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.
Quasiperiodicity and Persistent Kunneth Theorems
Explore quasiperiodicity in signals, persistent homology, and Kunneth theorems. Learn applications in time series analysis and computational chemistry through 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.
Introduction to Cubical Complexes and Persistence - 2020
Explore cubical complexes and cubical homology for efficient analysis of digital images using persistent homology, with applications in topological data analysis.
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.
Generalized Morse Theory of Distance Functions to Surfaces for Persistent Homology
Unifying distance fields, persistent homology, and Morse theory to quantify complex shape textures, with applications in characterizing vascular structures in leukemia samples.
Time Series and Biological Network Analysis via Directed Graphs
Explore robust techniques for analyzing biological time series data using directed acyclic graphs, focusing on extremal events and applications in genomic research and network analysis.
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.
Applications of Topology to Oncology Data
Exploring Persistent Homology in oncology: predicting leukaemia relapse risk and analyzing tumor microenvironments using topological data analysis and machine learning techniques.
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.
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.
The ABCs of Topological Data Analysis for Matrix Analysis
Explore topological data analysis for matrix structure, focusing on persistent homology and Betti curves. Learn applications in neuroscience, including analysis of neural correlation matrices.
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.
TDA for Chromatic Point Clouds
Generalizace persistentní homologie pro barevné bodové mraky. Detekce prostorových interakcí mezi různými typy bodů s aplikacemi v biologii a medicíně.
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.