Related papers: Map Projection
The classical Gauss Map is a piecewise continuous map from the unit interval to itself. From this map we retrieve the continued fraction expansion of irrational numbers and its dynamical properties give information about some arithmetic and…
We generalize our previous linear result [1] in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly…
The communications and interrelations between different locations on the Earth's surface have far-reaching implications for both social and natural systems. Effective spatial analytics ideally require a spatial representation, where…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…
Any subset of the plane can be approximated by a set of square pixels. This transition from a shape to its pixelation is rather brutal since it destroys geometric and topological information about the shape. Using a technique inspired by…
The aim of this paper and its sequel is to introduce and classify the holonomy algebras of the projective Tractor connection. After a brief historical background, this paper presents and analyses the projective Cartan and Tractor…
A momentum dependent projection of the Wegner-Hougton equation is derived for a scalar theory coupled to an external field. This formalism is useful to discuss the phase diagram of the theory. In particular we study some properties of the…
Current literature on posterior approximation for Bayesian inference offers many alternative methods. Does our chosen approximation scheme work well on the observed data? The best existing generic diagnostic tools treating this kind of…
In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…
Given two regular graphs with consistent rotation maps, we produce a constructive method for a consistent rotation map on their Cartesian product. This method will be given as a simple set of rules of addition and table look ups. We assume…
Immersions of graphs to the projective plane are studied. A classification of immersions up to regular homotopy is given. A complete invariant of immersions up to regular homotopy is constructed. Equivalence classes are described.
In this dissertation we study basic local differential geometry, projective differential geometry, and prolongations of overdetermined geometric partial differential equations. It is simple to prolong an n-th order linear ordinary…
Recently, 3D Gaussian Splatting has dominated novel-view synthesis with its real-time rendering speed and state-of-the-art rendering quality. However, during the rendering process, the use of the Jacobian of the affine approximation of the…
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and…
Generalized entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information…
The projection onto the epigraph or a level set of a closed proper convex function can be achieved by finding a root of a scalar equation that involves the proximal operator as a function of the proximal parameter. This paper develops the…
This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on $\mathbb{R}^2$ based on dense observations of a single realization of the deformed random field. Under this framework we…
We study conformal mappings in the Grushin plane and provide a number of their characterizations in terms of the Sobolev mappings and their geometry. Furthermore, we connect conformality on the Grushin plane with conformality on the complex…
We form a "map of tournaments" by adapting the map framework from the world of elections. By a tournament we mean a complete directed graph where the nodes are the players and an edge points from a winner of a game to the loser (with no…