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We use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by…

High Energy Physics - Theory · Physics 2016-04-20 Michele Cirafici

Topological data analysis (TDA) uses persistent homology to quantify loops and higher-dimensional holes in data, making it particularly relevant for examining the characteristics of images of cells in the field of cell biology. In the…

Methodology · Statistics 2024-05-06 Susan Glenn , Jessi Cisewski-Kehe , Jun Zhu , William M. Bement

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…

Quantitative Methods · Quantitative Biology 2025-09-09 James Boyle , Gregory Hamm , Eleanor Williams , Robin JG Hartman , Magnus Soderburg , Ian Henry , Michael Casey

Persistent homology (PH) is a recently developed theory in the field of algebraic topology to study shapes of datasets. It is an effective data analysis tool that is robust to noise and has been widely applied. We demonstrate a general…

Signal Processing · Electrical Eng. & Systems 2020-05-05 Yu-Min Chung , Chuan-Shen Hu , Yu-Lun Lo , Hau-Tieng Wu

This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…

Computational Geometry · Computer Science 2023-08-15 Audun Myers , David Muñoz , Firas Khasawneh , Elizabeth Munch

Topological Data Analysis (TDA) refers to an approach that uses concepts from algebraic topology to study the "shapes" of datasets. The main focus of this paper is persistent homology, a ubiquitous tool in TDA. Basing our study on this, we…

Probability · Mathematics 2016-04-15 Takashi Owada

In this paper, we introduce the persistence transformation, a novel methodology in Topological Data Analysis (TDA) for applications in time series data which can be obtained in various areas such as science, politics, economy, healthcare,…

Algebraic Topology · Mathematics 2024-01-31 Gideon Klaila , Anastasios Stefanou , Lena Ranke

With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. They are both examples of "functional data", which have become a prevailing…

Methodology · Statistics 2015-07-21 Jane-Ling Wang , Jeng-Min Chiou , Hans-Georg Mueller

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

Computer Vision and Pattern Recognition · Computer Science 2018-02-19 Christoph Hofer , Roland Kwitt , Marc Niethammer , Andreas Uhl

Time series analysis is critical for emerging net- work intelligent control and management functions. However, existing statistical-based and shallow machine learning models have shown limited prediction capabilities on multivariate time…

Machine Learning · Computer Science 2026-03-13 Yufeng Xin , Ethan Fan

Topological data analysis has emerged as a powerful tool for extracting the metric, geometric and topological features underlying the data as a multi-resolution summary statistic, and has found applications in several areas where data…

Probability · Mathematics 2024-02-16 Siddharth Vishwanath , Kenji Fukumizu , Satoshi Kuriki , Bharath Sriperumbudur

This paper investigates how Transformer language models (LMs) fine-tuned for acceptability classification capture linguistic features. Our approach uses the best practices of topological data analysis (TDA) in NLP: we construct directed…

Computation and Language · Computer Science 2023-10-04 Irina Proskurina , Irina Piontkovskaya , Ekaterina Artemova

A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields. Topological feature search of such data aims to reveal important properties useful to…

Computational Geometry · Computer Science 2024-06-06 Tripti Agarwal , Amit Chattopadhyay , Vijay Natarajan

Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and…

Algebraic Topology · Mathematics 2017-08-21 Massimo Ferri

The Mapper algorithm, a technique within topological data analysis (TDA), constructs a simplified graphical representation of high-dimensional data to uncover its underlying shape and structural patterns. The algorithm has attracted…

General Topology · Mathematics 2025-04-15 Vine Nwabuisi Madukpe , Bright Chukwuma Ugoala , Nur Fariha Syaqina Zulkepli

Graph models provide efficient tools to capture the underlying structure of data defined over networks. Many real-world network topologies are subject to change over time. Learning to model the dynamic interactions between entities in such…

Machine Learning · Computer Science 2025-01-03 Amirhossein Javaheri , Jiaxi Ying , Daniel P. Palomar , Farokh Marvasti

A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persistent homology, which encodes features of interest as…

Algebraic Topology · Mathematics 2026-02-04 Christian Lentz , Gregory Henselman-Petrusek , Lori Ziegelmeier

Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…

Physics and Society · Physics 2023-03-01 Andrea Santoro , Federico Battiston , Giovanni Petri , Enrico Amico

Nowadays, Machine Learning and Deep Learning methods have become the state-of-the-art approach to solve data classification tasks. In order to use those methods, it is necessary to acquire and label a considerable amount of data; however,…

Computer Vision and Pattern Recognition · Computer Science 2022-05-20 Adrián Inés , César Domínguez , Jónathan Heras , Gadea Mata , Julio Rubio

Childhood maltreatment may adversely affect brain development and consequently influence behavioral, emotional, and psychological patterns during adulthood. In this study, we propose an analytical pipeline for modeling the altered…

Neurons and Cognition · Quantitative Biology 2023-11-16 Moo K. Chung , Tahmineh Azizi , Jamie L. Hanson , Andrew L. Alexander , Richard J. Davidson , Seth D. Pollak