- 3 September 2017
- 4 September 2017
- 5 September 2017
- 6 September 2017
- 7 September 2017
- 8 September 2017

#### 15:00

**Meeting point at Catania airport with the School bus.Welcome.**

#### 08:30 - 9:00

##### Registration

#### 09:00 - 09:15

##### Introduction

#### 09:15 - 10:00

##### Presentation of students to the School

#### 10:00 - 13:00

##### Session I: STRUCTURE AND DYNAMICS OF MULTILAYER NETWORKS.

**Vito Latora (Queen Mary University of London)**

The constituents of a wide variety of real-world complex systems interact with each other in complicated patterns that can encompass multiple types of relationships and change in time. Recently, the interest of the research community towards such systems has increased because accounting for their "multilayer" features is a challenge. In this lecture, we will review the most recent advances in this new field, with main attention to the emergent properties induced by the structure of multiplex networks.

Topics covered:

- From complex systems to multilayer networks

- Structural properties of multilayer networks

- Reducibility of multilayer networks

- Dynamical properties of multulayer networks

#### 17:00 - 19:00

##### Student activities (TBD)

#### 09:30 - 12:30

##### Session II: Network Inference

**Tiago Peixoto (University of Bath, UK)**

Network structures are shaped by evolutionary mechanisms and determine the central aspects of how a system functions. However, differently from systems that are naturally embedded in space, we cannot simply "look" at network in order to extract its most important structural patterns. Instead, we must rely on well-founded algorithmic methods to extract this information from data in an interpretable way. In this lecture, we review a principled approach to this problem based on the elaboration of probabilistic models of network structure, and their statistical inference from empirical data.

We aim to cover the following topics:

- The stochastic block model (SBM) and its variants (degree correction, overlapping groups, etc.)

- Bayesian inference and model election: Distinguishing structure from noise.

- Generalizing from data: Prediction of missing and spurious links.

- Model extensions: Layered, dynamic SBMs, and generalized models on continuous latent spaces.

- Fundamental limits of inference: The undetectability transition.

- Efficient inference algorithms.

#### 17:00 - 19:00

##### Student activities (TBD)

#### 09:30 - 12:30

##### Focused Seminars Session

**Ernesto Estrada**

Communicability in networks

The concept of communicability will be motivated and introduced. Then, matrix functions will be used for its definition. Several theoretical properties of communicability functions and related parameters will be explained. Finally, a few examples of applications in neurosciences, social, ecological and infrastructural networks will be given.

**Eugenio Valdano**

Time-evolving networks and the spread of infectious diseases

Network epidemiology represents a powerful tool for assessing the vulnerability of a population to the introduction of a new infectious pathogen. The increased availability of highly resolved data tracking host interactions is making epidemic models potentially increasingly accurate. Integrating into them all the features emerging from these data, however, still represents a challenge. In particular, the interaction between disease dynamics and the time evolution of contact structures has been shown to impact the way pathogens spread. It changes, for instance, the conditions that lead to the wide-spreading regime, as encoded in epidemic threshold, which is the critical transmissibility value above which the epidemic breaks out. With a data-driven perspective, I will review the progress made in this field. I will show theoretical results and their applications, using both numerical and analytical techniques.

**Samir Suweis**

Adaptability and Stability in Mutualistic Ecological Networks

Mutualistic networks are formed when the interactions between two classes of species are mutually beneficial and they are important examples of cooperation shaped by evolution. The topological properties of the ecological interaction networks have been the subject of sparkling research and they indicate non-random pattern of community organization. Indeed, ecologists have collected extensive data on species interactions showing that, independently of species composition and latitude, mutualistic networks (such as plant-pollinator systems) have nested architectures: specialist species, with only few mutualistic links, tend to interact with a proper subset of the many mutualistic partners of any of the generalist species. I will show how nested interaction networks could emerge as a consequence of an optimization principle that also attenuates the impact of perturbation propagation on species abundance.

