Fractal Growth from Local Instabilities

We study, both with numerical simulations and theoretical methods, a cellular automata model for continuum equations describing growth processes in the presence of an external flux of particles. As a result of local instabilities we find a fractal regime of growth for small external fluxes. The growing tip is selected with probability proportional to the curvature in the point. A parameter $p$ gives the probability of lateral growth on the tip. The value of $p$ determines the fractal dimension of the aggregate. Furthermore, for each value of $p$ a cross-over between two different fractal dimensions is observed. Instead, the roughness exponent $\chi$ of the aggregates does not depend on $p$ ($\chi \simeq 0.5$). Fixed scale transformation approach is applied to compute theoretically the fractal dimension for one of the branches of the structure.Comment: 7 pages, 5 figures, submitted to EP

Damaging and Cracks in Thin Mud Layers

We present a detailed study of a two-dimensional minimal lattice model for the description of mud cracking in the limit of extremely thin layers. In this model each bond of the lattice is assigned to a (quenched) breaking threshold. Fractures proceed through the selection of the part of the material with the smallest breaking threshold. A local damaging rule is also implemented, by using two different types of weakening of the neighboring sites, corresponding to different physical situations. Some analytical results are derived through a probabilistic approach known as Run Time Statistics. 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, a formula for the mean weakening in time of the whole sample is obtained.Comment: 10 pages, 7 figures (9 postscript files), RevTe

Tackling information asymmetry in networks: a new entropy-based ranking index

Information is a valuable asset for agents in socio-economic systems, a significant part of the information being entailed into the very network of connections between agents. The different interlinkages patterns that agents establish may, in fact, lead to asymmetries in the knowledge of the network structure; since this entails a different ability of quantifying relevant systemic properties (e.g. the risk of financial contagion in a network of liabilities), agents capable of providing a better estimate of (otherwise) unaccessible network properties, ultimately have a competitive advantage. In this paper, we address for the first time the issue of quantifying the information asymmetry arising from the network topology. To this aim, we define a novel index - InfoRank - intended to measure the quality of the information possessed by each node, computing the Shannon entropy of the ensemble conditioned on the node-specific information. Further, we test the performance of our novel ranking procedure in terms of the reconstruction accuracy of the (unaccessible) network structure and show that it outperforms other popular centrality measures in identifying the "most informative" nodes. Finally, we discuss the socio-economic implications of network information asymmetry.Comment: 12 pages, 8 figure

Topologically biased random walk with application for community finding in networks

We present a new approach of topology biased random walks for undirected networks. We focus on a one parameter family of biases and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of biased random walks. This analogy is extended through the use of parametric equations of motion (PEM) to study the features of random walks {\em vs.} parameter values. Furthermore, we show an analysis of the spectral gap maximum associated to the value of the second eigenvalue of the transition matrix related to the relaxation rate to the stationary state. Applications of these studies allow {\em ad hoc} algorithms for the exploration of complex networks and their communities.Comment: 8 pages, 7 figure

Cold and Warm Denaturation of Proteins

We introduce a simplified protein model where the water degrees of freedom appear explicitly (although in an extremely simplified fashion). Using this model we are able to recover both the warm and the cold protein denaturation within a single framework, while addressing important issues about the structure of model proteins

Entropy-based randomisation of rating networks

In the last years, due to the great diffusion of e-commerce, online rating platforms quickly became a common tool for purchase recommendations. However, instruments for their analysis did not evolve at the same speed. Indeed, interesting information about users' habits and tastes can be recovered just considering the bipartite network of users and products, in which links have different weights due to the score assigned to items. With respect to other weighted bipartite networks, in these systems we observe a maximum possible weight per link, that limits the variability of the outcomes. In the present article we propose an entropy-based randomisation of (bipartite) rating networks by extending the Configuration Model framework: the randomised network satisfies the constraints of the degree per rating, i.e. the number of given ratings received by the specified product or assigned by the single user. We first show that such a null model is able to reproduce several non-trivial features of the real network better than other null models. Then, using it as a benchmark, we project the information contained in the real system on one of the layers, showing, for instance, the division in communities of music albums due to the taste of customers, or, in movies due the audience.Comment: 12 pages, 30 figure