Related papers: Higher-order Laplacian dynamics on hypergraphs wit…
In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in…
In this paper, we propose matrix-scaled consensus algorithms for linear dynamical agents interacting over an undirected network. Under the proposed algorithms, the state vectors of all agents to asymptotically agree up to some matrix…
Recently, graph neural networks have been widely used for network embedding because of their prominent performance in pairwise relationship learning. In the real world, a more natural and common situation is the coexistence of pairwise…
Networks are often interconnected, with one system wielding greater influence over another. However, the effects of such asymmetry on self-organized phenomena (e.g., consensus and synchronization) are not well understood. Here, we study…
Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable…
Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We propose a non-parametric statistical learning approach to…
Hypergraphs naturally represent higher-order interactions, which persistently appear from social interactions to neural networks and other natural systems. Although their importance is well recognized, a theoretical framework to describe…
This paper investigates agreement protocols over cooperative and cooperative--antagonistic multi-agent networks with coupled continuous-time nonlinear dynamics. To guarantee convergence for such systems, it is common in the literature to…
We present a relational graph learning approach for robotic crowd navigation using model-based deep reinforcement learning that plans actions by looking into the future. Our approach reasons about the relations between all agents based on…
Convolutional neural networks are nowadays witnessing a major success in different pattern recognition problems. These learning models were basically designed to handle vectorial data such as images but their extension to non-vectorial and…
Adaptive synchronization protocols for heterogeneous multi-agent network are investigated. The interaction between each of the agents is carried out through a directed graph. We highlight the lack of communication between agents and the…
Many networked datasets with units interacting in groups of two or more, encoded with hypergraphs, are accompanied by extra information about nodes, such as the role of an individual in a workplace. Here we show how these node attributes…
Hypergraph is a data structure that enables us to model higher-order associations among data entities. Conventional graph-structured data can represent pairwise relationships only, whereas hypergraph enables us to associate any number of…
This paper studies observability for non-uniform hypergraphs with inputs and outputs. To capture higher-order interactions, we define a canonical non-homogeneous dynamical system with nonlinear outputs on hypergraphs. We then construct…
We show that a general class of social impact models with higher-order interactions on hypergraphs can be exactly reduced to an equivalent model with pairwise interactions on a weighted projected network. This reduction is made by a mapping…
An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of $+1$ or $-1$. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian…
In this tutorial, we provide a didactic treatment of the emerging topic of signal processing on higher-order networks. Drawing analogies from discrete and graph signal processing, we introduce the building blocks for processing data on…
Recent empirical evidence has shown that in many real-world systems, successfully represented as networks, interactions are not limited to dyads, but often involve three or more agents at a time. These data are better described by…
Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random-walk models to…
This study develops an original and innovative matrix representation with respect to the information flow for networked multi-agent system. To begin with, the general concepts of the edge Laplacian of digraph are proposed with its algebraic…