Topology driven modeling: the IS metaphor
Résumé
In order to define a new method for analyzing
the immune system within the realm of Big Data, we bear
on the metaphor provided by an extension of Parisi’s
model, based on a mean field approach. The novelty is the
multilinearity of the couplings in the configurational variables.
This peculiarity allows us to compare the partition
function Z with a particular functor of topological field
theory—the generating function of the Betti numbers of the
state manifold of the system—which contains the same
global information of the system configurations and of the
data set representing them. The comparison between the
Betti numbers of the model and the real Betti numbers
obtained from the topological analysis of phenomenological
data, is expected to discover hidden n-ary relations
among idiotypes and anti-idiotypes. The data topological
analysis will select global features, reducible neither to a
mere subgraph nor to a metric or vector space. How the
immune system reacts, how it evolves, how it responds to
stimuli is the result of an interaction that took place among
many entities constrained in specific configurations which
are relational. Within this metaphor, the proposed method
turns out to be a global topological application of the
S[B] paradigm for modeling complex systems.