Related papers: Modelling Non-Linear Consensus Dynamics on Hypergr…
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…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…
In this paper, we study a class of equations representing nonlinear diffusion on networks. A particular instance of our model can be seen as a network equivalent of the porous-medium equation. We are interested in studying perturbations of…
We present a general framework that enables one to model high-order interaction among entangled dynamical systems, via hypergraphs. Several relevant processes can be ideally traced back to the proposed scheme. We shall here solely elaborate…
Modern sociology has profoundly uncovered many convincing social criteria for behavioural analysis. Unfortunately, many of them are too subjective to be measured and presented in online social networks. On the other hand, data mining…
Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a…
Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationships within these real-world systems, such as the encoding…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency…
While relations among individuals make an important part of data with scientific and business interests, existing statistical modeling of relational data has mainly been focusing on dyadic relations, i.e., those between two individuals.…
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…
We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…
The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…
The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and…
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
Individuals interact and cooperate in structured systems. Many studies represent this structure using static networks, where each link represents a permanent connection between two nodes. However, real interactions are generally not…
What kind of macroscopic structural and dynamical patterns can we observe in real-world hypergraphs? What can be underlying local dynamics on individuals, which ultimately lead to the observed patterns, beyond apparently random evolution?…
Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph…
I briefly survey several fascinating topics in networks and nonlinearity. I highlight a few methods and ideas, including several of personal interest, that I anticipate to be especially important during the next several years. These topics…