Discrete Morse Graph Skeletonization and Application to Local Structures of scRNA-seq Data
Explores topological data analysis for extracting graph skeletons from high-dimensional data, with applications in analyzing local structures of scRNA-seq datasets across brain regions.
Hardness Results in Discrete Morse Theory for 2-Complexes
Explore inapproximability and parameterized complexity in discrete Morse theory for 2-complexes, focusing on minimizing critical simplices and presenting new hardness results and an approximation algorithm.
Morse-Based Fibering of the Rank Invariant
Explore multi-parameter persistence in data analysis using discrete Morse theory to compute rank invariants, partition parameter space, and deduce persistence diagrams for equivalent classes of lines.
Ulrich Bauer: Ripser - Efficient Computation of Vietoris–Rips Persistence Barcodes
Explore efficient computation of Vietoris-Rips persistence barcodes using Ripser software. Learn about matrix reduction algorithms, persistent cohomology, and discrete Morse theory applications in topological data analysis.
Graph Reconstruction via Discrete Morse Theory
Explore graph reconstruction using discrete Morse theory, focusing on geometric graphs and density data. Learn about theoretical guarantees and applications in road network reconstruction.
Topological Methods in Discrete Geometry - New Developments
Explores recent advancements in topological methods for discrete geometry, focusing on configuration spaces in cooperative game theory and their connections to embedding problems in Euclidean spaces.
An Application of Discrete Morse Theory to Robot Motion Planning
Explore discrete Morse theory and its variants, learning how to apply this mathematical concept to develop continuous motion planning algorithms for autonomous devices.
Morse Theory for Group Presentations and the Persistent Fundamental Group
Discrete Morse theory refinement for CW-complexes, with applications in combinatorial group theory and topological data analysis, including persistent fundamental group computation.
Claudia Landi - Multi-parameter Persistence from the Viewpoint of Discrete Morse Theory
Explore multi-parameter persistence through discrete Morse theory, connecting combinatorial properties of critical cells to algebraic properties of persistence modules in topological data analysis.
Discrete Morse Theory Meets Multi-Parameter Persistence
Exploring connections between discrete Morse theory and multiparameter persistence in topological data analysis, focusing on critical cells, fibered rank invariant, and computational efficiency.
Topological Uncertainty and Representations for Biomedical Image Analysis
Innovative approach to biomedical image analysis using topological structures and uncertainty, enhancing segmentation accuracy and enabling interactive annotation for fine-scale delineation.
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.