Detecting Bifurcations in Dynamical Systems with Zigzag Persistent Homology
Explore zigzag persistent homology for efficient detection of bifurcations in dynamical systems, reducing computational costs and capturing topological changes in a single persistence diagram.
Alexander Wagner - Nonembeddability of Persistence Diagrams into Hilbert Spaces
Explore nonembeddability of persistence diagrams in Hilbert spaces, examining stability, metrics, and implications for machine learning applications in topological data analysis.
Computing Persistent Homology - Introduction
Explore the fundamentals of persistent homology computation, covering key concepts, intuition, and practical applications in topological data analysis.
Geometric and Topological Data Analysis of Enzyme Kinetics
Explore geometric and topological data analysis techniques applied to enzyme kinetics, focusing on ERK molecular dynamics and its implications for cancer and developmental defects.
Hengrui Luo - Generalized Penalty for Circular Coordinate Representation
Explore dimension reduction using circular coordinates and generalized penalties in topological data analysis. Enhance visualization of high-dimensional datasets while preserving topological structures.
Conley-Morse-Forman Theory for Generalized Combinatorial Multivector Fields
Generalized combinatorial multivector fields on finite topological spaces: extending Conley-Morse-Forman theory for data science applications, including isolated invariant sets, Conley index, and Morse decompositions.
Mean Estimation in High Dimension
Exploring recent advances in high-dimensional mean estimation, focusing on statistical challenges and computational aspects for independent, identically distributed data.
An Introduction to Persistent Homology
Explore persistent homology in applied topology, focusing on energy landscapes in chemistry. Learn about sublevelset analysis and its applications to real-valued functions and point cloud data.
Ulrich Bauer - Persistence Diagrams as Diagrams
Explore persistence diagrams as categorical functors, examining their structure, stability, and relationships to matchings. Learn about new constructions and theorems in this advanced algebraic topology lecture.
Vanessa Robins - Persistence Diagrams of Bead Packings
Exploring grain-scale mechanisms in granular crystallization using X-ray tomography and persistent homology, revealing key formation processes of tetrahedral and octahedral pores in spherical bead packings.
Persistence Images
Explore persistent homology and persistence images for topological data analysis. Learn to convert persistence diagrams into vector representations for machine learning applications.
Anthony Bak - Spaces of Shapes Persistent Homology for Drug Discovery
Explore persistent homology in drug discovery, focusing on structure-based design, chemical compound analysis, and machine learning applications for virtual screening and classification.
Harish Chintakunta - Topological Data Analysis and Signal Processing
Explore topological data analysis in signal processing, covering embedding techniques, harmonic effects, and applications in seizure prediction and power grid oscillation detection.
John Harer - Topological Data Analysis and Machine Learning
Explore topological data analysis and machine learning, covering methodology, examples, dimension reduction, and advanced techniques for feature extraction and classification.
Nonlinear Dynamics, High Dimensional Data, and Persistent Homology
Explore nonlinear dynamics, high-dimensional data analysis, and persistent homology with Konstantin Mischaikow. Learn about algebraic topology applications, persistence diagrams, and recent advancements in data science.
Gunnar Carlsson - Local to Global Principles in Persistent Homology
Explore persistent homology's local-to-global principles, computational methods, and applications in topology and data analysis with expert Gunnar Carlsson.
A Canonical Framework for Summarizing Persistence Diagrams
Explore a canonical framework for summarizing persistence diagrams in topological data analysis, including theoretical foundations, applications, and future developments.
Epsilon-Net Induced Lazy Witness Complex for Topological Data Analysis
Efficient topological data analysis using epsilon-net induced lazy witness complex. Improves scalability and approximation in persistent homology computation with theoretical guarantees and algorithmic implementations.
TALLEM - Topological Assembly of Locally Linear Euclidean Models
Explore a novel topological data analysis tool for nonlinear dimensionality reduction, assembling local Euclidean coordinates to create globally consistent maps that respect data topology.
Counting Embedded Spheres with the Same Persistence
Explores inverse problems in Topological Data Analysis, providing a formula for unbraided height equivalence classes of embedded two-spheres with prescribed level-set barcodes from z-axis projection.
Topological Data Analysis for Quantifying Plant Morphology
Explore topological data analysis for plant morphology using persistent homology and Euclidean Distance Transform. Learn applications in hurricane video data and XRay CT scans of plants.