Contagion-diffusion processes with recurrent mobility patterns of distinguishable agents.

The analysis of contagion-diffusion processes in metapopulations is a powerful theoretical tool to study how mobility influences the spread of communicable diseases. Nevertheless, many metapopulation approaches use indistinguishable agents to alleviate analytical difficulties. Here, we address the impact that recurrent mobility patterns, and the spatial distribution of distinguishable agents, have on the unfolding of epidemics in large urban areas. We incorporate the distinguishable nature of agents regarding both their residence and their usual destination. The proposed model allows both a fast computation of the spatiotemporal pattern of the epidemic trajectory and the analytical calculation of the epidemic threshold. This threshold is found as the spectral radius of a mixing matrix encapsulating the residential distribution and the specific commuting patterns of agents. We prove that the simplification of indistinguishable individuals overestimates the value of the epidemic threshold.

A metapopulation approach to identify targets for Wolbachia-based dengue control.

Over the last decade, the release of Wolbachia-infected Aedes aegypti into the natural habitat of this mosquito species has become the most sustainable and long-lasting technique to prevent and control vector-borne diseases, such as dengue, zika, or chikungunya. However, the limited resources to generate such mosquitoes and their effective distribution in large areas dominated by the Aedes aegypti vector represent a challenge for policymakers. Here, we introduce a mathematical framework for the spread of dengue in which competition between wild and Wolbachia-infected mosquitoes, the cross-contagion patterns between humans and vectors, the heterogeneous distribution of the human population in different areas, and the mobility flows between them are combined. Our framework allows us to identify the most effective areas for the release of Wolbachia-infected mosquitoes to achieve a large decrease in the global dengue prevalence.

Emergence, survival, and segregation of competing gangs.

In this paper, we approach the phenomenon of criminal activity from an infectious perspective by using tailored compartmental agent-based models that include the social flavor of the mechanisms governing the evolution of crime in society. Specifically, we focus on addressing how the existence of competing gangs shapes the penetration of crime. The mean-field analysis of the model proves that the introduction of dynamical rules favoring the simultaneous survival of both gangs reduces the overall number of criminals across the population as a result of the competition between them. The implementation of the model in networked populations with homogeneous contact patterns reveals that the evolution of crime substantially differs from that predicted by the mean-field equations. We prove that the system evolves toward a segregated configuration where, depending on the features of the underlying network, both gangs can form spatially separated clusters. In this scenario, we show that the beneficial effect of the coexistence of two gangs is hindered, resulting in a higher penetration of crime in the population.

Fear induced explosive transitions in the dynamics of corruption.

In this article, we analyze a compartmental model aimed at mimicking the role of imitation and delation of corruption in social systems. In particular, the model relies on a compartmental dynamics in which individuals can transit between three states: honesty, corruption, and ostracism. We model the transitions from honesty to corruption and from corruption to ostracism as pairwise interactions. In particular, honest agents imitate corrupt peers while corrupt individuals pass to ostracism due to the delation of honest acquaintances. Under this framework, we explore the effects of introducing social intimidation in the delation of corrupt people. To this aim, we model the probability that an honest delates a corrupt agent as a decreasing function of the number of corrupt agents, thus mimicking the fear of honest individuals to reprisals by those corrupt ones. When this mechanism is absent or weak, the phase diagram of the model shows three equilibria [(i) full honesty, (ii) full corruption, and (iii) a mixed state] that are connected via smooth transitions. However, when social intimidation is strong, the transitions connecting these states turn explosive leading to a bistable phase in which a stable full corruption phase coexists with either mixed or full honesty stable equilibria. To shed light on the generality of these transitions, we analyze the model in different network substrates by means of Monte Carlo simulations and deterministic microscopic Markov chain equations. This latter formulation allows us to derive analytically the different bifurcation points that separate the different phases of the system.

Analyzing the potential impact of BREXIT on the European research collaboration network.

