A roadmap for the computation of persistent homology

Single-cell topological RNA-seq analysis reveals insights into cellular differentiation and development

(2017) Abbas H Rizvi et al.   NATURE BIOTECHNOLOGY

Topological analysis of data

(2017) Alice Patania et al.   EPJ Data Science

Persistent homology analysis of brain artery trees

(2016) Paul Bendich et al.   Annals of Applied Statistics

What can topology tell us about the neural code?

(2016) Carina Curto   BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY

Two’s company, three (or more) is a simplex

(2016) Chad Giusti et al.   JOURNAL OF COMPUTATIONAL NEUROSCIENCE

Object-oriented persistent homology

(2016) Bao Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Topological persistence vineyard for dynamic functional brain connectivity during resting and gaming stages

(2016) Jaejun Yoo et al.   JOURNAL OF NEUROSCIENCE METHODS

Hierarchical structures of amorphous solids characterized by persistent homology

(2016) Yasuaki Hiraoka et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Inference of Ancestral Recombination Graphs through Topological Data Analysis

(2016) Pablo G. Cámara et al.   PLoS Computational Biology

A one-dimensional homologically persistent skeleton of an unstructured point cloud in any metric space

(2015) V. Kurlin   COMPUTER GRAPHICS FORUM

Persistent Homology for Path Planning in Uncertain Environments

(2015) Subhrajit Bhattacharya et al.   IEEE Transactions on Robotics

Topological trajectory classification with filtrations of simplicial complexes and persistent homology

(2015) Florian T. Pokorny et al.   INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH

Probabilistic Fréchet means for time varying persistence diagrams

(2015) Elizabeth Munch et al.   Electronic Journal of Statistics

Unveiling patterns of international communities in a global city using mobile phone data

(2015) Paolo Bajardi et al.   EPJ Data Science

Topological Data Analysis of Biological Aggregation Models

(2015) Chad M. Topaz et al.   PLoS One

Confidence sets for persistence diagrams

(2014) Brittany Terese Fasy et al.   ANNALS OF STATISTICS

Categorification of Persistent Homology

(2014) Peter Bubenik et al.   DISCRETE & COMPUTATIONAL GEOMETRY

Crackle: The Homology of Noise

(2014) Robert J. Adler et al.   DISCRETE & COMPUTATIONAL GEOMETRY

Fréchet Means for Distributions of Persistence Diagrams

(2014) Katharine Turner et al.   DISCRETE & COMPUTATIONAL GEOMETRY

Metrics for Generalized Persistence Modules

(2014) Peter Bubenik et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

Persistent homology analysis of protein structure, flexibility, and folding

(2014) Kelin Xia et al.   International Journal for Numerical Methods in Biomedical Engineering

A topological measurement of protein compressibility

(2014) Marcio Gameiro et al.   JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS

Persistent homology for the quantitative prediction of fullerene stability

(2014) Kelin Xia et al.   JOURNAL OF COMPUTATIONAL CHEMISTRY

Quantifying force networks in particulate systems

(2014) Miroslav Kramár et al.   PHYSICA D-NONLINEAR PHENOMENA

Reconceiving the hippocampal map as a topological template

(2014) Yuri Dabaghian et al.   eLife

Morse Theory for Filtrations and Efficient Computation of Persistent Homology

(2013) Konstantin Mischaikow et al.   DISCRETE & COMPUTATIONAL GEOMETRY

Linear-Size Approximations to the Vietoris–Rips Filtration

(2013) Donald R. Sheehy   DISCRETE & COMPUTATIONAL GEOMETRY

Persistent Homology of Collaboration Networks

(2013) C. J. Carstens et al.   MATHEMATICAL PROBLEMS IN ENGINEERING

Persistence of force networks in compressed granular media

(2013) M. Kramar et al.   PHYSICAL REVIEW E

Topology of viral evolution

(2013) J. M. Chan et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Alpha shape and Delaunay triangulation in studies of protein-related interactions

(2012) W. Zhou et al.   BRIEFINGS IN BIOINFORMATICS

Persistent homology for automatic determination of human-data based cost of bipedal walking

(2012) Ramanarayan Vasudevan et al.   Nonlinear Analysis-Hybrid Systems

Strong Homotopy Types, Nerves and Collapses

(2011) Jonathan Ariel Barmak et al.   DISCRETE & COMPUTATIONAL GEOMETRY

Random Geometric Complexes

(2011) Matthew Kahle   DISCRETE & COMPUTATIONAL GEOMETRY

Persistent Cohomology and Circular Coordinates

(2011) Vin de Silva et al.   DISCRETE & COMPUTATIONAL GEOMETRY

Dualities in persistent (co)homology

(2011) Vin de Silva et al.   INVERSE PROBLEMS

Probability measures on the space of persistence diagrams

(2011) Yuriy Mileyko et al.   INVERSE PROBLEMS

Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival

(2011) M. Nicolau et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Fast construction of the Vietoris-Rips complex

(2010) Afra Zomorodian   COMPUTERS & GRAPHICS-UK

Computing Robustness and Persistence for Images

(2010) P Bendich et al.   IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS

Topology and data

(2009) Gunnar Carlsson   BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY

Manifold Reconstruction in Arbitrary Dimensions Using Witness Complexes

(2009) Jean-Daniel Boissonnat et al.   DISCRETE & COMPUTATIONAL GEOMETRY

The Theory of Multidimensional Persistence

(2009) Gunnar Carlsson et al.   DISCRETE & COMPUTATIONAL GEOMETRY

Applications of computational homology to the analysis of treatment response in breast cancer patients

(2009) D. DeWoskin et al.   TOPOLOGY AND ITS APPLICATIONS

Reconstruction Using Witness Complexes

(2008) Leonidas J. Guibas et al.   DISCRETE & COMPUTATIONAL GEOMETRY

A weak characterisation of the Delaunay triangulation

(2008) Vin de Silva   GEOMETRIAE DEDICATA

Topological structures in the equities market network

(2008) G. Leibon et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA