Related papers: Persistent Dirac of Path and Hypergraph

As an outgrowth of our investigation of non-regular spaces within the context of quantum gravity and non-commutative geometry, we develop a graph Hilbert space framework on arbitrary (infinite) graphs and use it to study spectral properties…

Node clustering is a powerful tool in the analysis of networks. We introduce a graph neural network framework, named DIGRAC, to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic…

Metabolic networks are probably among the most challenging and important biological networks. Their study provides insight into how biological pathways work and how robust a specific organism is against an environment or therapy. Here we…

We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in…

In this article, we introduce a geometric and a spectral preorder relation on the class of weighted graphs with a magnetic potential. The first preorder is expressed through the existence of a graph homomorphism respecting the magnetic…

Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and…

We study the two-dimensional Dirac operator with an arbitrary combination of electrostatic and Lorentz scalar $\delta$-interactions of constant strengths supported on a smooth closed curve. For any combination of the coupling constants a…

Persistent homology (PH) has been widely applied to graph data to extract topological features. However, little attention has been paid to how different distance functions on a graph affect the resulting persistence barcodes and their…

Collective synchronization in complex systems arises from the interplay between topology and dynamics, yet how to design and control such patterns in higher-order networks remains unclear. Here we show that a Dirac spectral programming…

A directed hypergraph (dihypergraph) consists of a set of vertices and a set of hyperarcs, where each hyperarc is partitioned into a head and a tail. Directed hypergraphs are useful in many applications, including the study of chemical…

While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are frequently insensitive to localized structural fluctuations…

We study the electronic structure and the phase diagram of non-interacting fermions confined to hexagonal optical lattices. In the first part, we compare the properties of Dirac points arising in the eigenspectrum of either honeycomb or…

In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…

Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…

Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and…

Higher-order information is crucial for relational learning in many domains where relationships extend beyond pairwise interactions. Hypergraphs provide a natural framework for modeling such relationships, which has motivated recent…

Category theory has been recently used as a tool for constructing and modeling an information flow framework. Here, we show that the flow of information can be described using preradicals. We prove that preradicals generalize the notion of…

In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we will…

Predicting drug side-effects before they occur is a key task in keeping the number of drug-related hospitalizations low and to improve drug discovery processes. Automatic predictors of side-effects generally are not able to process the…

Recently, there has been a rising surge of momentum for deep representation learning in hyperbolic spaces due to theirhigh capacity of modeling data like knowledge graphs or synonym hierarchies, possessing hierarchical structure. We refer…