Optimizing Embedding Using Persistence
Explore optimizing Takens-type embeddings of time series using persistent (co)homology. Learn practical approaches for finding good embeddings and discuss the space of embeddings and open questions.
Parallel Decomposition of Persistence Modules Through Interval Bases
Explore parallel decomposition of persistence modules using interval bases, enhancing Topological Data Analysis with distributed computation and Hodge decomposition techniques.
L-P Metrics on Multiparameter Persistence Modules
Explores generalizations of p-Wasserstein distance for multi-parameter persistence modules, introducing d_I^p and d_M^p metrics. Examines their properties and applications in topological data analysis.
Edit Distance and Persistence Diagrams Over Lattices
Functorial pipeline for persistent homology: from filtered simplicial complexes to persistence diagrams. Addresses multiparameter persistent homology and functoriality of persistence diagrams.
Geometric Approaches on Persistent Homology
Explore geometric interpretations of persistence diagrams, focusing on quantitative descriptions of homology class size and persistence, with analysis of power filtration on unweighted graphs.
Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius
Explore geometric persistent homology, its isomorphism with Vietoris-Rips filtration, and applications in characterizing persistence barcodes, bounding intervals, and connecting to filling radius.
Vietoris-Rips Thickenings - Problems for Birds and Frogs
Explore open problems in Vietoris-Rips complexes, connecting diverse mathematical areas. Suitable for both broad theorists and problem-solving specialists in applied algebraic topology.
The Persistence Mayer-Vietoris Spectral Sequence
Explore the persistent Mayer-Vietoris spectral sequence, its applications in parallelizing persistent homology computations, and its ability to provide locality-enriched persistence barcodes.
Visualizing 2 Dimensional Persistent Homology
Explore techniques for visualizing 2D persistent homology, a powerful tool in topological data analysis, to gain insights into complex datasets and their underlying structures.
Algebraic Perspectives of Persistence
Explore algebraic approaches to persistent homology, focusing on the stability of persistence diagrams and their relation to input data changes in topological data analysis.
Novel Computational Perspectives of Persistence
Explore innovative computational approaches to persistence in algebraic topology, focusing on advanced techniques and their applications in data analysis and topological research.
Two-Parameter Persistent Homology of Second Configuration Spaces in Star Graphs
Explore configuration spaces in robot motion planning, focusing on 2-parameter persistent homology of second configuration spaces of star graphs with restraint parameters.
Classification of Euler Characteristic Transforms Using CNNs - 5/9/24
Explore how Euler Characteristic Transforms and CNNs can be used for shape classification, with a focus on leaf datasets. Learn about ECT-CNN pipeline, rotation equivariance, and practical applications.
Bounding the Interleaving Distance for Mapper Graphs with a Loss Function
Exploring interleaving distance for Mapper graphs, introducing a loss function to measure assignment quality and enable polynomial-time computation for data comparison and clustering.
Informational and Topological Signatures of Individuality in Network Neuroscience
Exploring brain function through topological data analysis, demonstrating improved individual and age discrimination using algebraic-topological features extracted from resting fMRI data compared to traditional methods.
Barcodes for the Topological Analysis of Gradient-Like Vector Fields
Explore topological analysis of gradient-like vector fields using barcodes. Learn about chain complexes, parametrization, and applications in smooth and discrete settings, with insights on stability and approximation.
Harmonic Persistent Homology for Disentangling Multiway Interaction in Data
Explore Harmonic Persistent Homology for analyzing multi-omics data, uncovering hidden patterns in complex diseases, and identifying biomarkers associated with latent biological pathways.
Topological Node2vec: Improving Graph Embeddings with Persistent Homology
Exploring persistent homology to enhance graph embeddings, combining topology with machine learning for improved data analysis and representation in complex networks.
Persistent Homology for Infinite Complexes - Extending Theory to Infinite CW Complexes
Explore the extension of persistent homology to infinite CW complexes, including key theorems and applications in topological data analysis.
Introduction to Perverse Sheaves
Dive into the fundamental concepts and theoretical foundations of perverse sheaves with expert mathematician Mark Goresky, exploring advanced mathematical structures and their applications.
Sheaves on Graphs, the Hanna Neumann Conjecture, and Algebraic Geometry Applications
Explore advanced graph theory concepts through sheaf theory and the Hanna Neumann conjecture, featuring innovative problem-solving approaches and applications in discrete mathematics.