5,635 research outputs found
Blocking light in compact Riemannian manifolds
We study compact Riemannian manifolds for which the light between any pair of
points is blocked by finitely many point shades. Compact flat Riemannian
manifolds are known to have this finite blocking property. We conjecture that
amongst compact Riemannian manifolds this finite blocking property
characterizes the flat metrics. Using entropy considerations, we verify this
conjecture amongst metrics with nonpositive sectional curvatures. Using the
same approach, K. Burns and E. Gutkin have independently obtained this result.
Additionally, we show that compact quotients of Euclidean buildings have the
finite blocking property.
On the positive curvature side, we conjecture that compact Riemannian
manifolds with the same blocking properties as compact rank one symmetric
spaces are necessarily isometric to a compact rank one symmetric space. We
include some results providing evidence for this conjecture.Comment: 19 page
PPI Induced Hypomagnesemic Hypoparathyroidism Leading to Posterio Reversible Encephalopathy Syndrome.
Quantifying the Artistic Experience with Perceptive Sketching Tools: Cognitive Technologies to Support Creativity Researchers
Creativity research has gradually moved away from controlled laboratory settings to more naturalistic and real world domains. As a result, new research methods are required to systematically analyze the artistic experience that includes the artist’s perception, behavior, and conception throughout the creative process. We use research findings from the Cognitive Science literature to create a framework called Perceptual Logic to categorize different types of artistic experience. This framework is applicable to open-ended artistic creativity. Empiri- cally validating such a framework requires new tools that provide insight into the naturalistic creative process. We describe the initial design of a set of digital sketching tools that enables creativity researchers to quantitatively analyze the artistic experience. These tools focus spe- cifically on understanding how visual digital artists perceive and interact with their drawings and paintings throughout their creative process
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