Session I

50'+ 10' Shlomo Havlin

Title: Cascading Failures and Recovery in Networks of Networks

Abstract: A framework for studying the vulnerability and the recovery of networks of interdependent networks will be presented. In interdependent networks, when nodes in one network fail, they cause dependent nodes in other networks to also fail. This is also the case when some nodes like certain locations play a role in two networks --multiplex. This may happen recursively and can lead to a cascade of failures and to a sudden fragmentation of the system. I will present analytical solutions for the critical thresholds and the giant component of a network of n interdependent networks. I will show, that the general theory has many novel features that are not present in the classical network theory. When recovery of components is possible global spontaneous recovery of the networks and hysteresis phenomena occur and the theory suggests an optimal repairing strategy for a system of systems. I will also show that interdependent networks embedded in space are significantly more vulnerable compared to non embedded networks. In particular, small localized attacks of zero fraction may lead to cascading failures and catastrophic consequences. Thus, analyzing real data and realistic models of network of networks is highly required to understand the system vulnerability.
50'+ 10' Jesús Gómez-Gardeñes

Title: Epidemics and Multiplex Metapopulations

Abstract: In this talk we study the impact that mobility patterns have on the onset of epidemics when different classes of individuals coexist within a metapopulation. Each class of individuals show different mobility patterns between the patches composing the metapopulation. Thus, the presence of M different types of individuals turns the usual networked metapopulation into a multiplex metapopulation of M layers, where each layer encodes the mobility network of each type of individuals. We will develop a Markovian formulation for calculating the time evolution of the infected individuals in each patch and compare our model with MonteCarlo agent based simulations. In addition, we focus on two particular datasets from the cities of Medellín and Bogotá, both in Colombia. Although mobility patterns in these two cities are similar from those typically found for large cities, these datasets provide additional information about the socioeconomic status of the individuals. This information is particularly important when the level of inequality in a society is large, as it is the case in Colombia. Thus, taking advantage of this additional information we will analyze how the different mobility pattern of each socioeconomic class affect the onset of epidemics.
15'+ 5' María Pereda

Title: On the emergence of cooperation under vigilance: a multiplex network approach

Abstract: Understanding the evolution of cooperation is one of the most fascinating challenges in many disciplines. There is a large amount of literature analysing the mechanisms for cooperation to emerge and to be sustained, both from theoretical and experimental studies. Another way to understand the evolution of cooperation in human societies consist in deciphering the cooperative behaviour in ancient communities from historical records. In a previous work we studied cooperation in the Yamana society that inhabited Argentina and observed that the emergence of an informal network of vigilance promoted cooperation. Several field studies have found evidence of humans exposing a pro-social behaviour when being observed by others and also under the presence of subtle cues of being watched. The observability effect (the increase of cooperation under vigilance) seems to be driven by our reputational concerns, bringing the indirect reciprocity mechanism into play. This work explores the effect of vigilance on cooperation in networked systems, in the framework of the Prisoners? Dilemma game. We study the bidirectionally-coupled vigilance and game dynamics. We quantify the impact of the topological structure of the network, and the interplay between vigilance and behaviour, on the outcome of cooperation. Moreover, we study the impact of vigilance on cooperation when the individuals have to afford a cost to become vigilant actors. We also analyse the influence of network multiplexity, i.e. the interconnection of different topological structures for the vigilance and the game networks, and the impact of layer-degree correlations, i.e. when node degrees of the multiplex layers are not randomly distributed but correlated. Our results show that vigilant actors can significantly affect the levels of cooperation, not only by enhancing cooperation in regions of the phase diagram where cooperation is expected to hold, but also by altering the critical point for the emergence of cooperation.
15'+ 5' Philip Chodrow (on behalf of Zeyad Al-Awwad; Shan Jiang and Marta Gonzalezs)

Title: Demand and Congestion in Multiplex Transportation Networks

Abstract: Recent studies of multimodal urban transportation networks have used the framework of multiplex network analysis to illuminate their structure and make analytic or simulation-based inferences about their dynamics. However, these systems are intrinsically sociotechnical, and their dynamical behavior depends not only on structure, but also on user behavior--particularly travel demand. We present the first study of an urban transportation system combining multiplex network analysis and validated Origin-Destination travel demand, using Riyadh's planned metro as a case study. First, we develop methods for analyzing the impact of additional transportation layers on existing dynamics, and show that the structure of demand plays a key role in determining qualitative system behavior. We then demonstrate the existence of fundamental limits to changes in traffic dynamics due to the intrinsic geometry of the metro layer. Finally, we develop a simple analytical framework for informing the planning of additional feeder layers (such as buses) to maximize the impact of the metro on global congestion. The techniques we present are computationally practical, easily extensible to arbitrary numbers of transportation layers, and implemented in open-source software.
15' + 5' Valerio Gemmetto (on behalf of Tiziano Squartini; Francesco Picciolo; Franco Ruzzenenti and Diego Garlaschelli)

