Related papers: Angles between subspaces and their tangents

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…

The purpose the present paper is to construct the hyperbolic trigonometry on Euclidean plane without refereing to hyperbolic plane. In this paper we show that the concept of hyperbolic angle and its functions forming the hyperbolic…

The imaging and spectroscopy of habitable worlds will require large-aperture space-based telescopes, to increase the collecting area and the angular resolution. These large telescopes will necessarily use segmented primaries to fit in a…

In Computer Vision, edge detection is one of the favored approaches for feature and object detection in images since it provides information about their objects boundaries. Other region-based approaches use probabilistic analysis such as…

The purpose of this paper is twofold. First, we define the new spaces and investigate some topological and structural properties. Also, we compute dual spaces of new spaces which are help us in the characterization of matrix mappings.…

Genuinely entangled subspaces (GESs) are the class of completely entangled subspaces that contain only genuinely multiparty entangled states. They constitute a particularly useful notion in the theory of entanglement but also have found an…

A new approach is suggested to quantum differential calculus on certain quantum varieties. It consists in replacing quantum de Rham complexes with differentials satisfying Leibniz rule by those which are in a sense close to Koszul complexes…

We propose a categorical semantics for machine learning algorithms in terms of lenses, parametric maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of…

We present an approach to semantic scene analysis using deep convolutional networks. Our approach is based on tangent convolutions - a new construction for convolutional networks on 3D data. In contrast to volumetric approaches, our method…

In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit. We introduce the manifold of uniform matrix product states, show how to compute different types of…

In this work, we propose "tangent images," a spherical image representation that facilitates transferable and scalable $360^\circ$ computer vision. Inspired by techniques in cartography and computer graphics, we render a spherical image to…

This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate…

We introduce a novel statistical way of analyzing the projected mass distribution in galaxy lenses based solely on the angular distribution of images in quads around the lens center. The method requires the knowledge of the lens center…

This is a survey paper on applications of mathematics of semirings to numerical analysis and computing. Concepts of universal algorithm and generic program are discussed. Relations between these concepts and mathematics of semirings are…

Results on matrix canonical forms are used to give a complete description of the higher rank numerical range of matrices arising from the study of quantum error correction. It is shown that the set can be obtained as the intersection of…

The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to…

Macaulay dual spaces provide a local description of an affine scheme and give rise to computational machinery that is compatible with the methods of numerical algebraic geometry. We introduce eliminating dual spaces, use them for computing…

Much of arithmetic geometry is concerned with the study of principal bundles. They occur prominently in the arithmetic of elliptic curves and, more recently, in the study of the Diophantine geometry of curves of higher genus. In particular,…

Past years have seen the development of a few proposals for quantum extensions of process calculi. The rationale is clear: with the development of quantum communication protocols, there is a need to abstract and focus on the basic features…

We study the branch divisors on the boundary of the canonical toroidal compactification of ball quotients. We show a criterion, the low slope cusp form trick, for proving that ball quotients are of general type. Moreover, we classify when…