Related papers: BPS Spectra, Barcodes and Walls

Type IIB string theory admits a BPS configuration in which three strings (of different type) meet at a point. Using this three string configuration we construct a string network and study its properties. In particular we prove supersymmetry…

Recently, persistent homology has had tremendous success in biomolecular data analysis. It works by examining the topological relationship or connectivity of a group of atoms in a molecule at a variety of scales, then rendering a family of…

The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…

We study the BPS spectrum in $D=4, N=4$ heterotic string compactifications, with some emphasis on intermediate $N=4$ BPS states. These intermediate states, which can become short in $N=2$ compactifications, are crucial for establishing an…

We study BPS jumping loci, or the subloci in moduli spaces of supersymmetric string vacua where BPS states come into existence discontinuously. This phenomenon is distinct from wall-crossing. We argue that these loci should be thought of as…

Persistent homology has been widely used to discover hidden topological structures in data across various applications, including music data. To apply persistent homology, a distance or metric must be defined between points in a point cloud…

Many attempts have been made in recent decades to integrate machine learning (ML) and topological data analysis. A prominent problem in applying persistent homology to ML tasks is finding a vector representation of a persistence diagram…

Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…

In this work we address a way to capture scalar field solutions on static spacetimes by using BPS formalism and relaxing the general covariance condition. We focus on configurations where the background geometry describes topological black…

We study the spectrum of BPS domain walls within the parameter space of N=1 U(N) gauge theories with adjoint matter and a cubic superpotential. Using a low energy description obtained by compactifying the theory on R^3 x S^1, we examine the…

This paper introduces an unsupervised method to estimate the class separability of text datasets from a topological point of view. Using persistent homology, we demonstrate how tracking the evolution of embedding manifolds during training…

Massless BPS-saturated states in toroidally compactified heterotic string were discussed first. Then, I constructed a large class of BPS-saturated states of toroidally compactified type II string theories. They were parametrized by four…

We discuss a set of heterotic and type II string theory compactifications to 1+1 dimensions that are characterized by factorized internal worldsheet CFTs of the form $V_1\otimes \bar V_2$, where $V_1, V_2$ are self-dual (super) vertex…

An Important tool in the field topological data analysis is known as persistent Homology (PH) which is used to encode abstract representation of the homology of data at different resolutions in the form of persistence diagram (PD). In this…

We obtain analytic and numerical results for the non-perturbative amplitudes of topological string theory on arbitrary, compact Calabi-Yau manifolds. Our approach is based on the theory of resurgence and extends previous special results to…

We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…

Spatial transcriptomics studies are becoming increasingly large and commonplace, necessitating simultaneous analysis of a large number of spatially resolved variables. Correspondingly, a diverse range of methodologies have been proposed to…

In this paper we study the persistent homology associated with topological crackle generated by distributions with an unbounded support. Persistent homology is a topological and algebraic structure that tracks the creation and destruction…

Magnitude homology is an emerging framework that captures the intrinsic topological and geometric features of metric spaces, demonstrating significant potential for topoplogical data analysis and geometric data analysis. This work…

We approach string phenomenology from the perspective of computational algebraic geometry, by providing new and efficient techniques for proving stability and calculating particle spectra in heterotic compactifications. This is done in the…