**Lectures**

**Susanna Manrubia**

**Viral war games: When evolution defeats imagination**Viruses count amongst the most amazing organisms on Earth regarding their evolutionary and adaptive abilities. They resort to several different forms of coding information in their genomes; together with an array of different mutational mechanisms, they have succeeded in infecting all cellular organisms and in escaping any antiviral strategy (natural or artificial). We will present two examples of viral adaptive strategies that can be formally addressed: the complex population response to combinations of antiviral drugs and the advantages of viruses with multipartite genomes. Finally, we will briefly discuss the origin of viruses and the role they may have played in the evolution of life.

**Fabrizio Lillo**

*Dynamical models of temporal networks*Many complex systems can be described as temporal networks, i.e. networks where links appear and disappear with time. Given the high dimensionality of the problem, suitable models are needed, especially if one is interested in parameter or hidden variable estimation, link forecasting, and analytical modelling the propagation of a signal on the network. In this lecture I will present some recent advancement in the field, introducing stationary and non-stationary models with application to financial and social temporal networks.

**Marián Boguñá**

**Network geometry. A geometric approach to complex networks**The main hypothesis of the network geometry program states that the architecture of real complex systems has a geometric origin. In a nutshell, the idea is that the elements of a complex system can be characterized by their positions in some underlying metric space so that the observable network topology —abstracting their patterns of interactions— is a reflection of their distances in this space. This simple idea has led to the development of a very general framework able to explain the most ubiquitous topological properties of real complex networks, namely, degree heterogeneity, the small-world property, and high levels of clustering. Network geometry is also able to explain in a very natural way non-trivial properties of real networks, like their self-similarity and community structure, their navigability properties, and is the basis for the definition of a renormalization group in complex networks. The same framework has also been successfully extended to weighted networks and multiplexes. In this lecture, I will review the work done in this field of research during the last ten years and discuss the applications of network geometry to many open problems in network science.

**Claudio Tessone**

**A complex systems approach to cryptocurrencies**Cryptocurrencies are possible because their public ledgers allow the storage of trustworthy information without the pre-requisite of trust between system participants. However, for this property to be preserved, ‘who’ writes these data into the ledger must be acceptable to all. Thus, centralisation of any kind is against the core principle of blockchain-based systems. Cryptocurrencies are the most widely adopted incarnation of blockchains. They are plagued with economic incentives, many of them obvious, some others put inadvertently. In this presentation we will review different links between microscopic agent behaviour and macroscopic emergent properties of cryptocurrencies.

The lecture consists of three parts: Wealth dynamics, financial markets and dark markets. In the first part of the lecture, we will explain the increasing concentration on wealth (and power!) in different cryptocurrencies, and link it to underlying design principles. In the second, we will explain the relationship between endogenous activity in cryptocurrencies and price dynamics with respect to fiat currencies. Finally, the third part will delve into the circulation (and relative size!) of illegal trades in cryptocurrencies.

Teamwork

**projects**

*Keep an eye on this page: we'll add them as we can confirm them*

1.

**Simplex2Vec embeddings for community detection in higher order interaction networks**(Tutor: Giovanni Petri)

Topological representations are rapidly becoming a popular way to capture and encode higher-order interaction in complex systems: they have found applications disciplines as different as cancer genomics, brain function and computational social science. Simplicial complexes, i.e. relational structures at the core of current topological descriptions, have hence become object of study, from both the modeling and descriptive perspectives. Surprisingly, scarce attention was given to defining a community structure on simplicial complexes. Here, we will adopt recent advances in symbolic embeddings (word2vec, node2vec) to produce an embedding based on the local dense structure of the complex and then exploit it to compute (simplicial) clusters. After investigating simplicial complexes coming from various fields (e.g. face-to-face contact data, brain functional activity), we will compare the results of this embedding route with the standard, and unsolved, problem of arbitrary simplicial complex embedding and quantify how much of the full combinatorial homological structure of the complexes is recovered by the embedding.

2.

