Yanxiang Tan  Ke Jing 《Mathematical Methods in the Applied Sciences》2016,39(11):2821-2839

In this paper, we study a class of delayed competitive neural networks with discontinuous activations. Without assuming the boundedness and local Lipschizian on the activation functions, some new criteria ensuring the existence and global exponential stability of almost periodic solutions for the neural network model considered in this work are established by constructing some suitable Lyapunov functionals and employing the theory of nonsmooth analysis. Finally, we present some applications and numerical examples with simulations to show the effectiveness of our main results. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

    

Rajan Rakkiyappan  Rathinasamy Sasirekha 《Complexity》2015,21(2):193-210

The synchronization problem for both continuous and discrete‐time complex dynamical networks with time‐varying delays is investigated. Using optimal partitioning method, time‐varying delays are partitioned into l subintervals and generalized results are derived in terms of linear matrix inequalities (LMIs). New delay‐dependent synchronization criteria in terms of LMIs are derived by constructing appropriate Lyapunov–Krasovskii functional, reciprocally convex combination technique and some inequality techniques. Numerical examples are given to illustrate the effectiveness and advantage of the proposed synchronization criteria. © 2014 Wiley Periodicals, Inc. Complexity 21: 193–210, 2015  相似文献   

    

Gennian Ge  Emre Kolotoğlu  Hengjia Wei 《组合设计杂志》2015,23(9):400-415

Grooming uniform all‐to‐all traffic in optical (SONET) rings with grooming ratio C requires the determination of a decomposition of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The determination of optimal C‐groomings has been considered for , and completely solved for . For , it has been shown that the lower bound for the drop cost of an optimal C‐grooming can be attained for almost all orders with 5 exceptions and 308 possible exceptions. For , there are infinitely many unsettled orders; especially the case is far from complete. In this paper, we show that the lower bound for the drop cost of a 6‐grooming can be attained for almost all orders by reducing the 308 possible exceptions to 3, and that the lower bound for the drop cost of a 7‐grooming can be attained for almost all orders with seven exceptions and 16 possible exceptions. Moreover, for the unsettled orders, we give upper bounds for the minimum drop costs.  相似文献   

    

Gennian Ge  Sihuang Hu  Emre Kolotoğlu  Hengjia Wei 《组合设计杂志》2015,23(6):233-273

A G‐design of order n is a decomposition of the complete graph on n vertices into edge‐disjoint subgraphs isomorphic to G. Grooming uniform all‐to‐all traffic in optical ring networks with grooming ratio C requires the determination of graph decompositions of the complete graph on n vertices into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The existence spectrum problem of G‐designs for five‐vertex graphs is a long standing problem posed by Bermond, Huang, Rosa and Sotteau in 1980, which is closely related to traffic groomings in optical networks. Although considerable progress has been made over the past 30 years, the existence problems for such G‐designs and their related traffic groomings in optical networks are far from complete. In this paper, we first give a complete solution to this spectrum problem for five‐vertex graphs by eliminating all the undetermined possible exceptions. Then, we determine almost completely the minimum drop cost of 8‐groomings for all orders n by reducing the 37 possible exceptions to 8. Finally, we show the minimum possible drop cost of 9‐groomings for all orders n is realizable with 14 exceptions and 12 possible exceptions.  相似文献   

    

《Nonlinear Analysis: Hybrid Systems》2014

In this paper, we investigate the stability and robust stability criteria for genetic regulatory networks with interval time-varying delays and Markovian jumping parameters. The genetic regulatory networks have a finite number of modes, which may jump from one mode to another according to the Markov process. By using Lyapunov–Krasovskii functional, some sufficient conditions are derived in terms of linear matrix inequalities to achieve the global asymptotic stability in the mean square of the considered genetic regulatory networks. Two numerical examples are provided to illustrate the usefulness of the obtained theoretical results.  相似文献   

    

Lokenath Debnath 《International Journal of Mathematical Education in Science & Technology》2013,44(6):769-785

