Immune networks: multi-tasking capabilities at medium load

The adaptive immune system of vertebrates can detect, respond to, and memorize diverse pathogens from past experience. While the clonal selection of T helper (Th) cells is the simple and established mechanism to better recognize new pathogens, the question that still remains unexplored is how the Th cells can acquire better ways to bias the responses of immune cells for eliminating pathogens more efficiently by translating the recognized antigen information into regulatory si...

In this work, we first revise some extensions of the standard Hopfield model in the low storage limit, namely the correlated attractor case and the multitasking case recently introduced by the authors. The former case is based on a modification of the Hebbian prescription, which induces a coupling between consecutive patterns and this effect is tuned by a parameter $a$. In the latter case, dilution is introduced in pattern entries, in such a way that a fraction $d$ of them is...

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 consider dense, associative neural-networks trained by a teacher (i.e., with supervision) and we investigate their computational capabilities analytically, via statistical-mechanics of spin glasses, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as quality and quantity of the training dataset, network storage and noise, that is valid in the limit of large netw...

A model of the columnar functional organization of neocortical association areas is studied. The neuronal network is composed of many Hebbian autoassociators, or modules, each of which interacts with a relatively small number of the others. Every module encodes and stores a number of elementary percepts, or features. Memory items, or patterns, are peculiar combinations of features sparsely distributed over the multi-modular network. Any feature stored in any module can be inv...

We numerically study a dynamical system model of an idiotypic immune network with a small number of degrees of freedom. The model was originally introduced by Varela et.al., and describes antibodies interacting in a body in order to prepare for the invasion of external antigens. The main purpose of this paper is to investigate the direction of change in the network system when antigens invade it. We investigate three models, original model, a modified model and a modified m...

Ever since the last two decades of the past century pioneering studies in the field of statistical physics had focused their efforts on developing models of neural networks that could display memory storage and retrieval. Though many associative memory models were easy to handle and still quite effective to explain the basic memory retrieval processes in the brain, they were not satisfactory under the biological point of view. It became clear to scientists that a biologically...

It is well known that a sparsely coded network in which the activity level is extremely low has intriguing equilibrium properties. In the present work, we study the dynamical properties of a neural network designed to store sparsely coded sequential patterns rather than static ones. Applying the theory of statistical neurodynamics, we derive the dynamical equations governing the retrieval process which are described by some macroscopic order parameters such as the overlap. It...

In the last 15 years, statistical physics has been a very successful framework to model complex networks. On the theoretical side, this approach has brought novel insights into a variety of physical phenomena, such as self-organisation, scale invariance, emergence of mixed distributions and ensemble non-equivalence, that display unconventional features on heterogeneous networks. At the same time, thanks to their deep connection with information theory, statistical physics and...

In this chapter we want to provide a review of the main results obtained in the modeling of epidemic spreading in scale-free networks. In particular, we want to show the different epidemiological framework originated by the lack of any epidemic threshold and how this feature is rooted in the extreme heterogeneity of the scale-free networks' connectivity pattern.