The stability of a graph partition: A dynamics-based framework for community detection

Recent years have seen a surge of interest in the analysis of complex networks, facilitated by the availability of relational data and the increasingly powerful computational resources that can be employed for their analysis. Naturally, the study of real-world systems leads to highly complex networks and a current challenge is to extract intelligible, simplified descriptions from the network in terms of relevant subgraphs, which can provide insight into the structure and function of the overall system. Sparked by seminal work by Newman and Girvan, an interesting line of research has been devoted to investigating modular community structure in networks, revitalising the classic problem of graph partitioning. However, modular or community structure in networks has notoriously evaded rigorous definition. The most accepted notion of community is perhaps that of a group of elements which exhibit a stronger level of interaction within themselves than with the elements outside the community. This concept has resulted in a plethora of computational methods and heuristics for community detection. Nevertheless a firm theoretical understanding of most of these methods, in terms of how they operate and what they are supposed to detect, is still lacking to date. Here, we will develop a dynamical perspective towards community detection enabling us to define a measure named the stability of a graph partition. It will be shown that a number of previously ad-hoc defined heuristics for community detection can be seen as particular cases of our method providing us with a dynamic reinterpretation of those measures. Our dynamics-based approach thus serves as a unifying framework to gain a deeper understanding of different aspects and problems associated with community detection and allows us to propose new dynamically-inspired criteria for community structure.Comment: 3 figures; published as book chapte

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com

Feedback control by online learning an inverse model

A model, predictor, or error estimator is often used by a feedback controller to control a plant. Creating such a model is difficult when the plant exhibits nonlinear behavior. In this paper, a novel online learning control framework is proposed that does not require explicit knowledge about the plant. This framework uses two learning modules, one for creating an inverse model, and the other for actually controlling the plant. Except for their inputs, they are identical. The inverse model learns by the exploration performed by the not yet fully trained controller, while the actual controller is based on the currently learned model. The proposed framework allows fast online learning of an accurate controller. The controller can be applied on a broad range of tasks with different dynamic characteristics. We validate this claim by applying our control framework on several control tasks: 1) the heating tank problem (slow nonlinear dynamics); 2) flight pitch control (slow linear dynamics); and 3) the balancing problem of a double inverted pendulum (fast linear and nonlinear dynamics). The results of these experiments show that fast learning and accurate control can be achieved. Furthermore, a comparison is made with some classical control approaches, and observations concerning convergence and stability are made

A General Framework for Complex Network Applications

Complex network theory has been applied to solving practical problems from different domains. In this paper, we present a general framework for complex network applications. The keys of a successful application are a thorough understanding of the real system and a correct mapping of complex network theory to practical problems in the system. Despite of certain limitations discussed in this paper, complex network theory provides a foundation on which to develop powerful tools in analyzing and optimizing large interconnected systems.Comment: 8 page