Fetching the paper…
Reading the bibliography…
In this paper we consider two topological transforms that are popular in applied topology: the Persistent Homology Transform (PHT) and the Euler Characteristic Transform (ECT).
H. Whitney, “Local properties of analytic varieties,” in A Symposium in Honor of M. Morse
1965
Earlier work this paper cites.
N. Alon, D. Haussler, and E. Welzl, “Partitioning and geometric embedding of range spaces of finite Vapnik-Chervonenkis dimension,” Proceedings of Symposium on Computational Geometry
1987
Earlier work this paper cites.
P. Schapira, “Operations on Constructible Functions,” in Journal of Pure and Applied Algebra
1991
Earlier work this paper cites.
P. Schapira, “Tomography of constructible functions,” in 11th Intl. Symp. on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
1995
Earlier work this paper cites.
Alex J. Wilkie. “Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function,” Journal of the American Mathematical Society
1996
Earlier work this paper cites.
M. Bestvina and N. Brady, “Morse theory and finiteness properties of groups,” Inventiones Mathematicae
1997
Earlier work this paper cites.
L. Van den Dries, Tame Topology and O-Minimal Structures
1998
Earlier work this paper cites.
P. K. Agarwal, H. Edelsbrunner, J. Harer, and Y. Wang, “Extreme elevation on a 2-manifold,” Discrete & Computational Geometry
2006
Earlier work this paper cites.
D. Cohen-Steiner, H. Edelsbrunner, J. Harer, “Stability of persistence diagrams,” Discrete & Computational Geometry
2007
Cited alongside, same era.
D. Cohen-Steiner, H. Edelsbrunner, J. Harer, Y. Mileyko: “Lipschitz functions have L p-stable persistence.” Foundations of Computational Mathematics
2010
Cited alongside, same era.
H. Edelsbrunner and J. Harer, “Computational Topology: An Introduction.” 241 pages. Applied Mathematics series. American Mathematical Society, Providence, RI. 2010
2010
Cited alongside, same era.
T. Lê Loi, “Lecture 2: Stratifications in O-minimal Structures,” in The Japanese-Australian Workshop on Real and Complex Singularities: JARCS III,
2010
Cited alongside, same era.
J. Curry, R. Ghrist, and M. Robinson, “Euler Calculus with Applications to Signals and Sensing,” in Proceedings of Symposia in Applied Mathematics
2012
D. Govc “On the Definition of the homological critical value,” Journal of Homotopy and Related Structures
2016
Later among the works it cites.
R. Ghrist, R. Levanger, and H. Mai, “Persistent Homology and Euler Integral Transforms” Journal of Applied and Computational Topology
2018
Closest in time.
G. Friedman Singular Intersection Homology (New Mathematical Monographs). Cambridge: Cambridge University Press, 2020. doi:10.1017/9781316584446. Citations here use the draft version available at http://faculty.tcu.edu/gfriedman/IHbook.pdf
2020
Closest in time.
2020
Closest in time.
K. Turner “Medians of populations of persistence diagrams,” Homology, Homotopy and Applications
2020
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
J. Curry “Sheaves, Cosheaves and Applications.” PhD dissertation, University of Pennsylvania, 2014
2014
Cited alongside, same era.
K. Turner, S. Mukherjee, and D. Boyer “Persistent Homology Transform for Modeling Shapes and Surfaces,” Information and Inference: A Journal of the IMA
2014
Cited alongside, same era.
J. Curry “Topological Data Analysis and Cosheaves,” Japan Journal of Industrial and Applied Mathematics
2015
Cited alongside, same era.
Y. Baryshnikov, R. Ghrist, and D. Lipsky “Inversion of Euler integral transforms with applications to sensor data,” Inverse Problems
Cited in the paper.
D.M. Boyer, J. Puente, J.T. Gladman, C. Glynn, S. Mukherjee, G.S. Yapuncich, and I. Daubechies “A New Fully Automated Approach for Aligning and Comparing Shapes,” The Anatomical Record, Volume 258, Issue 1, https://doi.org/10.1002/ar.23084
Cited in the paper.
Cited in the paper.
F. Chazal, V. de Silva, M. Glisse, S. Oudot, “Structure and Stability of Persistence Modules,” Springer Briefs in Mathematics
Cited in the paper.
Closest in time.
S.T. Wai, G.M. da Silva, H. Kirveslahti, E. Skeens, B. Feng, T. Sudijono, K.K. Yang, S. Mukherjee, B. Rubenstein, L. Crawford “A Topological Data Analytic Approach for Discovering Biophysical Signatures in Protein Dynamics,” bioRxiv preprint bioRxiv:2021.07.28.454240, 2021
2021
Closest in time.
B. Wang, T. Sudijono, H. Kirveslahti, T. Gao, DM. Boyer, S. Mukherjee, and L. Crawford “A statistical pipeline for identifying physical features that differentiate classes of 3D shapes,” Annals of Applied Statistics
2021
Closest in time.