Global synchronization of general delayed complex networks with stochastic disturbances

In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous-time networks with time-varying delay. Based on the stochastic Lyapunov stability theory, It?'s differential rule and the linear matrix inequality (LMI) optimization technique, several delay-dependent synchronous criteria are established, which guarantee the asymptotical mean-square synchronization of drive networks and response networks with stochastic disturbances. The criteria are expressed in terms of LMI, which can be easily solved using the Matlab LMI Control Toolbox. Finally, two examples show the effectiveness and feasibility of the proposed synchronous conditions.     

A weight’s agglomerative method for detecting communities in weighted networks based on weight’s similarity

This paper proposes the new definition of the community structure of the weighted networks that groups of nodes in which the edge's weights distribute uniformly but at random between them. It can describe the steady connections between nodes or some similarity between nodes' functions effectively. In order to detect the community structure efficiently, a threshold coefficient κ to evaluate the equivalence of edges' weights and a new weighted modularity based on the weight's similarity are proposed. Then, constructing the weighted matrix and using the agglomerative mechanism, it presents a weight's agglomerative method based on optimizing the modularity to detect communities. For a network with n nodes, the algorithm can detect the community structure in time O(n²log₂ⁿ). Simulations on networks show that the algorithm has higher accuracy and precision than the existing techniques. Furthermore, with the change of κ the algorithm discovers a special hierarchical organization which can describe the various steady connections between nodes in groups.     

Bifurcations and chaos control in discrete small-world networks

An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed. The control method is then applied to a discrete small-world network model. Qualitative analyses and simulations show that under a generic condition, the bifurcations and the chaos can be delayed or eliminated completely. In addition, the periodic orbits embedded in the chaotic attractor can be stabilized.     

Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique

The global stability problem of Takagi-Sugeno(T-S) fuzzy Hopfield neural networks(FHNNs) with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism.Firstly,using both Finsler’s lemma and an improved homogeneous matrix polynomial technique,and applying an affine parameter-dependent Lyapunov-Krasovskii functional,we obtain the convergent LMI-based stability criteria.Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique.Secondly,to further reduce the conservatism,a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs,which is suitable to the homogeneous matrix polynomials setting.Finally,two illustrative examples are given to show the efficiency of the proposed approaches.     

Multi-user cognitive radio network resource allocation based on the adaptive niche immune genetic algorithm

Multi-user cognitive radio network resource allocation based on the adaptive niche immune genetic algorithm is proposed, and a fitness function is provided. Simulations are conducted using the adaptive niche immune genetic algorithm, the simulated annealing algorithm, the quantum genetic algorithm and the simple genetic algorithm, respectively. The results show that the adaptive niche immune genetic algorithm performs better than the other three algorithms in terms of the multi-user cognitive radio network resource allocation, and has quick convergence speed and strong global searching capability, which effectively reduces the system power consumption and bit error rate.     

划分图上的正影响数

一个社会网络中通常包括具有正面影响和负面影响的两类人员,为了研究这个社会网络中人们之间相互影响的某些规律,引入了一个新的概念. 用划分图G=(V,E),V=V⁺ \cup V^-表示这样的一个社会网络,其中V⁺和V^- 分别表示正面人员的集合和负面人员的集合. 图G的一个点子集D\subseteq V^-被称为G的一个正影响集,若G的每个点的至少一半的邻点在D\cup V⁺中. G的所有正影响集的最小基数称为G的正影响数. 给出G的正影响数的几个下界并证明了这些界是紧的. 此外,还证明了求正影响数问题在二部图和弦图上都是NP-完全的.     

Information filtering in evolving online networks

Recommender systems use the records of users' activities and profiles of both users and products to predict users' preferences in the future. Considerable works towards recommendation algorithms have been published to solve the problems such as accuracy, diversity, congestion, cold-start, novelty, coverage and so on. However, most of these research did not consider the temporal effects of the information included in the users' historical data. For example, the segmentation of the training set and test set was completely random, which was entirely different from the real scenario in recommender systems. More seriously, all the objects are treated as the same, regardless of the new, the popular or obsoleted products, so do the users. These data processing methods always lose useful information and mislead the understanding of the system's state. In this paper, we detailed analyzed the difference of the network structure between the traditional random division method and the temporal division method on two benchmark data sets, Netflix and MovieLens. Then three classical recommendation algorithms, Global Ranking method, Collaborative Filtering and Mass Diffusion method, were employed. The results show that all these algorithms became worse in all four key indicators, ranking score, precision, popularity and diversity, in the temporal scenario. Finally, we design a new recommendation algorithm based on both users' and objects' first appearance time in the system. Experimental results showed that the new algorithm can greatly improve the accuracy and other metrics.     

Mean-field approximations of fixation time distributions of evolutionary game dynamics on graphs

The mean fixation time is often not accurate for describing the timescales of fixation probabilities of evolutionary games taking place on complex networks. We simulate the game dynamics on top of complex network topologies and approximate the fixation time distributions using a mean-field approach. We assume that there are two absorbing states. Numerically, we show that the mean fixation time is sufficient in characterizing the evolutionary timescales when network structures are close to the well-mixing condition. In contrast, the mean fixation time shows large inaccuracies when networks become sparse. The approximation accuracy is determined by the network structure, and hence by the suitability of the mean-field approach. The numerical results show good agreement with the theoretical predictions.     

Generalised expressions for the association and dissociation rate constants of molecules with multiple binding sites

ABSTRACT

Many proteins exhibit multiple binding patches. A patch may harbour a key chemical modification site, but may also simply act as a trap for the binding to another site. Here we consider the scenario in which one molecule (enzyme) binds another molecule (substrate) which contains two sites. We present microscopic expressions for the rate at which the enzyme binds to a particular site on the substrate, both for the scenario in which the enzyme directly binds the site without first visiting the other site, and for the case in which it may visit the other site an arbitrary number of times before binding to the site of interest. We also present the expressions for the corresponding dissociation reactions. These expressions can be used to compute in a single rare-event simulation of the dissociation pathway not only both the intrinsic and effective dissociation rate constants but also both association rate constants.