Related papers: Simplicial complexes: higher-order spectral dimens…

An ecological network is a formal representation of a specific type of interaction in a corresponding ecosystem. Such networks have traditionally been modelled as encoding exclusively pairwise interactions among the fundamental units of…

Over the last two decades, network science has greatly advanced our understanding of how the collective behaviors of a complex system emerge from the interactions among its basic units. Multiplex networks, i.e. networks with many layers,…

Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's…

Networks are often studied as graphs, where the vertices stand for entities in the world and the edges stand for connections between them. While relatively easy to study, graphs are often inadequate for modeling real-world situations,…

Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…

In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network…

The dynamics of complex networks, being a current hot topic of many scientific fields, is often coded through the corresponding Laplacian matrix. The spectrum of this matrix carries the main features of the networks' dynamics. Here we…

The aim of these notes is to introduce the intuition motivating the notion of a "complicial set", a simplicial set with certain marked "thin" simplices that witness a composition relation between the simplices on their boundary. By varying…

Combinatorial topology is used in distributed computing to model concurrency and asynchrony. The basic structure in combinatorial topology is the simplicial complex, a collection of subsets called simplices of a set of vertices, closed…

We outline a novel clustering scheme for simplicial complexes that produces clusters of simplices in a way that is sensitive to the homology of the complex. The method is inspired by, and can be seen as a higher-dimensional version of,…

Higher-order interactions have recently emerged as a promising framework for describing new dynamical phenomena in heterogeneous contagion processes. However, a fundamental open question is how to understand their contribution from the…

We study linear filters for processing signals supported on abstract topological spaces modeled as simplicial complexes, which may be interpreted as generalizations of graphs that account for nodes, edges, triangular faces etc. To process…

Lattice structures play a central role in spectral graph theory, offering analytical insight into diffusion, synchronization, and transport processes on regular discrete spaces. While their spectral properties are completely characterized…

The interactions between individuals play a pivotal role in shaping the structure and dynamics of social systems. Complex network models have proven invaluable in uncovering the underlying mechanisms that govern the formation and evolution…

We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular…

Cascades arise in many contexts (e.g., neuronal avalanches, social contagions, and system failures). Despite evidence that propagations often involve higher-order dependencies, cascade theory has largely focused on models with…

Multilayer networks represent systems in which there are several topological levels each one representing one kind of interaction or interdependency between the systems' elements. These networks have attracted a lot of attention recently…

Genetic regulatory networks are defined by their topology and by a multitude of continuously adjustable parameters. Here we present a class of simple models within which the relative importance of topology vs. interaction strengths becomes…

Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…

Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…