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We propose a method to optimally position a sensor system, which consists of multiple sensors, each has limited range and viewing angle, and they may fail with a certain failure rate. The goal is to find the optimal locations as well as the…
We obtain the distance of closest approach of the surfaces of two arbitrary ellipsoids valid at any orientation and separation, measured along their inter-center vector. This directional distance is derived from the Elliptic Contact…
In this paper, a piecewise quadratic nonconforming finite element method on rectangular grids for a fourth-order elliptic singular perturbation problem is presented. This proposed method is robustly convergent with respect to the…
We study the problem of minimum enclosing rectangle with outliers, which asks to find, for a given set of $n$ planar points, a rectangle with minimum area that encloses at least $(n-t)$ points. The uncovered points are regarded as outliers.…
We obtain a minimal supersymmetric extension of the Snyder algebra and study its representations. The construction differs from the general approach given in Hatsuda and Siegel ({\tt hep-th/0311002}), and does not utilize super-de Sitter…
The objective of the paper is to describe Besov spaces on general compact Riemannian manifolds in terms of the best approximation by eigenfunctions of elliptic differential operators.
A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.
This paper proposes localized subspace iteration (LSI) methods to construct generalized finite element basis functions for elliptic problems with multiscale coefficients. The key components of the proposed method consist of the localization…
We consider minimization problems with bisubmodular objective functions. We propose valid inequalities, namely the poly-bimatroid inequalities, and provide a complete linear description of the convex hull of the epigraph of a bisubmodular…
The outer Lowner-John method is widely used in sensor fusion applications to find the smallest ellipsoid that can approximate the intersection of a set of ellipsoids, described by positive definite covariance matrices modeling the quality…
We introduce the sparse operator compression to compress a self-adjoint higher-order elliptic operator with rough coefficients and various boundary conditions. The operator compression is achieved by using localized basis functions, which…
This paper studies the underlying combinatorial structure of a class of object rearrangement problems, which appear frequently in applications. The problems involve multiple, similar-geometry objects placed on a flat, horizontal surface,…
The problem of the minimization of least squares functionals with $\ell^1$ penalties is considered in an infinite dimensional Hilbert space setting. While there are several algorithms available in the finite dimensional setting there are…
We consider the problem of classifying trajectories on a discrete or discretised 2-dimensional manifold modelled by a simplicial complex. Previous works have proposed to project the trajectories into the harmonic eigenspace of the Hodge…
We consider the problem of learning uncertainty regions for parameter estimation problems. The regions are ellipsoids that minimize the average volumes subject to a prescribed coverage probability. As expected, under the assumption of…
Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire…
This paper presents a minimum displacement motion planning problem wherein obstacles are displaced by a minimum amount to find a feasible path. We define a metric for robot-obstacle intersection that measures the extent of the intersection…
We discuss vertex patch smoothers as overlapping domain decomposition methods for fourth order elliptic partial differential equations. We show that they are numerically very efficient and yield high convergence rates. Furthermore, we…
The difficulty for solving ill-posed linear operator equations in Hilbert space is reflected by the strength of ill-posedness of the governing operator, and the inherent solution smoothness. In this study we focus on the ill-posedness of…
A new approximation format for solutions of partial differential equations depending on infinitely many parameters is introduced. By combining low-rank tensor approximation in a selected subset of variables with a sparse polynomial…