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#Discrete Morse Theory

Showing: 12 courses
Institute for Pure & Applied Mathematics (IPAM)

Discrete Morse Graph Skeletonization and Application to Local Structures of scRNA-seq Data

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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.
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1 Lesons
52 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Hardness Results in Discrete Morse Theory for 2-Complexes

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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.
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13 Lesons
34 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Morse-Based Fibering of the Rank Invariant

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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.
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14 Lesons
54 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Ulrich Bauer: Ripser - Efficient Computation of Vietoris–Rips Persistence Barcodes

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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.
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19 Lesons
51 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Graph Reconstruction via Discrete Morse Theory

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Explore graph reconstruction using discrete Morse theory, focusing on geometric graphs and density data. Learn about theoretical guarantees and applications in road network reconstruction.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Topological Methods in Discrete Geometry - New Developments

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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.
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1 Lesons
42 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

An Application of Discrete Morse Theory to Robot Motion Planning

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Explore discrete Morse theory and its variants, learning how to apply this mathematical concept to develop continuous motion planning algorithms for autonomous devices.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Morse Theory for Group Presentations and the Persistent Fundamental Group

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Discrete Morse theory refinement for CW-complexes, with applications in combinatorial group theory and topological data analysis, including persistent fundamental group computation.
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1 Lesons
1 hour
On-Demand
Free-Video
Applied Algebraic Topology Network

Claudia Landi - Multi-parameter Persistence from the Viewpoint of Discrete Morse Theory

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Explore multi-parameter persistence through discrete Morse theory, connecting combinatorial properties of critical cells to algebraic properties of persistence modules in topological data analysis.
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1 Lesons
44 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Discrete Morse Theory Meets Multi-Parameter Persistence

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Exploring connections between discrete Morse theory and multiparameter persistence in topological data analysis, focusing on critical cells, fibered rank invariant, and computational efficiency.
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1 Lesons
52 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Topological Uncertainty and Representations for Biomedical Image Analysis

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Innovative approach to biomedical image analysis using topological structures and uncertainty, enhancing segmentation accuracy and enabling interactive annotation for fine-scale delineation.
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1 Lesons
55 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Bridging Persistent Homology and Discrete Morse Theory with Applications to Shape Reconstruction

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Explore the connection between persistent homology and discrete Morse theory, unifying key concepts and applying insights to shape reconstruction in computational topology.
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1 Lesons
56 minutes
On-Demand
Free-Video