Related papers: Asymptotics of Lower Dimensional Zero-Density Regi…

We propose a practical computational framework for detecting structural changes in parameter-dependent topological data. In many applications, such as time-series data analysis, anomaly detection, and monitoring of systems under changing…

Topological Data Analysis (TDA), an emerging field in investment sciences, harnesses mathematical methods to extract data features based on shape, offering a promising alternative to classical portfolio selection methodologies. We utilize…

The experiments on verification of the Kibble-Zurek mechanism showed that topological defects are formed most efficiently in the systems of small size or low (quasi-)dimensionality, whereas in the macroscopic two- and three-dimensional…

This research addresses a new tool for data analysis known as Topological Data Analysis TDA It underlies an area of Mathematics known as Combinatorial Algebra or more recently Algebraic Topology which through making strong use of…

Density Estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization,…

Quadratic systems with lossless quadratic terms arise in many applications, including models of atmosphere and incompressible fluid flows. Such systems have a trapping region if all trajectories eventually converge to and stay within a…

We generalize the topological response theory to detect the boundary anomalies of linear subsystem symmetries. This approach allows us to distinguish different subsystem symmetry-protected topological (SSPT) phases and uncover new ones. We…

The properties of topological systems are inherently tied to their dimensionality. Higher-dimensional physical systems exhibit topological properties not shared by their lower dimensional counterparts and, in general, offer richer physics.…

An important feature of turbulent boundary layers are persistent large-scale coherent structures in the flow. Here, we use Dynamic Mode Decomposition (DMD), a data-driven technique designed to detect spatio-temporal coherence, to construct…

Almost all statistical and machine learning methods in analyzing brain networks rely on distances and loss functions, which are mostly Euclidean or matrix norms. The Euclidean or matrix distances may fail to capture underlying subtle…

We use the nudged elastic band method from computational chemistry to analyze high-dimensional data. Our approach is inspired by Morse theory, and as output we produce an increasing sequence of small cell complexes modeling the dense…

Symmetry-protected topological phases host gapless modes at their boundary with a featureless environment of the same dimension or a trivial vacuum. In this study, we explore their behavior in a higher-dimensional environment, which itself…

We present a generalization of free fermionic topological insulators that are composed of topological subsystems of differing dimensionality. We specifically focus on topological subsystems of nonzero co-dimension are embedded within a…

Topological defects, which are singular points in a director field, play a major role in shaping active systems. Here, we experimentally study topological defects and the flow patterns around them, that are formed during the highly rapid…

We propose an unsupervised learning methodology with descriptors based on Topological Data Analysis (TDA) concepts to describe the local structural properties of materials at the atomic scale. Based only on atomic positions and without a…

Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced…

Topology has emerged as a fundamental property of many systems, manifesting in cosmology, condensed matter, high-energy physics and waves. Despite the rich textures, the topology has largely been limited to low dimensional systems that can…

Software libraries for Topological Data Analysis (TDA) offer limited support for interactive visualization. Most libraries only allow to visualize topological descriptors (e.g., persistence diagrams), and lose the connection with the…

Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology.…

This paper presents a principled approach for detecting out-of-distribution (OOD) samples in deep neural networks (DNN). Modeling probability distributions on deep features has recently emerged as an effective, yet computationally cheap…