Exact solution of the one-dimensional deterministic Fixed-Energy Sandpile

In reason of the strongly non-ergodic dynamical behavior, universality properties of deterministic Fixed-Energy Sandpiles are still an open and debated issue. We investigate the one-dimensional model, whose microscopical dynamics can be solved exactly, and provide a deeper understanding of the origin of the non-ergodicity. By means of exact arguments, we prove the occurrence of orbits of well-defined periods and their dependence on the conserved energy density. Further statistical estimates of the size of the attraction's basins of the different periodic orbits lead to a complete characterization of the activity vs. energy density phase diagram in the limit of large system's size.Comment: 4 pages, accepted for publication in Phys. Rev. Let

On a class of rational matrices and interpolating polynomials related to the discrete Laplace operator

Let \dlap be the discrete Laplace operator acting on functions(or rational matrices) $f:\mathbf{Q}_L\rightarrow\mathbb{Q}$,where $\mathbf{Q}_L$ is the two dimensional lattice of size $L$embedded in $\mathbb{Z}_2$. Consider a rational $L\times L$ matrix $\mathcal{H}$, whose inner entries $\mathcal{H}_{ij}$ satisfy \dlap\mathcal{H}_{ij}=0. The matrix $\mathcal{H}$ is thus theclassical finite difference five-points approximation of theLaplace operator in two variables. We give a constructive proofthat $\mathcal{H}$ is the restriction to $\mathbf{Q}_L$ of adiscrete harmonic polynomial in two variables for any L>2. Thisresult proves a conjecture formulated in the context ofdeterministic fixed-energy sandpile models in statisticalmechanics

Critical fluctuations in spatial complex networks

An anomalous mean-field solution is known to capture the non trivial phase diagram of the Ising model in annealed complex networks. Nevertheless the critical fluctuations in random complex networks remain mean-field. Here we show that a break-down of this scenario can be obtained when complex networks are embedded in geometrical spaces. Through the analysis of the Ising model on annealed spatial networks, we reveal in particular the spectral properties of networks responsible for critical fluctuations and we generalize the Ginsburg criterion to complex topologies.Comment: (4 pages, 2 figures

Preventing the Interaction between Coronaviruses Spike Protein and Angiotensin I Converting Enzyme 2: An In Silico Mechanistic Case Study on Emodin as a Potential Model Compound

Emodin, a widespread natural anthraquinone, has many biological activities including health-protective and adverse effects. Amongst beneficial effects, potential antiviral activity against coronavirus responsible for the severe acute respiratory syndrome outbreak in 2002–2003 has been described associated with the inhibition of the host cells target receptors recognition by the viral Spike protein. However, the inhibition mechanisms have not been fully characterized, hindering the rational use of emodin as a model compound to develop more effective analogues. This work investigates emodin interaction with the Spike protein to provide a mechanistic explanation of such inhibition. A 3D molecular modeling approach consisting of docking simulations, pharmacophoric analysis and molecular dynamics was used. The plausible mechanism is described as an interaction of emodin at the protein–protein interface which destabilizes the viral protein-target receptor complex. This analysis has been extended to the Spike protein of the coronavirus responsible for the current pandemic hypothesizing emodin’s functional conservation. This solid knowledge-based foothold provides a possible mechanistic rationale of the antiviral activity of emodin as a future basis for the potential development of efficient antiviral cognate compounds. Data gaps and future work on emodin-related adverse effects in parallel to its antiviral pharmacology are explored

Non-equilibrium mean-field theories on scale-free networks

Many non-equilibrium processes on scale-free networks present anomalous critical behavior that is not explained by standard mean-field theories. We propose a systematic method to derive stochastic equations for mean-field order parameters that implicitly account for the degree heterogeneity. The method is used to correctly predict the dynamical critical behavior of some binary spin models and reaction-diffusion processes. The validity of our non-equilibrium theory is furtherly supported by showing its relation with the generalized Landau theory of equilibrium critical phenomena on networks.Comment: 4 pages, no figures, major changes in the structure of the pape

Non-equilibrium phase transition in negotiation dynamics

We introduce a model of negotiation dynamics whose aim is that of mimicking the mechanisms leading to opinion and convention formation in a population of individuals. The negotiation process, as opposed to ``herding-like'' or ``bounded confidence'' driven processes, is based on a microscopic dynamics where memory and feedback play a central role. Our model displays a non-equilibrium phase transition from an absorbing state in which all agents reach a consensus to an active stationary state characterized either by polarization or fragmentation in clusters of agents with different opinions. We show the exystence of at least two different universality classes, one for the case with two possible opinions and one for the case with an unlimited number of opinions. The phase transition is studied analytically and numerically for various topologies of the agents' interaction network. In both cases the universality classes do not seem to depend on the specific interaction topology, the only relevant feature being the total number of different opinions ever present in the system.Comment: 4 pages, 4 figure

Topology-induced coarsening in language games

We investigate how very large populations are able to reach a global consensus, out of local “microscopic” interaction rules, in the framework of a recently introduced class of models of semiotic dynamics, the so-called naming game. We compare in particular the convergence mechanism for interacting agents embedded in a low-dimensional lattice with respect to the mean-field case. We highlight that in low dimensions consensus is reached through a coarsening process that requires less cognitive effort of the agents, with respect to the mean-field case, but takes longer to complete. In one dimension, the dynamics of the boundaries is mapped onto a truncated Markov process from which we analytically computed the diffusion coefficient. More generally we show that the convergence process requires a memory per agent scaling as N and lasts a time N1+2∕d in dimension d⩽4 (the upper critical dimension), while in mean field both memory and time scale as N3∕2, for a population of N agents. We present analytical and numerical evidence supporting this picture

Network dismantling

We study the network dismantling problem, which consists in determining a minimal set of vertices whose removal leaves the network broken into connected components of sub-extensive size. For a large class of random graphs, this problem is tightly connected to the decycling problem (the removal of vertices leaving the graph acyclic). Exploiting this connection and recent works on epidemic spreading we present precise predictions for the minimal size of a dismantling set in a large random graph with a prescribed (light-tailed) degree distribution. Building on the statistical mechanics perspective we propose a three-stage Min-Sum algorithm for efficiently dismantling networks, including heavy-tailed ones for which the dismantling and decycling problems are not equivalent. We also provide further insights into the dismantling problem concluding that it is an intrinsically collective problem and that optimal dismantling sets cannot be viewed as a collection of individually well performing nodes.Comment: Source code and data can be found at https://github.com/abraunst/decycle

Statistical Mechanics of maximal independent sets

The graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory. A maximal independent set is defined by the set of occupied nodes that satisfy some packing and covering constraints. It is known that finding minimum and maximum-density maximal independent sets are hard optimization problems. In this paper, we use cavity method of statistical physics and Monte Carlo simulations to study the corresponding constraint satisfaction problem on random graphs. We obtain the entropy of maximal independent sets within the replica symmetric and one-step replica symmetry breaking frameworks, shedding light on the metric structure of the landscape of solutions and suggesting a class of possible algorithms. This is of particular relevance for the application to the study of strategic interactions in social and economic networks, where maximal independent sets correspond to pure Nash equilibria of a graphical game of public goods allocation