We propose a generalized curvature that is motivated by the optimal transport problem on $\mathbb{R}^d$ with cost induced Tonelli Lagrangian $L$. show non-negativity of implies displacement convexity entropy functional $L-$Wasserstein space along $C^2$ interpolants.

We present a table driven approach to performing Catmull-Clark subdivision in parallel utilizing one thread per output mesh vertex. We apply the procedure one or two times in order to isolate extraordinary vertices and simplify the input patch structures consumed by the hardware unit responsible for adaptive tessellation. From this simplified mesh, we evaluate the performance Stam’s direct eval...

Background Right ventricular (RV) pressure overload results in interventricular septal displacement (IVSD) towards left ventricle in patients with pulmonary arterial hypertension (PAH). There is however scarce data on the duration of IVSD during cardiac cycle as expressed by curvature duration index (CDi) and its potential role in the evaluation of PAH patients. The aim of our study is to revea...

We consider a mathematical model for the quasi-static deformation of a thinning sheet. The model couples a first-order equation for the thickness of the sheet to a prescribed curvature equation for the displacement of the sheet. We prove a local in time existence and uniqueness theorem for this system when the sheet can be written as a graph. A contact problem is formulated for a sheet constrai...

We present a new method for enhancing shape features of a mesh surface by moving mesh vertices from low-curvature regions to high-curvature regions or feature regions. The movement of the vertices, also called vertex flow, is driven by minimizing an objective function defined to take into account several important considerations in mesh improvement. First, a new edge-based energy term is used t...

We construct geodesics in the Wasserstein space of probability measures along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show that a local Poincaré inequality and the measure contraction property follow from the Ricci curvature bounds defined by Sturm. We also show for a large class o...

In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals de ned on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto-Westdickenberg in ...

Kinematic analysis has provided important insights into the biology of growth by revealing the distribution of expansion within growing organs. Modern methods of kinematic analysis have made use of new image-tracking algorithms and computer-assisted evaluation, but these methods have yet to be adapted for examination of growth in a variety of plant species or for analysis of graviresponse. Ther...

Using the visual search method, we show that stimuli that contain curvature discontinuities (i.e., points where the second derivative along an image contour is not defined) are easily found among stimuli containing only smooth changes in curvature. Curved stimuli that lack curvature discontinuities, however, are difficult to find among distractors that have them. These results suggest that the ...

During physiological spontaneous breathing maneuvers, the diaphragm displaces volume while maintaining curvature. However, with maximal diaphragm activation, curvature decreases sharply. We tested the hypotheses that the relationship between diaphragm muscle shortening and volume displacement (VD) is nonlinear and that curvature is a determinant of such a relationship. Radiopaque markers were s...