In the pose-estimation problem we need to align a set of n markers (points in 3D space) and choose one of their n! permutations, so that the sum of squared corresponding distances to another ordered set of n markers is minimized. We prove that every set has a weighted subset (core-set) of constant size (independent of n), such that computing the optimal orientation of the small core-set would y...

This paper investigates a discontinuous neural network which is used as a model of the mammalian olfactory system and can more generally be applied to solve non-negative sparse approximation problems. By inherently limiting the systems integrators to having non-negative outputs, the system function becomes discontinuous since the integrators switch between being inactive and being active. It is...

1 1 INTRODUCTION 2 1 Introduction Classical calculus is a basic tool in analysis. We use it so often that we forget that its construction needed considerable time and effort. Especially in the last decade, the progresses made in the field of analysis in metric spaces make us reconsider this calculus. Along this line of thought, all started with the definition of Pansu derivative [24] and its ve...

1. The technique used by the author (Grigorov, 2006) relies on singular-spectrum analysis (SSA). While the author has claimed to have used a nonlinear time series approach, SSA by very definition is a linear decomposition technique. The lag-correlation matrix constructed as a part of the SSA technique is a measure of linear correlation between the samples in the time series, hence representativ...

The sufficient conditions of solvability and unique solvability of the two-point boundary value problems of Vallèe-Poussin and Cauchy-Niccoletti have been found for a system of ordinary differential equations of the form u(n) = f(t, u, u′, . . . , u(n−1)), where the vector function f :]a, b[×Rnl → Rl has nonintegrable singularities with respect to the first argument at the points a and b. § 1. ...

whereΔp is the p-Laplacian, Ω ∈ C0,1 be a bounded domain inRN . Let p ≥ 2, λ > 0 and f : Ω×R −→ R be a caratheodory function which is decreasing with respect to the second variable, i.e., f(x, s1) ≥ f(x, s2) for a.a. x ∈ Ω ands1, s2 ∈ R, s1 ≤ s2 (2) Assume, moreover, that there exists f0 ∈ Lp(Ω), p′ = p p−1 and c > 0 such that ∣f(x, s)∣ ≤ f0(x) + c∣s∣p−1 (3) We considered such problems with num...

In the pose-estimation problem we need to align a set of n markers (points in 3D space) and choose one of their n! permutations, so that the sum of squared corresponding distances to another ordered set of n markers is minimized. We prove that every set has a weighted subset (core-set) of constant size (independent of n), such that computing the optimal orientation of the small core-set would y...

We study several canonical decision problems arising from some well-known theorems from combinatorial geometry. Among others, we show that computing the minimum size of a Caratheodory set and a Helly set and certain decision versions of the ham-sandwich cut problem are W[1]-hard (and NP-hard) if the dimension is part of the input. This is done by fpt-reductions (which are actually ptime-reducti...

function, 51 Riemann integral, 51 adjoint bilinear form, 65 almost separably valued, 53 Ascoli Theorem, 8 Banach space reflexive, 6 separable, 2 Banach-Steinhaus Theorem, 5 Bessel’s inequality, 9 biharmonic, 61 bilinear form, 55, 58 bounded, 58 strongly positive, 58 Bochner-Pettis Theorem Theorem, 53 Bounded Inverse Theorem, 6 Calculus in W 1,p(I;X) Theorem, 54 Campanato ’63 Theorem, 86 Campana...