Abstract: We introduce a network valuation model (hereafter NEVA) for the ex-ante valuation of claims among financial institutions connected in a network of liabilities. Similar to previous work, the new framework allows to endogenously determine the recovery rate on all claims upon the default of some institutions. In addition, it also allows to account for ex-ante uncertainty on the asset values, in particular the one arising when the valuation is carried out at some time before the maturity of the claims. The framework encompasses as special cases both the ex-post approaches of Eisenberg and Noe and its previous extensions, as well as the ex-ante approaches, in the sense that each of these models can be recovered exactly for special values of the parameters. We characterize the existence and uniqueness of the solutions of the valuation problem under general conditions on how the value of each claim depends on the equity of the counterparty. Further, we define an algorithm to carry out the network valuation and we provide sufficient conditions for convergence to the maximal solution.

Abstract: In multi-layer networks with directed links, introducing measures of dependency between different layers requires more than a straightforward extension of the multiplexity measures that have been developed for undirected multiplexes. In particular, one should take into account the effects of reciprocity, i.e. the tendency of pairs of vertices to establish mutual connections. In single-layer networks, reciprocity is a crucial structural property affecting several dynamical processes. Here we extend it to multiplexes and introduce the notion of multireciprocity, defined as the tendency of links in one layer to be reciprocated by links in a different layer. While ordinary reciprocity reduces to a scalar quantity, multireciprocity requires a square matrix generated by all the possible pairs of layers.

Abstract: The Japanese banking crisis in the late 1990s has been considered a significant turning point in the history of the Japanese banking system. This period has attracted researchers' interest in studying the increase of bad debt on Japanese banks? balance sheets, which led to the crisis of the 1990s. Here we investigate the risk propagating through a bipartite banking network consisting of two kinds of nodes: assets on one hand and banks on the other. Using a Cascading Failure Model (CFM), originally proposed by Huang et al. [1], to describe the propagation of failures in the network, we attempt to understand the main culprit provoking the crisis and the systemic conditions that amplified or repressed the ?chain reaction? of bankruptcies

Abstract: Bipartite networks are currently regarded as providing a major insight into the organization of real-world systems, unveiling the mechanisms shaping the interactions occurring between distinct groups of nodes. One of the major problems encountered when dealing with bipartite networks is obtaining a (monopartite) projection over the layer of interest which preserves as much as possible the information encoded into the original bipartite structure. In the present paper we propose an algorithm to obtain statistically-validated monopartite projections of bipartite networks, which implements a entropy-based null-model We analyze a social network (i.e. the MovieLens dataset, a bipartite network of users and rated movies) and an economic network (i.e. the countries-products World Trade Web representation): while, in the first case, projecting Movie- Lens on the films layer allows clusters of movies belonging to similar genres to be detected, in the second case, projecting the World Trade Web on the countries layer reveals a modular structure of similarly-industrialized clusters of nations.

Abstract: We introduce two models of inclusion hierarchies: random graph hierarchy (RGH) and limited random graph hierarchy (LRGH). In both models a set of nodes at a given hierarchy level is connected randomly, as in the Erdos-Renyi random graph, with a fixed average degree equal to a system parameter c. Clusters of the resulting network are treated as nodes at the next hierarchy level and they are connected again at this level and so on, until the process cannot continue. In the RGH model we use all clusters, including those of size 1, when building the next hierarchy level, while in the LRGH model clusters of size 1 stop participating in further steps. We find that in both models the number of nodes at a given hierarchy level h decreases approximately exponentially with h. The height of the hierarchy H, i.e. the number of all hierarchy levels, increases logarithmically with the system size N, i.e. with the number of nodes at the first level. The height H decreases monotonically with the connectivity parameter c in the RGH model and it reaches a maximum for a certain c(max) in the LRGH model. The distribution of separate cluster sizes in the LRGH model is a power law with an exponent about -1.25. The above results follow from approximate analytical calculations and have been confirmed by numerical simulations.

Abstract: Information diffusion and epidemics outbreaks share a similar non linear dynamics which is studied in many scientific fields, including biology, engineering and physics.?The problem of controlling such types of dynamics in complex systems has recently been studied in different contexts. We shall provide an overview of recent? results obtained both in the case of control, i.e., when a central decision can be?operated and agents comply to the central controller, and strategic versions of the same?problems, where some of the agents may comply or not, or to a certain degree,? depending on their own utility, both in the case of cooperative behaviors and in the? case of competitive ones.?

Abstract: Worldwide firms interact with each other to form complex networks of financial relations. These financial interactions are partly captured by the ownership relations between them. We constructed the weighted and directed network of 800,000 companies forming multinational firms, with respect to their 1.2 million ownership relations (UNIL-GeoDivercity-Orbis, 2013) and extracted the corresponding directed network of the cities that harbor these firms. The firms, and therefore the cities, are then classified into five categories according to their main field of activity, i.e. high-tech, low-tech, knowledge-intensive services, low knowledge-intensive services and other (OECD, 2009). We employed this classification to divide the network into activity-specific relation networks that are connected through the cities they have in common, thus constructing a weighted and directed, multi-layered, partial-multiplex network of cities.

