A novel methodology for epidemic risk assessment of COVID-19 outbreak.

We propose a novel data-driven framework for assessing the a-priori epidemic risk of a geographical area and for identifying high-risk areas within a country. Our risk index is evaluated as a function of three different components: the hazard of the disease, the exposure of the area and the vulnerability of its inhabitants. As an application, we discuss the case of COVID-19 outbreak in Italy. We characterize each of the twenty Italian regions by using available historical data on air pollution, human mobility, winter temperature, housing concentration, health care density, population size and age. We find that the epidemic risk is higher in some of the Northern regions with respect to Central and Southern Italy. The corresponding risk index shows correlations with the available official data on the number of infected individuals, patients in intensive care and deceased patients, and can help explaining why regions such as Lombardia, Emilia-Romagna, Piemonte and Veneto have suffered much more than the rest of the country. Although the COVID-19 outbreak started in both North (Lombardia) and Central Italy (Lazio) almost at the same time, when the first cases were officially certified at the beginning of 2020, the disease has spread faster and with heavier consequences in regions with higher epidemic risk. Our framework can be extended and tested on other epidemic data, such as those on seasonal flu, and applied to other countries. We also present a policy model connected with our methodology, which might help policy-makers to take informed decisions.

Stability of synchronization in simplicial complexes.

Various systems in physics, biology, social sciences and engineering have been successfully modeled as networks of coupled dynamical systems, where the links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We show that complete synchronization exists as an invariant solution, and give the necessary condition for it to be observed as a stable state. Moreover, in some relevant instances, such a necessary condition takes the form of a Master Stability Function. This generalizes the existing results valid for pairwise interactions to the case of complex systems with the most general possible architecture.

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.

Emergent explosive synchronization in adaptive complex networks.

Adaptation plays a fundamental role in shaping the structure of a complex network and improving its functional fitting. Even when increasing the level of synchronization in a biological system is considered as the main driving force for adaptation, there is evidence of negative effects induced by excessive synchronization. This indicates that coherence alone cannot be enough to explain all the structural features observed in many real-world networks. In this work, we propose an adaptive network model where the dynamical evolution of the node states toward synchronization is coupled with an evolution of the link weights based on an anti-Hebbian adaptive rule, which accounts for the presence of inhibitory effects in the system. We found that the emergent networks spontaneously develop the structural conditions to sustain explosive synchronization. Our results can enlighten the shaping mechanisms at the heart of the structural and dynamical organization of some relevant biological systems, namely, brain networks, for which the emergence of explosive synchronization has been observed.

Mobility and Congestion in Dynamical Multilayer Networks with Finite Storage Capacity.

Multilayer networks describe well many real interconnected communication and transportation systems, ranging from computer networks to multimodal mobility infrastructures. Here, we introduce a model in which the nodes have a limited capacity of storing and processing the agents moving over a multilayer network, and their congestions trigger temporary faults which, in turn, dynamically affect the routing of agents seeking for uncongested paths. The study of the network performance under different layer velocities and node maximum capacities reveals the existence of delicate trade-offs between the number of served agents and their time to travel to destination. We provide analytical estimates of the optimal buffer size at which the travel time is minimum and of its dependence on the velocity and number of links at the different layers. Phenomena reminiscent of the slower is faster effect and of the Braess' paradox are observed in our dynamical multilayer setup.

Hybrid recommendation methods in complex networks.

We propose two recommendation methods, based on the appropriate normalization of already existing similarity measures, and on the convex combination of the recommendation scores derived from similarity between users and between objects. We validate the proposed measures on three data sets, and we compare the performance of our methods to other recommendation systems recently proposed in the literature. We show that the proposed similarity measures allow us to attain an improvement of performances of up to 20% with respect to existing nonparametric methods, and that the accuracy of a recommendation can vary widely from one specific bipartite network to another, which suggests that a careful choice of the most suitable method is highly relevant for an effective recommendation on a given system. Finally, we study how an increasing presence of random links in the network affects the recommendation scores, finding that one of the two recommendation algorithms introduced here can systematically outperform the others in noisy data sets.

Nonlinear growth and condensation in multiplex networks.

Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of nonlinear preferential attachment rules. We show, both numerically and analytically, that by tuning the level of nonlinearity these models allow us to reproduce either homogeneous or heterogeneous degree distributions, together with positive or negative degree correlations across layers. In particular, we derive the condition for the appearance of a condensed state in which one node in each layer attracts an extensive fraction of all the edges.

Growing multiplex networks.

We propose a modeling framework for growing multiplexes where a node can belong to different networks. We define new measures for multiplexes and we identify a number of relevant ingredients for modeling their evolution such as the coupling between the different layers and the distribution of node arrival times. The topology of the multiplex changes significantly in the different cases under consideration, with effects of the arrival time of nodes on the degree distribution, average shortest path length, and interdependence.

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.

