Interacting urns on a finite directed graph

Self Organization of Interacting Polya Urns

We introduce a simple model which shows non-trivial self organized critical properties. The model describes a system of interacting units, modelled by Polya urns, subject to perturbations and which occasionally break down. Three equivalent formulations stochastic, quenched and deterministic are shown to reproduce the same dynamics. Among the novel features of the model are a non-homogeneous sta...

Naming on a Directed Graph

We address how the structure of a social communication system affects language coordination. The naming game is an abstraction of lexical acquisition dynamics, in which N agents try to find an agreement on the names to give to objects. Most results on naming games are specific to certain communication network topologies. We present two important results that are general to any graph topology: t...

Synchronization and fluctuation theorems for interacting Friedman urns

Directed prime graph of non-commutative ring

Prime graph of a ring R is a graph whose vertex set is the whole set R any any two elements $x$ and $y$ of $R$ are adjacent in the graph if and only if $xRy = 0$ or $yRx = 0$.  Prime graph of a ring is denoted by $PG(R)$. Directed prime graphs for non-commutative rings and connectivity in the graph are studied in the present paper. The diameter and girth of this graph are also studied in the pa...

Interacting Particles on Finite

There is a well-established topic \interacting particle systems", treated in the books by Griieath 14], Liggett 17], and Durrett 11], which studies diierent models for particles on the innnite lattice Z d. All these models make sense, but mostly have not been systematically studied, in the context of nite graphs. Some of these models { the voter model, the antivoter model, and the exclusion pro...