Related papers: Optimal separator for an ellipse; Application to l…

We describe a generalised method for ellipsoid fitting against a minimum set of data points. The proposed method is numerically stable and applies to a wide range of ellipsoidal shapes, including highly elongated and arbitrarily oriented…

This paper is concerned with the development and analysis of an iterative solver for high-dimensional second-order elliptic problems based on subspace-based low-rank tensor formats. Both the subspaces giving rise to low-rank approximations…

This paper considers the problem of optimally deploying omnidirectional sensors, with potentially limited sensing radius, in a network-like environment. This model provides a compact and effective description of complex environments as well…

In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing the area of a surface subject to a prescribed boundary…

In this paper, we propose a novel method for transforming data into a low-dimensional space optimized for one-class classification. The proposed method iteratively transforms data into a new subspace optimized for ellipsoidal encapsulation…

This paper investigates realisations of elliptic differential operators of general order on manifolds with boundary following the approach of B\"ar-Ballmann to first order elliptic operators. The space of possible boundary values of…

We establish new results concerning projectors on max-plus spaces, as well as separating half-spaces, and derive an explicit formula for the distance in Hilbert's projective metric between a point and a half-space over the max-plus…

An extended interference pattern close to surface may result in both a transmissive or evanescent surface fields for large area manipulation of trapped particles. The affinity of differing particle sizes to a moving standing wave light…

Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical…

Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…

We propose a simple derivation of an upper bound for the perimeter of an ellipse. The procedure, which relies on the use of elliptic integrals, consists in introducing, via inequalities and convexity properties, specific integrals which can…

Associating distinct groups of objects (clusters) with contiguous regions of high probability density (high-density clusters), is central to many statistical and machine learning approaches to the classification of unlabelled data. We…

We characterize all possible relative positions between a hyperboloid of one sheet and a sphere through the roots of a characteristic polynomial associated to these quadrics. The classification is also suitable for a hyperboloid and a…

Using orthogonal projections, we investigate distance of a given elasticity tensor to classes of elasticity tensors exhibiting particular material symmetries. These projections depend on the orientation of the elasticity tensor, hence the…

A small variation of the circular shape of the hodograph theorem states that for every elliptical solution of the two-body problem, it is possible to find an appropriate inertial frame such that the speed of the bodies is constant. We use…

A new closed-form solver is proposed minimizing the algebraic error optimally, in the least-squares sense, to estimate the relative planar motion of two calibrated cameras. The main objective is to solve the over-determined case, i.e., when…

The landscapes of a polyhedron are subsets of its nets one must consider to identify all shortest paths. Landscapes of cubes and tetrahedra have been used to identify coordinate based formulas for the lengths of the shortest paths between…

We present an efficient preconditioner for the orbital minimization method when the Hamiltonian is discretized using planewaves (i.e., pseudospectral method). This novel preconditioner is based on an approximate Fermi operator projection by…

We provide novel linear combination of unitaries decompositions for a class of discrete elliptic differential operators. Specifically, Poisson problems augmented with periodic, Dirichlet, Neumann, Robin, and mixed boundary conditions are…

Numerical homogenization aims to efficiently and accurately approximate the solution space of an elliptic partial differential operator with arbitrarily rough coefficients in a $d$-dimensional domain. The application of the inverse operator…