Related papers: Approximate Distribution of Hitting Probabilities …
For polyhedral convex cones in ${\mathbb R}^d$, we give a proof for the conic kinematic formula for conic curvature measures, which avoids the use of characterization theorems. For the random cones defined as typical cones of an isotropic…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
In the first part of this paper, we obtain symmetric formulae for the probabilities that a plane convex body hits exactly 1, 2, 3, 4, 5 or 6 triangles of a lattice of congruent triangles in the plane. Furthermore, a very simple formula for…
We explore some probabilistic applications arising in connections with $K$-theoretic symmetric functions. For instance, we determine certain corner distributions of random lozenge tilings and plane partitions. We also introduce some…
In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these…
This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective on the complement of visible umbilical sets.
Given a model in algebraic statistics and some data, the likelihood function is a rational function on a projective variety. Algebraic algorithms are presented for computing all critical points of this function, with the aim of identifying…
The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is…
Given cell-average data values of a piecewise smooth bivariate function $f$ within a domain $\Omega$, we look for a piecewise adaptive approximation to $f$. We are interested in an explicit and global (smooth) approach. Bivariate…
This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective in a well-chosen subset of arbitrarily small measure.
We theoretically determine the probability distribution function of the net field of the random planar structure of dipoles which represent polarized particles. At small surface concentrations c of the point dipoles this distribution is…
The preservation of ambient isotopic equivalence under piecewise linear (PL) approximation for smooth knots are prominent in molecular modeling and simulation. Sufficient conditions are given regarding: (1) Hausdorff distance, and (2) a sum…
We prove a general theorem providing smoothed analysis estimates for conic condition numbers of problems of numerical analysis. Our probability estimates depend only on geometric invariants of the corresponding sets of ill-posed inputs.…
The derivative expansion approach to the calculation of the interaction between two surfaces, is a generalization of the proximity force approximation, a technique of widespread use in different areas of physics. The derivative expansion…
A formalism is introduced for the non-perturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of light from two-dimensional penetrable rough surfaces. As an example, we apply this formalism to study the…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
We study the problem of quantization of discrete probability distributions, arising in universal coding, as well as other applications. We show, that in many situations this problem can be reduced to the covering problem for the unit…
Some ball-quotient orbifolds are related by covering maps. We exploit these coverings to find infinite towers of orbifolds uniformized by the complex 2-ball and some orbifolds over K3 surfaces uniformized by the 2-ball. Corresponding…