Coevolutionary dynamics of a variant of the cyclic Lotka-Volterra model with three-agent interactions

We study a variant of the cyclic Lotka-Volterra model with three-agent interactions. Inspired by a multiplayer variation of the Rock-Paper-Scissors game, the model describes an ideal ecosystem in which cyclic competition among three species develops through cooperative predation. Its rate equations in a well-mixed environment display a degenerate Hopf bifurcation, occurring as reactions involving two predators plus one prey have the same rate as reactions involving two preys plus one predator. We estimate the magnitude of the stochastic noise at the bifurcation point, where finite size effects turn neutrally stable orbits into erratically diverging trajectories. In particular, we compare analytic predictions for the extinction probability, derived in the Fokker-Planck approximation, with numerical simulations based on the Gillespie stochastic algorithm. We then extend the analysis of the phase portrait to heterogeneous rates. In a well-mixed environment, we observe a continuum of degenerate Hopf bifurcations, generalizing the above one. Neutral stability ensues from a complex equilibrium between different reactions. Remarkably, on a two-dimensional lattice, all bifurcations disappear as a consequence of the spatial locality of the interactions. In the second part of the paper, we investigate the effects of mobility in a lattice metapopulation model with patches hosting several agents. We find that strategies propagate along the arms of rotating spirals, as they usually do in models of cyclic dominance. We observe propagation instabilities in the regime of large wavelengths. We also examine three-agent interactions inducing nonlinear diffusion.Comment: 22 pages, 13 figures. v2: version accepted for publication in EPJ

Behavior of Aeromonas hydrophila in Bottled Mineral Waters

The growth and survival of Aeromonas hydrophila in three types of natural mineral waters were investigated. Mineral waters with different levels of mineral content (low, medium, and high) were experimentally contaminated with A. hydrophila, stored at different temperatures (10 degrees C and 20 degrees C), and analyzed at intervals over a 60-day period. Water samples that were not experimentally contaminated were investigated for indigenous A. hydrophila. The results confirmed that A. hydrophila may occur naturally in mineral waters and showed that the level of mineral content, temperature, length of storage, and, in some cases, the type of container used may favor the growth of A. hydrophila. The greatest proliferation was observed in water with a low mineral content stored in PET bottles at 10 degrees C, in which A. hydrophila peaked at day 28 (4.47 +/- 0.01 log CFU/100 ml). At 20 degrees C, the same load was observed at day 60. The presence of high densities of A. hydrophila in bottled mineral water can constitute a risk for some groups of consumers, such as elderly and immunocompromised persons

Numerical Reconstruction of the Covariance Matrix of a Spherically Truncated Multinormal Distribution

We relate the matrix SB of the second moments of a spherically truncated normal multivariate to its full covariance matrix Σ and present an algorithm to invert the relation and reconstruct Σ from SB. While the eigenvectors of Σ are left invariant by the truncation, its eigenvalues are nonuniformly damped. We show that the eigenvalues of Σ can be reconstructed from their truncated counterparts via a fixed point iteration, whose convergence we prove analytically. The procedure requires the computation of multidimensional Gaussian integrals over an Euclidean ball, for which we extend a numerical technique, originally proposed by Ruben in 1962, based on a series expansion in chi-square distributions. In order to study the feasibility of our approach, we examine the convergence rate of some iterative schemes on suitably chosen ensembles of Wishart matrices. We finally discuss the practical difficulties arising in sample space and outline a regularization of the problem based on perturbation theory

A perturbative approach to the reconstruction of the eigenvalue spectrum of a normal covariance matrix from a spherically truncated counterpart

In this paper we propose a perturbative method for the reconstruction of the covariance matrix of a multinormal distribution, under the assumption that the only available information amounts to the covariance matrix of a spherically truncated counterpart of the same distribution. We expand the relevant equations up to the fourth perturbative order and discuss the analytic properties of the first few perturbative terms. We finally compare the proposed approach with an exact iterative algorithm (presented in Palombi et al. (2017)) in the hypothesis that the spherically truncated covariance matrix is estimated from samples of various sizes.Comment: 39 pages, 7 figures. v2: version accepted for publication in J. Comp. Appl. Mat

Using a calibration experiment to assess gene-specific information: full Bayesian and empirical Bayesian models for two-channel microarray data.

MOTIVATION: Microarray studies permit to quantify expression levels on a global scale by measuring transcript abundance of thousands of genes simultaneously. A difficulty when analysing expression measures is how to model variability for the whole set of genes. It is usually unrealistic to assume a common variance for each gene. Several approaches to model gene-specific variances are proposed. We take advantage of calibration experiments, in which the probes hybridized on the two channels come from the same population (self-self experiment). In this case it is possible to estimate the gene-specific variance, to be incorporated in comparative experiments on the same tissue, cellular line or species. RESULTS: We present two approaches to introduce prior information on gene-specific variability from a calibration experiment: an empirical Bayes model and a full Bayesian hierarchical model. We apply the methods in the analysis of human lipopolysaccharide-stimulated leukocyte experiments. AVAILABILITY: The calculations are implemented in WinBugs. The codes are available on request from the authors

Un modello bayesiano gerarchico per l'analisi di regressione logistica con errore di misura nelle variabili esplicative: applicazione allo studio della relazione tra leucemia in eta' adulta ed esposizione domestica a radon

Dottorato di ricerca in statistica applicata. 12. ciclo. Relatore A. Biggeri. Coordinatore G. M. MarchettiConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Topological Aspects of the Multi-Language Phases of the Naming Game on Community-Based Networks

The Naming Game is an agent-based model where individuals communicate to name an initially unnamed object. On a large class of networks continual pairwise interactions lead the system to an ultimate consensus state, in which agents onverge on a globally shared name. Soon after the introduction of the model, it was observed in literature that on community-based networks the path to consensus passes through metastable multi-language states. Subsequently, it was proposed to use this feature as a mean to discover communities in a given network. In this paper we show that metastable states correspond to genuine multi-language phases, emerging in the thermodynamic limit when the fraction of links connecting communities drops below critical thresholds. In particular, we study the transition to multi-language states in the stochastic block model and on networks with community overlap. We also xamine the scaling of critical thresholds under variations of topological properties of the network, such as the number and relative size of communities and the structure of intra-/inter-community links. Our results provide a theoretical justification for the proposed use of the model as a community-detection algorithm