Mark Kac Seminar

March 2, 2007

introduction talks archive contact location

The seminar takes place in Utrecht, Kromme Nieuwegracht 80, room 132.
Note: order of talks has been reversed (Thursday, March 1)

11:15-13:00 speaker: Thierry Bodineau (Paris 7) title: Phase coexistence for lattice models (2)

This is the second lecture, in a series of three.
For an abstract see the linked pdf-file.
 
14:15-16:00 speaker: Ellen Baake (Bielefeld) title: Mutation-selection models, quantum chains and branching processes


abstract: 

We consider the evolution of biological populations under the joint action of mutation and selection. The genotypes are linear arrangements of N sites, each of which may take the value +1 or -1; the evolution of an infinite population is then described by a dynamical system for a probability distribution on {-1,+1}^N.

We first show that this model is exactly equivalent to an Ising quantum chain.
In this picture, the fitness of a configuration corresponds to the interaction energy of the spins within the chain, whereas mutation corresponds to interaction of the spins with a transversal field. This equivalence is exploited to obtain exact equilibrium solutions for representative fitness landscapes, with special emphasis on phase transitions.

We then reinterpret the approach in the framework of branching processes.
This admits a plausible biological interpretation of the quantum-mechanical observables that appeared `enigmatic' in the previous approach. The key to the connection is the time-reversed Markov process and its stationary distribution (i.e., the type distribution of the individuals that are ancestral to today's population).
 

 
Mark Kac Seminar 2006-2007  

last updated: 01 Mrz 2007 by Markus