Statistical physics of the Schelling model of segregation

We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics methods shed light on the rich phenomenology of this simple model, exhibiting static phase transitions typical of kinetic constrained models, nontrivial coarsening like in driven-particle systems and percolation-related phenomena.Comment: 4 pages, 3 figure

A unified framework for Schelling's model of segregation

Schelling's model of segregation is one of the first and most influential models in the field of social simulation. There are many variations of the model which have been proposed and simulated over the last forty years, though the present state of the literature on the subject is somewhat fragmented and lacking comprehensive analytical treatments. In this article a unified mathematical framework for Schelling's model and its many variants is developed. This methodology is useful in two regards: firstly, it provides a tool with which to understand the differences observed between models; secondly, phenomena which appear in several model variations may be understood in more depth through analytic studies of simpler versions.Comment: 21 pages, 3 figure

Enhancing Robustness and Immunization in geographical networks

We find that different geographical structures of networks lead to varied percolation thresholds, although these networks may have similar abstract topological structures. Thus, the strategies for enhancing robustness and immunization of a geographical network are proposed. Using the generating function formalism, we obtain the explicit form of the percolation threshold $q_{c}$ for networks containing arbitrary order cycles. For 3-cycles, the dependence of $q_c$ on the clustering coefficients is ascertained. The analysis substantiates the validity of the strategies with an analytical evidence.Comment: 6 pages, 8 figure

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

Optimization in task--completion networks

We discuss the collective behavior of a network of individuals that receive, process and forward to each other tasks. Given costs they store those tasks in buffers, choosing optimally the frequency at which to check and process the buffer. The individual optimizing strategy of each node determines the aggregate behavior of the network. We find that, under general assumptions, the whole system exhibits coexistence of equilibria and hysteresis.Comment: 18 pages, 3 figures, submitted to JSTA

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

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

Consensus and ordering in language dynamics

We consider two social consensus models, the AB-model and the Naming Game restricted to two conventions, which describe a population of interacting agents that can be in either of two equivalent states (A or B) or in a third mixed (AB) state. Proposed in the context of language competition and emergence, the AB state was associated with bilingualism and synonymy respectively. We show that the two models are equivalent in the mean field approximation, though the differences at the microscopic level have non-trivial consequences. To point them out, we investigate an extension of these dynamics in which confidence/trust is considered, focusing on the case of an underlying fully connected graph, and we show that the consensus-polarization phase transition taking place in the Naming Game is not observed in the AB model. We then consider the interface motion in regular lattices. Qualitatively, both models show the same behavior: a diffusive interface motion in a one-dimensional lattice, and a curvature driven dynamics with diffusing stripe-like metastable states in a two-dimensional one. However, in comparison to the Naming Game, the AB-model dynamics is shown to slow down the diffusion of such configurations.Comment: 7 pages, 6 figure

Aflatoxins M1 and M2 in the milk of donkeys fed with naturally contaminated diet

For its nutritional composition, donkey milk is an excellent alternative to breast milk for infants suffering from cow’s milk allergies. Even in donkeys, a passage of aflatoxin from contaminated feed to milk could occur, as reported by many authors in other dairy species, but there are no studies on this topic. This work was aimed at studying the excretion of aflatoxin M1 (AFM1) and M2 (AFM2) in milk after feeding trials with contaminated feed. Six donkeys, at the end of lactation, received a diet with naturally contaminated corn containing 202 and 11 μg.kg−1 of aflatoxin B1 (AFB1) and aflatoxin B2 (AFB2), respectively. Individual milk samples were analyzed for AFM1 and AFM2 for 15 days after the contaminated feed administration. Amounts of AFM1 and AFM2 were detected in the milk. The steady state condition was reached after 6 days. No AFM1 or AFM2 were detected in milk after 28 h from the last contaminated feed administration. The carryover from AFB1 to AFM1 and from AFB2 to AFM2 was found to be 0.02 and 0.31%, respectively. The results obtained in this study are thus a further step toward understanding the possible carryover of aflatoxin in donkey milk