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Persistent Homology Analysis of Brain Artery Trees.
TLDR
The correlation with age continues to be significant even after controlling for correlations from earlier significant summaries, and novel approaches to the statistical analysis lead to heightened correlations with covariates such as age and sex relative to earlier analyses of this data set. Expand
Evaluating genetic markers and neurobiochemical analytes for fluoxetine response using a panel of mouse inbred strains
TLDR
A candidate genetic locus that associates with baseline depressive-like behavior contains a gene that encodes for cellular proliferation/adhesion molecule (Cadm1), supporting a genetic basis for the role of neuro/gliogenesis in depression. Expand
Optimization Method for Fr\'echet Means in BHV Treespace
For a dataset of points from a metric space, the Fréchet function is the sum of squared distances from a variable point to the data points. The Fréchet mean is the minimizer of the Fréchet function.Expand
Sticky central limit theorems on open books
Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of whenExpand
Tree-Oriented Analysis of Brain Artery Structure
TLDR
This analysis of MRA data shows a statistically significant effect of age and sex on brain artery structure, and variation in the proximity of brain arteries to the cortical surface results in strong statistical difference between sexes and statistically significant age effect. Expand
Branch order regression for modeling brain vasculature
TLDR
A novel parametrization preserves an important aspect of tree structure, namely its branch order, and is amenable to standard methods of analysis, like generalized linear/additive models. Expand
Relative Optimality Conditions and Algorithms for Treespace Fréchet Means
TLDR
By analyzing the differential properties of the Frechet function along geodesics in treespace, a theorem describing a decomposition of the derivative along a geodesic is obtained that is used to formulate optimality conditions which are used as a logical basis for an algorithm to verify relative optimality at points where theFrechet function gradient does not exist. Expand
Dynamic Geodesics in Treespace via Parametric Maximum Flow
Shortest paths in treespace, which represent minimal deformations between trees, are unique and can be computed in polynomial time. The ability to quickly compute shortest paths has enabled newExpand
Computing Affine Combinations, Distances, and Correlations for Recursive Partition Functions
TLDR
Taking advantage of the recursive structure in trees, this work formulated fast algorithms for computing affine combinations, distances and correlations in a vector subspace of recursive partition functions. Expand
Tree Oriented Data Analysis
TLDR
Property of the Fr\'echet function are used to develop an algorithmic system for computing Fr‐echet means and a sticky law of large numbers is described which describes a surprising stability of the topological tree structure of sample Fr¬echet mean at that of the population Frµechetmean. Expand
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