Quality assessment and community detection methods for anonymized mobility data in the Italian Covid context.

We discuss how to assess the reliability of partial, anonymized mobility data and compare two different methods to identify spatial communities based on movements: Greedy Modularity Clustering (GMC) and the novel Critical Variable Selection (CVS). These capture different aspects of mobility: direct population fluxes (GMC) and the probability for individuals to move between two nodes (CVS). As a test case, we consider movements of Italians before and during the SARS-Cov2 pandemic, using Facebook users' data and publicly available information from the Italian National Institute of Statistics (Istat) to construct daily mobility networks at the interprovincial level. Using the Perron-Frobenius (PF) theorem, we show how the mean stochastic network has a stationary population density state comparable with data from Istat, and how this ceases to be the case if even a moderate amount of pruning is applied to the network. We then identify the first two national lockdowns through temporal clustering of the mobility networks, define two representative graphs for the lockdown and non-lockdown conditions and perform optimal spatial community identification on both graphs using the GMC and CVS approaches. Despite the fundamental differences in the methods, the variation of information (VI) between them assesses that they return similar partitions of the Italian provincial networks in both situations. The information provided can be used to inform policy, for example, to define an optimal scale for lockdown measures. Our approach is general and can be applied to other countries or geographical scales.

The folding space of proteinß2-microglobulin is modulated by a single disulfide bridge.

Protein beta-2-microglobulin (ß2m) is classically considered the causative agent of dialysis related amyloidosis, a conformational disorder that affects patients undergoing long-term hemodialysis. The wild type (WT) form, the ΔN6 structural variant, and the D76N mutant have been extensively used as model systems ofß2m aggregation. In all of them, the native structure is stabilized by a disulfide bridge between the sulphur atoms of the cysteine residues 25 (at B strand) and 80 (at F strand), which has been considered fundamental inß2m fibrillogenesis. Here, we use extensive discrete molecular dynamics simulations of a full atomistic structure-based model to explore the role of this disulfide bridge as a modulator of the folding space ofß2m. In particular, by considering different models for the disulfide bridge, we explore the thermodynamics of the folding transition, and the formation of intermediate states that may have the potential to trigger the aggregation cascade. Our results show that the dissulfide bridge affects folding transition and folding thermodynamics of the considered model systems, although to different extents. In particular, when the interaction between the sulphur atoms is stabilized relative to the other intramolecular interactions, or even locked (i.e. permanently established), the WT form populates an intermediate state featuring a well preserved core and two unstructured termini, which was previously detected only for the D76N mutant. The formation of this intermediate state may have important implications in our understanding ofß2m fibrillogenesis.

Large deviations of random walks on random graphs.

We study the rare fluctuations or large deviations of time-integrated functionals or observables of an unbiased random walk evolving on Erdös-Rényi random graphs, and construct a modified, biased random walk that explains how these fluctuations arise in the long-time limit. Two observables are considered: the sum of the degrees visited by the random walk and the sum of their logarithm, related to the trajectory entropy. The modified random walk is used for both quantities to explain how sudden changes in degree fluctuations, similar to dynamical phase transitions, are related to localization transitions. For the second quantity, we also establish links between the large deviations of the trajectory entropy and the maximum entropy random walk.

Attractor nonequilibrium stationary states in perturbed long-range interacting systems.

Isolated long-range interacting particle systems appear generically to relax to nonequilibrium states ("quasistationary states" or QSSs) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness" of these states when the system is not isolated. In this paper we explore, using both analytical and numerical approaches to a paradigmatic one-dimensional model, the effect of a simple class of perturbations. We call them "internal local perturbations" in that the particle energies are perturbed at collisions in a way which depends only on the local properties. Our central finding is that the effect of the perturbations is to drive all the very different QSSs we consider towards a unique QSS. The latter is thus independent of the initial conditions of the system, but determined instead by both the long-range forces and the details of the perturbations applied. Thus in the presence of such a perturbation the long-range system evolves to a unique nonequilibrium stationary state, completely different from its state in absence of the perturbation, and it remains in this state when the perturbation is removed. We argue that this result may be generic for long-range interacting systems subject to perturbations which are dependent on the local properties (e.g., spatial density or velocity distribution) of the system itself.

Scaling quasistationary states in long-range systems with dissipation.

Hamiltonian systems with long-range interactions give rise to long-lived out-of-equilibrium macroscopic states, so-called quasistationary states. We show here that, in a suitably generalized form, this result remains valid for many such systems in the presence of dissipation. Using an appropriate mean-field kinetic description, we show that models with dissipation due to a viscous damping or due to inelastic collisions admit "scaling quasistationary states," i.e., states that are quasistationary in rescaled variables. A numerical study of one-dimensional self-gravitating systems confirms the relevance of these solutions and gives indications of their regime of validity in line with theoretical predictions. We underline that the velocity distributions never show any tendency to evolve towards a Maxwell-Boltzmann form.

Finite-N corrections to Vlasov dynamics and the range of pair interactions.

We explore the conditions on a pair interaction for the validity of the Vlasov equation to describe the dynamics of an interacting N-particle system in the large N limit. Using a coarse graining in phase space of the exact Klimontovich equation for the N-particle system, we evaluate, neglecting correlations of density fluctuations, the scalings with N of the terms describing the corrections to the Vlasov equation for the coarse-grained one-particle phase space density. Considering a generic interaction with radial pair force F(r), with F(r)∼1/r(γ) at large scales, and regulated to a bounded behavior below a "softening" scale ɛ, we find that there is an essential qualitative difference between the cases γd, i.e., depending on the the integrability at large distances of the pair force. In the former case, the corrections to the Vlasov dynamics for a given coarse-grained scale are essentially insensitive to the softening parameter ɛ, while for γ>d the amplitude of these terms is directly regulated by ɛ, and thus by the small scale properties of the interaction. This corresponds to a simple physical criterion for a basic distinction between long-range (γ≤d) and short-range (γ>d) interactions, different from the canonical one (γ≤d+1 or γ>d+1) based on thermodynamic analysis. This alternative classification, based on purely dynamical considerations, is relevant notably to understanding the conditions for the existence of so-called quasistationary states in long-range interacting systems.