Large‐scale digitization projects such as# ScanAllFishes and oVert are generating high‐
resolution microCT scans of vertebrates by the thousands. Data from these projects are …

As a means of improving analysis of biological shapes, we propose an algorithm for
sampling a Riemannian manifold by sequentially selecting points with maximum uncertainty …

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 …

Clustering in high-dimensions poses many statistical challenges. While traditional distance-
based clustering methods are computationally feasible, they lack probabilistic interpretation …

This paper derives rates of convergence of approximations of observers and controllers
arising in the native space embedding method for adaptive estimation and control of a class …

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 …

We develop a geometric framework, based on the classical theory of fibre bundles, to
characterize the cohomological nature of a large class of synchronization-type problems in …

We present results of a long-term team collaboration of mathematicians and biologists. We
focus on building a mathematical framework for the shape space constituted by a collection …

Kernel-based nonlinear dimensionality reduction methods, such as Local Linear Embedding
(LLE) and Laplacian Eigenmaps, rely heavily upon pairwise distances or similarity scores …

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 …