Abstract: When assessing the security or robustness of a complex system, including the fact that many nodes may fail together is essential. Though complex network studies typically assume that nodes are identical with respect to their vulnerability to failure or attack, this is often inaccurate.Surprisingly, this heterogeneity can be utilized to improve the system's functionality using a new ``color-avoiding percolation'' theory.We illustrate this with a new topological approach to cybersecurity.If there are many eavesdroppers, each tapping many nodes, we propose to split the message, and transmit each piece on a path that avoids all the nodes which are vulnerable to one of the eavesdroppers.Our theory determines which nodes can securely communicate and is applicable to a wide range of systems, from economic networks to epidemics

Abstract: The project TOPDRIM envisioned a new mathematical and computational framework based on topological data analysis for probing data spaces and extracting manifold hidden relations (patterns) that exist among data. While pursuing this objective, a general program aiming to construct an innovative methodology to perform data analytics has been devised. This program proposes the realization of a Field Theory of Data starting from topological data analysis, passing through field theory and returning an automaton as a recognizer of the data language. TOPDRIM contributed mainly to the first stage of the program by giving evidence that topological data analysis is a viable tool to tame the wild collection of data and to detect changes in complex networks. However, TOPDRIM already went beyond the concept of networks by considering instead simplicial complexes, which allow the study of n-dimensional objects (n>=2). An alternative approach to machine learning has been put forward, where data mining starts without receiving any initial input.

Abstract: Multilayer infrastructure is often interdependent, with nodes in one layer depending on nearby nodes in another layer to function. The links in each layer are often of limited length, due to the construction cost of longer links. Here, we model such systems as a multiplex network, in which each layer has links of characteristic geographic length. This is equivalent to a system of interdependent spatially embedded networks in which the connectivity links are constrained in length but varied while the length of the dependency links is always zero. We find two distinct percolation transition behaviors depending on the characteristic length of the links. When this value is longer than a certain critical value, abrupt, first-order transitions take place, while for shorter values the transition is continuous.

Abstract: In this talk, we will give a topological characterization of functional and behavioural features of complex systems. In particular we propose an interpretation of languages of regular expressions as the outcome of global topological features of the space intrinsically generated by the formal representation of processes constrained over the space. Our goal is a new scheme, (in the sense of Grothendieck) allowing for a new characterization of regular expressions and the study of a different axiomatic structure, analogous to Kleene algebras, but encompassing non-deterministic process interpretation.

Abstract: Developing, and managing predictive, causal models for smart cities must involve stakeholders with conflicting requirements, limited available data, limited knowledge and different ?city-subsystems? which interacts. Challenges can be summarized: (1) Present initiatives mostly focus on closed sets of topics leading to a narrow domain view. (2) Current simulations rely on small-scale, isolated models of real-world environments, where changes and migration of simulation results to real-world must be carried out manually. (3) Predictive causal models have to prove additional benefit by including smart cities ?behaviour? e.g. dynamic feedback loops of domains. Interdisciplinary, holistic approaches should integrate big static and dynamic data, the city emits from sources including IoT, documents or citizens. Data must be managed to provide the fundament for hybrid simulation models operated by multi-domain experts. This provides decision support for governance stakeholders, industry and citizens to influence the city.

Abstract: Social media are increasingly reflecting and influencing behavior of other complex systems. We investigate the relations between Twitter and stock market, in particular the Dow Jones Industrial Average contituents. In our previous work we adapted the well-known \event study" from economics to the analysis of Twitter data. We defined \events" as peaks of Twitter activity, and automatically classified sentiment in Twitter posts. During the Twitter peaks, we found significant dependence between the Twitter sentiment and stock returns: the sentiment polarity implies the direction of Cumulative Abnormal Returns

Abstract: Social interactions are composite, involve different communication layers and evolve in time. However, a rigorous analysis of the whole complexity of social networks has been hindered so far by lack of suitable data. Here we consider both the multi-layer and dynamic nature of social relations by analysing a diverse set of empirical temporal multiplex networks. We focus on the measurement and characterization of inter-layer correlations to investigate how activity in one layer affects social acts in another layer. We define observables able to detect when genuine correlations are present in empirical data, and single out spurious correlation induced by the bursty nature of human dynamics. We show that such temporal correlations do exist in social interactions where they act to depress the tendency to concentrate long stretches of activity on the same layer and imply some amount of potential predictability in the connection patterns between layers. Our work sets up a general framework to measure temporal correlations in multiplex networks, and we anticipate that it will be of interest to researchers in a broad array of fields.

Abstract: Most of complex physical systems are characterised by an emergent behaviour arising from the interaction of many particles dynamics. The resulting patterns at the macroscopic level can thus be linked to functional states of the system, which strongly depend on the topological features of the connections, on the single node intrinsic dynamics and environmental inputs. Nowadays these concepts are generalised and applied to a plethora of fields, including social dynamics, epidemics spreading, information flows and, in this particular case, also to the physiology of excitable biological media. In this perspective, we analysed emergent dynamics of the endocrine b-cells in the pancreas, as a typical example of biological electrically-coupled oscillators which release insulin in response to appropriate blood glucose levels. The primary focus was to establish a link between the underlying physical connectivity of the nodes and the functional state of the global network, modulated by specific operating conditions. A functional state was determined by looking at the robustness of the emergent electrical oscillations and the synchronisation patterns, investigated through a functional network approach. Indeed, a deep bond exists between the original physical network and the induced functional network. The possibile presence of multiplex via connections with other networks will also be discussed.