Multi-atlas segmentation has been widely used to segment various anatomical structures. The success of this technique partly relies on the selection of atlases that are best mapped to a new target image after registration. Recently, manifold learning has been proposed as a method for atlas selection. Each manifold learning technique seeks to optimize a unique objective function. Therefore, diff...

Let f be a continuous function on Rn, and suppose f is continuously differentiable on an open dense subset. Such functions arise in many applications, and very often minimizers are points at which f is not differentiable. Of particular interest is the case where f is not convex, and perhaps not even locally Lipschitz, but is a function whose gradient is easily computed where it is defined. We p...

Given a commutative noetherian non-positive DG-ring with bounded cohomology which has dualizing DG-module, we study its regular, Gorenstein and Cohen-Macaulay loci. We give sufficient condition for the regular locus to be open, show that is always open. However, both of these loci are often empty: no matter how nice H0(A) is, there examples where A empty. then DG-module contains dense open set....

Abstract Erdős proved that every real number is the sum of two Liouville numbers. A set W complex numbers said to have property if members . Mahler divided all transcendental into three disjoint classes S , T and U such that, in particular, any which are algebraically dependent lie same class. The a proper subset has Lebesgue measure zero. It here, using theorem Weil on locally compact groups, ...

In the spirit of Kolmogorov typicality, we introduce notion germ-typicality: in a space dynamics, it encompasses all these phenomena that occur for dense and open subset parameters any generic parametrized family contained an set systems. For 2≤r<∞, prove Newhouse phenomenon (the coexistence infinitely many sinks) is locally Cr-germ-typical, nearby dissipative bicycle: homoclinic tangency linke...

For a row finite directed graph E, Kumjian, Pask, and Rae-burn proved that there exists a universal C *-algebra C * (E) generated by a Cuntz-Krieger E-family. In this paper we consider two density problems of invertible elements in graph C *-algebras C * (E), and it is proved that C * (E) has stable rank one, that is, the set of all invertible elements is dense in C * (E) (or in its unitization...