Non-Diffusive Vortexes at Transition State of Activated Process by Persistent Homology
Exploring non-diffusive dynamics in molecular transitions using persistent homology, revealing reactive vortexes and rotational fluxes at transition states of alanine-dipeptide isomerization.
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.
A Topological Understanding of Neuronal Morphologies
Exploring topological data analysis for neuronal morphologies, from single cells to networks. Highlights applications in classification, clustering, and solving inverse problems in neuroscience.
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.
Geometry and Topology of Data
Explore hyperconvexity and generalized curvature in metric spaces, linking topological data analysis with geometric concepts for a deeper understanding of data structures.
The Generalized Persistence Diagram Encodes the Bigraded Betti Numbers
Explore how generalized persistence diagrams encode bigraded Betti numbers in 2-parameter persistence modules, with implications for RIVET software and interval decomposable modules.
Persistent Topological Laplacians
Explores persistent topological Laplacians to address limitations in topological data analysis, enhancing the handling of complex data and uncovering SARS-CoV-2 evolution mechanisms.
Small Density Vacuum and How to Find Them Robustly
Explore a new TDA method for identifying small density vacuums in high-density regions, with proven robustness and bounded persistence. Includes simulations and theoretical insights.
Topological Time Series Analysis for Hurricanes and Dynamical Systems
Explore topological data analysis applications in studying hurricane satellite imagery and dynamical system bifurcations using persistent homology and zigzag persistence techniques.
Ephemeral Persistence Modules and Distance Comparison
Exploring sheaf theoretic methods in persistent homology, comparing approaches using Alexandrov's and gamma-topology, and examining pseudo-distances in persistence module spaces.
Homotopical Decompositions of Simplicial and Vietoris Rips Complexes
Explore homotopical decompositions of simplicial complexes, focusing on obstruction complexes and their applications in topological data analysis, with insights on Vietoris-Rips complexes.
Differential Calculus on Persistence Barcodes
Explore differential calculus on persistence barcodes, covering differentiability concepts, lifts to ordered barcodes, and applications in topological data analysis.
Studying the Space of Persistence Diagrams Using Optimal Partial Transport II
Exploring persistence diagrams through optimal transport theory, bridging topological data analysis with measure spaces to characterize convergence and prove new results in random settings.
Studying the Space of Persistence Diagrams Using Optimal Partial Transport - Part I
Exploring persistence diagrams through optimal partial transport, bridging topological data analysis with measure theory. Novel approach enables new insights into convergence, continuity, and random settings in TDA.
TopoAct - Visually Exploring the Shape of Activations in Deep Learning
Explore the shape of neuron activations in deep learning using topological data analysis. Gain insights into learned representations of image classifiers with TopoAct visualization system.
On the Metric Distortion of Embedding Persistence Diagrams into RKHS
Explores embedding Persistence Diagrams into Reproducing Kernel Hilbert Spaces, analyzing metric properties and stability guarantees for machine learning applications in Topological Data Analysis.
Multiple Hypothesis Testing with Persistent Homology
Exploring methods for multiple hypothesis testing in persistent homology, including family-wise error rates and false discovery rates, with applications to Mapper complex validation.
Quantifying Lung Structure in COPD and Solubility of Chemical Compounds
Explore topological data analysis applications in medicine and chemistry, focusing on lung structure in COPD and chemical compound solubility using persistent homology as a key tool.