In this work, we study the impact that the withdrawal of institutions from the United Kingdom caused by BREXIT has on the European research collaboration networks. To this aim, we consider BREXIT as a targeted attack to those graphs composed by the European institutions that have collaborated in research projects belonging to the three main H2020 programs (Excellent Science, Industrial Leadership, and Societal Challenges). The consequences of this attack are analyzed at the global, mesoscopic, and local scales and compared with the changes suffered by the same collaboration networks when a similar quantity of nodes is randomly removed from the network. Our results suggest that changes depend on the specific program, with Excellent Science being the most affected by BREXIT perturbation. However, the structure of the integrated collaboration network is not significantly affected by BREXIT compared to the variations observed after the random removal of institutions.

The structure and dynamics of multilayer networks.

In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal- or context-related properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.

Diffusion dynamics on multiplex networks.

We study the time scales associated with diffusion processes that take place on multiplex networks, i.e., on a set of networks linked through interconnected layers. To this end, we propose the construction of a supra-laplacian matrix, which consists of a dimensional lifting of the laplacian matrix of each layer of the multiplex network. We use perturbative analysis to reveal analytically the structure of eigenvectors and eigenvalues of the complete network in terms of the spectral properties of the individual layers. The spectrum of the supra-laplacian allows us to understand the physics of diffusionlike processes on top of multiplex networks.

Explosive first-order transition to synchrony in networked chaotic oscillators.

Critical phenomena in complex networks, and the emergence of dynamical abrupt transitions in the macroscopic state of the system are currently a subject of the outmost interest. We report evidence of an explosive phase synchronization in networks of chaotic units. Namely, by means of both extensive simulations of networks made up of chaotic units, and validation with an experiment of electronic circuits in a star configuration, we demonstrate the existence of a first-order transition towards synchronization of the phases of the networked units. Our findings constitute the first prove of this kind of synchronization in practice, thus opening the path to its use in real-world applications.

Emerging meso- and macroscales from synchronization of adaptive networks.

We consider a set of interacting phase oscillators, with a coupling between synchronized nodes adaptively reinforced, and the constraint of a limited resource for a node to establish connections with the other units of the network. We show that such a competitive mechanism leads to the emergence of a rich modular structure underlying cluster synchronization, and to a scale-free distribution for the connection strengths of the units.

Norm violation versus punishment risk in a social model of corruption.

We analyze the onset of social-norm-violating behaviors when social punishment is present. To this aim, a compartmental model is introduced to illustrate the flows among the three possible states: honest, corrupt, and ostracism. With this simple model we attempt to capture some essential ingredients such as the contagion of corrupt behaviors to honest agents, the delation of corrupt individuals by honest ones, and the warning to wrongdoers (fear like that triggers the conversion of corrupt people into honesty). In nonequilibrium statistical physics terms, the former dynamics can be viewed as a non-Hamiltonian kinetic spin-1 Ising model. After developing in full detail its mean-field theory and comparing its predictions with simulations made on regular networks, we derive the conditions for the emergence of corrupt behaviors and, more importantly, illustrate the key role of the warning-to-wrongdoers mechanism in the latter.

Social network reciprocity as a phase transition in evolutionary cooperation.

In evolutionary dynamics the understanding of cooperative phenomena in natural and social systems has been the subject of intense research during decades. We focus attention here on the so-called "lattice reciprocity" mechanisms that enhance evolutionary survival of the cooperative phenotype in the prisoner's dilemma game when the population of Darwinian replicators interact through a fixed network of social contacts. Exact results on a "dipole model" are presented, along with a mean-field analysis as well as results from extensive numerical Monte Carlo simulations. The theoretical framework used is that of standard statistical mechanics of macroscopic systems, but with no energy considerations. We illustrate the power of this perspective on social modeling, by consistently interpreting the onset of lattice reciprocity as a thermodynamical phase transition that, moreover, cannot be captured by a purely mean-field approach.

Effects of mobility in a population of prisoner's dilemma players.

