inference theory for social organization of less repetitive endeavors such as one-of-a-kind projects. These challenges need to be addressed in order for active inference to provide a unifying framework for different types of social organization employing human and artificial intelligence.     

单调类定理的一个集合论证明

本文利用集合论中的序数理论和超限归纳法,给出概率测度论中一个集族生成的最小σ代数,最小λ类和最小单调类的具体形式,并给出单调类定理一个直接的证明.     

A Characterization Theorem for the Canonical Basis of a Closure Operator

The purpose of this paper is to provide a characterization result for the canonical basis of an arbitrary closure operator. This theorem strengthens the result of Burosch, Demetrovics and Katona, who propose a characterization of the generating system of a closure operator defined by the quasi-closed sets of the closure operator.