Related papers: Predictability of bursts of a recurrent nova using…
The relationship between the macroscopic response of the slope and the macrostructure of the force chain network under the action of the metal plate was studied by the particle discrete element method and the persistent homology. The…
We present the evolution of the optical spectra of the 2021 outburst of RS Ophiuchi (RS Oph) over about a month after the outburst. The spectral evolution is similar to the previous outbursts. Early spectra show prominent P Cygni profiles…
Topological data analysis is an approach to study shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions.…
We explore the recently introduced persistent reachability homology (PRH) of digraph data, i.e. data in the form of directed graphs. In particular, we study the effectiveness of PRH in network classification task in a key neuroscience…
In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…
In recent years, cosmic shear has emerged as a powerful tool to study the statistical distribution of matter in our Universe. Apart from the standard two-point correlation functions, several alternative methods like peak count statistics…
For nearly three decades, spatial games have produced a wealth of insights to the study of behavior and its relation to population structure. However, as different rules and factors are added or altered, the dynamics of spatial models often…
Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…
This article studies the robust version of persistent homology based on trimming methodology to capture the geometric feature through support of the data in presence of outliers. Precisely speaking, the proposed methodology works when the…
We present a topological pipeline for automated multiclass emotion recognition from eye-tracking data. Delay embeddings of gaze trajectories are analyzed using persistent homology. From the resulting persistence diagrams, we extract…
Persistent Homology is a fairly new branch of Computational Topology which combines geometry and topology for an effective shape description of use in Pattern Recognition. In particular it registers through "Betti Numbers" the presence of…
Persistent homology is currently one of the more widely known tools from computational topology and topological data analysis. We present in this note a brief survey on the evolution of the subject. The goal is to highlight the main ideas,…
Persistence-based topological optimization deforms a point cloud $X \subset \mathbb{R}^d$ by minimizing objectives of the form $L(X) = \ell(\mathrm{Dgm}(X))$, where $\mathrm{Dgm}(X)$ is a persistence diagram. In practice, optimization is…
We address the problem of estimating multiple modes of a multivariate density using persistent homology, a central tool in Topological Data Analysis. We introduce a method based on the preliminary estimation of the $H_0$-persistence diagram…
Recent studies have actively employed persistent homology (PH), a topological data analysis technique, to analyze the topological information in time series data. Many successful studies have utilized graph representations of time series…
Oscillations observed in the light curve of Nova V1974 Cygni 1992 since summer 1994 have been interpreted as permanent superhumps. From simple calculations based on the Tidal-Disk Instability model of Osaki, and assuming that the accretion…
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…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
Over the last 40 years, multi-frequency observations, coupled with advances in theoretical modelling, have led to a much fuller understanding of the nova phenomenon. Here I give a brief review of the current state of knowledge of Classical…
RS Oph has persistently displayed flickering at optical wavelengths when observed away from its repeating nova outbursts. During the 2006 eruption the flickering disappeared, and this repeated during the recent 2021 event. We have been…