We establish a semi-group solution concept for morphological differential equations, such as the mean curvature flow equation. The proposed method consists in generating flows from generalized minimizers of nonconvex energy functionals. We use relaxation and convexification to define generalized minimizers. The main part of this work consists in verification of the solution concept by comparing...

We study stability of non-compact gradient Kähler-Ricci flow solitons with positive holomorphic bisectional curvature. Our main result is that any compactly supported perturbation and appropriately decaying perturbations of the Kähler potential of the soliton will converge to the original soliton under Kähler-Ricci flow as time tends to infinity. To obtain this result, we construct appropriate ...

Two main assumptions which underlie the Stoney formula relating substrate curvature to mismatch strain in a bonded thin film are that the film is very thin compared to the substrate, and the deformations are infinitesimally small. Expressions for the curvature-strain relationship are derived for cases in which these assumptions are relaxed, thereby providing a basis for interpretation of experi...

Detectability of contours may be affected by long-range interactions between neurons in early stages of visual cortex. Specifically, neurons with receptive fields arrayed along the length of a contour may facilitate each other in a position- and orientation-dependent manner. Accordingly, the overall geometry of a contour should significantly influence both the strength of these long-range inter...

This paper explores the possibilities of very simple analysis on derivation of spiral regions for a single segment of cubic function matching positional, tangential, and curvature end conditions. Spirals are curves of monotone curvature with constant sign and have the potential advantage that the minimum and maximum curvature exists at their end points. Therefore, spirals are free from singular...

The use of point sets instead of meshes became more popular during the last years. We present a new method for anisotropic fairing of a point sampled surface using an anisotropic geometric mean curvature ßow. The main advantage of our approach is that the evolution removes noise from a point set while it detects and enhances geometric features of the surface such as edges and corners. We derive...

We describe an efficient implementation of an interior-point algorithm for non-convex problems that uses directions of negative curvature. These directions should ensure convergence to second-order KKT points and improve the computational efficiency of the procedure. Some relevant aspects of the implementation are the strategy to combine a direction of negative curvature and a modified Newton d...

For linear optimization (LO) problems, we consider a curvature integral first introduced by Sonnevend et al. (1991). Our main result states that in order to establish an upper bound for the total Sonnevend curvature of the central path, it is sufficient to consider only the case when n = 2m. This also implies that the worst cases of LO problems for path-following algorithms can be reconstructed...

The B subunit of the bacterial cholera toxin (CTxB) is responsible for the toxin binding to the cell membrane and its intracellular trafficking. CTxB binds to the monosialotetrahexosyl ganglioside at the plasma membrane of the target cell and mediates toxin internalization by endocytosis. CTxB induces a local membrane curvature that is essential for its clathrin-independent uptake. Using all-at...

In this paper, we address the topic of monogenic curvature scale-space. Combining methods of tensor algebra, monogenic signal and quadrature filter, the monogenic curvature signal, as a novel model for intrinsically two-dimensional (i2D) structures, is derived in an algebraically extended framework. It is unified with a scale concept by employing damped spherical harmonics as basis functions. T...