Mon, 17 Oct 2005
15:45
DH 3rd floor SR

Lattice gases and the Lov

Dr Alex Scott
(Mathematical Institute, Oxford)
Abstract

Given a family of independent events in a probability space, the probability

that none of the events occurs is of course the product of the probabilities

that the individual events do not occur. If there is some dependence between the

events, however, then bounding the probability that none occurs is a much less

trivial matter. The Lov

Fri, 14 Oct 2005
16:15

Frozen Light

Lene Hau
(Harvard)
Abstract

In Clarendon Lab

Mon, 10 Oct 2005
17:00
L1

Coupled Systems: Theory and Examples

Martin Golubitsky
(University of Houston)
Abstract
A coupled cell system is a collection of interacting dynamical systems.
Coupled cell models assume that the output from each cell is important and that signals from two or more cells can be compared so that patterns of synchrony can emerge. We ask: How much of the qualitative dynamics observed in coupled cells is the product of network architecture and how much depends on the specific equations?

The ideas will be illustrated through a series of examples and theorems. One theorem classifies spatio-temporal symmetries of periodic solutions and a second gives necessary and sufficient conditions for synchrony in terms of network architecture.
Mon, 10 Oct 2005
15:45
DH 3rd floor SR

Self-interacting Random Walks

Dr Pierre Tarres
(Mathematical Institute, Oxford)
Abstract

A self-interacting random walk is a random process evolving in an environment depending on its past behaviour.

The notion of Edge-Reinforced Random Walk (ERRW) was introduced in 1986 by Coppersmith and Diaconis [2] on a discrete graph, with the probability of a move along an edge being proportional to the number of visits to this edge. In the same spirit, Pemantle introduced in 1988 [5] the Vertex-Reinforced Random Walk (VRRW), the probability of move to an adjacent vertex being then proportional to the number of visits to this vertex (and not to the edge leading to the vertex). The Self-Interacting Diffusion (SID) is a continuous counterpart to these notions.

Although introduced by similar definitions, these processes show some significantly different behaviours, leading in their understanding to various methods. While the study of ERRW essentially requires some probabilistic tools, corresponding to some local properties, the comprehension of VRRW and SID needs a joint understanding of on one hand a dynamical system governing the general evolution, and on the other hand some probabilistic phenomena, acting as perturbations, and sometimes changing the nature of this dynamical system.

The purpose of our talk is to present our recent results on the subject [1,3,4,6].

Bibliography

[1] M. Bena

Mon, 10 Oct 2005
14:15
DH 3rd floor SR

A Markov History of Partial Observations

Mr Max Skipper
(Mathematical Institute, Oxford)
Abstract

Numerous physical systems are justifiably modelled as Markov processes. However,

in practical applications the (usually implicit) assumptions concerning accurate

measurement of the system are often a fair departure from what is possible in

reality. In general, this lack of exact information is liable to render the