We address the problem of how the survival of cooperation in a social system depends on the motion of the individuals. Specifically, we study a model in which prisoner's dilemma players are allowed to move in a two-dimensional plane. Our results show that cooperation can survive in such a system provided that both the temptation to defect and the velocity at which agents move are not too high. Moreover, we show that when these conditions are fulfilled, the only asymptotic state of the system is that in which all players are cooperators. Our results might have implications for the design of cooperative strategies in motion coordination and other applications including wireless networks.

Explosive transitions induced by interdependent contagion-consensus dynamics in multiplex networks.

We introduce a model to study the interplay between information spreading and opinion formation in social systems. Our framework consists in a two-layer multiplex network where opinion dynamics takes place in one layer, while information spreads on the other one. The two dynamical processes are mutually coupled in such a way that the control parameters governing the dynamics of the node states at one layer depend on the dynamical states at the other layer. In particular, we consider the case in which consensus is favored by the common adoption of information, while information spreading is boosted between agents sharing similar opinions. Numerical simulations of the model point out that, when the coupling between the dynamics of the two layers is strong enough, a double explosive transition, i.e., a discontinuous transition both in consensus dynamics and in information spreading appears. Such explosive transitions lead to bi-stability regions in which the consensus-informed states and the disagreement-uninformed states are both stable solutions of the intertwined dynamics.

Markovian approach to tackle the interaction of simultaneous diseases.

The simultaneous emergence of several abrupt disease outbreaks or the extinction of some serotypes of multistrain diseases are fingerprints of the interaction between pathogens spreading within the same population. Here, we propose a general and versatile benchmark to address the unfolding of both cooperative and competitive interacting diseases. We characterize the explosive transitions between the disease-free and the epidemic regimes arising from the cooperation between pathogens and show the critical degree of cooperation needed for the onset of such abrupt transitions. For the competing diseases, we characterize the mutually exclusive case and derive analytically the transition point between the full-dominance phase, in which only one pathogen propagates, and the coexistence regime. Finally, we use this framework to analyze the behavior of the former transition point as the competition between pathogens is relaxed.

Graph analysis of cell clusters forming vascular networks.

This manuscript describes the experimental observation of vasculogenesis in chick embryos by means of network analysis. The formation of the vascular network was observed in the area opaca of embryos from 40 to 55 h of development. In the area opaca endothelial cell clusters self-organize as a primitive and approximately regular network of capillaries. The process was observed by bright-field microscopy in control embryos and in embryos treated with Bevacizumab (Avastin®), an antibody that inhibits the signalling of the vascular endothelial growth factor (VEGF). The sequence of images of the vascular growth were thresholded, and used to quantify the forming network in control and Avastin-treated embryos. This characterization is made by measuring vessels density, number of cell clusters and the largest cluster density. From the original images, the topology of the vascular network was extracted and characterized by means of the usual network metrics such as: the degree distribution, average clustering coefficient, average short path length and assortativity, among others. This analysis allows to monitor how the largest connected cluster of the vascular network evolves in time and provides with quantitative evidence of the disruptive effects that Avastin has on the tree structure of vascular networks.

Solitons in the Salerno model with competing nonlinearities.

We consider a lattice equation (Salerno model) combining onsite self-focusing and intersite self-defocusing cubic terms, which may describe a Bose-Einstein condensate of dipolar atoms trapped in a strong periodic potential. In the continuum approximation, the model gives rise to solitons in a finite band of frequencies, with sechlike solitons near one edge, and an exact peakon solution at the other. A similar family of solitons is found in the discrete system, including a peakon; beyond the peakon, the family continues in the form of cuspons. Stability of the lattice solitons is explored through computation of eigenvalues for small perturbations, and by direct simulations. A small part of the family is unstable (in that case, the discrete solitons transform into robust pulsonic excitations); both peakons and cuspons are stable. The Vakhitov-Kolokolov criterion precisely explains the stability of regular solitons and peakons, but does not apply to cuspons. In-phase and out-of-phase bound states of solitons are also constructed. They exchange their stability at a point where the bound solitons are peakons. Mobile solitons, composed of a moving core and background, exist up to a critical value of the strength of the self-defocusing intersite nonlinearity. Colliding solitons always merge into a single pulse.

