Related papers: Network effects in default clustering for large sy…

We present classes of models in which particles are dropped on an arbitrary fixed finite connected graph, obeying adhesion rules with screening. We prove that there is an invariant distribution for the resulting height profile, and Gaussian…

The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…

We study the scenario of graph-based clustering algorithms such as spectral clustering. Given a set of data points, one first has to construct a graph on the data points and then apply a graph clustering algorithm to find a suitable…

A/B testing is a standard approach for evaluating the effect of online experiments; the goal is to estimate the `average treatment effect' of a new feature or condition by exposing a sample of the overall population to it. A drawback with…

Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and…

The classical reduced-form and filtration expansion framework in credit risk is extended to the case of multiple, non-ordered defaults, assuming that conditional densities of the default times exist. Intensities and pricing formulas are…

Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…

We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…

We study the behavior of the clustering coefficient in tagged networks. The rich variety of tags associated with the nodes in the studied systems provide additional information about the entities represented by the nodes which can be…

The recent high level of interest in weighted complex networks gives rise to a need to develop new measures and to generalize existing ones to take the weights of links into account. Here we focus on various generalizations of the…

Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms, and various pattern formations. Because of noise in each component, collective dynamics inevitably involve…

Emergent design failures are ubiquitous in complex systems, and often arise when system elements cluster. Approaches to systematically reduce clustering could improve a design's resilience, but reducing clustering is difficult if it is…

Graph pooling is a central component of a myriad of graph neural network (GNN) architectures. As an inheritance from traditional CNNs, most approaches formulate graph pooling as a cluster assignment problem, extending the idea of local…

In the new field of financial systemic risk, the network of interbank counterparty relationships can be described as a directed random graph. In "cascade models" of systemic risk, this "skeleton" acts as the medium through which financial…

Many machine learning algorithms are based on the assumption that training examples are drawn independently. However, this assumption does not hold anymore when learning from a networked sample because two or more training examples may…

A simple banking network model is proposed which features multiple waves of bank defaults and is analytically solvable in the limiting case of an infinitely large homogeneous network. The model is a collection of nodes representing…

We consider a general tractable model for default contagion and systemic risk in a heterogeneous financial network, subject to an exogenous macroeconomic shock. We show that, under some regularity assumptions, the default cascade model…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…

We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak convergence result for the fluctuation process and use it for…

The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…