Compared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied fo...

In this paper, the norm attaining operators in Frechet spaces are considered. These characterized based on their density, normality, linearity and compactness. It is shown that image dense for a normal injective operator space, as well its inverse given self-adjoint. A space also to be if adjoint attains condition under which attainability normality of an coincides given. Furthermore, between l...

Summary This paper formalizes in Mizar [1], [2], that the isometric isomorphisms between spaces formed by an ( n + 1)-dimensional multilinear map and -fold composition of linear maps on real normed spaces. result is used to describe space nth-order derivatives Frechet derivative as a space. In Section 1, we discuss 1-dimensional 0-fold compositions preparation, 2, extend discussion compositions...

We address the problem of performing efficient similarity join for large sets of moving objects trajectories. Unlike previous approaches which use a dedicated index in a transformed space, our premise is that in many applications of location-based services, the trajectories are already indexed in their native space, in order to facilitate the processing of common spatio-temporal queries, e.g., ...

The minimum backward Fréchet distance (MBFD) problem is a natural optimization problem for the weak Fréchet distance, a variant of the well-known Fréchet distance. In this problem, a threshold ε and two polygonal curves, T1 and T2, are given. The objective is to find a pair of walks on T1 and T2, which minimizes the union of the portions of backward movements while the distance between the movi...

Various researchers have studied examples of innnite-dimensional dynamical systems. In most of the cases, the phase space consisted of a Hilbert or Banach space or a Frechet space of functions. In this article we propose to study a dynamical system, namely the geodesic ow, over more structurally complex manifolds, the tangent bundles of a family of Hilbert Grassmannians. Using the high degree o...

Let Sf be the Schwartz space of all rapidly decreasing functions on R, Sf be the topological dual space of Sf and for each positive integer p,Sfp be the space of all elements of £f' which are continuous in the p-th norm defining the nuclear Frechet topology of Sf. The main purpose of the present paper is to show that if {Xtί t e [0, + oo)} is an ^'-valued Gaussian process and for any fixed φβ^ ...

We present a new approach to treat nonlinear operators in reduced basis approximations of parametrized evolution equations. Our approach is based on empirical interpolation of nonlinear differential operators and their Frechet derivatives. Efficient offline/online decomposition is obtained for discrete operators that allow an efficient evaluation for a certain set of interpolation functionals. ...

Let F be a continuous function from an open subset D of a separable Banach space X into a Banach space Y. We show that if there is a dense G8 subset A of D and a Gs subset H of X whose closure has nonempty interior, such that for each a E A and each x E H the directional derivative DxF(a) of F at a in the direction x exists, then F is Giteaux differentiable on a dense G8 subset of D. If X is re...

Motivated by symplectic geometry, we give a detailed account of differential forms and currents on orbifolds with corners, the pull-back push-forward operations, their fundamental properties. We work within formalism where category corners is obtained as localization etale proper groupoids corners. Constructions proofs are formulated in terms structure maps groupoids, avoiding use orbifold char...