We construct SRB measures for endomorphisms satisfying conditions far weaker than the usual non-uniform expansion. As a consequence, the definition of a non-uniformly expanding map can be weakened. We also prove the existence of an absolutely continuous invariant measure for local diffeomorphisms, only assuming the existence of hyperbolic times for Lebesgue almost every point in the manifold.

We consider the problem of constructing quasi-conformal mappings between surfaces by solving Beltrami equations. This is of great importance for shape registration. In the physical world, most surface deformations can be rigorously modeled as quasi-conformal maps. The local deformation is characterized by a complex-value function, Beltrami coefficient, which describes the deviation from conform...

Object localization is an important computer vision problem with a variety of applications. The lack of large scale object-level annotations and the relative abundance of image-level labels makes a compelling case for weak supervision in the object localization task. Deep Convolutional Neural Networks are a class of state-of-the-art methods for the related problem of object recognition. In this...

We extend the definition of quasi-finite complexes by considering not necessarily countable complexes. We provide a characterization of quasi-finite complexes in terms of L-invertible maps and dimensional properties of compactifications. Several results related to the class of quasi-finite complexes are established, such as completion of metrizable spaces, existence of universal spaces and a ve...

In this paper, we introduce the notion of an ordered rational proximal contraction in partially ordered b-quasi metric spaces. We shall then prove some best proximity point theorems in partially ordered b-quasi metric spaces.

The object of this paper is to establish a theorem for a unique common fixed point of four self mappings, weakly compatibile in pairs and satisfying a generalized contractive condition in a cone metric space. Our result generalizes and synthesizes the results of Abbas– Jungck [1], Arshad et al. [2], Huang–Zhang [3] and Vetro [8].