Related papers: Aggregation models on hypergraphs
We use the first Betti number of a complex to characterize the morphological structure of granular samples in mechanical equilibrium. We analyze two-dimensional granular packings after a tapping process by means of both simulations and…
In this paper, we propose a novel hypergraph based method (called HF) to fit and segment multi-structural data. The proposed HF formulates the geometric model fitting problem as a hypergraph partition problem based on a novel hypergraph…
Understanding feature-outcome associations in high-dimensional data remains challenging when relationships vary across subpopulations, yet standard methods assuming global associations miss context-dependent patterns, reducing statistical…
In recent years, networks with higher-order interactions have emerged as a powerful tool to model complex systems. Comparing these higher-order systems remains however a challenge. Traditional similarity measures designed for pairwise…
We consider complements of standard Seifert surfaces of special alternating links. On these handlebodies, we use Honda's method to enumerate those tight contact structures whose dividing sets are isotopic to the link, and find their number…
The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of…
Detecting statistical interactions between input features is a crucial and challenging task. Recent advances demonstrate that it is possible to extract learned interactions from trained neural networks. It has also been observed that, in…
The study of complex systems has captured widespread attention in recent years, emphasizing the exploration of interactions and emergent properties among system units. Network analysis based on graph theory has emerged as a powerful…
Modeling higher-order interactions (HOI) has emerged as a crucial challenge in complex systems analysis, as many phenomena cannot be fully captured by pairwise relationships alone. Hypergraphs, which generalize graphs by allowing…
We consider the problem of estimating the topology of spatial interactions in a discrete state, discrete time spatio-temporal graphical model where the interactions affect the temporal evolution of each agent in a network. Among other…
Hypergraphs that can depict interactions beyond pairwise edges have emerged as an appropriate representation for modeling polyadic relations in complex systems. With the recent surge of interest in researching hypergraphs, the centrality…
Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order models (ROMs) have a place to alleviate the computational…
There are two rather distinct approaches to Morse theory nowadays: smooth and discrete. We propose to study a real valued function by assembling all associated sections in a topological category. From this point of view, Reeb functions on…
In this paper we study topology of the variety of closed planar polygons with given side lengths. We describe the Betti numbers of the moduli spaces as functions of the length vector. We also find sharp upper bounds on the sum of Betti…
Topological constraints (TCs) between polymers determine the behaviour of complex fluids such as creams, oils and plastics. Most of the polymer solutions used every day life employ linear chains; their behaviour is accurately captured by…
Networks are important structures used to model complex systems where interactions take place. In a basic network model, entities are represented as nodes, and interaction and relations among them are represented as edges. However, in a…
Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
We consider a social learning problem, where a network of agents is interested in selecting one among a finite number of hypotheses. We focus on weakly-connected graphs where the network is partitioned into a sending part and a receiving…
Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…