We address the problem of single image super-resolution by exploring the manifold properties. Given a set of low resolution image patches and their corresponding high resolution patches, we assume they respectively reside on two non-linear manifolds that have similar locallylinear structure. This manifold correlation can be realized by a threelayer Markov network that connects performing super-...

To process massive high -dimensional datasets, we utilize the underlying assumption that data on manifold is approximately linear in sufficiently small patches (or neighborhoods of points) that are sampled with sufficient density from the manifold. Under this assumption, each patch can be represented (up to a small approximation error) by a tangent space of the manifold in its area and the tang...

We first make a little survey of the twistor theory for hypercomplex, generalized quaternionic or manifolds. This last was initiated by Pantilie (Ann. Mat. Pura. Appl. 193 (2014) 633–641), and allows one to extend Penrose correspondence from quaternion case. He showed that any almost manifold equipped with an appropriate connection admit space which comes naturally tautological complex structur...

a. csaszar introduced and extensively studied the notionof generalized open sets. following csazar, we introduce a new notionsuperconnected. the main purpose of this paper is to study generalizedsuperconnected spaces. various characterizations of generalized super-connected spaces and preservation theorems are discussed.

Let (M, f,G) be a manifold, a function and a Riemann metric on the manifold. Topologists would use these data in order to analyze the manifold by means of Morse theory, that is by studying the dynamical system ẋ = ±∇f . Many recent applications of physics to topology are based on another point of view suggested in E. Witten’s paper Supersymmetry and Morse theory J. Diff. Geom. (1982). Given the...

In this paper we address the problem of building valid representations for non-manifold d-dimensional objects. To this aim, we have developed a combinatorial approach based on decomposing a non-manifold d-dimensional object into an assembly of more regular components, that we call initial quasi-manifolds. We present a decomposition algorithm, whose complexity is slightly super-linear in the tot...

We construct a three-dimensional topological sigma model which is induced from a generalized complex structure on a target generalized complex manifold. This model is constructed from maps from a three-dimensional manifold X to an arbitrary generalized complex manifold M . The theory is invariant under the diffeomorphism on the world volume and the b-transformation on the generalized complex st...

‎Two types of properties for linear connections (natural and almost paracontact metric) are discussed in almost paracontact metric geometry with respect to four linear connections‎: ‎Levi-Civita‎, ‎canonical (Zamkovoy)‎, ‎Golab and generalized dual‎. ‎Their relationship is also analyzed with a special view towards their curvature‎. ‎The particular case of an almost paracosymplectic manifold giv...

A connection between the conifold locus of the type II string on the W P 4 11226 Calabi-Yau manifold and the geometry of the quantum moduli of N =2 SU(2) super Yang-Mills is presented. This relation is obtained from the anomalous behaviour of the SU(2) super Yang-Mills special coordinates under S-duality transformation in Sl(2;Z)/Γ2.