Persistent Homology Analysis of Brain Artery Trees.
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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.
Published Version (Please cite this version)10.1214/15-AOAS886
Publication InfoBendich, Paul; Marron, JS; Miller, Ezra; Pieloch, Alex; & Skwerer, Sean (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.
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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
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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