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Intrinsic inference on the mean geodesic of planar shapes and tree discrimination by leaf growth
 ANN. STATIST
, 2011
"... For planar landmark based shapes, taking into account the nonEuclidean geometry of the shape space, a statistical test for a common mean first geodesic principal component (GPC) is devised which rests on one of two asymptotic scenarios. For both scenarios, strong consistency and central limit theo ..."
Abstract

Cited by 9 (2 self)
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For planar landmark based shapes, taking into account the nonEuclidean geometry of the shape space, a statistical test for a common mean first geodesic principal component (GPC) is devised which rests on one of two asymptotic scenarios. For both scenarios, strong consistency and central limit theorems are established, along with an algorithm for the computation of a Ziezold mean geodesic. In application, this allows to verify the geodesic hypothesis for leaf growth of Canadian black poplars and to discriminate genetically different trees by observations of leaf shape growth over brief time intervals. With a test based on Procrustes tangent space coordinates, not involving the shape space’s curvature, neither can be achieved.
of objects with application in manufacturing
, 2010
"... Statistical performance of tests for factor effects on the shape ..."
RESEARCH STATEMENT
"... My research is in Lie theory, the study of groups with a compatible manifold structure, and has connections to representation theory and combinatorics. I study loop groups, the simplest class of infinitedimensional Lie groups. The elements of a loop group are smooth maps from the circle into a fini ..."
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My research is in Lie theory, the study of groups with a compatible manifold structure, and has connections to representation theory and combinatorics. I study loop groups, the simplest class of infinitedimensional Lie groups. The elements of a loop group are smooth maps from the circle into a finitedimensional Lie group. Loop groups are related to the study of solitons and integrable systems in PDE, and to quantum field theory (QFT). They are spaces of fields for twodimensional versions of the standard model of particle physics. Quantizing these fields requires constructing suitable probability measures on loop groups. Choosing the correct coordinates is the key to many problems in mathematics. One goal of my research is finding the right coordinates for studying the invariant measure on a loop group. Coordinates on a compact, semisimple Lie group K in which the invariant measure can be written as a product appear in the work of Lu [35] and Soibelman [49]. These coordinates are connected to the geometry and topology of the flag manifold of K. In [39], my advisor Doug Pickrell used the framework of KacMoody Lie algebras, in which loop groups are generalizations of semisimple Lie groups, to prove the existence of an analogous coordinate system on the group of loops into SU(2). In [41], Pickrell and I prove that such a coordinate system exists on the group of loops into any compact, simple group K. Besides conjecturally factoring the invariant measure on the loop group of K, these coordinates provide a new tool for probing the analytic properties of this
Journal of Multivariate Analysis 131 (2014) 174–196 Contents lists available at ScienceDirect Journal of Multivariate Analysis
"... journal homepage: www.elsevier.com/locate/jmva ..."
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2. “Shape Space Geometry”, and
"... The authors wish to thank the discussants for their very interesting and stimulating contributions indicating various directions for future research and clarifying issues raised in our contribution. It seems that the following three major topics 1. “Simple and Parsimonious Descriptors for Shape Data ..."
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The authors wish to thank the discussants for their very interesting and stimulating contributions indicating various directions for future research and clarifying issues raised in our contribution. It seems that the following three major topics 1. “Simple and Parsimonious Descriptors for Shape Data”,