Spin glasses on Bethe Lattices for large coordination number

We study spin glasses on random lattices with finite connectivity. In the infinite connectivity limit they reduce to the Sherrington Kirkpatrick model. In this paper we investigate the expansion around the high connectivity limit. Within the replica symmetry breaking scheme at two steps, we compute the free energy at the first order in the expansion in inverse powers of the average connectivity (z), both for the fixed connectivity and for the fluctuating connectivity random lattices. It is well known that the coefficient of the 1/z correction for the free energy is divergent at low temperatures if computed in the one step approximation. We find that this annoying divergence becomes much smaller if computed in the framework of the more accurate two steps breaking. Comparing the temperature dependance of the coefficients of this divergence in the replica symmetric, one step and two steps replica symmetry breaking, we conclude that this divergence is an artefact due to the use of a finite number of steps of replica symmetry breaking. The 1/z expansion is well defined also in the zero temperature limit.Comment: 17 pages and 6 figure

Dynamical correlations in the escape strategy of Influenza A virus

The evolutionary dynamics of human Influenza A virus presents a challenging theoretical problem. An extremely high mutation rate allows the virus to escape, at each epidemic season, the host immune protection elicited by previous infections. At the same time, at each given epidemic season a single quasi-species, that is a set of closely related strains, is observed. A non-trivial relation between the genetic (i.e., at the sequence level) and the antigenic (i.e., related to the host immune response) distances can shed light into this puzzle. In this paper we introduce a model in which, in accordance with experimental observations, a simple interaction rule based on spatial correlations among point mutations dynamically defines an immunity space in the space of sequences. We investigate the static and dynamic structure of this space and we discuss how it affects the dynamics of the virus-host interaction. Interestingly we observe a staggered time structure in the virus evolution as in the real Influenza evolutionary dynamics.Comment: 14 pages, 5 figures; main paper for the supplementary info in arXiv:1303.595

Maximum entropy models capture melodic styles

We introduce a Maximum Entropy model able to capture the statistics of melodies in music. The model can be used to generate new melodies that emulate the style of the musical corpus which was used to train it. Instead of using the $n-$body interactions of $(n-1)-$order Markov models, traditionally used in automatic music generation, we use a $k-$nearest neighbour model with pairwise interactions only. In that way, we keep the number of parameters low and avoid over-fitting problems typical of Markov models. We show that long-range musical phrases don't need to be explicitly enforced using high-order Markov interactions, but can instead emerge from multiple, competing, pairwise interactions. We validate our Maximum Entropy model by contrasting how much the generated sequences capture the style of the original corpus without plagiarizing it. To this end we use a data-compression approach to discriminate the levels of borrowing and innovation featured by the artificial sequences. The results show that our modelling scheme outperforms both fixed-order and variable-order Markov models. This shows that, despite being based only on pairwise interactions, this Maximum Entropy scheme opens the possibility to generate musically sensible alterations of the original phrases, providing a way to generate innovation

Opinion dynamics with disagreement and modulated information

Opinion dynamics concerns social processes through which populations or groups of individuals agree or disagree on specific issues. As such, modelling opinion dynamics represents an important research area that has been progressively acquiring relevance in many different domains. Existing approaches have mostly represented opinions through discrete binary or continuous variables by exploring a whole panoply of cases: e.g. independence, noise, external effects, multiple issues. In most of these cases the crucial ingredient is an attractive dynamics through which similar or similar enough agents get closer. Only rarely the possibility of explicit disagreement has been taken into account (i.e., the possibility for a repulsive interaction among individuals' opinions), and mostly for discrete or 1-dimensional opinions, through the introduction of additional model parameters. Here we introduce a new model of opinion formation, which focuses on the interplay between the possibility of explicit disagreement, modulated in a self-consistent way by the existing opinions' overlaps between the interacting individuals, and the effect of external information on the system. Opinions are modelled as a vector of continuous variables related to multiple possible choices for an issue. Information can be modulated to account for promoting multiple possible choices. Numerical results show that extreme information results in segregation and has a limited effect on the population, while milder messages have better success and a cohesion effect. Additionally, the initial condition plays an important role, with the population forming one or multiple clusters based on the initial average similarity between individuals, with a transition point depending on the number of opinion choices

A fast no-rejection algorithm for the Category Game

The Category Game is a multi-agent model that accounts for the emergence of shared categorization patterns in a population of interacting individuals. In the framework of the model, linguistic categories appear as long lived consensus states that are constantly reshaped and re-negotiated by the communicating individuals. It is therefore crucial to investigate the long time behavior to gain a clear understanding of the dynamics. However, it turns out that the evolution of the emerging category system is so slow, already for small populations, that such an analysis has remained so far impossible. Here, we introduce a fast no-rejection algorithm for the Category Game that disentangles the physical simulation time from the CPU time, thus opening the way for thorough analysis of the model. We verify that the new algorithm is equivalent to the old one in terms of the emerging phenomenology and we quantify the CPU performances of the two algorithms, pointing out the neat advantages offered by the no-rejection one. This technical advance has already opened the way to new investigations of the model, thus helping to shed light on the fundamental issue of categorization.Comment: 17 pages, 7 figure

Modeling the emergence of contact languages

Contact languages are born out of the non-trivial interaction of two (or more) parent languages. Nowadays, the enhanced possibility of mobility and communication allows for a strong mixing of languages and cultures, thus raising the issue of whether there are any pure languages or cultures that are unaffected by contact with others. As with bacteria or viruses in biological evolution, the evolution of languages is marked by horizontal transmission; but to date no reliable quantitative tools to investigate these phenomena have been available. An interesting and well documented example of contact language is the emergence of creole languages, which originated in the contacts of European colonists and slaves during the 17th and 18th centuries in exogenous plantation colonies of especially the Atlantic and Indian Ocean. Here, we focus on the emergence of creole languages to demonstrate a dynamical process that mimics the process of creole formation in American and Caribbean plantation ecologies. Inspired by the Naming Game (NG), our modeling scheme incorporates demographic information about the colonial population in the framework of a non-trivial interaction network including three populations: Europeans, Mulattos/Creoles, and Bozal slaves. We show how this sole information makes it possible to discriminate territories that produced modern creoles from those that did not, with a surprising accuracy. The generality of our approach provides valuable insights for further studies on the emergence of languages in contact ecologies as well as to test specific hypotheses about the peopling and the population structures of the relevant territories. We submit that these tools could be relevant to addressing problems related to contact phenomena in many cultural domains: e.g., emergence of dialects, language competition and hybridization, globalization phenomena

Innovation processes for inference

In this letter, we introduce a new approach to quantify the closeness of symbolic sequences and test it in the framework of the authorship attribution problem. The method, based on a recently discovered urn representation of the Pitman-Yor process, is highly accurate compared to other state-of-the-art methods, featuring a substantial gain in computational efficiency and theoretical transparency. Our work establishes a clear connection between urn models critical in interpreting innovation processes and nonparametric Bayesian inference. It opens the way to design more efficient inference methods in the presence of complex correlation patterns and non-stationary dynamics