Related papers: BPS Spectra, Barcodes and Walls
In this paper, we give lower bounds for the homology of the fibers of a map to a manifold. Using new sheaf theoretic methods, we show that these lower bounds persist over whole open sets of the manifold, and that they are stable under…
$P$-brane solutions of low-energy string actions have traditionally provided the first evidence for the existence of string dualities, in which fundamental and solitonic $p$-branes are identified with perturbative and non-perturbative BPS…
We probe the geometry around an elementary BPS (EBPS) state in heterotic string theory compactified on a six-torus by scattering a massless scalar off it and comparing with the corresponding experiment in which the EBPS state is replaced by…
We study classical and quantum aspects of D=4, N=2 BPS black holes for T_2 compactification of D=6, N=1 heterotic string vacua. We extend dynamical relaxation phenomena of moduli fields to background consisting of a BPS soliton or a black…
Persistent homology was shown by Carlsson and Zomorodian to be homology of graded chain complexes with coefficients in the graded ring $\kk[t]$. As such, the behavior of persistence modules -- graded modules over $\kk[t]$ is an important…
Persistent homology theory is a relatively new but powerful method in data analysis. Using simplicial complexes, classical persistent homology is able to reveal high dimensional geometric structures of datasets, and represent them as…
We compute the spectrum of quarter BPS dyons in freely acting Z_2 and Z_3 orbifolds of type II string theory compactified on a six dimensional torus. For large charges the result for statistical entropy computed from the degeneracy formula…
In this work, we present a generalization of extended persistent homology to filtrations of graded sub-groups by defining relative homology in this setting. Our work provides a more comprehensive and flexible approach to get an algebraic…
Persistent homology is a tool from Topological Data Analysis (TDA) used to summarize the topology underlying data. It can be conveniently represented through persistence diagrams. Observing a noisy signal, common strategies to infer its…
We discuss topologically stable solitons in two-dimensional theories with the extended supersymmetry assuming that the spatial coordinate is compact. This problem arises in the consideration of the domain walls in the popular theories with…
Combining toric geometry techniques and $\mathcal{N}=2$ supergravity formalisms, we study 5D black branes in the M-theory compactification on a four parameter Calabi-Yau threefold. First, we investigate 5D BPS and non-BPS black holes that…
It is well known that in string compactifications on toric Calabi-Yau manifolds one can introduce refined BPS invariants that carry information not only about the charge of the BPS state but also about the spin content. In this paper we…
Topological data analysis is a recent and fast growing field that approaches the analysis of datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH), has seen a notable increase in applications in the…
We discuss discrete symmetries in several string compactification schemes. The same constraints on the light spectra as for Gepner models \cite{rosss} are found in various cases for non-$R$ symmetries. The analogous constraints for $R$…
Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining…
We propose a functorial framework for persistent homology based on finite topological spaces and their associated posets. Starting from a finite metric space, we associate a filtration of finite topologies whose structure maps are…
Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of…
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
This paper introduces persistent homology, which is a powerful tool to characterize the shape of data using the mathematical concept of topology. We explain the fundamental idea of persistent homology from scratch using some examples. We…
Until now all known static multi black hole solutions described BPS states with charges of the same sign. Such solutions could not be related to flat directions in the space of BPS states. The total number of such states could not…