This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Königsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real physical systems are included. We also mention some important and modern applications of graph theory or network problems from transportation to telecommunications. Graphs or networks are effectively used as powerful tools in industrial, electrical and civil engineering, communication networks in the planning of business and industry. Graph theory and combinatorics can be used to understand the changes that occur in many large and complex scientific, technical and medical systems. With the advent of fast large computers and the ubiquitous Internet consisting of a very large network of computers, large-scale complex optimization problems can be modelled in terms of graphs or networks and then solved by algorithms available in graph theory. Many large and more complex combinatorial problems dealing with the possible arrangements of situations of various kinds, and computing the number and properties of such arrangements can be formulated in terms of networks. The Knight's tour problem, Hamilton's tour problem, problem of magic squares, the Euler Graeco-Latin squares problem and their modern developments in the twentieth century are also included.  相似文献   

    

TROY TASSIER 《The Journal of mathematical sociology》2013,37(3):233-262

I construct a Markov model of referral hiring to look at two issues: inequality between groups and workplace segregation. The model differs from most models of referral hiring in that it explicitly considers a firm structure where employment opportunities arise. The model suggests that referral hiring does not directly produce inequality between groups at the population level, even though firms have a bias toward hiring workers from the same group they already employ. The result highlights a difference between outcomes of referral hiring at the population and individual levels in that individual firm biases balance out when aggregated. However, referral hiring does produce segregation of groups across firms in a given industry, and the degree of segregation monotonically increases in the amount of referral hiring.  相似文献   

    

DAVID R. GIBSON 《The Journal of mathematical sociology》2013,37(4):295-323

Network ties are thought to be concurrent—one can “have” many friends at once, for instance—but their concrete enactment is largely serial and episodic, guided by priorities that steer a person from one encounter to the next. Further, dyadic encounters require that two people be simultaneously available to interact, creating the need for coordinated scheduling. Here I study the consequences of scheduling for network diffusion, using a computer simulation that interposes a scheduling process between a pre-existing network and instances of contagion. The pace and extent of diffusion are shown to depend upon the interaction of network topology, contagion rule (on first-contact versus at some threshold), and whether actors try to remedy past scheduling imperfections. Scheduling turns central actors into diffusion bottlenecks, but can also trigger early adoption by giving actors false readings on the status of their network alters. The implications of scheduling extend beyond diffusion, to other outcomes such as decision-making, as well as to network evolution.  相似文献   

    

NOAH E. FRIEDKIN 《The Journal of mathematical sociology》2013,37(2):146-155

This article presents a multilevel event history model of social diffusion and applies it to Coleman, Katz, and Menzel's (1966 Coleman , J. S. , Katz , E. , &; Menzel , H. ( 1966 ). Medical Innovation: A Diffusion Study . Indianapolis , IN : Bobbs-Merrill . [Google Scholar]) data on the adoption of tetracycline by physicians. The simplest form of a multilevel model allows a random intercept. In the present application of this simple model to the Medical Innovation data, structured for an event history analysis, the physicians are nested in city and time. Random intercepts capture effects of contextual conditions that are shared by event history cases with the same city–time status. The intercepts also reflect any baseline internal contagion effects, that is, the proportion of physicians in the city–time network who have adopted the drug at time t ? 1. Here, I show that Van den Bulte and Lilien's (2001 Van den Bulte , C. &; Lilien , G. L. ( 2001 ). Medical innovation revisited: social contagion versus marketing effort . American Journal of Sociology , 106 , 1409 – 1435 .[Crossref], [Web of Science ®] , [Google Scholar]) finding of an important contextual effect of drug firms' marketing effort is misleading. I also show that the social network in which physicians are situated significantly contributes to their adoptions, controlling for baseline internal contagion effects and individual-level characteristics of physicians, which have been emphasized in investigations of these data.  相似文献   

    

MATTHEW S. BOTHNER  RICHARD HAYNES  WONJAE LEE  EDWARD BISHOP SMITH 《The Journal of mathematical sociology》2013,37(2):80-114

Two key problems in the study of longitudinal networks are determining when to chunk continuous time data into discrete time periods for network analysis and identifying periodicity in the data. In addition, statistical process control applied to longitudinal social network measures can be biased by the effects of relational dependence and periodicity in the data. Thus, the detection of change is often obscured by random noise. Fourier analysis is used to determine statistically significant periodic frequencies in longitudinal network data. Two approaches are then offered: using significant periods as a basis to chunk data for longitudinal network analysis or using the significant periods to filter the longitudinal data. E-mail communication collected at the United States Military Academy is examined.  相似文献