Geometric Interpretation of Persistence
Explore geometric interpretations of persistence in algebraic topology, covering space reconstruction, one-dimensional persistent homology classification, and detection of contractible geodesics using higher-dimensional features.
Persistence in Functional Topology
Explore functional topology's evolution, connecting persistent homology to critical point theory and calculus of variations. Gain insights into Morse's theory and its application to minimal surfaces.
Conversation on the Paper "Persistent Extension and Analogous Bars" by Yoon, Ghrist, Giusti
Explore persistent homology extensions and analogous bars in topological data analysis, discussing novel methods for comparing persistence barcodes and their applications in data science.
Geometry and Topology of Periodic Point Sets, for Example Crystals
Explore geometric and topological tools for characterizing crystalline materials, including Brillouin zones and persistent homology, and discuss challenges in defining persistent homology for periodic point sets.
Henry Adams - Vietoris-Rips Complexes of Hypercube Graphs
Explore Vietoris-Rips complexes of hypercube graphs, their homotopy types, and applications in genetic recombination and persistent homology. Discover formulas, open questions, and conjectures in this fascinating area of applied algebraic topology.
Other Persistence Invariants - Homotopy and the Cohomology Ring
Explore persistent homotopy groups and cohomology rings, focusing on fundamental groups, rational homotopy, and cup-length diagrams. Learn about new tools complementing persistent homology in topological data analysis.
Massimo Ferri - Selection of Points in Persistence Diagrams
Explore point selection in persistence diagrams, including Kurlin's criterion and the Ziqqurat method, for noise reduction and improved data analysis in topological data analysis.
Marian Mrozek - Combinatorial vs. Classical Dynamics: Recurrence
Explore combinatorial dynamics in data science, its ties to classical dynamics, and applications in computer-assisted proofs. Learn about topological invariants and recent developments in recurrent behavior analysis.
On Characterizing Rare Events in Persistent Homology
Explore rare events in persistent homology, focusing on indecomposables in multi-parameter settings. Learn about large deviation principles and laws of large numbers in topological data analysis.
Star Clusters in Clique Complexes and the Vietoris-Rips Complex of Planar Sets
Explore star clusters in simplicial complexes and their applications to independence complexes and Vietoris-Rips complexes of planar sets, with insights on homotopy information and related conjectures.
Vietoris-Rips Complexes of Hypercube Graphs
Explore Vietoris-Rips complexes of hypercube graphs, their collapsibility, and applications in genetic trees and persistent homology. Gain insights into simplicial complexes and topological data analysis.
Approximation of Compact Metric Spaces by Finite Samples
Explore topological data analysis through finite approximations of compact metric spaces, connecting Shape Theory and Persistence for robust feature extraction from noisy datasets.
Discrete Homotopy Theory and Applications
Explore discrete homotopy theory's evolution, applications in topology, geometry, and group theory. Learn simplified approaches to fundamental groups and covering spaces, with insights into various mathematical domains.
Barbara Giunti - Average Complexity of Barcode Computation for Vietoris-Rips Filtrations
Explore algorithmic complexity of persistent homology in random Vietoris-Rips filtrations, focusing on boundary matrix fill-up and its implications for computational efficiency.
Principled Simplicial Neural Networks for Trajectory Prediction
Learn advanced techniques for trajectory prediction using simplicial neural networks, exploring their principles and applications in data science and signal processing.
Minimal Cycle Representatives in Persistent Homology Using Linear Programming
Explores optimization techniques for selecting minimal cycle representatives in persistent homology, comparing effectiveness and computational costs of various algorithms using linear programming methods.
The Directional Transform
Explore the directional transform in topological data analysis, its applications in understanding complex structures, and its potential for enhancing machine learning models and data shape quantification.
A Topological Study of the Space of Planar Pentagons
Exploring topology of planar pentagons as a model for molecular conformation spaces, using topological data analysis for dimensionality reduction and visualization.
Persistent Cycle Registration and Topological Bootstrap
Novel approach for comparing persistent homology representations, utilizing spatial placement of persistent cycles. Demonstrates application in topological inference to differentiate signal from noise in point cloud data.
Henry Adams - Topology in Machine Learning
Explore persistent homology in machine learning, covering applications in materials science, computer vision, and agent-based modeling. Learn how topology relates to dataset geometry and explainable AI.
Swap, Shift and Trim to Edge Collapse a Flag Filtration
Exploring efficient algorithms for reducing flag filtrations in persistent homology, with focus on edge collapse techniques and their applications in computational topology.