**Temporal and correlational topology of Alzheimer's Disease**(Tutor: Giovanni Petri)

Recent evidence showed that neuronal dynamics in fMRI recordings during rest and task conditions converges on a low-dimensional manifold, that is thought to facilitate the execution of diverse task states. The properties of this manifold and of the flow defined on it correlated with individual cognitive measures. We will investigate the deformation of the manifold in pathological conditions, in particular in Alzheimer's Disease (AD), in two ways: first, by characterizing its topological deviations from the healthy case via the homological properties of the fabric of functional correlations; second, by comparing the global temporal topology of healthy and AD subjects captured by geometrization and symbolic techniques (Taken's embedding and word2vec)

3.

**How to protect sex workers from HIV: simulating the impact of different prevention strategies**

on an empirical network of sexual contacts(Tutor: Eugenio Valdano)

on an empirical network of sexual contacts

Sexual contacts are the main spreading route of the Human Immunodeficiency Virus (HIV). This puts sex workers at higher risk of infection even in populations where prevalence (average fraction of population infected) is moderate or low. Female sex workers with heterosexual clients are particularly at risk, given the higher probability of male-to-female transmission than female-to-male. Protecting female sex workers from HIV infection not only positively affects the welfare of an often stigmatized group with poor access to healthcare. It is also a key step in eliminating the HIV epidemic by reducing the prevalence in a bridge population. Female sex workers have two main ways to protect themselves: condoms, and Pre-Exposure Prophylaxis (PrEP). PrEP consists in taking a pill every day, and protects uninfected individuals from acquiring HIV, even when they engage in condom-less acts. Many factors drive diffusion and adherence both to condom use and to PrEP. We will use an empirical network of sexual contacts. We will simulate the spread of HIV and the adoption and adherence to condom use and PrEP. We will compare the impact of the two prevention strategies on the number of prevented infections.

4.

**Network analysis of the global carbon trade flows**

**(Tutor: Angelo Facchini)**

The aim of the project is to apply complex networks methods to the global CO2 flows associated to the commerce of goods and commodities between world countries. Starting from Multi-Regional Input Output (MRIO) data, we derive a network to apply centrality measures and community detection methods to find vulnerabilites and hidden patterns in the global trade system. Results have a direct impact on carbon reduction policies as well as highlighting potential effects of protectism-oriented policies.

5.

**Grand challenges in social physics: In pursuit of moral behavior**(Tutor: Valerio Capraro)

Methods of statistical physics have proven valuable for studying the evolution of cooperation in social dilemma games. However, recent empirical research shows that cooperative behavior in social dilemmas is only one kind of a more general class of behavior, namely moral behavior, which includes reciprocity, respecting others' property, honesty, equity, efficiency, as well as many others. Inspired by these experimental works, in [1] we argued that it is time to go beyond the borders of cooperation and start applying methods of statistical physics to other behaviors. In[2] we did a first step in this direction, by applying the Monte Carlo method to study the evolution of honesty in well-mixed populations. But this is only a first step and a lot of questions remain to be addressed. This is a far-reaching direction for future research that can help us answer fundamental questions about human sociality. Why did our societies evolve as they did? What moral principles are more likely to emerge? What happens when different moral principles clash? Can we predict the break out of moral conflicts in advance and contribute to their solution? These are amongst the most important questions of our time, and methods of statistical physics could lead to new insights and contribute toward finding answers.

[1] Capraro V, Perc M (2018) Grand challenges in social physics: In pursuit of moral behavior. Frontiers in Physics, 6, 107.

[2] Capraro V, Perc M, Vilone D (2019) The evolution of lying in well-mixed populations. Under Review.

6.

**Polarization dynamics in echo chambers on social media**(Tutor: Michele Starnini)

Echo chambers in online social networks, in which users prefer to interact only with ideologically-aligned peers, are believed to facilitate misinformation spreading and contribute to hamper democratic debate [1]. Data-driven research efforts have recently quantified echo-chambers effects on the spreading of information, revealing that the capability of users in propagating the content they produce strongly depends on their polarization [2]. However, the polarization of a user is often assumed to be a static quantity, averaged over a certain time interval. How can we quantify the evolution of polarization in time on different social media (e.g. Twitter, Facebook, Reddit)? Is the network of interactions between users affected by such polarization dynamics? Can echo chambers, i.e. the combination of users' polarization and their interaction network, be reproduced by time-varying network models? In this project, we will combine data analysis with temporal network approaches to shed light on these questions.

[1] M. Del Vicario et al., “The spreading of misinformation online,” PNAS 113, 554 (2016).

