Tricritical behavior in epidemic dynamics with vaccination

We scrutinize the phenomenology arising from a minimal vaccination-epidemic (MVE) dynamics using three methods: mean-field approach, Monte Carlo simulations, and finite-size scaling analysis. The mean-field formulation reveals that the MVE model exhibits either a continuous or a discontinuous active-to-absorbing phase transition, accompanied by bistability and a tricritical point. However, on square lattices, we detect no signs of bistability, and we disclose that the active-to-absorbing state transition has a scaling invariance and critical exponents compatible with the continuous transition of the directed percolation universality class. Additionally, our findings indicate that the tricritical and crossover behaviors of the MVE dynamics belong to the universality class of mean-field tricritical directed percolation.Comment: 12 pages, 6 figures and 2 tables. Version closer to the published pape

Random networks with q-exponential degree distribution

We use the configuration model to generate networks having a degree distribution that follows a $q$-exponential, $P_q(k)=(2-q)\lambda[1-(1-q)\lambda k]^{1/(q-1)}$, for arbitrary values of the parameters $q$ and $\lambda$. We study the assortativity and the shortest path of these networks finding that the more the distribution resembles a pure power law, the less well connected are the corresponding nodes. In fact, the average degree of a nearest neighbor grows monotonically with $\lambda^{-1}$. Moreover, our results show that $q$-exponential networks are more robust against random failures and against malicious attacks than standard scale-free networks. Indeed, the critical fraction of removed nodes grows logarithmically with $\lambda^{-1}$ for malicious attacks. An analysis of the $k_s$-core decomposition shows that $q$-exponential networks have a highest $k_s$-core, that is bigger and has a larger $k_s$ than pure scale-free networks. Being at the same time well connected and robust, networks with $q$-exponential degree distribution exhibit scale-free and small-world properties, making them a particularly suitable model for application in several systems.Comment: 6 pages, 8 figure

Mandala Networks: ultra-small-world and highly sparse graphs

The increasing demands in security and reliability of infrastructures call for the optimal design of their embedded complex networks topologies. The following question then arises: what is the optimal layout to fulfill best all the demands? Here we present a general solution for this problem with scale-free networks, like the Internet and airline networks. Precisely, we disclose a way to systematically construct networks which are robust against random failures. Furthermore, as the size of the network increases, its shortest path becomes asymptotically invariant and the density of links goes to zero, making it ultra-small world and highly sparse, respectively. The first property is ideal for communication and navigation purposes, while the second is interesting economically. Finally, we show that some simple changes on the original network formulation can lead to an improved topology against malicious attacks.ISSN:2045-232

Ising-like model replicating time-averaged spiking behaviour of in vitro neuronal networks

We analyze time-averaged experimental data from in vitro activities of neuronal networks. Through a Pairwise Maximum-Entropy method, we identify through an inverse binary Ising-like model the local fields and interaction couplings which best reproduce the average activities of each neuron as well as the statistical correlations between the activities of each pair of neurons in the system. The specific information about the type of neurons is mainly stored in the local fields, while a symmetric distribution of interaction constants seems generic. Our findings demonstrate that, despite not being directly incorporated into the inference approach, the experimentally observed correlations among groups of three neurons are accurately captured by the derived Ising-like model. Within the context of the thermodynamic analogy inherent to the Ising-like models developed in this study, our findings additionally indicate that these models demonstrate characteristics of second-order phase transitions between ferromagnetic and paramagnetic states at temperatures above, but close to, unity. Considering that the operating temperature utilized in the Maximum-Entropy method is To= 1 , this observation further expands the thermodynamic conceptual parallelism postulated in this work for the manifestation of criticality in neuronal network behavior