- Guido Caldarelli
**Systemic Risk in Financial Networks and Beyond**
We will report on our recent advancements in the theoretical framework to measure systemic risk in global financial market and financial networks. Moreover, we will present the new projects and opportunities intended to boost both the theoretical and the applied aspects of network science. - Leonardo Dueñas-Osorio
**The role of interdependencies in the probabilistic risk assessment of coupled infrastructure systems**
The increasing interdependence across critical infrastructure systems enables them to operate more efficiently while bridging the gap between increasing demand for services and the slow pace of infrastructure renewal and upgrade. However, when facing contingencies from random failures or natural hazards, interdependencies across lifeline systems worsen the performance of systems already affected by the hazard actions. This talk will highlight the advances in quantifying the effects of network interdependencies in the context of deterioration, earthquake and hurricane hazards. Interdependency models built with tools from infrastructure engineering and network theory are validated with post-disaster field data, including methods to quantify the strength of coupling across systems from restoration curves, which after calibration enable the risk assessment of coupled systems and support practical decision making. - Erol Gelenbe
**Networks of Networks in the Digital Society**
Our digital society relies on commerce, work, food provisioning, transportation,energy, information and data networks, and many others, that interact to make the system as a whole "work". For the first time in human history, all of these networks have a common mediator and representation system: the information and data networks. Thus we can envision to model and understand these complex networks as an observable and formal mathematical system. This talk will present a mathematical approach based on stochastic networks that leads to closed form mathematical solutions, and we will illustrate this approach through specific results for stochastic networks that simultaneously model commerce, transportation, ICT and energy consumption - Shlomo Havlin
**The Extreme Vulnerability of Network of Interdependent Networks**
Network research and percolation theory have been focused on the properties of a single isolated network that does not interact or depends on other networks. In reality, many real-networks interact with other networks. We present a framework for studying percolation of interacting networks. In interdependent networks, when nodes in one network fail, they cause dependent nodes in other networks to also fail. This may happen recursively and can lead to a cascade of failures and to a sudden fragmentation of the system. I will present exact analytical solutions for the critical threshold and giant component of a network of n interdependent networks which generalize the case of n=1 studied in percolation theory and graph theory for many years. I will show, that the general theory has many novel features that are not present in classical percolation theory. For example, while a failure of a fraction of nodes in a single network can lead only to small damage to the system, in interacting network it can lead to a sudden (discontinuous) collapse due to cascading failures. However, reducing the coupling between the networks leads to a change from a discontinuous percolation transition to a smooth transition at a critical coupling. We also show that interdependent networks embedded in space are significantly more vulnerable compared to random networks. - Irena Vodenska
**Cascading Failures in Bi-partite Graphs: Model for Systemic Risk Propagation**
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