Activation clustering in neural and social networks

Questions related to the evolution of the structure of networks have received recently a lot of attention in the literature. But what is the state of the network given its structure? For example, there is the question of how the structures of neural networks make them behave? Or, in the case of a network of humans, the question could be related to the states of humans in general, given the structure of the social network. The models based on stochastic processes developed in this article, do not attempt to capture the fine details of social or neural dynamics. Rather they aim to describe the general relationship between the variables describing the network and the aggregate behavior of the network. A number of nontrivial results are obtained using computer simulations. © 2005 Wiley Periodicals, Inc. Complexity 10: 42–50, 2005     

Viability in dynamic social networks

Two examples, Sampson's monks and Padgett and Ansell’ Florentines, illustrate the viability approach of dynamic networks. Notably, the relationship with centrality is studied. Historical processes involving networks are discussed.

Networks are presented as controls in controlled dynamic systems. Viability is the property for a state x that there exists a trajectory starting from x and satisfying the constraints until the time horizon. To obtain this, connection matrices must be selected at each time and each visited state among a specific set, the regulation map, which is carefully defined and built.     

Mittag-Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field

Fractional order quaternion-valued neural networks are a type of fractional order neural networks for which neuron state, synaptic connection strengths, and neuron activation functions are quaternion. This paper is dealing with the Mittag-Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field. The fractional order quaternion-valued neural networks are separated into four real-valued systems forming an equivalent four real-valued fractional order neural networks, which decreases the computational complexity by avoiding the noncommutativity of quaternion multiplication. Via some fractional inequality techniques and suitable Lyapunov functional, a brand new criterion is proposed first to ensure the Mittag-Leffler stability for the addressed neural networks. Besides, the combination of quaternion-valued adaptive and impulsive control is intended to realize the asymptotically synchronization between two fractional order quaternion-valued neural networks. Ultimately, two numerical simulations are provided to check the accuracy and validity of our obtained theoretical results.     

Stability of Hopfield-type neural networks II

The global asympatotic stability and asymptotic stability for Hopfield-type neural networks with delays are investigated. Project supported by the National Natural Science Foundation of China.     

Approximation by radial bases and neural networks

In this paper, we study approximation by radial basis functions including Gaussian, multiquadric, and thin plate spline functions, and derive order of approximation under certain conditions. Moreover, neural networks are also constructed by wavelet recovery formula and wavelet frames.     

Object oriented modeling of social networks

The aim of this paper is to explain principles of object oriented modeling in the scope of modeling dynamic social networks. As such, the approach of object oriented modeling is advocated within the field of organizational research that focuses on networks.We provide a brief introduction into the field of social networks and present an overview of existing network models and methods. Subsequently we introduce an elementary problem field in the social sciences in general, and in studies of organizational change and design in particular: the micro-macro link. We argue that the most appropriate way to hadle this problem is the principle of methodological individualism. For social network analysis, to contribute to this theoretical perspective, it should include an individual choice mechanism and become more dynamically oriented. Subsequently, object oriented modeling is advocated as a tool to meet these requirements for social network analysis. We show that characteristics of social systems that are emphasized in the methodological individualistic approach have their direct equivalences in object oriented models. The link between the micro level where actors act, and the macro level where phenomena occur as a consequence and cause of these actions, can be modelled in a straightforward way.     

The effect of gossip on social networks

In this article, we develop a simple model for the effect of gossip spread on social network structure. We define gossip as information passed between two individuals A and B about a third individual C which affects the strengths of all three relationships: it strengthens A‐B and weakens both B‐C and A‐C. We find, in both an analytic derivation and model simulations, that if gossip does not spread beyond simple triads, it destroys them but if gossip propagates through large dense clusters, it strengthens them. Additionally, our simulations show that the effect of gossip on network metrics (clustering coefficient, average‐path‐length, and sum‐of‐strengths) varies with network structure and average‐node‐degree. © 2010 Wiley Periodicals, Inc. Complexity 16: 39‐47, 2011     

Hopfield神经网络的周期解存在性及其全局吸引性

利用重合度理论和微分不等式分析等技巧，给出了Hopfield神经网络周期解存在性及其全局吸引性的判别准则。     

An improved determination approach to the structure and parameters of dynamic structure-based neural networks

Dynamic structure-based neural networks are being extensively applied in many fields of science and engineering. A novel dynamic structure-based neural network determination approach using orthogonal genetic algorithm with quantization is proposed in this paper. Both the parameter (the threshold of each neuron and the weight between neurons) and the transfer function (the transfer function of each layer and the network training function) of the dynamic structure-based neural network are optimized using this approach. In order to satisfy the dynamic transform of the neural network structure, the population adjustment operation was introduced into orthogonal genetic algorithm with quantization for dynamic modification of the population’s dimensionality. A mathematical example was applied to evaluate this approach. The experiment results suggested that this approach is feasible, correct and valid.     

