Franco Bagnoli

Damage spreading and Lyapunov exponents in cellular automata

Abstract Using the concept of the Boolean derivative we study local damage spreading for one-dimensional elementary cellular automata and define their maximal Lyapunov exponent. A random matrix approximation describes quite well the behavior of “chaotic” cellular automata and predicts a directed percolation-type phase transition. After the introduction of a small amount of noise elementary cellular automata reveal the same type of transition.

Modeling HIV quasispecies evolutionary dynamics

BackgroundDuring the HIV infection several quasispecies of the virus arise, which are able to use different coreceptors, in particular the CCR5 and CXCR4 coreceptors (R5 and X4 phenotypes, respectively). The switch in coreceptor usage has been correlated with a faster progression of the disease to the AIDS phase. As several pharmaceutical companies are starting large phase III trials for R5 and X4 drugs, models are needed to predict the co-evolutionary and competitive dynamics of virus strains.ResultsWe present a model of HIV early infection which describes the dynamics of R5 quasispecies and a model of HIV late infection which describes the R5 to X4 switch. We report the following findings: after superinfection (multiple infections at different times) or coinfection (simultaneous infection by different strains), quasispecies dynamics has time scales of several months and becomes even slower at low number of CD4+ T cells. Phylogenetic inference of chemokine receptors suggests that viral mutational pathway may generate a large variety of R5 variants able to interact with chemokine receptors different from CXCR4. The decrease of CD4+ T cells, during AIDS late stage, can be described taking into account the X4-related Tumor Necrosis Factor dynamics.ConclusionThe results of this study bridge the gap between the within-patient and the inter-patients (i.e. world-wide) evolutionary processes during HIV infection and may represent a framework relevant for modeling vaccination and therapy.

EPIDEMIC SPREADING AND RISK PERCEPTION IN MULTIPLEX NETWORKS: A SELF-ORGANIZED PERCOLATION METHOD

In this paper we study the interplay between epidemic spreading and risk perception on multiplex networks. The basic idea is that the effective infection probability is affected by the perception of the risk of being infected, which we assume to be related to the fraction of infected neighbors, as introduced by Bagnoli et al. [Phys. Rev. E 76, 061904 (2007)PLEEE81539-375510.1103/PhysRevE.76.061904]. We rederive previous results using a self-organized method that automatically gives the percolation threshold in just one simulation. We then extend the model to multiplex networks considering that people get infected by physical contacts in real life but often gather information from an information network, which may be quite different from the physical ones. The similarity between the physical and the information networks determines the possibility of stopping the infection for a sufficiently high precaution level: if the networks are too different, there is no means of avoiding the epidemics.

SYNCHRONIZATION AND MAXIMUM LYAPUNOV EXPONENTS OF CELLULAR AUTOMATA

We study the synchronization of totalistic one dimensional cellular automata (CA). The CA with a non zero synchronization threshold exhibit complex non periodic space time patterns and conversely. This synchronization transition is related to directed percolation. We study also the maximum Lyapunov exponent for CA, defined in analogy with continuous dynamical systems as the exponential rate of expansion of the linear map induced by the evolution rule of CA, constructed with the aid of the Boolean derivatives. The synchronization threshold is strongly correlated to the maximum Lyapunov exponent and we propose approximate relations between these quantities. The value of this threshold can be used to parametrize the space time complexity of CA.

Kinetic phase transitions in a surface reaction model with local interactions

The steady‐state properties of the CO oxidation on a catalyst surface are investigated by Monte Carlo simulations. We extend the irreversible model of Ziff, Gulari, and Barshad [Phys. Rev. Lett. 56, 2553 (1986)] by means of adsorption probabilities depending on the instantaneous local coverages. We almost follow Kaukonen and Nieminen [J. Chem. Phys. 91, 4380 (1989)] simulation procedure. It results in a qualitative change in the original phase diagram with, especially, the vanishing of the second order phase transition of the adsorbate. We also show how the addition of the diffusion of CO in our simulations shifts the transition points obtained so far.

Speciation as Pattern Formation by Competition in a Smooth Fitness Landscape

We investigate the problem of speciation and coexistence in simple ecosystems when the competition among individuals is included in the Eigen model for quasispecies. By suggesting an analogy between the competition among strains and the diffusion of a chemical inhibitor in a reaction-diffusion system, the speciation phenomenon is considered the analogous of chemical pattern formation in genetic space. In the limit of vanishing mutation rate we obtain analytically the conditions for speciation. Using different forms of the competition interaction we show that the speciation is absent for the genetic equivalent of a normal diffusing inhibitor, and is present for shorter-range interactions.

Information dynamics algorithm for detecting communities in networks

Abstract The problem of community detection is relevant in many scientific disciplines, from social science to statistical physics. Given the impact of community detection in many areas, such as psychology and social sciences, we have addressed the issue of modifying existing well performing algorithms by incorporating elements of the domain application fields, i.e. domain-inspired. We have focused on a psychology and social network-inspired approach which may be useful for further strengthening the link between social network studies and mathematics of community detection. Here we introduce a community-detection algorithm derived from the van Dongen’s Markov Cluster algorithm (MCL) method [4] by considering networks’ nodes as agents capable to take decisions. In this framework we have introduced a memory factor to mimic a typical human behavior such as the oblivion effect . The method is based on information diffusion and it includes a non-linear processing phase. We test our method on two classical community benchmark and on computer generated networks with known community structure. Our approach has three important features: the capacity of detecting overlapping communities, the capability of identifying communities from an individual point of view and the fine tuning the community detectability with respect to prior knowledge of the data. Finally we discuss how to use a Shannon entropy measure for parameter estimation in complex networks.

Some facts of life

We study the statistics of the time evolution of the Game of Life. We recognize three different time regimes of which the most interesting one is the long time glider regime, which has properties typical of a critical state. We introduce mean field approximations able to give some insights on the time evolution of the density of the density of living cells. Extended simulations are reported which deal with the evolution of the density, damage spreading and the measurements of a finite size exponent. A simple dynamical model explains some aspects of the asymptotic glider regime. We study also the dependence of the asymptotic density on the initial density both analytically and numerically.

EIGEN'S ERROR THRESHOLD AND MUTATIONAL MELTDOWN IN A QUASISPECIES MODEL

We introduce a toy model for interacting populations connected by mutations and limited by a shared resource. We study the presence of Eigens error threshold and mutational meltdown. The phase diagram of the system shows that the extinction of the whole population due to mutational meltdown can occur well before an eventual error threshold transition.

BOOLEAN DERIVATIVES AND COMPUTATION OF CELLULAR AUTOMATA

The derivatives of a Boolean function are defined up to any order. The Taylor and MacLaurin expansions of a Boolean function are thus obtained. The last corresponds to the ring sum expansion (RSE) of a Boolean function, and is a more compact form than the usual canonical disjunctive form. For totalistic functions the RSE allows the saving of a large number of Boolean operations. The algorithm has natural applications to the simulations of cellular automata using the multi-site coding technique. Several already published algorithms are analyzed, and expressions with fewer terms are generally found.