95,870 research outputs found

    The Physics of Communicability in Complex Networks

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    A fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and applied to a wide variety of real-world networks in recent years. Several such communicability functions are reviewed in this paper. It is emphasized that communication and correlation in networks can take place through many more routes than the shortest paths, a fact that may not have been sufficiently appreciated in previously proposed correlation measures. In contrast to these, the communicability measures reviewed in this paper are defined by taking into account all possible routes between two nodes, assigning smaller weights to longer ones. This point of view naturally leads to the definition of communicability in terms of matrix functions, such as the exponential, resolvent, and hyperbolic functions, in which the matrix argument is either the adjacency matrix or the graph Laplacian associated with the network. Considerable insight on communicability can be gained by modeling a network as a system of oscillators and deriving physical interpretations, both classical and quantum-mechanical, of various communicability functions. Applications of communicability measures to the analysis of complex systems are illustrated on a variety of biological, physical and social networks. The last part of the paper is devoted to a review of the notion of locality in complex networks and to computational aspects that by exploiting sparsity can greatly reduce the computational efforts for the calculation of communicability functions for large networks.Comment: Review Article. 90 pages, 14 figures. Contents: Introduction; Communicability in Networks; Physical Analogies; Comparing Communicability Functions; Communicability and the Analysis of Networks; Communicability and Localization in Complex Networks; Computability of Communicability Functions; Conclusions and Prespective

    Network Identification for Diffusively-Coupled Systems with Minimal Time Complexity

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    The theory of network identification, namely identifying the (weighted) interaction topology among a known number of agents, has been widely developed for linear agents. However, the theory for nonlinear agents using probing inputs is less developed and relies on dynamics linearization. We use global convergence properties of the network, which can be assured using passivity theory, to present a network identification method for nonlinear agents. We do so by linearizing the steady-state equations rather than the dynamics, achieving a sub-cubic time algorithm for network identification. We also study the problem of network identification from a complexity theory standpoint, showing that the presented algorithms are optimal in terms of time complexity. We also demonstrate the presented algorithm in two case studies.Comment: 12 pages, 3 figure

    Swarm shape manipulation through connection control

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    The control of a large swarm of distributed agents is a well known challenge within the study of unmanned autonomous systems. However, it also presents many new opportunities. The advantages of operating a swarm through distributed means has been assessed in the literature for efficiency from both operational and economical aspects; practically as the number of agents increases, distributed control is favoured over centralised control, as it can reduce agent computational costs and increase robustness on the swarm. Distributed architectures, however, can present the drawback of requiring knowledge of the whole swarm state, therefore limiting the scalability of the swarm. In this paper a strategy is presented to address the challenges of distributed architectures, changing the way in which the swarm shape is controlled and providing a step towards verifiable swarm behaviour, achieving new configurations, while saving communication and computation resources. Instead of applying change at agent level (e.g. modify its guidance law), the sensing of the agents is addressed to a portion of agents, differentially driving their behaviour. This strategy is applied for swarms controlled by artificial potential functions which would ordinarily require global knowledge and all-to-all interactions. Limiting the agents' knowledge is proposed for the first time in this work as a methodology rather than obstacle to obtain desired swarm behaviour
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