Related papers: Spectral Theory for Networks with Attractive and R…
We study the effects of network topology on the response of networks of coupled discrete excitable systems to an external stochastic stimulus. We extend recent results that characterize the response in terms of spectral properties of the…
Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph…
Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
We consider the problem of finding universal bounds of "isoperimetric" or "isodiametric" type on the spectral gap of the Laplacian on a metric graph with natural boundary conditions at the vertices, in terms of various analytical and…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
How the architecture of gene regulatory networks ultimately shapes gene expression patterns is an open question, which has been approached from a multitude of angles. The dominant strategy has been to identify non-random features in these…
We introduce a new class of filtrations indexed by attracting levels in dynamical systems, providing novel inputs for persistent homology and related methods in topological data analysis. These filtrations quantify, in a forward direction,…
Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…
We introduce a new family of algorithms for detecting and estimating a rank-one signal from a noisy observation under prior information about that signal's direction, focusing on examples where the signal is known to have entries biased to…
Higher-order networks encode the many-body interactions existing in complex systems, such as the brain, protein complexes, and social interactions. Simplicial complexes are higher-order networks that allow a comprehensive investigation of…
The notion of Laplacian of a graph can be generalized to simplicial complexes and hypergraphs, and contains information on the topology of these structures. Even for a graph, the consideration of associated simplicial complexes is…
The eigenvalues of the Laplacian matrix for a class of directed graphs with both positive and negative weights are studied. First, a class of directed signed graphs is investigated in which one pair of nodes (either connected or not) is…
A certain degree of inhibition is a common trait of dynamical networks in nature, ranging from neuronal and biochemical networks, to social and technological networks. We study here the role of inhibition in a representative dynamical…
To describe the flow of a miscible quantity on a network, we introduce the graph wave equation where the standard continuous Laplacian is replaced by the graph Laplacian. This is a natural description of an array of inductances and…
Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social, biological or computer sciences involve interactions among…
This paper addresses the problem of identifying the graph structure of a dynamical network using measured input/output data. This problem is known as topology identification and has received considerable attention in recent literature. Most…
Heterogeneous and complex networks represent intertwined interactions between real-world elements or agents. Determining the multi-scale mesoscopic organization of clusters and intertwined structures is still a fundamental and open problem…
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…
Spectral analysis has been successfully applied at the detection of community structure of networks, respectively being based on the adjacency matrix, the standard Laplacian matrix, the normalized Laplacian matrix, the modularity matrix,…