LECTURES & TUTORIALS

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.

Multiresolution Filterbanks to Enhance Signal Contrast 
(Speaker: Jacob Billings)
The tutorial explores the use of wavelet filters to enhance feature detection among time series. Wavelet filters are especially useful at localizing deviations from ongoing dynamics. The tutorial will demonstrate the use of several wavelet filtration schema–including continuous, discrete, and bi-orthogonal–to enhance data-driven feature detection in time-series.

Unravelling the topological arrangements and selected reaction parameters from global measurements of an extended neural model
(Speaker: Ihusan Adam)
Living brains show immensely complex dynamics that are often modelled by ensembles of simple neuron models connected through a network of intricate structure. The complexity displayed by these systems stem from the topology of the network support. To gain an insight into this problem, we propose and test a procedure that is aimed at reconstructing the a priori unknown architecture of the embedding network. To this end we consider and extended model of Leaky-Integrate and Fire (LIF) neurons with short-term plasticity. The neurons are coupled to directed network and display a level of heterogeneity in the associated current a, which dictates the  ring regime in which a neuron is operating in. The aim of the method is to recover the distribution of connectivity k ̃ of the underlying networks as well as the distribution of the assigned a. Our approach to the inverse problem makes use of the celebrated Heterogenous Mean-Field (HMF) approximation to rewrite the dynamics of the system by splitting the types of neurons into classes which re ect the associated a and in-degree k ̃. The HMF reduction scheme allows us to in essence, create a mesh on the space de ned by the variables a and k ̃ in such a way that all possible neurons fall within this space. The two sought distributions of P(a) and P(k ̃) are then the correct solutions that sum the classes of neurons to reproduce the global  eld that was obtained by simulating the original model. We have tested this on synthetic data, where the global  eld was generated by a random network and a bell-shaped distribution of currents, and here the method captures the two distributions remarkably well and manages to almost exactly reproduce the global field.

The Origins of Social Balance in Signed Networks
(Speaker: Sofia Teixeira Monteiro)
Social media often reveals a complex interplay between positive and negative ties. And real online social networks are proven to show high social balance. Yet, the origin of such complex patterns of interaction remains largely elusive. In this work we study how third parties may sway our perception of others. We build a model of peer-influence relying on the analysis of all triadic relations taking into account the relations with common friends. We show that this simple peer-influence mechanism, based on balance theory of social sciences, is able to promptly increase the social balance of a signed network.