The estimate for approximation error of spherical neural networks

Compared with planar hyperplane, fitting data on the sphere has been an important and an active issue in geoscience, metrology, brain imaging, and so on. In this paper, with the help of the Jackson‐type theorem of polynomial approximation on the sphere, we construct spherical feed‐forward neural networks to approximate the continuous function defined on the sphere. As a metric, the modulus of smoothness of spherical function is used to measure the error of the approximation, and a Jackson‐type theorem on the approximation is established. Copyright © 2011 John Wiley & Sons, Ltd.     

Compressing strongly connected subgroups in social networks: An entropy-based approach

To detect and study cohesive subgroups of actors is a main objective in social network analysis. What are the respective relations inside such groups and what separates them from the outside. Entropy-based analysis of network structures is an up-and-coming approach. It turns out to be a powerful instrument to detect certain forms of cohesive subgroups and to compress them to superactors without loss of information about their embeddedness in the net: Compressing strongly connected subgroups leaves the whole net’s and the (super-)actors’ information theoretical indices unchanged; i.e., such compression is information-invariant. The actual article relates on the reduction of networks with hundreds of actors. All entropy-based calculations are realized in an expert system shell.     

Passivity and passification of quaternion-valued memristive neural networks

In this paper, a class of memristive neural networks with quaternion-valued connection weights is studied. By starting from some basic quaternion-valued algorithms, the quaternion-valued memristive system is obtained; then, some passivity criteria for the memristive neural networks are presented based on some appropriate auxiliary functions. Furthermore, to tackle with the passification problem, two kinds of control protocols are designed. What should be mentioned is that, in the above derived conclusions, the partial order is employed, which can be employed to compare the “magnitude” of two different quaternions, and thus, the closed convex hull consisted by quaternion can be derived correspondingly. In the end, the analytical design are substantiated with two numerical results.     

A graph-theoretic approach to exponential stability of BAM neural networks with delays and reaction-diffusion

This paper deals with the problem of global exponential stability for bidirectional associate memory (BAM) neural networks with time-varying delays and reaction-diffusion terms. By using some inequality techniques, graph theory as well as Lyapunov stability theory, a systematic method of constructing a global Lyapunov function for BAM neural networks with time-varying delays and reaction-diffusion terms is provided. Furthermore, two different kinds of sufficient principles are derived to guarantee the exponential stability of BAM neural networks. Finally, a numerical example is carried out to demonstrate the effectiveness and applicability of the theoretical results.     

Evolution of social networks

Modeling the evolution of networks is central to our understanding of large communication systems, and more general, modern economic and social systems. The research on social and economic networks is truly interdisciplinary and the number of proposed models is huge. In this survey we discuss a small selection of modeling approaches, covering classical random graph models, and game-theoretic models to analyze the evolution of social networks. Based on these two basic modeling paradigms, we introduce co-evolutionary models of networks and play as a potential synthesis.     

New LMI-based criteria for global robust stability of delayed neural networks

Some novel, linear matrix inequality based, criteria for the uniqueness and global robust stability of the equilibrium point of Hopfield-type neural networks with delay are presented. A comparison of the present criteria with the previous criteria is made.     

Approximating smooth and sparse functions by deep neural networks: Optimal approximation rates and saturation

Constructing neural networks for function approximation is a classical and longstanding topic in approximation theory. In this paper, we aim at constructing deep neural networks with three hidden layers using a sigmoidal activation function to approximate smooth and sparse functions. Specifically, we prove that the constructed deep nets with controllable magnitude of free parameters can reach the optimal approximation rate in approximating both smooth and sparse functions. In particular, we prove that neural networks with three hidden layers can avoid the phenomenon of saturation, i.e., the phenomenon that for some neural network architectures, the approximation rate stops improving for functions of very high smoothness.     

Synchronization of memristor‐based delayed BAM neural networks with fractional‐order derivatives

This article deals with the problem of synchronization of fractional‐order memristor‐based BAM neural networks (FMBNNs) with time‐delay. We investigate the sufficient conditions for adaptive synchronization of FMBNNs with fractional‐order 0 < α < 1. The analysis is based on suitable Lyapunov functional, differential inclusions theory, and master‐slave synchronization setup. We extend the analysis to provide some useful criteria to ensure the finite‐time synchronization of FMBNNs with fractional‐order 1 < α < 2, using Mittag‐Leffler functions, Laplace transform, and linear feedback control techniques. Numerical simulations with two numerical examples are given to validate our theoretical results. Presence of time‐delay and fractional‐order in the model shows interesting dynamics. © 2016 Wiley Periodicals, Inc. Complexity 21: 412–426, 2016     

Unanimous opinions in social influence networks

In this paper, I show that persons reach unanimous opinions even when they have different initial opinions and different social influences in social influence networks. Friedkin and Johnsen introduced a model of social influence networks, and identified conditions for initially diverse opinions to converge. However, they did not examine conditions of “unanimous” convergence. Hence, I provide sufficient conditions of such unanimous consensus by focusing on three typical but conflicting social influences: the equal influence, the influence of the lowest opinion, and no influence. I show that unanimous opinions occur even when persons have antagonistic social influences such as the equal influence and the influence of the lowest opinion. I also demonstrate that the most cooperative type is the equal influence, but the most central type is the no influence.