Communication in networks with hierarchical branching

We present a simple model of communication in networks with hierarchical branching. We analyze the behavior of the model from the viewpoint of critical systems under different situations. For certain values of the parameters, a continuous phase transition between a sparse and a congested regime is observed and accurately described by an order parameter and the power spectra. At the critical point the behavior of the model is totally independent of the number of hierarchical levels. Also scaling properties are observed when the size of the system varies. The presence of noise in the communication is shown to break the transition. The analytical results are a useful guide to forecasting the main features of real networks.

Optimal network topologies for local search with congestion

The problem of searchability in decentralized complex networks is of great importance in computer science, economy, and sociology. We present a formalism that is able to cope simultaneously with the problem of search and the congestion effects that arise when parallel searches are performed, and we obtain expressions for the average search cost both in the presence and the absence of congestion. This formalism is used to obtain optimal network structures for a system using a local search algorithm. It is found that only two classes of networks can be optimal: starlike configurations, when the number of parallel searches is small, and homogeneous-isotropic configurations, when it is large.

Synchronization reveals topological scales in complex networks

We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular structures corresponding to well-defined communities of nodes emerge in different time scales, ordered in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology, and spectral graph analysis.

Self-organized criticality and synchronization in a coupled map lattice model of integrate-and-fire oscillators

We introduce two coupled map lattice models with nonconservative interactions and a continuous nonlinear driving. Depending on both the degree of conservation and the convexity of the driving we find different behaviors, ranging from self-organized criticality, in the sense that the distribution of events (avalanches) obeys a power law, to a macroscopic synchronization of the population of oscillators, with avalanches of the size of the system.

Synchronization in a lattice model of pulse-coupled oscillators

We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interactions that ensures, in a general context, the existence of a fully synchronized regime. This condition turns out to be the same as that obtained for the globally coupled population. When the condition is not completely satisfied we find different spatial structures. This also gives some hints about self-organized criticality.

Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators

We analyze the physical mechanisms leading either to synchronization or to the formation of spatiotemporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we study a one-dimensional ring with unidirectional coupling. In such a situation, exact results concerning the stability of the fixed of the dynamic evolution of the lattice can be obtained. Furthermore, we show that this stability is the responsible for the different behaviors.

Self-similar community structure in a network of human interactions

We propose a procedure for analyzing and characterizing complex networks. We apply this to the social network as constructed from email communications within a medium sized university with about 1700 employees. Email networks provide an accurate and nonintrusive description of the flow of information within human organizations. Our results reveal the self-organization of the network into a state where the distribution of community sizes is self-similar. This suggests that a universal mechanism, responsible for emergence of scaling in other self-organized complex systems, as, for instance, river networks, could also be the underlying driving force in the formation and evolution of social networks.

Modelling diffusion of innovations in a social network

A simple model of diffusion of innovations in a social network with upgrading costs is introduced. Agents are characterized by a single real variable, their technological level. According to local information, agents decide whether to upgrade their level or not, balancing their possible benefit with the upgrading cost. A critical point where technological avalanches display a power-law behavior is also found. This critical point is characterized by a macroscopic observable that turns out to optimize technological growth in the stationary state. Analytical results supporting our findings are found for the globally coupled case.

Self-organized evolution in a socio-economic environment

We propose a general scenario to analyze technological changes in socio-economic environments. We illustrate the ideas with a model that incorporating the main trends is simple enough to extract analytical results and, at the same time, sufficiently complex to display a rich dynamic behavior. Our study shows that there exists a macroscopic observable that is maximized in a regime where the system is critical, in the sense that the distribution of events follow power laws. Computer simulations show that, in addition, the system always self-organizes to achieve the optimal performance in the stationary state.

Impact of community structure on information transfer

The observation that real complex networks have internal structure has important implication for dynamic processes occurring on such topologies. Here we investigate the impact of community structure on a model of information transfer able to deal with both search and congestion simultaneously. We show that networks with fuzzy community structure are more efficient in terms of packet delivery than those with pronounced community structure. We also propose an alternative packet routing algorithm which takes advantage of the knowledge of communities to improve information transfer and show that in the context of the model an intermediate level of community structure is optimal. Finally, we show that in a hierarchical network setting, providing knowledge of communities at the level of highest modularity will improve network capacity by the largest amount.

Exact long-time behavior of a network of oscillators under random fields

We present an exact solution for the order parameters that characterize the stationary behavior of a population of Kuramotos phase oscillators under random external fields [Y. Kuramoto, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Vol. 39 (Springer, Berlin, 1975), p. 420]. From these results it is possible to generate the phase diagram of models with an arbitrary distribution of random frequencies and random fields.

O-chromosome lethal frequencies in Serbian and Montenegrin Drosophila subobscura populations

Lethal chromosomal frequencies were obtained from three Drosophila subobscura samples from the Mt. Avala (Serbia) population in September 2003 (0.218), June 2004 (0.204) and September 2004 (0.250). These values and those from other Balkan populations studied previously (Petnica, Kamariste, Zanjic and Djerdap) were used to analyze the possible effect of population, year, month and altitude above sea level on lethal chromosomal frequencies. According to ANOVAS no effect were observed. Furthermore, the lethal frequencies of the Balkan populations did not vary according to latitude. This is probably due to the relative proximity and high gene flow between these populations. From a joint study of all the Palearctic D. subobscura populations so far analyzed, it can be deduced that the Balkan populations are located in the central area of the species distribution. Finally, it seems that lethal chromosomal frequencies are a consequence of the genetic structure of the populations.

Coisas velhas em coisas novas: novas "velhas tecnologias"

A intenção é oferecer discussão atualizada em torno das espetaculares inovações tecnológicas, realçando tanto rompimento quanto continuidades. Assim como se defende que as tecnologias demonstram um sentido de convergência, também demonstram continuidades. Os hackers e outros defensores do software livre pregam liberdade e libertação, imaginando computador e internet como arenas da liberdade. Apenas em parte isto parece correto, também porque os mesmos hackers que se proclamam libertários se submetem a estruturas tacanhas de poder (chefes autocráticos, por exemplo). Ao mesmo tempo, a internet acaba subordinando-se ao poder dos Estados (ao contrário de sua pretensa vocação "globalizante"), porque ainda são a instância jurídica de ordenamento. A França impôs mudanças em conteúdos de sites e é notória a resistência da China e de outros regimes (mais fechados) ao fluxo desimpedido da informação. Aquela aura inicial de liberdade, consagrada na estrutura do computador de ser customizado e formatado na linha final, está sendo fortemente contestada, seja por conta de fluxos ilegais e imorais, seja pela invasão de spams e marketing, seja pela contaminação de vírus. A assim dita "internet generativa" vai cedendo, sob pressão também de usuários que querem produtos acabados, garantidos e mais fáceis de manipular,premida pelos abusos da liberdade. É notório o caso da Wikipédia: constantes guerras de edição conturbam seu ambiente (ainda que isto não impeça a produção de uma enciclopédia de grande interesse e originalidade).