Benoît Mandelbrot (1924–2010) születésének 100. évfordulóján felidézzük néhány személyes találkozásunkhoz kötődő emlékeinket. A „fraktálok atyja” a munkásságán keresztül megismert csodás természeti objektumokhoz hasonlóan igen komplex személyiség volt. Nagy...

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...

Two independent approaches, the box counting and the sand box methods are used for the determination of the generalized dimensions (Dq) associated with the geometrical structure of growing deterministic fractals. We find that the multifractal nature of the geometry results in an unusually slow...

We study the behavior of the clustering coefficient in tagged networks. The rich variety of tags associated with the nodes in the networks we considered provide additional relevant information about the entities represented by the nodes. Such specific features can be important for practical...

Several recent studies of complex networks have suggested algorithms for locating network communities, also called modules or clusters, which are mostly defined as groups of nodes with dense internal connections. Along with the rapid development of these clustering techniques, the ability of...

We discuss biologically inspired, inherently non-equilibrium models of self-propelled particles, in which the particles interact with their neighbors by choosing at each time step the local average direction of motion. We summarize some of the results of large-scale simulations and theoretical...

Self-affine functions F(x) with multiscaling height correlations cq(x) ∼xqHq are described in terms of the standard multifractal formalism with a modified assumption for the partition. The corresponding quantities and expressions are shown to exhibit some characteristic differences from the...

In this paper we present our detailed investigations on the nature of the phase transition in the scalar noise model (SNM) of collective motion. Our results confirm the original findings of Vicsek et al. [Phys. Rev. Lett. 75 (1995) 1226] that the disorder–order transition in the SNM is a...

To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables us to establish an equivalence between the equilibrium...

Bacterial colonies have developed sophisticated modes of cooperative behavior which enable them to respond to adverse growth conditions. It has been shown that such behavior can be manifested in formation of complex colonial patterns. Certain Bacillus species exhibit collective migration,...