Related papers: Spectral Theory of Hypergraphs: A Survey
Hyperspectral imaging (HSI) unlocks the huge potential to a wide variety of applications relied on high-precision pathology image segmentation, such as computational pathology and precision medicine. Since hyperspectral pathology images…
We propose the spectral degree exponent as a novel graph metric. Although Hofmeister \cite{HofmeisterThesis} has studied the same metric, we generalise Hofmeister's work to weighted graphs. We provide efficient iterative formulas and bounds…
The Hermitian adjacency matrices of digraphs based on the sixth root of unity were introduced in [B. Mohar, A new kind of Hermitian matrices for digraphs, Linear Alg. Appl. (2020)]. They appear to be the most natural choice for the spectral…
One of the hot topics in machine learning is the field of GNN. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph…
Square matrices often arise in microeconomics, particularly in network models addressing applications from opinion dynamics to platform regulation. Spectral theory provides powerful tools for analyzing their properties. We present an…
In this paper, we define the adjacency matrix of a semigraph. We give the conditions for a matrix to be semigraphical and give an algorithm to construct a semigraph from the semigraphical matrices. We derive lower and upper bounds for…
Providing an abstract representation of natural and human complex structures is a challenging problem. Accounting for the system heterogenous components while allowing for analytical tractability is a difficult balance. Here I introduce…
Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…
In this paper extremal problems for uniform hypergraphs are studied in the general setting of hereditary properties. It turns out that extremal problems about edges are particular cases of a general analyic problem about a recently…
Graph based representation is widely used in visual tracking field by finding correct correspondences between target parts in consecutive frames. However, most graph based trackers consider pairwise geometric relations between local parts.…
Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random…
The representations of neural networks are often compared to those of biological systems by performing regression between the neural network responses and those measured from biological systems. Many different state-of-the-art deep neural…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
In this paper we investigate the traces of the adjacency tensor of hypergraphs (simply called the traces of hypergraphs). We give new expressions for the traces of hypertrees and linear unicyclic hypergraphs by the weight function assigned…
We give the first exact and stability results for a hypergraph Tur\'{a}n problem with infinitely many extremal constructions that are far from each other in edit-distance. This includes an example of triple systems with Tur\'{a}n density…
In many real world datasets arising from social networks, there are hidden higher order relations among data points which cannot be captured using graph modeling. It is natural to use a more general notion of hypergraphs to model such…
The magnitude homology, introduced by R. Hepworth and S. Willerton, offers a topological invariant that enables the study of graph properties. Hypergraphs, being a generalization of graphs, serve as popular mathematical models for data with…
Hypergraphs are useful mathematical representations of overlapping and nested subsets of interacting units, including groups of genes or brain regions, economic cartels, political or military coalitions, and groups of products that are…
We provide a detailed description of the maps associated with spectral interlacing, for rank one perturbations and bordering of symmetric and Hermitian matrices. The arguments rely on standard techniques of nonlinear analysis.
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…