Nonlinear Stochastic Differential Equations and Self-Organized Criticality

Several nonlinear stochastic differential equations have been proposed in connection with self-organized critical phenomena. Due to the threshold condition involved in its dynamic evolution an infinite number of nonlinearities arises in a hydrodynamic description. We study two models with different noise correlations which make all the nonlinear contribution to be equally relevant below the upper critical dimension. The asymptotic values of the critical exponents are estimated from a systematic expansion in the number of coupling constants by means of the dynamic renormalization group.Comment: RevTeX 3.0, no figure

Dynamical properties of the Zhang model of Self-Organized Criticality

Critical exponents of the infinitely slowly driven Zhang model of self-organized criticality are computed for $d=2,3$ with particular emphasis devoted to the various roughening exponents. Besides confirming recent estimates of some exponents, new quantities are monitored and their critical exponents computed. Among other results, it is shown that the three dimensional exponents do not coincide with the Bak, Tang, and Wiesenfeld (abelian) model and that the dynamical exponent as computed from the correlation length and from the roughness of the energy profile do not necessarily coincide as it is usually implicitly assumed. An explanation for this is provided. The possibility of comparing these results with those obtained from Renormalization Group arguments is also briefly addressed.Comment: 8 pages, 12 PostScript figures, RevTe

Synchronization in dynamical networks of locally coupled self-propelled oscillators

Systems of mobile physical entities exchanging information with their neighborhood can be found in many different situations. The understanding of their emergent cooperative behaviour has become an important issue across disciplines, requiring a general conceptual framework in order to harvest the potential of these systems. We study the synchronization of coupled oscillators in time-evolving networks defined by the positions of self-propelled agents interacting in real space. In order to understand the impact of mobility in the synchronization process on general grounds, we introduce a simple model of self-propelled hard disks performing persistent random walks in 2$d$ space and carrying an internal Kuramoto phase oscillator. For non-interacting particles, self-propulsion accelerates synchronization. The competition between agent mobility and excluded volume interactions gives rise to a richer scenario, leading to an optimal self-propulsion speed. We identify two extreme dynamic regimes where synchronization can be understood from theoretical considerations. A systematic analysis of our model quantifies the departure from the latter ideal situations and characterizes the different mechanisms leading the evolution of the system. We show that the synchronization of locally coupled mobile oscillators generically proceeds through coarsening verifying dynamic scaling and sharing strong similarities with the phase ordering dynamics of the 2$d$ XY model following a quench. Our results shed light into the generic mechanisms leading the synchronization of mobile agents, providing a efficient way to understand more complex or specific situations involving time-dependent networks where synchronization, mobility and excluded volume are at play

Modeling the Internet

We model the Internet as a network of interconnected Autonomous Systems which self-organize under an absolute lack of centralized control. Our aim is to capture how the Internet evolves by reproducing the assembly that has led to its actual structure and, to this end, we propose a growing weighted network model driven by competition for resources and adaptation to maintain functionality in a demand and supply ``equilibrium''. On the demand side, we consider the environment, a pool of users which need to transfer information and ask for service. On the supply side, ASs compete to gain users, but to be able to provide service efficiently, they must adapt their bandwidth as a function of their size. Hence, the Internet is not modeled as an isolated system but the environment, in the form of a pool of users, is also a fundamental part which must be taken into account. ASs compete for users and big and small come up, so that not all ASs are identical. New connections between ASs are made or old ones are reinforced according to the adaptation needs. Thus, the evolution of the Internet can not be fully understood if just described as a technological isolated system. A socio-economic perspective must also be considered.Comment: Submitted to the Proceedings of the 3rd International Conference NEXT-SigmaPh

Synchronization of moving integrate and fire oscillators

We present a model of integrate and fire oscillators that move on a plane. The phase of the oscillators evolves linearly in time and when it reaches a threshold value they fire choosing their neighbors according to a certain interaction range. Depending on the velocity of the ballistic motion and the average number of neighbors each oscillator fires to, we identify different regimes shown in a phase diagram. We characterize these regimes by means of novel parameters as the accumulated number of contacted neighbors.Comment: 9 pages, 5 figure

Community analysis in social networks

We present an empirical study of different social networks obtained from digital repositories. Our analysis reveals the community structure and provides a useful visualising technique. We investigate the scaling properties of the community size distribution, and that find all the networks exhibit power law scaling in the community size distributions with exponent either -0.5 or -1. Finally we find that the networks' community structure is topologically self-similar using the Horton-Strahler index.Comment: Submitted to European Physics Journal

Food-bridging: a new network construction to unveil the principles of cooking

In this manuscript we propose, analyse, and discuss a possible new principle behind traditional cuisine: the Food-bridging hypothesis and its comparison with the food-pairing hypothesis using the same dataset and graphical models employed in the food-pairing study by Ahn et al. [Scientific Reports, 1:196 (2011)]. The Food-bridging hypothesis assumes that if two ingredients do not share a strong molecular or empirical affinity, they may become affine through a chain of pairwise affinities. That is, in a graphical model as employed by Ahn et al., a chain represents a path that joints the two ingredients, the shortest path represents the strongest pairwise chain of affinities between the two ingredients. Food-pairing and Food-bridging are different hypotheses that may describe possible mechanisms behind the recipes of traditional cuisines. Food-pairing intensifies flavour by mixing ingredients in a recipe with similar chemical compounds, and food-bridging smoothes contrast between ingredients. Both food-pairing and food-bridging are observed in traditional cuisines, as shown in this work. We observed four classes of cuisines according to food-pairing and food-bridging: (1) East Asian cuisines, at one extreme, tend to avoid food-pairing as well as food-bridging; and (4) Latin American cuisines, at the other extreme, follow both principles. For the two middle classes: (2) Southeastern Asian cuisines, avoid food-pairing and follow food-bridging; and (3) Western cuisines, follow food-pairing and avoid food-bridging