A topological data analytic approach for discovering biophysical signatures in protein dynamics
Identifying structural differences among proteins can be a non-trivial task. When contrasting
ensembles of protein structures obtained from molecular dynamics simulations, biologically …
ensembles of protein structures obtained from molecular dynamics simulations, biologically …
Euler characteristic surfaces
G Beltramo, R Andreeva, Y Giarratano… - arXiv preprint arXiv …, 2021 - arxiv.org
We study the use of the Euler characteristic for multiparameter topological data analysis.
Euler characteristic is a classical, well-understood topological invariant that has appeared in …
Euler characteristic is a classical, well-understood topological invariant that has appeared in …
Persistent magnitude
D Govc, R Hepworth - Journal of Pure and Applied Algebra, 2021 - Elsevier
In this paper we introduce the persistent magnitude, a new numerical invariant of (sufficiently
nice) graded persistence modules. It is a weighted and signed count of the bars of the …
nice) graded persistence modules. It is a weighted and signed count of the bars of the …
[PDF][PDF] Randomness and statistical inference of shapes via the smooth Euler characteristic transform
K Meng, J Wang, L Crawford… - arXiv preprint arXiv …, 2022 - researchgate.net
In this paper, we provide the mathematical foundations for the randomness of shapes and
the distributions of smooth Euler characteristic transform. Based on these foundations, we …
the distributions of smooth Euler characteristic transform. Based on these foundations, we …
Reconstructing embedded graphs from persistence diagrams
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding
the size and prominence of topological features at varying scales, the PD provides important …
the size and prominence of topological features at varying scales, the PD provides important …
The weighted Euler curve transform for shape and image analysis
Abstract The Euler Curve Transform (ECT) of Turner et al. is a complete invariant of an
embedded simplicial complex, which is amenable to statistical analysis. We generalize the …
embedded simplicial complex, which is amenable to statistical analysis. We generalize the …
A statistical pipeline for identifying physical features that differentiate classes of 3D shapes
A statistical pipeline for identifying physical features that differentiate classes of 3D shapes
Page 1 The Annals of Applied Statistics 2021, Vol. 15, No. 2, 638–661 https://doi.org/10.1214/20-AOAS1430 …
Page 1 The Annals of Applied Statistics 2021, Vol. 15, No. 2, 638–661 https://doi.org/10.1214/20-AOAS1430 …
Randomness of Shapes and Statistical Inference on Shapes via the Smooth Euler Characteristic Transform
K Meng, J Wang, L Crawford… - Journal of the American …, 2024 - Taylor & Francis
In this article, we establish the mathematical foundations for modeling the randomness of
shapes and conducting statistical inference on shapes using the smooth Euler characteristic …
shapes and conducting statistical inference on shapes using the smooth Euler characteristic …
Ordering Topological Descriptors
Recent developments in shape reconstruction and comparison call for the use of many
different types of topological descriptors (persistence diagrams, Euler characteristic …
different types of topological descriptors (persistence diagrams, Euler characteristic …