**Miguel Angel Muñoz**

Complex synchronization patterns and Griffiths phases in brain networks

In this talk, I will discuss how the special features of the connectivity patterns of (human) brain networks, severely affect dynamical processes --relevant in neurodynamics, information processing, and ultimately in cognition-- occurring on top of them. Particular emphasis will be put onto the hierarchical and modular organization of the network of anatomical connections, and how the heterogeneity of its modules induces new behaviors --absent in more regular networks-- such as critical-like features such as generic slow relaxations, large correlation lengths and responses, etc (i.e. Griffiths phases) and highly variable synchronization patterns, matching empirical observations from functional magnetic resonance recordings.

**Massimo Stella**

What can network theory tell us about the human mind?

Representing words in the human mind as a network opened new scenarios in cognitive science, providing new quantitative tools for the investigation of linguistic and cognitive patterns. This talk will review the impact that network models have in psycholinguistic applications, such as: (i) the identification of constraints over sound similarities in words, and the (ii) quantification of word learning strategies in young children and adults. Well known cognitive effects like phonological competition or lexical learning will be quantified and related to network features like centrality measures or multiplexity within models of network growth.

**Marco Javarone**

Evolutionary Game Theory: a brief introduction.

Evolutionary Game Theory (EGT) represents the attempt to describe the evolution of populations by combining the mathematical framework of Game Theory with the Darwinian principles of evolution. Nowadays, a long list of applications of EGT spans from biology to socio-economic systems, aiming to describe the behavior of complex phenomena. In particular, the discovering (and the understanding) of mechanisms able to trigger the emergence of cooperation constitutes one of the most interesting challenges in this area. Here, networkedtopologies play a very important role, in particular in relation to the phenomenon known as 'network-reciprocity'. During this brief tutorial, participants will have the opportunity to learn about the preliminary concepts in EGT, with a focus on two famous games, i.e. the Prisoner's Dilemma and the Public Goods Game. In addition, some use cases, related to the modeling of social behaviors will be discussed, in order to stimulate the interest of students coming from different areas, e.g. from physics to computational social science.

**Jacob Biamonte **

Quantum vs stochastic walks on complex networks.

Dynamical stochastic processes can be formulated in a way reminiscent of quantum theory [BB17, BFD17]. This sets a stage for contrasting stochastic and quantum mechanics in terms of walks on complex networks. We will recall the exactly solved model in [Phys. Rev. X 3, 041007 (2013)] and conclude with ideas appearing in quantum statistical mechanics to formulate entropy for general complex networks [Phys. Rev. X 6, 041062 (2016)].

[BB17] 274 page book on using quantum techniques to model stochastic processes https://arxiv.org/abs/1209.3632

[BFD17] survey article â€˜complex networks: from classical to quantumâ€™ https://arxiv.org/abs/1702.08459

#### 16:00 - 20:00

##### Social boat tour.

#### 09:30 - 12:30

##### Session III: Spreading Processes in Complex Networks

**Jesús Gómez-Gardeñes (Universidad de Zaragoza)**

In this lecture we will cover the fundamentals of contagion processes in complex networks. We will start by introducing the so-called compartmental models and show the main techniques aimed at studying this framework in populations whose interaction backbone is a graph. Then we will explore matapopulations dynamics to tackle the analysis of spreading processes in realistic scenarios. We will show how real mobility patterns, described as origin-destination matrices, can be incorporated in metapopulation models to obtain predictions about the epidemic onset.

The outline of this lecture is:

- Introduction

- Compartmental models

- The heterogenenous mean field approach

- The microscopic Markovian framework

- Metapopulation models

- The Markovian formulation of metapopulation dynamics

- Vector-borne diseases

#### 20:00 - 23:00

##### Social dinner

#### 09:30 - 12:30

##### Session IV: Ecological Networks

**Sonia Kéfi (Université de Montpellier/CNRS)**

Networks provide powerful tools to visualize and quantify the complexity of ecological systems. In this lecture, I'll present some of the broad questions that have been addressed with networks in ecology. I'll give an overview of recent (and less recent) studies on the structural regularities of ecological networks, and what we know about the links between these structural properties and ecological network dynamics, and in particular their resilience to perturbations.

Topics covered (tentative):

- The complexity-stability debate in ecology

- Food webs: data and theory

- Mutualistic networks: data and theory

- Toward multiplex ecological networks