# Immune networks: multitasking capabilities near saturation

E. Agliari, A. Annibale, A. Barra, A. Coolen, D. Tantari

*Journal of Physics A* 46, 415003 (2013)

#spinsystems#biomathematics#statisticalphysics

The immune system must simultaneously recall multiple defense strategies because many antigens can attack the host at the same time.

Pattern-diluted associative networks were introduced recently as models for the immune system, with nodes representing T-lymphocytes and stored patterns representing signalling protocols between T- and B-lymphocytes. It was shown earlier that in the regime of extreme pattern dilution, a system with NT T-lymphocytes can manage a number $N_B!=!\order(N_T^\delta)$ of B-lymphocytes simultaneously, with δ!<!1. Here we study this model in the extensive load regime NB!=!αNT, with also a high degree of pattern dilution, in agreement with immunological findings. We use graph theory and statistical mechanical analysis based on replica methods to show that in the finite-connectivity regime, where each T-lymphocyte interacts with a finite number of B-lymphocytes as NT→∞, the T-lymphocytes can coordinate effective immune responses to an extensive number of distinct antigen invasions in parallel. As α increases, the system eventually undergoes a second order transition to a phase with clonal cross-talk interference, where the system's performance degrades gracefully. Mathematically, the model is equivalent to a spin system on a finitely connected graph with many short loops, so one would expect the available analytical methods, which all assume locally tree-like graphs, to fail. Yet it turns out to be solvable. Our results are supported by numerical simulations.

#### Degree-correlations in a bursting dynamic network model

F. Vanni, P. Barucca

*Journal of Economic Interaction and Coordination*

#### Phase transition creates the geometry of the continuum from discrete space

R. Farr, T. Fink

*Physical Review E*

#### Intelligently chosen interventions have potential to outperform the diode bridge in power conditioning

F. Liu, Y. Zhang, O. Dahlsten, F. Wang

*Scientific Reports *

#### Portfolio analysis and geographical allocation of renewable sources: A stochastic approach

A. Scala, A. Facchini, U. Perna, R. Basosi

*Energy Policy*

#### Changes to Gate Closure and its impact on wholesale electricity prices: The case of the UK

A. Facchini, A. Rubino, G. Caldarelli, G. Liddo

*Energy Policy*

#### The statistical physics of real-world networks

G. Cimini, T. Squartini, F. Saracco, D. Garlaschelli, A. Gabrielli, G. Caldarelli

*Nature Reviews Physics*

#### PopRank: Ranking pages’ impact and users’ engagement on Facebook

A. Zaccaria, M. Vicario, W. Quattrociocchi, A. Scala, L. Pietronero

*PLoS ONE *

128 / 128 papers