Title: Patterns of multiplexity and multireciprocity in directed multiplexes

Abstract: In multi-layer networks with directed links, introducing measures of dependency between different layers requires more than a straightforward extension of the multiplexity measures that have been developed for undirected multiplexes. In particular, one should take into account the effects of reciprocity, i.e. the tendency of pairs of vertices to establish mutual connections. In single-layer networks, reciprocity is a crucial structural property affecting several dynamical processes. Here we extend it to multiplexes and introduce the notion of multireciprocity, defined as the tendency of links in one layer to be reciprocated by links in a different layer. While ordinary reciprocity reduces to a scalar quantity, multireciprocity requires a square matrix generated by all the possible pairs of layers. We introduce multireciprocity metrics valid for both binary and weighted multiplexes and provide an empirical analysis of the World Trade Multiplex, representing the import-export relationships between world countries in different products. We show that several pairs of layers exhibit strong multiplexity, an effect which is however largely encoded into the degree or strength sequences of individual layers. We also find that most pairs of commodities are characterised by positive multireciprocity, and that such values are significantly lower than the usual reciprocity measured on the aggregated network. Moreover, layers with low (high) internal reciprocity are embedded within groups of layers with low (high) mutual multireciprocity. We finally identify robust empirical patterns showing that joint multi-layer connection probabilities can be reconstructed from marginal ones via the multireciprocity matrix. Therefore the latter can bridge the gap between single-layer properties and truly multiplex information.
50'+ 10' Vito Latora

Title: Collective phenomena induced by multiplexity

Abstract: Focusing on the dynamics of multiplex networks, we discuss some examples where multiplexity gives rise to the emergence of novel dynamical behaviors, otherwise unobserved in the dynamics of single-layer networks.


Session II

50'+ 10' Marc Barthelemy

Title: Transportation systems: a multilayer network approach

Abstract: Multilayer networks provide a natural framework for studying transportation systems. Within this approach I will show on practical examples how we can understand the structure of these systems and quantify the impact of the coupling between different modes. I will also discuss how a simple dynamical model on these systems allows to explain some statistical patterns observed for human mobility.
50'+ 10' Marta Gonzalez

Title: Collective benetfits in traffic during large events via the use of information technologies

Abstract: Information technologies today can inform drivers about their alternatives for shortest paths from origins to destinations, but they do not contain incentives or information that promote collective benefits. To obtain such benefits, we need to have not only good estimates of how the traffic is formed but also to have target strategies to reduce enough vehicles from the best possible roads in a feasible way. Moreover, to reach the target vehicle reduction is not trivial, it requires individual sacrifices such as drivers taking alternative routes, shifts in departure times or even changes in modes of transportation. The opportunity is that during large events (Carnivals, Festivals, Races, etc.) the traffic inconveniences in large cities are unusually high, yet temporary, and the entire population may be more willing to adopt collective recommendations for social good. In this paper, we integrate for the first time big data resources to quantify the impact of events and propose target strategies for collective good at urban scale. In the context of the Olympic Games in Rio de Janeiro, we first predict the increase in traffic by integrating data from: mobile phones, schedules and venues of sport matches, Airbnb, Waze and transit information. Second, we evaluate the impact of Olympic Games to the travel of commuters, and propose different route choice scenarios during the morning and evening peak hours. Moreover, we pinpoint the trips which have greatest contribution to the global congestion and propose reasonable collective reduction. Interestingly, we show that (i) following new route options with individual shortest path can save more collective travel time than keeping routine routes, uncovering the positive value of information technologies during events; (ii) if a small targeted proportion of people from specific areas switch from driving to public transport, the collective travel time can be reduced to a great extent.
15'+ 5' Ludvig Bohlin (on behalf of Manlio De Domenico; Christian Persson; Daniel Edler and Martin Rosvall)

