Phase transitions for the cavity approach to the clique problem on random graphs

We give a rigorous proof of two phase transitions for a disordered system designed to find large cliques inside Erdos random graphs. Such a system is associated with a conservative probabilistic cellular automaton inspired by the cavity method originally introduced in spin glass theory.Comment: 36 pages, 4 figure

Shaken Dynamics: An Easy Way to Parallel Markov Chain Monte Carlo

We define a class of Markovian parallel dynamics for spin systems on arbitrary graphs with nearest neighbor interaction described by a Hamiltonian function H(sigma). These dynamics turn out to be reversible and their stationary measure is explicitly determined. Convergence to equilibrium and relation of the stationary measure to the usual Gibbs measure are discussed when the dynamics is defined on Z(2). Further it is shown how these dynamics can be used to define natively parallel algorithms to face problems in the context of combinatorial optimization

Effects of boundary conditions on irreversible dynamics

We present a simple one-dimensional Ising-type spin system on which we define a completely asymmetric Markovian single spin-flip dynamics. We study the system at a very low, yet non-zero, temperature and we show that for empty boundary conditions the Gibbs measure is stationary for such dynamics, while introducing in a single site a $+$ condition the stationary measure changes drastically, with macroscopical effects. We achieve this result defining an absolutely convergent series expansion of the stationary measure around the zero temperature system. Interesting combinatorial identities are involved in the proofs

Finite morphic pp-groups

According to Li, Nicholson and Zan, a group $G$ is said to be morphic if, for every pair $N_{1}, N_{2}$ of normal subgroups, each of the conditions $G/N_{1} \cong N_{2}$ and $G/N_{2} \cong N_{1}$ implies the other. Finite, homocyclic $p$-groups are morphic, and so is the nonabelian group of order $p^{3}$ and exponent $p$, for $p$ an odd prime. It follows from results of An, Ding and Zhan on self dual groups that these are the only examples of finite, morphic $p$-groups. In this paper we obtain the same result under a weaker hypotesis.Comment: 7 pages. Critical reference added, and manuscript revised accordingl

Elements of prime order in the upper central series of a group of prime-power order

We investigate the occurrence of elements of order $p$ in the upper central series of a finite $p$-group.Comment: 6 page

The analyticity region of the hard sphere gas. Improved bounds

We find an improved estimate of the radius of analyticity of the pressure of the hard-sphere gas in $d$ dimensions. The estimates are determined by the volume of multidimensional regions that can be numerically computed. For $d=2$, for instance, our estimate is about 40% larger than the classical one.Comment: 4 pages, to appear in Journal of Statistical Physic

2011: TwoMediterranean landscape types and their interface as a case study for »landscape red-listing

Abstract Landscapes can be viewed as one of the levels in which biodiversity is hierarchically arranged; hence, it may prove important to develop lists of endangered landscape types. Among the landscape systems (sensu Keywords: flysch, hierarchical land classification, Italy, landscape boundaries, landscape protection, land-use changes, pyroclastic flow, urban sprawl. Riassunto Il paesaggio può essere considerato uno dei livelli di organizzazione della biodiversità; potrebbe pertanto essere utile sviluppare metodiche per la stesura di liste rosse di paesaggi minacciati. Il Lazio nord-occidentale comprende due sistemi di paesaggio (sensu Parole chiave: cambiamenti di uso del suolo, classificazione del paesaggio, conservazione del paesaggio, flysch, piroclastiti, urbanizzazione diffusa

Ideal gas approximation for a two-dimensional rarefied gas under Kawasaki dynamics

Article / Letter to editorMathematisch Instituu