Although the basal ganglia have been shown to be critical for the expression of emotion in prosody and facial expressions, it is unclear whether they are also critical for recognition of emotions.â€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

2008

We use heat kernels or eigenfunctions of the Laplacian to construct local coordinates on large classes of Euclidean domains and Riemannian manifolds (not necessarily smooth, e.g., with (alpha)â€¦ (More)

We use heat kernels or eigenfunctions of the Laplacian to construct local coordinates on large classes of Euclidean domains and Riemannian manifolds (not necessarily smooth, e.g. with CÎ± metric).â€¦ (More)

We study one dimensional sets (Hausdorff dimension) lying i n a Hilbert space. The aim is to classify subsets of Hilbert spaces that are contained in a connected set of finite Hausdorff length. We doâ€¦ (More)

We repurpose tools from the theory of quantitative rectifiability to study the qualitative rectifiability of measures in R, n â‰¥ 2. To each locally finite Borel measure Î¼, we associate a functionâ€¦ (More)

A measure is 1-recti able if there is a countable union of nite length curves whose complement has zero measure. We characterize 1-recti able Radon measures Î¼ in n-dimensional Euclidean space for allâ€¦ (More)

The serotonergic antagonist, methysergide, administered into the periaqueductal gray matter (PAG), inhibited the antinociceptive effect of morphine, but not of glutamate, also administered into theâ€¦ (More)

We have used magnetic resonance imaging (MRI) of the living rat brain to longitudinally analyze the ontogenesis of an ibotenic acid lesion targeted at the piriform cortex. The MRI data wereâ€¦ (More)

The purpose of this essay is to present a partial survey of a family of theorems that are usually referred to as analystâ€™s traveling salesman theorems (also referred to as geometric travelingâ€¦ (More)