The relationship between semicircular canal radius of curvature and afferent sensitivity has not been experimentally determined. We characterized mouse semicircular canal afferent responses to sinusoidal head rotations to facilitate interspecies and intraspecies comparisons of canal size to sensitivity. The interspecies experiment compared the horizontal canal afferent responses among animals r...

Despite the growth in traffic volumes, average operating speeds on rural highways have increased by as much as 8 kilometers per hour (kmh) in the past decade.1 But in most cases, horizontal and vertical alignments of these roads have remained unchanged. Together these two events have created geometric inconsistencies in certain locations because of the required curvature (demand) being greater ...

The Riemannian geometry of elastica in one and two dimensions is considered. Two examples from engineering science are given. The first is the deflexion or Frenet curvature of the elastic filament rod where the Riemannian curvature vanishes, since the curve is one dimensional. However the Frenet curvature scalar appears on the LeviCivita-Christoffel symbol of the Riemannian geometry. A second e...

In this paper, an optimal inequality involving the delta curvature is exposed. With help of some characterizations about vertical motion and horizontal divergence are obtained.

We show that if a distribution does not depend on the vertical coordinates, then Schouten curvature tensor coincides with Riemannian curvature. The and nonholonomicity are used to write Jacobi equation for distribution. This leads study of second-order optimality conditions horizontal geodesics in sub-Riemannian geometry. conjugate points Heisenberg group as an example.

in this paper, the time-like hyperruled surfaces in the minkowski 4-space and their algebraicinvariants are worked. also some characteristic results are found about these algebraic invariants.

In Euclidean vector spaces, dimensionality reduction can be centered at the data mean. In contrast, distances do not split into orthogonal components and centered analysis distorts inter-point distances in the presence of curvature. In this paper, we define a dimensionality reduction procedure for data in Riemannian manifolds that moves the analysis from a center point to local distance measure...

In this article we provide a vertical height estimate for compact special Weingarten surfaces of elliptic type in M2(c) × R, i.e. surfaces whose mean curvature H and extrinsic Gauss curvature Ke satisfy H = f(H2 −Ke) with 4x(f ′(x))2 < 1, for all x ∈ [0,+∞). The vertical height estimate generalizes a result by Rosenberg and Sa Earp and applies only to surfaces verifying a height estimate condit...

PURPOSE To investigate the variation of lamina cribrosa (LC) structure based on the baseline intraocular pressure (IOP) in eyes with primary open-angle glaucoma (POAG) and healthy individuals using swept-source optical coherence tomography. METHODS A total of 108 eyes with POAG and 61 healthy eyes were recruited. Based on the baseline IOP, the POAG eyes were divided into higher-baseline IOP (...