Inferring and Characterizing Neuronal Connectivity with Deep Geometry and Topology
Exploring novel geometric and topological methods to decode neural connectivity rules in C. elegans, revealing insights into embryonic development and nervous system architecture.
Parallel Decomposition of Persistence Modules Through Interval Bases
Exploring parallel decomposition of persistence modules using interval bases, with applications in Topological Data Analysis and connections to the Hodge Laplacian.
Katharine Turner - PCA of Persistent Homology Rank Functions with Case Studies
Explore persistent homology rank functions through PCA, featuring case studies and insights into topological data analysis techniques.
Multiparameter Persistence for Machine Learning in Topological Data Analysis
Explore advanced Topological Data Analysis through multiparameter persistence, focusing on practical machine learning applications using MMA decomposition and signed barcode techniques.
Persistent Homology Analysis of Phase Transitions in Quantum Systems
Explore persistent homology for analyzing phase transitions in complex physical systems. Learn how this topological machine learning method extracts meaningful information from sparse data in condensed matter physics.
Persistent Homology of Plant-Pollinator Interactions - The Importance of Flowering Plant Surveys
Explore persistent homology in plant-pollinator interactions, analyzing topological features and the impact of flowering plant surveys on understanding community structures.
Spectral Relaxations of the Persistent Rank Invariant - Applied Algebraic Topology Network
Spectral relaxations of persistent rank invariant: A framework for continuous relaxations, offering stability and differentiability while preserving key properties and enabling efficient GPU-parallelized computation.
Bridging Persistent Homology and Discrete Morse Theory with Applications to Shape Reconstruction
Explore the connection between persistent homology and discrete Morse theory, unifying key concepts and applying insights to shape reconstruction in computational topology.