Discrete solitons and vortices in the two-dimensional Salerno model with competing nonlinearities.

An anisotropic lattice model in two spatial dimensions, with on-site and intersite cubic nonlinearities (the Salerno model), is introduced, with emphasis on the case in which the intersite nonlinearity is self-defocusing, competing with on-site self-focusing. The model applies, for example, to a dipolar Bose-Einstein condensate trapped in a deep two-dimensional (2D) optical lattice. Soliton families of two kinds are found in the model: ordinary ones and cuspons, with peakons at the border between them. Stability borders for the ordinary solitons are found, while all cuspons (and peakons) are stable. The Vakhitov-Kolokolov criterion does not apply to cuspons, but for the ordinary solitons it correctly identifies the stability limits. In direct simulations, unstable solitons evolve into localized pulsons. Varying the anisotropy parameter, we trace a transition between the solitons in 1D and 2D versions of the model. In the isotropic model, we also construct discrete vortices of two types, on-site and intersite centered (vortex crosses and squares, respectively), and identify their stability regions. In simulations, unstable vortices in the noncompeting model transform into regular solitons, while in the model with the competing nonlinearities they evolve into localized vortical pulsons, which maintain their topological character. Bound states of regular solitons and vortices are constructed too, and their stability is identified.

Explosive Contagion in Networks.

The spread of social phenomena such as behaviors, ideas or products is an ubiquitous but remarkably complex phenomenon. A successful avenue to study the spread of social phenomena relies on epidemic models by establishing analogies between the transmission of social phenomena and infectious diseases. Such models typically assume simple social interactions restricted to pairs of individuals; effects of the context are often neglected. Here we show that local synergistic effects associated with acquaintances of pairs of individuals can have striking consequences on the spread of social phenomena at large scales. The most interesting predictions are found for a scenario in which the contagion ability of a spreader decreases with the number of ignorant individuals surrounding the target ignorant. This mechanism mimics ubiquitous situations in which the willingness of individuals to adopt a new product depends not only on the intrinsic value of the product but also on whether his acquaintances will adopt this product or not. In these situations, we show that the typically smooth (second order) transitions towards large social contagion become explosive (first order). The proposed synergistic mechanisms therefore explain why ideas, rumours or products can suddenly and sometimes unexpectedly catch on.

Layer-layer competition in multiplex complex networks.

The coexistence of multiple types of interactions within social, technological and biological networks has moved the focus of the physics of complex systems towards a multiplex description of the interactions between their constituents. This novel approach has unveiled that the multiplex nature of complex systems has strong influence in the emergence of collective states and their critical properties. Here we address an important issue that is intrinsic to the coexistence of multiple means of interactions within a network: their competition. To this aim, we study a two-layer multiplex in which the activity of users can be localized in each of the layers or shared between them, favouring that neighbouring nodes within a layer focus their activity on the same layer. This framework mimics the coexistence and competition of multiple communication channels, in a way that the prevalence of a particular communication platform emerges as a result of the localization of user activity in one single interaction layer. Our results indicate that there is a transition from localization (use of a preferred layer) to delocalization (combined usage of both layers) and that the prevalence of a particular layer (in the localized state) depends on the structural properties.

Enhancing the stability of the synchronization of multivariable coupled oscillators.

Synchronization processes in populations of identical networked oscillators are the focus of intense studies in physical, biological, technological, and social systems. Here we analyze the stability of the synchronization of a network of oscillators coupled through different variables. Under the assumption of an equal topology of connections for all variables, the master stability function formalism allows assessing and quantifying the stability properties of the synchronization manifold when the coupling is transferred from one variable to another. We report on the existence of an optimal coupling transference that maximizes the stability of the synchronous state in a network of Rössler-like oscillators. Finally, we design an experimental implementation (using nonlinear electronic circuits) which grounds the robustness of the theoretical predictions against parameter mismatches, as well as against intrinsic noise of the system.