Immune networks: multi-tasking capabilities at medium load

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