Session I

09:00 - 09:45 Albert Diaz-Guilera

Dynamics in multiplex networks

The Science of Complex Systems is an emergent discipline rather successful in the last years. However, further progress in the physics is hampered by the lack of deep knowledge about how multi-level complex systems organize and operate. Preliminary results show that interactions at different levels behave in a significantly different way than in an isolated level. For example, such dependencies may induce cascading failures and sudden collapses of the entire system. This makes the science of complex networks particularly suitable for the exploration of the many challenges that we face today, including critical infrastructures and communication systems, as well as techno-social and socioeconomic networks.
We have been working in the development of a mathematical, computational and algorithmic framework for the study of the physics of multiscale complex systems. The chosen framework consists in a set of layers in such a way that every single layer has exactly the same set of nodes, but they can have different patterns of connectivity. A clear example can be that of social networks, where a layer can be a set of Twitter users having its respective set of following and followed users and another layer can be the same set of Facebook users. A user can have different sets of neighbours in each network because one can think on more familiar or more professional links. But the set of users is exactly the same. In this case, one can imagine that information can flow in any of the two layers and shifting from one to the other when one of the users decide to do it.
In this talk we emphasize on the dynamic properties of multiplex networks by looking at different phenomenologies and different types of interaction within and between layers.
09:45 - 10:30 Osman Yagan

Robustness of electrical power systems against cascading failures

Electrical power systems are one of the most important infrastructures that support our society. However, their vulnerabilities have raised great concern recently due to several large-scale blackouts around the world. In this talk, we will present several results concerning the robustness of power systems against cascading failures initiated by a random attack. This will be done under a simple yet useful model based on global and equal redistribution of load upon failures. We provide a comprehensive understanding of system robustness under this model by (i) deriving an expression for the final system size as a function of the size of initial attacks; (ii) deriving the critical attack size after which system breaks down completely; (iii) showing that complete system breakdown takes place through a first-order (i.e., discontinuous) transition in terms of the attack size; and (iv) establishing the optimal load-capacity distribution that maximizes robustness. In particular, we show that robustness is maximized when the difference between the capacity and initial load is the same for all lines; i.e., when all lines have the same redundant space regardless of their initial load. This is in contrast with the intuitive and commonly used setting where capacity of a line is a fixed factor of its initial load. We will also consider the case where an adversary can launch a targeted attack, and present several results on the hardness of attacking optimally. Time permitting, we will present several other application areas for the same model with pointers for future work.

Coffee break

11:00 - 11:45 Marta Gonzalez

Planning for Electric Vehicles Coupled with Urban Mobility -

The rising adoption of plug-in electric vehicles (PEVs) leads to the alignment of their electricity and their mobility demands. Therefore, transportation and power infrastructures are becoming increasingly interdependent. In this work, we uncover patterns of PEV mobility by integrating for the first time two unique data sets: (i) mobile phone activity of 1.39 million Bay Area residents and (ii) charging activity of PEVs in 580,000 sessions obtained in the same region. We present a method to estimate individual mobility of PEV drivers at fine temporal and spatial resolution integrating survey data with mobile phone data and income information obtained from census. Thereupon, we recommend changes in PEVs charging times of commuters at their work stations that take into account individual travel needs and shave the pronounced peak in power demand. Informed by the tariff of electricity, we calculate the monetary gains to incentivize the adoption of the recommendations. These results open avenues for planning for the future of coupled transportation and electricity needs using personalized data.
11:45 - 12:30 Hiroki Sayama

Formulating Evolutionary Dynamics of Organism-Environment Couplings Using Graph Product Multilayer Networks

A conventional view of biological evolution typically assumes that the fitness is an attribute of individual organisms or genes. However, this simplistic view is known to be invalid in realistic scenarios where organisms' fitnesses depend on their surrounding environments. Here we present a theoretical framework that mathematically formulates the evolutionary dynamics of such organism-environment couplings using graph product multilayer networks. Specifically, one factor network represents different options of environments and their mutual physical accessibility, and another factor network represents possible types of organisms and their mutual evolutionary accessibility. The organism-environment coupling space is given by a Cartesian product of these two networks, whose nodes represent specific organism-environment combinations. We studied a simple evolutionary model using a reaction-diffusion equation on this organism-environment coupling space. We numerically measured correlations between the inherent fitness of organisms and the actual average fitness obtained from the graph product-based evolutionary model, varying the spatial diffusion rate while keeping the type diffusion rate small. Results demonstrated that, when the spatial diffusion is sufficiently slow (i.e., when the system is effectively spatial), the correlation between inherent and actual fitnesses drops significantly, where it is no longer valid to assume that fitness can be attributed only to organisms.


