# Emanuela Merelli visits South Denmark University

## October 24, 2013 • meeting

Emanuela Merelli from University of Camerino visited the Topdrim partner SDU at IMADA in the period of 16th-23th Oct., 2013, where she gave a talk on October, 21 on **Topology driven modelling – the IS metaphor**.

Abstract:

In my talk I will introduce a new approach for data-driven modelling based on a model of the immune system (IS), that is a generalization of the IS à la Hopfiel-Parisi model, in which only two-body interaction are present, by many-body interactions (n-ary relations) based on a mean field approach, as is the case of many models in the literature. The novelty is the multilinearity in the configurational variables that allows us to extend the mean field from local to non-local. This peculiarity allows us to show that the partition function Z is similar to that in a topological field theory, as it contains the same global information about the system configurations. One of its functors is the generating function of the Betti numbers of the state manifold of the system. Comparison between the Betti numbers of the model and the real Betti numbers obtained from the topological analysis of phenomenological data of immune systems, is expected to discover hidden n-ary relations among idiotypes and anti-idiotypes: in fact the topological analysis allows to select global features that cannot be reduced neither to a mere subgraph nor to a metric or vector space. The n-ary relations reveal that living matter is not only complex, but relies on the evolution of those constraints, which harness the execution and the emergence of collective functions; principle underlying the S[B] modeling framework proposed in TOPDRIM project (FP7-ICT-2011-8/318121).

Also, a series of talks on Algebraic Topology are presented to Emanuela Merelli by the group members of SDU. The programme of these talks was:

- Introduction to Topology space, quotient topology, 3 hours
- surface, connected sum, gluing and slicing of polygon, 3 hours
- fundamental groups, 3 hours
- homology, 3 hours.
- Delta and singular homology, Euler Characteristics 3 hours.