Title: Generalized mapping of dynamics in multilayer and interconnected systems

Abstract: To connect structure and dynamics in interconnected systems, flow-based methods have proven useful for identifying modular dynamics in weighted and directed networks that capture constraints on flow processes. However, many interconnected systems consist of elements with multiple layers of interactions. The information-theoretic and flow-based method known as the map equation was recently generalized to multilayer networks. However, it has been unclear how to further generalize the method to any type of layered network, such as multiplex networks, interconnected multiplex networks, interdependent networks, and interconnected multilayer networks. Here we show that discriminating between physical nodes for describing the concrete elements that flow entities can visit and abstract state nodes for representing the dynamics allows for completely generalized mapping. The generalized mapping framework applies to dynamics in multilayer and interconnected systems as well as any higher-order Markov chain model. We demonstrate how representations that are true to the system at hand provide the most effective analysis.
50'+ 10' Osman Yagan

Title: Analysis of Contagions in Multi-layer and Multiplex Networks

Abstract: Dynamical processes on complex networks has been an active research area over the past decade. In this talk, we will present recent results on two major and related classes of dynamical processes: i) Information propagation, also known as simple contagion, and ii) Influence propagation, also known as complex contagion. With regard to simple contagions, we will consider a clustered multi-layer network model to capture the fact that information may propagate simultaneously over multiple social networks. Assuming that information propagates according to the SIR model and with different information transmissibility across the networks, we give results for the conditions, probability, and size of information epidemics. We present analogous results for complex contagions over clustered multiplex networks under a generalized linear threshold model. Collecting, we demonstrate several non-trivial results concerning the impact of clustering on contagion dynamics. Last but not least, we compare the dynamics of complex contagions over multiplex networks and their monoplex projections and demonstrate that ignoring link types and aggregating network layers may lead to inaccurate conclusions about contagion dynamics, particularly when the correlation of degrees between layers is high.
15'+ 5' Andrea Santoro (on behalf of Vito Latora; Giuseppe Nicosia and Vincenzo Nicosia)

Title: Strategic growth of multilayer airline networks

Abstract: The airline transportation system is a paradigmatic example of multiplex network, where nodes represent airports, edges stand for direct flights between two locations, and each layer contains all the routes operated by the same carrier. In this work we propose a genuinely multiplex model of network growth, based on a trade-off between the maximisation of the number of potential travellers and the minimisation of competition on each route. By using real data about the six continental air transportation networks, we show that the model is able to reproduce quite accurately the structural properties of these systems, and in particular the observed patterns of egde overlap and node activity distribution. The results suggest that each airline really tends to organise its network in order to optimise a trade-off between efficiency and competition, and that the networks of all the airlines of a continent are indeed placed very close to the theoretical Pareto front in the efficiency-competition plane. We finally explain how this simple model can be used to suggest which routes should be added to an existing network in order to improve the overall performance of an airline. This work sheds light on the fundamental role played by multiplexity in shaping the structure of continental air transportation systems, and provides new interesting insight about effective strategies for network optimisation based exclusively on structural considerations.
15'+ 5' Nicolás Deschle (on behalf of Andreas Daffertshofer)

Title: Quantifying topology transfer in interconnected networks of phase oscillators using relaxation time

Abstract: In the last decade or so, the study of interconnected complex networks gained much interest across the scientific community. In neuroscience, in particular, systems are often composed of many networks that interact on different spatial and temporal scales. This may result in activity that is synchronized within and/or across networks, in its simplest form in-phase oscillations. We studied numerically the synchronizability of two interconnected oscillator networks of finite-size. In contrast to other studies that assessed synchronizability by the asymptotic state of (local) Kuramoto order parameter, we quantified is by the (local) relaxation time towards that asymptotic state. In view of finite-size effects, the latter was expected to be quite erratic which motivated using a statistical approach often employed to quantify stochastic dynamics: We determined the serial-lag auto-correlation function of the simulated time series of the networks? order parameters. The envelope of the auto-correlation function decayed exponentially (as in the case of a linear response system), which allowed for estimating the relaxation time. We first tested procedures in the case of two fully connected, symmetric networks and compared. Our numerical estimates of the relaxation times closely resembled the analytically known bifurcation scheme. Next we changed the topology of one of the networks to be random (Erdos-Rényi), scale free (Barabási-Albert) and small world (Newman-Watts) by guarantying that the asymptotic value of local synchronization in that that network remained constant. Dependent of the relation of average degree and within-network vis-á-vis between-network coupling strength, topology transferred from one network to the other. Quantifying synchronizability through the (local) relaxation time appears a useful tool when it comes to interactions between oscillator networks.