In order to preserve singularities in denoising, we propose a new scheme by adding dilated singularity prior to noisy images. The singularities are detected by canny operator firstly and then dilated using mathematical morphology for finding pixels “near” singularities instead of “on” singularities. The denoising results for pixels near singularities are obtained by nonlocal means in spatial do...

The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS) in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine the relationship between the singularities and the principal integrability feature of multidimensiona...

This paper presents a coordinate-invariant differential geometric analysis of kinematic singularities for closed kinematic chains containing both active and passive joints. Using the geometric framework developed in Park and Kim (1996) for closed chain manipulability analysis, we classify closed chain singularities into three basic types: (i) those corresponding to singular points of the joint ...

This paper deals with the basic approximation properties of the h-p version of the boundary element method (BEM) in IR 3. We extend the results on the exponential convergence of the h-p version of the boundary element method on geometric meshes from problems in polygonal domains to problems in polyhedral domains. In 2D elliptic boundary value problems the solutions have only corner singularitie...

By a series of discoveries during the past thirty years, a distinguished list of researchers have provided us with a marvelous vista of singularity theory as it applies to isolated singularities, especially isolated complete intersection singularities. This began with Milnor’s seminal monograph on isolated hypersurfaces singularities [Mi], which introduced as a principal tool in the study of is...

Skip connections made the training of very deep networks possible and have become an indispensable component in a variety of neural architectures. A completely satisfactory explanation for their success remains elusive. Here, we present a novel explanation for the benefits of skip connections in training very deep networks. The difficulty of training deep networks is partly due to the singulari...

Abstract It is demonstrated that for the isospin I = 1/2 πN scattering amplitude, T =1/2 ( s , t ), s = m N</...

Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmololgies ar...