A perturbative approach to the Bak-Sneppen Model

We study the Bak-Sneppen model in the probabilistic framework of the Run Time Statistics (RTS). This model has attracted a large interest for its simplicity being a prototype for the whole class of models showing Self-Organized Criticality. The dynamics is characterized by a self-organization of almost all the species fitnesses above a non-trivial threshold value, and by a lack of spatial and temporal characteristic scales. This results in {\em avalanches} of activity power law distributed. In this letter we use the RTS approach to compute the value of $x_c$, the value of the avalanche exponent $\tau$ and the asymptotic distribution of minimal fitnesses.Comment: 4 pages, 3 figures, to be published on Physical Review Letter

Gravitational force distribution in fractal structures

We study the (newtonian) gravitational force distribution arising from a fractal set of sources. We show that, in the case of real structures in finite samples, an important role is played by morphological properties and finite size effects. For dimensions smaller than d-1 (being $d$ the space dimension) the convergence of the net gravitational force is assured by the fast decaying of the density, while for fractal dimension D>d-1 the morphological properties of the structure determine the eventual convergence of the force as a function of distance. We clarify the role played by the cut-offs of the distribution. Some cosmological implications are discussed.Comment: 9 pages, latex, 2 postscript figures, also available at http://www.phys.uniroma1.it/DOCS/PIL/pil.html Accepted for Publication in Europhysics Letters. Minor modifications adde

The systemic lupus erythematosus IRF5 risk haplotype is associated with systemic sclerosis

Systemic sclerosis (SSc) is a fibrotic autoimmune disease in which the genetic component plays an important role. One of the strongest SSc association signals outside the human leukocyte antigen (HLA) region corresponds to interferon (IFN) regulatory factor 5 (IRF5), a major regulator of the type I IFN pathway. In this study we aimed to evaluate whether three different haplotypic blocks within this locus, which have been shown to alter the protein function influencing systemic lupus erythematosus (SLE) susceptibility, are involved in SSc susceptibility and clinical phenotypes. For that purpose, we genotyped one representative single-nucleotide polymorphism (SNP) of each block (rs10488631, rs2004640, and rs4728142) in a total of 3,361 SSc patients and 4,012 unaffected controls of Caucasian origin from Spain, Germany, The Netherlands, Italy and United Kingdom. A meta-analysis of the allele frequencies was performed to analyse the overall effect of these IRF5 genetic variants on SSc. Allelic combination and dependency tests were also carried out. The three SNPs showed strong associations with the global disease (rs4728142: P = 1.34×10<sup>−8</sup>, OR = 1.22, CI 95% = 1.14–1.30; rs2004640: P = 4.60×10<sup>−7</sup>, OR = 0.84, CI 95% = 0.78–0.90; rs10488631: P = 7.53×10<sup>−20</sup>, OR = 1.63, CI 95% = 1.47–1.81). However, the association of rs2004640 with SSc was not independent of rs4728142 (conditioned P = 0.598). The haplotype containing the risk alleles (rs4728142*A-rs2004640*T-rs10488631*C: P = 9.04×10<sup>−22</sup>, OR = 1.75, CI 95% = 1.56–1.97) better explained the observed association (likelihood P-value = 1.48×10<sup>−4</sup>), suggesting an additive effect of the three haplotypic blocks. No statistical significance was observed in the comparisons amongst SSc patients with and without the main clinical characteristics. Our data clearly indicate that the SLE risk haplotype also influences SSc predisposition, and that this association is not sub-phenotype-specific

Statistical properties of fractures in damaged materials

We introduce a model for the dynamics of mud cracking in the limit of of extremely thin layers. In this model the growth of fracture proceeds by selecting the part of the material with the smallest (quenched) breaking threshold. In addition, weakening affects the area of the sample neighbour to the crack. Due to the simplicity of the model, it is possible to derive some analytical results. In particular, we find that the total time to break down the sample grows with the dimension L of the lattice as L^2 even though the percolating cluster has a non trivial fractal dimension. Furthermore, we obtain a formula for the mean weakening with time of the whole sample.Comment: 5 pages, 4 figures, to be published in Europhysics Letter

Percolation in real Wildfires

This paper focuses on the statistical properties of wild-land fires and, in particular, investigates if spread dynamics relates to simple invasion model. The fractal dimension and lacunarity of three fire scars classified from satellite imagery are analysed. Results indicate that the burned clusters behave similarly to percolation clusters on boundaries and look more dense in their core. We show that Dynamical Percolation reproduces this behaviour and can help to describe the fire evolution. By mapping fire dynamics onto the percolation models the strategies for fire control might be improved.Comment: 8 pages, 3 figures, epl sytle (epl.cls included

1-d gravity in infinite point distributions

The dynamics of infinite, asymptotically uniform, distributions of self-gravitating particles in one spatial dimension provides a simple toy model for the analogous three dimensional problem. We focus here on a limitation of such models as treated so far in the literature: the force, as it has been specified, is well defined in infinite point distributions only if there is a centre of symmetry (i.e. the definition requires explicitly the breaking of statistical translational invariance). The problem arises because naive background subtraction (due to expansion, or by "Jeans' swindle" for the static case), applied as in three dimensions, leaves an unregulated contribution to the force due to surface mass fluctuations. Following a discussion by Kiessling, we show that the problem may be resolved by defining the force in infinite point distributions as the limit of an exponentially screened pair interaction. We show that this prescription gives a well defined (finite) force acting on particles in a class of perturbed infinite lattices, which are the point processes relevant to cosmological N-body simulations. For identical particles the dynamics of the simplest toy model is equivalent to that of an infinite set of points with inverted harmonic oscillator potentials which bounce elastically when they collide. We discuss previous results in the literature, and present new results for the specific case of this simplest (static) model starting from "shuffled lattice" initial conditions. These show qualitative properties (notably its "self-similarity") of the evolution very similar to those in the analogous simulations in three dimensions, which in turn resemble those in the expanding universe.Comment: 20 pages, 8 figures, small changes (section II shortened, added discussion in section IV), matches final version to appear in PR

Theory of Self-organized Criticality for Problems with Extremal Dynamics

We introduce a general theoretical scheme for a class of phenomena characterized by an extremal dynamics and quenched disorder. The approach is based on a transformation of the quenched dynamics into a stochastic one with cognitive memory and on other concepts which permit a mathematical characterization of the self-organized nature of the avalanche type dynamics. In addition it is possible to compute the relevant critical exponents directly from the microscopic model. A specific application to Invasion Percolation is presented but the approach can be easily extended to various other problems.Comment: 11 pages Latex (revtex), 3 postscript figures included. Submitted to Europhys. Let