In this work we present a model for a systemic approach to the immune system. In particular we develop a model to describe the idiotypic network, namely the network formed by different B-cell clones that interact via an antibody/anti-antibody mechanism. The immunoglobulines are modeled as binary strings and the (weighted) interaction is based on complementarily rule. In the nodes of the resulting network families of Ising spins are placed, whose states represents the quiescent/firing state of a linfocite. With this model the most important features of immune system such as low-dose tolerance, dynamical memory, bell shaped response and self/non-self distinction are recovered as emergent properties.

We present the project SciCafé that has the goal of networking the science cafés of all Europe and neighboring countries. A science café is a method of science popularization based on participation: "normal" people and experts discuss on the same ground, in a location where people, and not experts, feel at home. The discussion is guided by participants, and not by the speakers. In other words, it concerns more the "participation" than "communication".

We illustrate how dynamical transitions in nonlinear semiclassical models can be recognized as phase transitions in the corresponding -- inherently linear -- quantum model, where, in a Statistical Mechanics framework, the thermodynamic limit is realized by letting the particle population go to infinity at fixed size. We focus on lattice bosons described by the Bose-Hubbard (BH) model and Discrete Self-Trapping (DST) equations at the quantum and semiclassical level, respectively.
After showing that the gaussianity of the quantum ground states is broken at the phase transition, we work out the exact value of the critical exponents and provide numerical evidence confirming the relevant scaling hypothesis. Our analytical results rely on a general scheme obtained from a large-population expansion of the eigenvalue equation of the BH model. In this approach the DST equations resurface as solutions of the zeroth-order problem.

We study the emergence of several magnetic phases in dipolar bosonic gases subject to three- body loss mechanism employing numerical simulations based on the density matrix renormalization group(DMRG) algorithm. After mapping the original Hamiltonian in spin language, we find a strong parallelism between the bosonic theory and the spin-1 Heisenberg model with single ion anisotropy and long-range interactions. A rich phase diagram, including ferromagnetic, antiferromagnetic and non-local ordered phases, emerges in the one-dimensional case, and is preserved even in presence of a trapping potential.

In the presence of strong competition, individuals carrying rare (genetic or phenotypic) traits may be able to exploit new resources, survive predation or better adapt to an evolving environment. In the framework of population genetics, this advantage is summarized by the concept of "balancing (or negative frequency dependent) selection". In well-mixed infinite populations, a non-zero balancing selection is sufficient to maintain polymorphism and biodiversity. Here we show that the behavior is different when the population is embedded in low-dimensional spaces. In particular, in one dimension polymorphism needs a critical threshold of balancing selection, below which the population undergoes genetic demixing and eventually fixation.

This is joint work with L. Dall'Asta (Dipartimento di Fisica and Centre for Computational Sciences - Politecnico di Torino) and D. Beghé (Dipartimento di Biologia Evolutiva e Funzionale, Universita degli Studi di Parma)

Both inference and applied aspects of recent contributions to the bio-interactome fields will be examined, in particular with reference to the idea of identifying differential structures depending on conditions.

The cell is a structural and functional unit, the building block of any living systems. Cells are constituted by a tiny membrane, made of lipid bilayer, which encloses a finite volume and protects the genetic material stored inside. Modern cells with their complex machineries, result from evolution of ancient supposedly minimalistic cell entity, the protocell. It is customarily believed that autocatalytic reactions might have be at play in primordial protocell. The shared view is that protocell's volume might have been occupied by interacting families of replicators, organized in autocatalytic cycles. A chemical reaction is called autocatalytic if one of the reaction products is itself a catalyst for the chemical reaction. Even if only a small amount of the catalyst is present, the reaction may start off slowly, but will quickly speed up once more catalyst is produced. If the reactant is not replaced, the process will again slow down producing the typical sigmoid shape for the concentration of the product. All this is for a single chemical reaction, but of greater interest is the case of many chemical reactions, where one or more reactions produce a catalyst for some of the other reactions. Then the whole collection of constituents is called an autocatalytic set. The study of the dynamical evolution of interacting species of homologous quantities defines the field of population dynamics, which finds particularly important applications within the realm of life science. Population is indeed a technical term which is referred to various, completely distinct fields of applications. The classical deterministic approach to population dynamics relies on characterizing quantitatively the densities of species through a system of ordinary differential equations which incorporate the specific interactions being at play. As opposed to this formulation, a different (stochastic) level of modeling can be invoked which instead focuses on the individual-based description. This amounts to characterizing the microscopic dynamics via explicit rules governing the interactions among individuals and with the surrounding environment. The stochasticity is intrinsic to the systems and stems from the microscopic finiteness of the investigated medium. Remarkably, inherent demographic perturbations might induce regular behaviours at the macroscopic level, emerging as a spontaneous colletive self-organized phenomenon.In this paper, we investigate the stochastic dynamics of a complex network of autocatalytic reactions, within a spatially bounded domain, so to mimick a primordial cell back at the orgin of life [1,2]. The role of stochastic fluctuations is elucidated through the use of the van Kampen system-size expansion and shown to induce regular oscillations in time of in the concentration amount [3]. Corrections beyond the Gaussian approximation are analytically computed within the van Kampen operative ansatz. An extended Fokker-Planck equation is obtained and the moments of the multivariate non Gaussian distribution of fluctuations quantified. The theory predictions are challenged versus direct stochastic simulations and shown to return an excellent agreement. Possible implications of our findings as concerns protocells origin and evolution are addressed

