858 research outputs found
Self-organization and complex networks
No full textIn this chapter we discuss how the results developed within the theory of fractals and Self-Organized Criticality (SOC) can be fruitfully exploited as ingredients of adaptive network models. In order to maintain the presentation self-contained, we first review the basic ideas behind fractal theory and SOC. We then briefly review some results in the field of complex networks, and some of the models that have been proposed. Finally, we present a self-organized model recently proposed by Garlaschelli et al. (Nat. Phys. 3: 813, 2007) that couples the fitness network model defined by Caldarelli et al. (Phys. Rev. Lett. 89: 258702, 2002) with the evolution model proposed by Bak and Sneppen (Phys. Rev. Lett. 71: 4083, 1993) as a prototype of SOC. Remarkably, we show that the results obtained for the two models separately change dramatically when they are coupled together. This indicates that self-organized networks may represent an entirely novel class of complex systems, whose properties cannot be straightforwardly understood in terms of what we have learnt so far. © 2009 Springer-Verlag Berlin Heidelberg
A Network Analysis of Countries’ Export Flows: Firm Grounds for the Building Blocks of the Economy
No full textIn this paper we analyze the bipartite network of countries and products from UN data on country production. We define the country-country and product-product projected networks and introduce a novel method of filtering information based on elements’ similarity. As a result we find that country clustering reveals unexpected socio-geographic links among the most competing countries. On the same footings the products clustering can be efficiently used for a bottom-up classification of produced goods. Furthermore we mathematically reformulate the “reflections method” introduced by Hidalgo and Hausmann as a fixpoint problem; such formulation highlights some conceptual weaknesses of the approach. To overcome such an issue, we introduce an alternative methodology (based on biased Markov chains) that allows to rank countries in a conceptually consistent way. Our analysis uncovers a strong non-linear interaction between the diversification of a country and the ubiquity of its products, thus suggesting the possible need of moving towards more efficient and direct non-linear fixpoint algorithms to rank countries and products in the global market.</p
Reply to the Comment by H. Tephany and J. Nahmias on "Percolation in real wildfires" by G. Caldarelli et al.
No full textIn a previous paper we analyzed the satellite images of three big wildfires in the Mediterranean area. The main result of this analysis is that the burnt area is quite compact, with a fractalperimeter (at least up to a characteristic scale), with a fractal dimension D = 4/3.In their comment to our paper, Tephany et al. propose another mechanism for the stopping of the progress of the wildfire and the formation of such a perimeter. Following their argument the spread is stopped by a pinning mechanism due to the “reaching of a critical local value of reactants average concentration” for many possible reasons (fuel variations, metereological conditions, topography, and human intervention).We agree completely with Tephany et al. that these are the real causes of the stopping. However, once these causes are identified, one needs a universal mechanism of formation of afractal perimeter with D = 4/3.We then want to stress the fact that our model takes into account the above mechanism in an effective way justified by the universality of the percolation properties
Cellular models for river networks
No full textA cellular model introduced for the evolution of the fluvial landscape is revisited using extensive numerical and scaling analyses. The basic network shapes and their recurrence especially in the aggregation structure are then addressed. The roles of boundary and initial conditions are carefully analyzed as well as the key effect of quenched disorder embedded in random pinning of the landscape surface. It is found that the above features strongly affect the scaling behavior of key morphological quantities. In particular, we conclude that randomly pinned regions (whose structural disorder bears much physical meaning mimicking uneven landscape-forming rainfall events, geological diversity or heterogeneity in surficial properties like vegetation, soil cover or type) play a key role for the robust emergence of aggregation patterns bearing much resemblance to real river networks
Mean field theory for ordinary and hot sandpiles
No full textA mean field theory is discussed for a sandpile model, a cellular automaton prototype of systems showing self-organized criticality. The previous formulation of the mean field does not take into account the dissipation effects that take place on boundaries. This gives rise to some inconsistencies that are eliminated by carefully considering the boundaries effects, as it is shown in this paper. We present here a revised version of the MF equations. The main result is that criticality arises in the thermodynamic limit for sandpile systems, confirming numerical observations on the behavior of the order parameter.
The mean field approach is also generalized by applying it to the more general case of sandpiles in thermal equilibrium where a temperature-like parameter T is introduced. In this case we show that criticality is not destroyed at T> 0
Complex Networks: Principles, Methods and Applications by Vito Latora, Vincenzo Nicosia and Giovanni Russo
No full textInvasion percolation on a tree and queueing models
No full textWe study the properties of the Barabasi model of queuing [A.-L. Barabasi, Nature (London) 435, 207 (2005); J. G. Oliveira and A.-L. Barabasi, Nature (London) 437, 1251 (2005)] in the hypothesis that the number of tasks grows with time steadily. Our analytical approach is based on two ingredients. First we map exactly this model into an invasion percolation dynamics on a Cayley tree. Second we use the theory of biased random walks. In this way we obtain the following results: the stationary-state dynamics is a sequence of causally and geometrically connected bursts of execution activities with scale-invariant size distribution. We recover the correct waiting-time distribution P(W)(tau)similar to tau(-3/2) at the stationary state (as observed in different realistic data). Finally we describe quantitatively the dynamics out of the stationary state quantifying the power-law slow approach to stationarity both in single dynamical realization and in average. These results can be generalized to the case of a stochastic increase in the queue length in time with limited fluctuations. As a limit case we recover the situation in which the queue length fluctuates around a constant average value
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