Probabilistic Approach to Structural Change Prediction in Evolving Social Networks

We propose a predictive model of structural changes in elementary subgraphs of social network based on Mixture of Markov Chains. The model is trained and verified on a dataset from a large corporate social network analyzed in short, one day-long time windows, and reveals distinctive patterns of evolution of connections on the level of local network topology. We argue that the network investigated in such short timescales is highly dynamic and therefore immune to classic methods of link prediction and structural analysis, and show that in the case of complex networks, the dynamic subgraph mining may lead to better prediction accuracy. The experiments were carried out on the logs from the Wroclaw University of Technology mail server

On Invariance and Selectivity in Representation Learning

We discuss data representation which can be learned automatically from data, are invariant to transformations, and at the same time selective, in the sense that two points have the same representation only if they are one the transformation of the other. The mathematical results here sharpen some of the key claims of i-theory -- a recent theory of feedforward processing in sensory cortex

Deterministic Scale-Free Networks

Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are stochastic, that is they create networks in which the nodes appear to be randomly connected to each other. Here we propose a simple model that generates scale-free networks in a deterministic fashion. We solve exactly the model, showing that the tail of the degree distribution follows a power law

The role of clustering and gridlike ordering in epidemic spreading

The spreading of an epidemic is determined by the connectiviy patterns which underlie the population. While it has been noted that a virus spreads more easily on a network in which global distances are small, it remains a great challenge to find approaches that unravel the precise role of local interconnectedness. Such topological properties enter very naturally in the framework of our two-timestep description, also providing a novel approach to tract a probabilistic system. The method is elaborated for SIS-type epidemic processes, leading to a quantitative interpretation of the role of loops up to length 4 in the onset of an epidemic.Comment: Submitted to Phys. Rev. E; 15 pages, 11 figures, 5 table

Scale-free networks in complex systems

In the past few years, several studies have explored the topology of interactions in different complex systems. Areas of investigation span from biology to engineering, physics and the social sciences. Although having different microscopic dynamics, the results demonstrate that most systems under consideration tend to self-organize into structures that share common features. In particular, the networks of interaction are characterized by a power law distribution, $P(k)\sim k^{-\alpha}$, in the number of connections per node, $k$, over several orders of magnitude. Networks that fulfill this propriety of scale-invariance are referred to as ``scale-free''. In the present work we explore the implication of scale-free topologies in the antiferromagnetic (AF) Ising model and in a stochastic model of opinion formation. In the first case we show that the implicit disorder and frustration lead to a spin-glass phase transition not observed for the AF Ising model on standard lattices. We further illustrate that the opinion formation model produces a coherent, turbulent-like dynamics for a certain range of parameters. The influence, of random or targeted exclusion of nodes is studied.Comment: 9 pages, 4 figures. Proceeding to "SPIE International Symposium Microelectronics, MEMS, and Nanotechnology", 11-15 December 2005, Brisbane, Australi