Flow graphs: interweaving dynamics and structure.

The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential because different dynamical processes may be affected very differently by network topology. A full characterization of such systems thus requires a formalization that encompasses both aspects simultaneously, rather than relying only on the topological adjacency matrix. To achieve this, we introduce the concept of flow graphs, namely weighted networks where dynamical flows are embedded into the link weights. Flow graphs provide an integrated representation of the structure and dynamics of the system, which can then be analyzed with standard tools from network theory. Conversely, a structural network feature of our choice can also be used as the basis for the construction of a flow graph that will then encompass a dynamics biased by such a feature. We illustrate the ideas by focusing on the mathematical properties of generic linear processes on complex networks that can be represented as biased random walks and their dual consensus dynamics, and show how our framework improves our understanding of these processes.

Small-world behavior in time-varying graphs.

Connections in complex networks are inherently fluctuating over time and exhibit more dimensionality than analysis based on standard static graph measures can capture. Here, we introduce the concepts of temporal paths and distance in time-varying graphs. We define as temporal small world a time-varying graph in which the links are highly clustered in time, yet the nodes are at small average temporal distances. We explore the small-world behavior in synthetic time-varying networks of mobile agents and in real social and biological time-varying systems.

Functional modularity of background activities in normal and epileptic brain networks.

We analyze the connectivity structure of weighted brain networks extracted from spontaneous magnetoencephalographic signals of healthy subjects and epileptic patients (suffering from absence seizures) recorded at rest. We find that, for the activities in the 5-14 Hz range, healthy brains exhibit a sparse connectivity, whereas the brain networks of patients display a rich connectivity with a clear modular structure. Our results suggest that modularity plays a key role in the functional organization of brain areas during normal and pathological neural activities at rest.

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.

Community structure of cortical networks in spinal cord injured patients.

In the present study, we estimated the cortical networks were from high-resolution EEG recordings in a group of spinal cord injured patients and in a group of healthy subjects, during the preparation of a limb movement. Then, we use the Markov Clustering method to analyse the division of the network into community structures. The results indicate large differences between the injured patients and the healthy subjects. In particular, the networks of spinal cord injured patient exhibited a higher density of clusters. In the Alpha (7-12 Hz) frequency band, the two observed largest communities were mainly composed by the cingulate motor areas with the supplementary motor areas, and by the pre-motor areas with the right primary motor area of the foot. This functional separation could reflect the partial alteration in the primary motor areas because of the effects of the spinal cord injury.

Analysis of self-organized criticality in the Olami-Feder-Christensen model and in real earthquakes.

We perform an analysis on the dissipative Olami-Feder-Christensen model on a small world topology considering avalanche size differences. We show that when criticality appears, the probability density functions (PDFs) for the avalanche size differences at different times have fat tails with a q-Gaussian shape. This behavior does not depend on the time interval adopted and is found also when considering energy differences between real earthquakes. Such a result can be analytically understood if the sizes (released energies) of the avalanches (earthquakes) have no correlations. Our findings support the hypothesis that a self-organized criticality mechanism with long-range interactions is at the origin of seismic events and indicate that it is not possible to predict the magnitude of the next earthquake knowing those of the previous ones.

Detecting complex network modularity by dynamical clustering.

Based on cluster desynchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and real-world networks whose modular structure is already known or has been studied by means of other methods. The algorithm attains a high level of precision, especially when the modular units are very mixed and hardly detectable by the other methods, with a computational effort O(KN) on a generic graph with N nodes and K links.

Quantifying the relevance of different mediators in the human immune cell network.

MOTIVATION: Immune cells coordinate their efforts for the correct and efficient functioning of the immune system (IS). Each cell type plays a distinct role and communicates with other cell types through mediators such as cytokines, chemokines and hormones, among others, that are crucial for the functioning of the IS and its fine tuning. Nevertheless, a quantitative analysis of the topological properties of an immunological network involving this complex interchange of mediators among immune cells is still lacking. RESULTS: Here we present a method for quantifying the relevance of different mediators in the immune network, which exploits a definition of centrality based on the concept of efficient communication. The analysis, applied to the human IS, indicates that its mediators differ significantly in their network relevance. We found that cytokines involved in innate immunity and inflammation and some hormones rank highest in the network, revealing that the most prominent mediators of the IS are molecules involved in these ancestral types of defence mechanisms which are highly integrated with the adaptive immune response, and at the interplay among the nervous, the endocrine and the immune systems. CONTACT: claudio.franceschi@unibo.it.

Non-Gaussian equilibrium in a long-range Hamiltonian system.

We study the dynamics of a system of N classical spins with infinite-range interaction. We show that, if the thermodynamic limit is taken before the infinite-time limit, the system does not relax to the Boltzmann-Gibbs equilibrium, but exhibits different equilibrium properties, characterized by stable non-Gaussian velocity distributions, Lévy walks, and dynamical correlation in phase space.