Inferring Network Topology from Complex Dynamics

Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation of one collective dynamical trajectory. The general theoretical framework is applicable to arbitrary network dynamical systems described by ordinary differential equations. No interference (external driving) is required and the type of dynamics is not restricted in any way. In particular, the observed dynamics may be arbitrarily complex; stationary, invariant or transient; synchronous or asynchronous and chaotic or periodic. Presupposing a knowledge of the functional form of the dynamical units and of the coupling functions between them, we present an analytical solution to the inverse problem of finding the network topology. Robust reconstruction is achieved in any sufficiently long generic observation of the system. We extend our method to simultaneously reconstruct both the entire network topology and all parameters appearing linear in the system's equations of motion. Reconstruction of network topology and system parameters is viable even in the presence of substantial external noise.Comment: 11 pages, 4 figure

Thesaurus as a complex network

A thesaurus is one, out of many, possible representations of term (or word) connectivity. The terms of a thesaurus are seen as the nodes and their relationship as the links of a directed graph. The directionality of the links retains all the thesaurus information and allows the measurement of several quantities. This has lead to a new term classification according to the characteristics of the nodes, for example, nodes with no links in, no links out, etc. Using an electronic available thesaurus we have obtained the incoming and outgoing link distributions. While the incoming link distribution follows a stretched exponential function, the lower bound for the outgoing link distribution has the same envelope of the scientific paper citation distribution proposed by Albuquerque and Tsallis. However, a better fit is obtained by simpler function which is the solution of Ricatti's differential equation. We conjecture that this differential equation is the continuous limit of a stochastic growth model of the thesaurus network. We also propose a new manner to arrange a thesaurus using the ``inversion method''.Comment: Contribution to the Proceedings of `Trends and Perspectives in Extensive and Nonextensive Statistical Mechanics', in honour of Constantino Tsallis' 60th birthday (submitted Physica A

Complex network analysis and nonlinear dynamics

This chapter aims at reviewing complex network and nonlinear dynamical models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the field of complex networks, the present summary introduces some applications of complex networks to economics, finance, epidemic spreading of innovations, and regional trade and developments. The chapter also reviews results involving applications of complex networks to other relevant socioeconomic issue

Investigation of a Protein Complex Network

The budding yeast {\it Saccharomyces cerevisiae} is the first eukaryote whose genome has been completely sequenced. It is also the first eukaryotic cell whose proteome (the set of all proteins) and interactome (the network of all mutual interactions between proteins) has been analyzed. In this paper we study the structure of the yeast protein complex network in which weighted edges between complexes represent the number of shared proteins. It is found that the network of protein complexes is a small world network with scale free behavior for many of its distributions. However we find that there are no strong correlations between the weights and degrees of neighboring complexes. To reveal non-random features of the network we also compare it with a null model in which the complexes randomly select their proteins. Finally we propose a simple evolutionary model based on duplication and divergence of proteins.Comment: 19 pages, 9 figures, 1 table, to appear in Euro. Phys. J.