Related papers: Balanced Hodge Laplacians Optimize Consensus Dynam…
Consensus over networked agents is typically studied using undirected or directed communication graphs. Undirected graphs enforce symmetry in information exchange, leading to convergence to the average of initial states, while directed…
Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted in order to admit global synchronization, a condition called Laplacian coupling.…
Complex networks represent the natural backbone to study epidemic processes in populations of interacting individuals. Such a modeling framework, however, is naturally limited to pairwise interactions, making it less suitable to properly…
Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…
Disease spreading models such as the ubiquitous SIS compartmental model and its numerous variants are widely used to understand and predict the behaviour of a given epidemic or information diffusion process. A common approach to imbue more…
We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…
As key subjects in spectral geometry and combinatorial graph theory respectively, the (continuous) Hodge Laplacian and the combinatorial Laplacian share similarities in revealing the topological dimension and geometric shape of data and in…
Heterogeneous graphs have multiple node and edge types and are semantically richer than homogeneous graphs. To learn such complex semantics, many graph neural network approaches for heterogeneous graphs use metapaths to capture multi-hop…
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…
Weighing the topological domain over which data can be represented and analysed is a key strategy in many signal processing and machine learning applications, enabling the extraction and exploitation of meaningful data features and their…
Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social…
We study discrete Laplacians on two-dimensional lattices under modular iterations, focusing on the emergence of nontrivial large-scale patterns. While purely binary or constant modular sequences quickly collapse into strict periodicity, the…
Simplicial complexes have recently been in the limelight of higher-order network analysis, where a minority of simplices play crucial roles in structures and functions due to network heterogeneity. We find a significant inconsistency…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
Persistent homology has been studied to better understand the structural properties and topology features of weighted networks. It can reveal hidden layers of information about the higher-order structures formed by non-pairwise interactions…
We consider decentralized optimization problems where one aims to minimize a sum of convex smooth objective functions distributed between nodes in the network. The links in the network can change from time to time. For the setting when the…
Our previous multiscale graph basis dictionaries/graph signal transforms -- Generalized Haar-Walsh Transform (GHWT); Hierarchical Graph Laplacian Eigen Transform (HGLET); Natural Graph Wavelet Packets (NGWPs); and their relatives -- were…
This work addresses the edge-based synchronization problem in first-order multi-agent systems containing both cooperative and antagonistic interactions with one or multiple leader groups. The presence of multiple leaders and antagonistic…
We study symplectic Laplacians on compact symplectic manifolds with boundary. These Laplacians are associated with symplectic cohomologies of differential forms and can be of fourth-order. We introduce several natural boundary conditions on…
The closed loops or cycles in a brain network embeds higher order signal transmission paths, which provide fundamental insights into the functioning of the brain. In this work, we propose an efficient algorithm for systematic identification…