We consider cooperative reactions and we study the effects of the interaction strength among the system components on the reaction rate, hence realizing a connection between microscopic and macroscopic observables. Our approach is based on statistical mechanics models and it is developed analytically via mean-field techniques. First of all, we show that, when the coupling strength is set positive, a cooperative behavior naturally emerges from the model; in particular, by means of various cooperative measures previously introduced, we highlight how the degree of cooperativity depends on the interaction strength among components. Furthermore, we introduce a criterion to discriminate between weak and strong cooperativity, based on a measure of ``susceptibility''. We also properly extend the model in order to account for multiple attachments phenomena: this is realized by incorporating within the model p-body interactions, whose non-trivial cooperative capability is investigated too.

We study the Renyi entropy of the 1-d XYZ spin-1/2 chain in the entirety of its phase diagram. The model has several quantum critical lines corresponding to rotated XXZ chains in their paramagnetic phase, and four tri-critical points where these phases join.
Two of these points are described by a conformal FT and close to them the entropy scales as the logarithm of its mass gap (BKT PT).
The other two points are not conformal and the entropy has a peculiar singular behavior in their neighbors, characteristic of an essential singularity (First order PT). Depending on the approach to these points, the entropy can take any positive value from 0 to ∞. We propose the entropy as an efficient tool to determine the nature of a PT

We show how entanglement entropies allow for the estimation of quasi-long-range order in one dimensional systems whose low-energy physics is well captured by the Tomonaga-Luttinger liquid universality class. First, we check our procedure in the exactly solvable XXZ spin-1/2 chain in its entire critical region, finding very good agreement with Bethe ansatz results. Then, we show how phase transitions between different dominant orders may be efficiently estimated by considering the superfluid-charge density wave transition in a system of one-dimensional dipolar bosons. Finally, we discuss the application of this method to multispecies systems such as the one-dimensional Hubbard model.

In several problems concerning 1D dynamics, e.g., quantum-state transmission, one is faced with the dispersive evolution of an input wavepacket, whose Fourier-space components are determined by its initial shape. The evolution occurs along a `wire' and is substantially ruled by its dispersion relation, which is usually a nonlinear function of the (quasi-) momentum when the wire is realized by discrete arrays of physical objects. It is textbook knowledge that a Gaussian packet broadens with a rate depending on the second derivative of the dispersion relation.
In order to preserve as much as possible the wavepacket shape one must avoid dispersion: it is therefore convenient to initialize the wavepacket with its components sitting aroung an inflection point of the dispersion relation, so that higher-order terms determine the dispersion.
In the literature the role of the cubic nonlinearity of is accounted for in the case of a Gaussian packet. However, there are reasons to look for an extension of this result: besides the possibility that cubic terms could also vanish (e.g., by symmetry), one could be interested in a non-Gaussian initial shape of the wavepacket. In this work such an extension is obtained in terms of rather simple formulas. These permit to obtain an optimal initial width, which shows peculiar scaling as a function of the wire length.

I propose an exactly solvable simplified statistical mechanical model for the thermodynamics of beta-amyloid aggregation, generalizing a well-studied model for protein folding. The monomer concentration is explicitly taken into account as well as a nontrivial dependence on the microscopic degrees of freedom of the single peptide chain, both in the alpha-helix folded isolated state and in the fibrillar one. The phase diagram of the model is studied and compared to the outcome of fibril formation experiments which is qualitatively reproduced.