Persistent Homology Analysis of Brain Artery Trees.
Abstract
New representations of tree-structured data objects, using ideas from topological
data analysis, enable improved statistical analyses of a population of brain artery
trees. A number of representations of each data tree arise from persistence diagrams
that quantify branching and looping of vessels at multiple scales. Novel approaches
to the statistical analysis, through various summaries of the persistence diagrams,
lead to heightened correlations with covariates such as age and sex, relative to earlier
analyses of this data set. The correlation with age continues to be significant even
after controlling for correlations from earlier significant summaries.
Type
Journal articlePermalink
https://hdl.handle.net/10161/11157Published Version (Please cite this version)
10.1214/15-AOAS886Publication Info
(n.d.). Persistent Homology Analysis of Brain Artery Trees. Ann Appl Stat, 10(1). pp. 198-218. 10.1214/15-AOAS886. Retrieved from https://hdl.handle.net/10161/11157.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Paul L Bendich
Associate Research Professor of Mathematics
I work in computational topology, which for me means adapting and using tools from
algebraic topology in order to study noisy and high-dimensional datasets arising from
a variety of scientific applications.
My thesis research involved the analysis of datasets for which the number of degrees
of freedom varies across the parameter space. The main tools are local homology and
intersection homology, suitably redefined in this fuzzy multi-scale context.
I am also working on building connections bet
Ezra Miller
Professor of Mathematics
Professor Miller's research centers around problems in geometry, algebra, topology,
combinatorics, statistics, probability, and computation originating in mathematics
and the sciences, including biology, chemistry, computer science, and imaging.The
techniques range, for example, from abstract algebraic geometry or commutative algebra
of ideals and varieties to concrete metric or discrete geometry of polyhedral spaces;
from deep topological constructions such as equivariant K-theory a
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