Related papers: Nonlocal network dynamics via fractional graph Lap…
Evolutionary dynamics have been traditionally studied in the context of homogeneous populations, mainly described my the Moran process. Recently, this approach has been generalized in \cite{LHN} by arranging individuals on the nodes of a…
Extensive research on graph-based dynamics and control of multi-agent systems has successfully demonstrated control of robotic swarms, where each robot is perceived as an independent agent virtually connected by a network topology. The…
We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity…
Dynamic graph neural networks (DyGNNs) have demonstrated powerful predictive abilities by exploiting graph structural and temporal dynamics. However, the existing DyGNNs fail to handle distribution shifts, which naturally exist in dynamic…
Motivated by the relationship between the eigenvalue spectrum of the Laplacian matrix of a network and the behavior of dynamical processes evolving in it, we propose a distributed iterative algorithm in which a group of $n$ autonomous…
The movement of organisms and cells can be governed by occasional long distance runs, according to an approximate L\'evy walk. For T cells migrating through chronically-infected brain tissue, runs are further interrupted by long pauses, and…
The fundamental lemma from behavioral systems theory yields a data-driven non-parametric system representation that has shown great potential for the data-efficient control of unknown linear and weakly nonlinear systems, even in the…
In this paper, we study the leaderless consensus problem for multiple Lagrangian systems in the presence of parametric uncertainties and external disturbances under directed graphs. For achieving asymptotic behavior, a robust continuous…
It is now well known that ultracontractive properties of semigroups with infinitesimal generator given by an undirected graph Laplacian operator can be obtained through an understanding of the geometry of the underlying infinite weighted…
Foundation models have shown great promise in various fields of study. A potential application of such models is in computer network traffic analysis, where these models can grasp the complexities of network traffic dynamics and adapt to…
Dynamic transportation networks have been analyzed for years by means of static graph-based indicators in order to study the temporal evolution of relevant network components, and to reveal complex dependencies that would not be easily…
The dynamical behavior of networked complex systems is shaped not only by the direct links among the units, but also by the long-range interactions occurring through the many existing paths connecting the network nodes. In this work, we…
Time-evolving graphs arise frequently when modeling complex dynamical systems such as social networks, traffic flow, and biological processes. Developing techniques to identify and analyze communities in these time-varying graph structures…
We develop a general theory of random walks on hypergraphs which includes, as special cases, the different models that are found in literature. In particular, we introduce and analyze general random walk Laplacians for hypergraphs, and we…
We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…
We address the problem of identifying the topology of an unknown weighted, directed network of LTI systems stimulated by wide-sense stationary noises of unknown power spectral densities. We propose several reconstruction algorithms based on…
A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high…
Several variants of the graph Laplacian have been introduced to model non-local diffusion processes, which allow a random walker to {\textquotedblleft jump\textquotedblright} to non-neighborhood nodes, most notably the transformed path…
Networks of dynamical systems play an important role in various domains and have motivated many studies on the control and analysis of linear dynamical networks. For linear network models considered in these studies, it is typically…
Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more…