Effect of Topology Structures on Synchronization Transition in Coupled Neuron Cells System

In this paper,by the help of evolutionary algorithm and using Hindmarsh–Rose(HR)neuron model,we investigate the efect of topology structures on synchronization transition between diferent states in coupled neuron cells system.First,we build diferent coupling structure with N cells,and found the efect of synchronized transition contact not only closely with the topology of the system,but also with whether there exist the ring structures in the system.In particular,both the size and the number of rings have greater efects on such transition behavior.Secondly,we introduce synchronization error to qualitative analyze the efect of the topology structure.Furthermore,by fitting the simulation results,we find that with the increment of the neurons number,there always exist the optimization structures which have the minimum number of connecting edges in the coupling systems.Above results show that the topology structures have a very crucial role on synchronization transition in coupled neuron system.Biological system may gradually acquire such efcient topology structures through the long-term evolution,thus the systems’information process may be optimized by this scheme.     

Model of line preserving field line motions using Euler potentials

We consider behavior of finite magnetic field lines during reconnection processes. We portray field line motions using Euler potentials representation. Here, we propose a new insight into plasma flow fields related with magnetic reconnection. In this approach reconnection is treated as a breakage of magnetic topology, which results in deviation from the line preserving flow regime. We derive constraints and the general equations for these flows. In our approach the flux preserving flows are treated as a special case of line preserving regime. We also derive a constraint on a non-ideal term in Ohm’s Law within diffusion regions, which relates plasma flow with resistivity, and which must hold for non-reconnective diffusion. We also propose a new method of detecting magnetic reconnection.     

车间作业调度的可行化判定及不可行解的纠正

生产调度过程中出现不可行解是调度研究经常遇到的问题之一.提出了对JSP调度方案进行可行化判定和纠正不可行解的可行算子,算子包括了基于有向图拓扑排序原理对车间作业调度方案进行可行判定的方法和将不可行解纠正为可行解的算法.证明了该纠正算法总能成功,并对算子的功能进行了拓展使之还可应用于不完备调度.最后讨论了可行算子的特点、时间效率和应用前景.     

Strong Statistical Convergence in Probabilistic Metric Spaces

Abstract

In this article, we introduce the concepts of strongly statistically convergent sequence and strong statistically Cauchy sequence in a probabilistic metric (PM) space endowed with the strong topology, and establish some basic facts. Next, we define the strong statistical limit points and the strong statistical cluster points of a sequence in this space and investigate the relations between these concepts.     

Cartesian closed categories of FƵ-domains

A subset system Z assigns to each partially ordered set P a certain collection Z（P） of subsets. In this paper, a new kind of subset systems called directable subset systems is introduced. For a directable subset system Z, the concepts of FZ-way-below relation and FZ-domain are introduced. The well-known Scott topology is naturally generalized to the Z-level and the resulting topology is called FZ-Scott topology, and the continuous functions with respect to this topology are characterized by preserving the suprema of directed Z-sets. Then, we mainly consider a generalization of the cartesian closedness of the categories DCPO of directed complete posets, BF of bifinite domains and FS of FS-domains to the Z-level. Corresponding to them, it is proved that, for a suitable subset system Z, the categories FZCPO of Z-complete posets, FSFZ of finitely separated FZ-domains and BFFZ of bifinite FZ-domains are all cartesian closed. Some examples of these categories are given.     

基于CA的结构拓扑优化中变量更新规则研究

针对连续体结构拓扑优化中数值不稳定问题,借鉴控制系统中反馈控制和误差放大器的原理,构建了一种无梯度约束的变量更新规则,以结构应变能密度均匀分布为优化目标,建立了基于元胞自动机的拓扑优化模型,进行了二维连续体结构的拓扑优化设计,得到材料在设计域内的最优分布。通过求解三个经典的算例,探讨了不同的误差放大系数对优化结果的影响,试验结果表明,该更新规则能够有效地抑制棋盘格和网格依赖性问题。     

解决约束违背问题的一种自适应调整方法

带约束的优化问题的目的是要找到满足等式或者不等式约束的最优点。在某些情况下,优化求解得到的"最优点"可能会使得某个或某几个约束条件超出目标约束限,或者在所有约束条件中的最大值远远小于目标约束限。针对这一类问题,本文提出一种在寻优过程的每一次迭代中自适应调整约束限的方法,通过动态调整迭代过程中迭代模型约束限的值,将约束条件中最大值的约束条件变为等式约束,使得迭代解始终在可行域范围内,且收敛后的最优解不违背任何约束条件。本文将该方法成功应用于位移约束下结构重量最小化拓扑优化模型,原来不满足约束条件的情况在使用该方法后都能使约束得到满足,解决了约束条件被违背的问题。     

基于等效静态载荷法的区间参数结构可靠性拓扑优化

研究了用等效静态载荷法,解决动态响应约束下的区间参数结构可靠性拓扑优化问题。对等效静态载荷赋予了新的含义:由等效静态载荷产生的区间静态响应与由动态载荷产生的区间动态响应,其对应的中值与离差均相等。利用泰勒展开计算出区间参数结构动态响应所有可能值组成的集合,再根据集合映射获得包含结构所有不确定信息的等效静态载荷集合,继而建立静态可靠性拓扑优化数学模型。通过集合映射和区间自然扩展,获得静态位移响应区间。基于区间非概率可靠性指标的定义,给出区间非概率可靠性约束的伴随法灵敏度分析算法。采用移动渐近线法完成此优化问题的求解。数值算例验证了模型的正确性和算法的有效性。     

基于综合故障的无线传感器网络无标度容错拓扑模型研究

针对无线传感器网络实际应用中遇到的环境损毁和能量耗尽的问题,本文首先对网络综合故障进行建模,获取满足综合故障容忍能力和网络生命期双重需求的网络节点度和节点度上限值的取值规律,并结合由无标度特征导出的两者关系,从而求得最优节点度上限值,最终引入关于节点度上限值的适应度函数,提出了容忍环境损毁和能量耗尽综合故障的无标度容错拓扑演化模型.仿真实验结果表明,该模型演化生成的无标度拓扑对环境损毁和能量耗尽具有较好的容错性,并能够有效地延长网络生命期.     

Fuzzy Perfect Mappings and Q-Compactness in Smooth Fuzzy Topological Spaces

We point out that the product of two fuzzy closed sets of smooth fuzzy topological spaces need not be fuzzy closed with respect to the the existing notion of product smooth fuzzy topology. To get this property, we introduce a new suitable product smooth fuzzy topology. We investigate whether $F_1\times F_2$ and $(F,H)$ are weakly smooth fuzzy continuity whenever $F_1$, $F_2$, $F$ and $H$ are weakly smooth fuzzy continuous. Using this new product smooth fuzzy topology, we define smooth fuzzy perfect mapping and prove that composition of two smooth fuzzy perfect mappings is smooth fuzzy perfect under some additional conditions. We also introduce two new notions of compactness called $Q$-compactness and $Q$-$\alpha$-compactness; and discuss the compactness of the image of a $Q$-compact set ($Q$-$\alpha$-compact set) under a weakly smooth fuzzy continuous function ($(\alpha ,\beta )$-weakly smooth fuzzy continuous function).