Description of the project
Complex systems with competitive and cooperative behaviour are part of everyday experience.
The recent financial crisis and economic turmoil represent an example of the difficulty in predicting and controlling global behaviour of a complex network of interacting agents.
Can Mathematics be helpful in the description of a complex system?
Hard sciences, like Physics, have been successful in describing complex physical systems which are made by a large number of interacting components via the use of simplified mathematical models.
A useful paradigm which has emerged in this description is the one of disordered systems and in particular spin-glasses, where random interactions give rise to a very rich structure, characterized by multiple equilibrium states.
Social, Economical and Biological sciences face nowadays a challenge similar to the one of physical sciences, to a higher level.
The goal of the present proposal is to apply the tools and methodology of Statistical Mechanics and Probability Theory to two problems.
The first is a problem in population genetics, i.e. to describe the random genealogies that appear in realistic models of evolutions, which incorporate recombination and selection.
Modern methods to localize disease genes increasing rely on models of the stochastic processes that have shaped present-day genomes.
The second problem is crucial in social sciences, i.e. the problem of giving a quantitative description of interactions.
We would like to study the so-called inverse problem, i.e. the estimation of interaction parameters starting from the knowledge of average values and correlations.
We argue that Mathematics is very likely going to have a pivotal beneficial mutual exchange with Social and Biological sciences, especially through the study of complex system statistical mechanics models.