Retrieving Infinite Numbers of Patterns in a Spin-Glass Model of Immune Networks

Many components of the IS are constructed as modular units which do not need to communicate with each other such that the number of components increases but the size remains constant. However, a sub-modular IS architecture in which lymph node number and size both increase sublinearly with body size is shown to efficiently balance the requirements of communication and migration, consistent with experimental data. We hypothesize that the IS architecture optimizes the tradeoff b...

We study the influence of network topology on retrieval properties of recurrent neural networks, using replica techniques for diluted systems. The theory is presented for a network with an arbitrary degree distribution $p(k)$ and applied to power law distributions $p(k) \sim k^{-\gamma}$, i.e. to neural networks on scale-free graphs. A bifurcation analysis identifies phase boundaries between the paramagnetic phase and either a retrieval phase or a spin glass phase. Using a po...

We introduce a bipartite, diluted and frustrated, network as a sparse restricted Boltzman machine and we show its thermodynamical equivalence to an associative working memory able to retrieve multiple patterns in parallel without falling into spurious states typical of classical neural networks. We focus on systems processing in parallel a finite (up to logarithmic growth in the volume) amount of patterns, mirroring the low-level storage of standard Amit-Gutfreund-Sompolinsky...

In this work we use belief-propagation techniques to study the equilibrium behaviour of a minimal model for the immune system comprising interacting T and B clones. We investigate the effect of the so-called idiotypic interactions among complementary B clones on the system's activation. Our result shows that B-B interactions increase the system's resilience to noise, making clonal activation more stable, while increasing the cross-talk between different clones. We derive anal...

Storing memory for molecular recognition is an efficient strategy for responding to external stimuli. Biological processes use different strategies to store memory. In the olfactory cortex, synaptic connections form when stimulated by an odor, and establish distributed memory that can be retrieved upon re-exposure. In contrast, the immune system encodes specialized memory by diverse receptors that recognize a multitude of evolving pathogens. Despite the mechanistic difference...

This is a review to appear as a contribution to the edited volume "Spin Glass Theory & Far Beyond - Replica Symmetry Breaking after 40 Years", World Scientific. It showcases a selection of contributions from the spin glass community at large to high-dimensional statistics, by focusing on three important graph-based models and methodologies having deeply impacted the field: inference of graphs (a.k.a. direct coupling analysis), inference from graphs (the community detection pr...

We study the emergence of the collective spatio-temporal macroscopic properties of the immune system, by representing individually the elementary interactions between its microscopic components (antibodies, antigens, cytokines). The results of this detailed explicit analysis are compared with the traditional procedure of averaging over individuals and representing the collective dynamics in terms of densities that obey partial differential equations (PDE). The simulations sho...

In this thesis, we review and examine the replica method from several viewpoints. The replica method is a mathematical technique to calculate general moments of stochastic variables. This method provides a systematic way to evaluate physical quantities and becomes one of the most important tools in the theory of spin glasses and in the related discipline including information processing tasks. In spite of the effectiveness of the replica method, it is known that several pro...

The repertoire of lymphocyte receptors in the adaptive immune system protects organisms from diverse pathogens. A well-adapted repertoire should be tuned to the pathogenic environment to reduce the cost of infections. We develop a general framework for predicting the optimal repertoire that minimizes the cost of infections contracted from a given distribution of pathogens. The theory predicts that the immune system will have more receptors for rare antigens than expected from...

Complex macroscopic behaviour can arise in many-body systems with only very simple elements as a consequence of the combination of competition and inhomogeneity. This paper attempts to illustrate how statistical physics has driven this recognition, has contributed new insights and methodologies of wide application influencing many fields of science, and has been stimulated in return.