Session II

14:30 - 15:15 Danielle Bassett

Perturbation and Control of Human Brain Network Dynamics

The human brain is a complex organ characterized by heterogeneous patterns of interconnections across disparate physical scales and phenomenological levels. New non-invasive imaging techniques now allow for these patterns to be carefully and comprehensively mapped in individual humans, paving the way for a better understanding of how wiring supports our thought processes. While a large body of work now focuses on descriptive statistics to characterize these wiring patterns at a single scale, a critical open question lies in how the organization of these networks across scales constrains the potential repertoire of brain dynamics. In this talk, I will describe an approach for understanding how perturbations to brain dynamics propagate through complex writing patterns, driving the brain into new states of activity. Drawing on a range of disciplinary tools – from graph theory to network control theory and optimization – I will identify control points in brain networks, characterize trajectories of brain activity states following perturbation to those points, and propose a mechanism for how network control evolves in our brains as we grow from children into adults. Finally, I will describe how these computational tools and approaches can be used to better understand how the brain controls its own dynamics (and we in turn control our own behavior), but also how we can inform stimulation devices to control abnormal brain dynamics, for example in patients with severe epilepsy.
15:15 - 16:00 Federico Battiston

Mesoscale organization of multiplex collaboration and brain networks

Embedding relations of different types across several layers, multiplex networks encode an additional level of richness which can be observed across different scales, from motifs to community and core-periphery structure. In the first part of this talk I will revisit two historical network datasets (a co-authorship network of scientists and a co-starring network of actors) with a multilayer perspective. I will show the emergence of non-trivial multiplex communities spanning different research areas or movie genres, and introduce a simple model of network evolution which mimics the real mechanisms by which collaborations grow and is able to reproduce the empirical findings. In the second part of this talk I will build the theory behind multilayer motif analysis, and discuss a new algorithm to extract cores in multiplex networks. The methods are applied to multimodal brain networks built from the joint analysis of structural and functional connectivity, confirming the non-trivial relationship between the two and highlighting novel regions of interest neglected from previous analyses.

Coffee break

16:30 - 17:15 Sergio Gomez

Microscopic Analysis of Spreading Processes in Multilayer Networks

Mean field approximations have allowed an important advancement in the understanding of spreading processes in networks, e.g. yielding first approximations to the epidemic thresholds for different models of networks. However, they are not appropriate for the analysis of a given network, only for families of them with well-defined statistical structural properties. The Microscopic Markov Chain Approach (MMCA) constitutes the main analytical alternative for the theoretical examination of discrete-time spreading processes in fixed (synthetic or real) networks. It has been applied to diverse dynamics such as SIS epidemic spreading, threshold-like models, the coupling of epidemic and information spreading in multiplex networks, metapopulation models, and routing dynamics. In this presentation, we will review MMCA in several single-layer and multiplex dynamics, and we will introduce a new paradigm in which the microscopic variables are defined at the level of links instead of nodes. We will show the derivation of Epidemic Link Equations for a SIS dynamics, which leads to important concepts such as the conductance of the links or the hostility felt by a node.
17:15 - 18:00 Elisa Omodei

Multilayer network analysis for socio-economic development and humanitarian response

Over the last decades network science, and more recently the methods developed for the study of multilayer networks, have been successfully applied to study problems in diverse fields, from sociology to biology. In this talk, I will give an overview of applications of multilayer network methods for socio-economic development and humanitarian response. I will focus in particular on a study investigating the diffusion of microfinance within rural India villages accounting for the whole multilayer structure of the underlying social networks. We define a new measure of node centrality on multilayer networks, diffusion versatility, and show that this is a better predictor of microfinance participation rate than previously introduced measures defined on aggregated single-layer social networks. Moreover, we untangle the role played by each social dimension and find that the most prominent role is played by the nodes that are central on the layers related to trust (asking for help in a medical emergency, asking for money if in need, and asking for advice), shedding new light on the key triggers of the diffusion of microfinance.