[2] W. Cota et al., "Quantifying echo chamber effects in information spreading over political communication networks", Under review (2019).

7.

**Maximum entropy and maximum likelihood approach to network ensembles: network reconstruction from partial information and null models**(Tutor: Andrea Gabrielli)

In this project students will be involved in a theoretical and numerical study of the most advanced methods of network modeling based on the concepts of constrained maximum entropy and maximum likelihood. This approach is very important in all situations in which we would like to build an ensemble of network configurations all sharing some minimal mean features without introducing arbitrary and uncontrolled statistical biases. This is crucial in particular in two cases: (i) when we want to reconstruct the properties of a real network about which only partial information is accessible; (ii) when we want to test, by constructing appropriate null models, the statistical hypothesis whether “high order” statistical properties of an observed networks can be derived from its simpler “low order” ones.

8.

**Geometric embeddings vs. community detection in complex networks**(Tutor: Marián Boguñá)

Random graphs in latent metric spaces represent nowadays the simplest class of models able to explain most of the complex topological properties of real networks, including heterogeneous degree distributions, high levels of clustering, degree-degree correlations, small-worldness, self-similarity, community structure, etc. This seems to indicate that, indeed, the topology of real networks has a geometric origin. If this is true, finding faithful embeddings of complex networks may provide a wealth of novel information, as it allows us to quantify single interactions among elements of the system. In this project, students will make use of Mercator, a new algorithm that provides very accurate embeddings of complex networks. Using Mercator, a large set of real complex networks will be embedded in the hyperbolic plane. After assessing the quality of the embedding, the obtained geometric information can be used to detect communities in the system. Already tested algorithms will be compared to new proposals and finally, communities found from the embeddings will be compared to those found by well stablished community detection methods.

9.

**Low-dimensional representation of temporal networks**(Tutor: Laetitia Gauvin)

The use of dimensionality reduction techniques has been proven to be powerful in various domains. For what regards temporal networks such techniques can help recovering missing data, detect anomalies and extract latent structures. Here we will take advantage of the flexibility of tensor factorization methods, a well known unsupervised machine learning technique, to tackle some of these problems and will possibly extend to more general techniques of embeddings. We will consider several possible applications such as the analysis of streams of user-generated content in social media that exhibit patterns of collective attention across diverse topics, with temporal structures determined both by exogenous factors and endogenous factors. Another possible case study will be related to social networks, online or offline. Because social interactions represent the main transmission route of diseases and information, there is a crucial need to develop techniques able to deal with the structures encountered in temporal networks that entail complex correlations of topological features and activity patterns. Low-dimensionality representations can be of help in these different case studies, indeed they can allow to extract topics out of unstructured texts in social media or to extract community-like structure that have an impact on diffusion processes relevant to information/disease propagation.

10.

**Evolution and the interplay between interaction and competition**(Tutor: Ennio Bilancini)

The evolution of behaviors (or phenotypes) in a structured population depends on both the structure of interaction and the structure of competition. The structure of interaction specifies how agents are matched (e.g., in a uniformly random manner or assortatively under some respect). Together with agents' behaviors (or phenotypes), the interaction structure allows to compute fitness. The structure of competition specifies instead which agents compete with each other to spread their behaviors (or phenotypes) over time. Among competing agents, selection of phenotypes is based on fitness. Despite the literature has only indirectly focused on this aspect, the evolution of phenotypes may largely depend on the interplay between interaction and competition structures. We strongly encourage investigations of the effects of this interplay on the results of evolutionary selection. Such investigations are likely to require focusing on complex systems, which are not easily studied analytically but may be worked out through simulations.

11.

**Understanding the meso-scale dynamics of the Blockchain economy**(Tutor: Claudio J. Tessone)

Blockchain-based systems are the backbone technology for several crypto-currencies and allow for trust to emerge in distributed systems without the need for central authorities. These registries contain the full story of economic transactions within this closed economy. As such, they constitute a unique (yet immense) dataset that can be exploited in multiple ways. Within the system, thousands of entities (the largest ones) can be identified and the wealth flow measured. In this project, the interested students will apply statistical network models to assert the topological effects that are significant in the formation, evolution and growth of the Bitcoin economy. They will be presented with a curated dataset of manageable size, covering most of the system history.

**Tutorials**

**TBA**