Immune networks: multi-tasking capabilities at medium load

Abstract

Associative network models featuring multi-tasking properties have been
\nintroduced recently and studied in the low-load regime, where the number
\nP of simultaneously retrievable patterns scales with the number N of nodes as
\nP ∼ logN. In addition to their relevance in artificial intelligence, these models
\nare increasingly important in immunology, where stored patterns represent
\nstrategies to fight pathogens and nodes represent lymphocyte clones. They
\nallow us to understand the crucial ability of the immune system to respond
\nsimultaneously to multiple distinct antigen invasions. Here we develop further
\nthe statistical mechanical analysis of such systems, by studying the mediumload regime, P ∼ Nδ with δ ∈ (0, 1]. We derive three main results. First,
\nwe reveal the nontrivial architecture of these networks: they exhibit a high
\ndegree of modularity and clustering, which is linked to their retrieval abilities.
\nSecond, by solving the model we demonstrate for δ < 1 the existence of
\nlarge regions in the phase diagram where the network can retrieve all stored
\npatterns simultaneously. Finally, in the high-load regime δ = 1 we find that the
\nsystem behaves as a spin-glass, suggesting that finite-connectivity frameworks
\nare required to achieve effective retrieval.