*(updated January 31, 2020)*

**Monday, 18 May, morning (9.30-12.30)**

**Introduction to Complex Networks** **(Mendes)**: In this introductory lecture I will present topics in a simple and intuitive form about complex networks that does not require any specific knowledge on the field. I will present and explore some of the main features of networks from the node degree to the global properties. I will review the state-of-the-art in network science given attention to network models, percolation properties, phase transitions, etc.

**Monday, 18 May, afternoon (14.30-17.30)**

**Spreading Processes in Mono- and Multilayer Networks ****(Moreno)**: Introduction to the structure of multilayer networks. Disease spreading models: SIS and SIR dynamics. Individual-based description of spreading processes: Microscopic Markov Chain Approach. Mean-field descriptions. Some notes about numerical simulations. Disease spreading in undirected and directed multilayer networks. Localization of diseases. Rumor dynamics. Diffusion dynamics in undirected and directed multilayer networks. Application: measuring the epidemic reproduction number in data-driven contact networks.

**Tuesday, 19 May, morning (9.30-12.30)**

** Percolation Processes on Multiplex Networks (Mendes)**: Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each layer having its own kind of edges, represented by different colours. An important fundamental structural feature of networks is their resilience to damage, the percolation transition. Generalisation of these concepts to multiplex networks requires careful definition of what we mean by connected clusters. In this course I will present results about the percolation transition in these systems.

**Tuesday, 19 May, afternoon **

* short talks by students* (see page Application)

**Wednesday, 20 May, morning (9.30-12.30)**

**Computational Human Dynamics ****(Karsai)**: Human actions and interactions appear neither deterministic nor completely random for an external observer. They are driven by several confounding factors like personal decisions and preferences, inter-personal influence, or impulses arriving from the environment just to mention a few. Consequently, their characterization, modeling and understanding have to consider simultaneously their stochastic but correlated nature, which can be conveniently approached by computational methods. Early simulation studies of human dynamics focused on the mechanistic modeling of emergent social phenomena like the social structure or any collective process taking place on it. Multivariate statistical models have been also developed to identify correlations and causal patterns in the temporal sequence of decisions, mobility, or adoption patterns of individuals or groups. However, the recent availability of large digitally behavioral datasets radically changed this landscape and opened up novel opportunities for the application and development of computational methods borrowed from statistical learning and artificial intelligence. This lead researcher to achieve better understanding of human behavior, and to build predictive models with ever seen precision about processes driven by the many aspects of human dynamics. In this lecture we are going to discuss examples regarding these aspects of computational human dynamics. We will identify some ways human dynamical data can be collected and will introduce several computational models, built on mechanistic or statistical learning conventions, to describe human dynamics at the individual, group and collective level. More precisely, we will discuss the characterization and potential explanations of bursty patterns of individual dynamics; we will focus on temporal networks and their different ways of modeling and representations; and we will see how statistical learning methods can be use to infer characteristics of individuals like their language usage or socioeconomic status.

**Wednesday, 20 May, afternoon (14.30-17.30)**

**Brain networks ****(De Vico Fallani)**: In the last decades, network science has become essential for studying complex interconnected systems. Combined with neuroimaging, network science has allowed to visualize brain connectivity patterns and quantify their key organizational properties. Within this expanding multidisciplinary field many issues remain open, from how modeling temporally dynamic brain networks to how integrating information from multimodal connectivity. In this presentation, I will focus on these challenges and discuss the potential impact through a selection of results obtained in human neuroscience.

**Wednesday, 20 May, evening (20.00)**

**social dinner**

**Thursday, 21 May, morning (9.30-12.30)**

**Biological Networks (I)****(Pržulj)**: Dealing with complex “omic” data is computationally intractable. Hence, we must develop methods for extracting new biomedical knowledge from them. In this lecture, we will present new computational methods from our lab to address these challenges. Our new computational methods uncover the patterns in molecular networks and in the multi-scale network organization indicative of biological function, translating the information hidden in the network topology into biomedical knowledge. Also, we introduce a versatile data fusion (integration) framework to address key challenges in precision medicine: better patient stratification, prediction of driver genes in cancer, and re-purposing of approved drugs to particular patients and patient groups. Our new methods stem from novel network science approaches coupled with machine learning, such as graph-regularized non-negative matrix tri-factorization. We utilize our new methodologies for performing other related tasks, including uncovering new cancer mechanisms and disease re-classification from modern, heterogeneous molecular level data, inferring new Gene Ontology relationships, and aligning multiple molecular networks.

**Thursday, 21 May, afternoon (14.30-17.30)**

**Biological Networks (II)****(Calzone)**: Cancer is often referred to as a network disease, because the genes that are mutated or altered affect or even rewire the original (healthy) network leading to different outcomes. The complexity of the processes and events that contribute to the development of the disease calls for formal and precise theoretical approaches to explain in details these complex biological phenomena, provide predictions that can be tested experimentally, and formulate plausible scenarios of a complex biological behaviour when intuition is not sufficient anymore. For that purpose, we start with the analyses of omics data and the gathering of prior information (from published experiments and databases) and organise the acquired knowledge in the form of a network. The network includes the main actors of the signalling pathways that participate in the tumorigenesis. The network is then translated into a mathematical model with the appropriate formalism (chemical kinetics, logical approach, etc.) that will depend on the initial biological question and the type of networks. The model aims at predicting and anticipating the effect of a perturbation, either from an intrinsic point of view (e.g., mutations) or from an extrinsic point of view (e.g. drug treatment). After introducing some key concepts of network construction and mathematical formalisms, I will show some examples of such analyses with logical models of signalling pathways which are known to be altered in cancer.

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