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.
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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 am a mathematician whose main research focus lies in adapting theory from ostensibly
pure areas of mathematics, such as topology, geometry, and abstract algebra, into
tools that can be broadly used in many data-centeredapplications.My initial training
was in a recently-emerging field called topological data analysis (TDA). I have beenresponsible
for several essential and widely-used elements of its theoretical toolkit, with a
particularfocus on building TDA methodology
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-theor
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