Related papers: Geometric Interpretations of the Normalized Epipol…
The real projective plane has three well know isomorphic constructions: the extended euclidean plane, unit (hemi)sphere, and three dimensional vector space over the reals. In this paper we find the isomorphisms that map between these three…
We examine the problem of construction of confidence intervals within the basic single-parameter, single-iteration variation of the method of quasi-optimal weights. Two kinds of distortions of such intervals due to insufficiently large…
The space ${\Bbb{L}}$ of oriented lines, or rays, in ${\Bbb{R}}^3$ is a 4-dimensional space with an abundance of natural geometric structure. In particular, it boasts a neutral K\"ahler metric which is closely related to the Euclidean…
The immediate purpose of the paper was neither to review the basic definitions of percolation theory nor to rehearse the general physical notions of universality and renormalization (an important technique to be described in Part Two). It…
This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been…
In a neutral particle gas detector, the parallax error resulting from the perpendicular projection on the detection plane or wire of the radial particle trajectories emanating from a point like source (such as a scattering sample) can…
In this paper, a geometrical interpretation of light diffraction is given using an infinity of fluctuating geodesics that represent paths of least time in an homogeneous space. Without using the wave theory, we provide a geometrical…
We consider the problem of recovering an unknown matching between a set of $n$ randomly placed points in $\mathbb{R}^d$ and random perturbations of these points. This can be seen as a model for particle tracking and more generally, entity…
The recently developed information-theoretic approach to crystallographic symmetry classifications and quantifications in two dimensions (2D) from digital transmission electron and scanning probe microscope images is adapted for the…
Random geometric graphs are random graph models defined on metric measure spaces. A random geometric graph is generated by first sampling points from a metric space and then connecting each pair of sampled points independently with a…
When the regressors of a econometric linear model are nonorthogonal, it is well known that their estimation by ordinary least squares can present various problems that discourage the use of this model. The ridge regression is the most…
This work is concerned with the proof of \emph{a posteriori} error estimates for fully-discrete Galerkin approximations of the Allen-Cahn equation in two and three spatial dimensions. The numerical method comprises of the backward Euler…
We consider the problem of recovering linear image $Bx$ of a signal $x$ known to belong to a given convex compact set ${\cal X}$ from indirect observation $\omega=Ax+\xi$ of $x$ corrupted by random noise $\xi$ with finite covariance matrix.…
Using a recently derived integral in terms of elementary functions, we derive new asymptotic expansions of the normal inverse Gaussian cumulative distribution function. One of the asymptotic representations is in terms of the normal…
We show that measures with finite support on the real line are the unique solution to an algorithm, named generalized minimal extrapolation, involving only a finite number of generalized moments (which encompass the standard moments, the…
We prove residual-type a posteriori error estimates in the maximum norm for a linear scalar elliptic convection-diffusion problem that may be singularly perturbed. Similar error analysis in the energy norm by Verf\"{u}rth indicates that a…
Geometrical optical illusions have been object of many studies due to the possibility they offer to understand the behaviour of low-level visual processing. They consist in situations in which the perceived geometrical properties of an…
In this work, we present a novel error analysis for recovering a spatially dependent diffusion coefficient in an elliptic or parabolic problem. It is based on the standard regularized output least-squares formulation with an $H^1(\Omega)$…
Working with electrodynamics in the geometrical optics approximation we derive the expression representing an effectively curved geometry which guides the propagation of electromagnetic waves in material media whose physical properties…
It is often convenient to use Gaussian blur in studying image quality or in data augmentation pipelines for training convoluional neural networks. Because of their convenience, Guassians are sometimes used as first order approximations of…