Related papers: New Bounds for Hypergeometric Creative Telescoping
For many years, exact metric search relied upon the property of triangle inequality to give a lower bound on uncalculated distances. Two exclusion mechanisms derive from this property, generally known as pivot exclusion and hyperplane…
We present a new, far simpler family of counter-examples to Kushnirenko's Conjecture. Along the way, we illustrate a computer-assisted approach to finding sparse polynomial systems with maximally many real roots, thus shedding light on the…
We develop a new technique for computing higher limits of functors over filtered posets by constructing explicit fibrant replacements within a suitable model category structure. We apply this procedure to develop two systematic vanishing…
We show tight lower bounds for the entire trade-off between space and query time for the Approximate Near Neighbor search problem. Our lower bounds hold in a restricted model of computation, which captures all hashing-based approaches. In…
We develop quantitative algorithmic information bounds for orthogonal projections and distances in the plane. Under mild independence conditions, the distance $|x-y|$ and a projection coordinate $p_e x$ each retain at least half the…
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…
New lower bounds on the minimum distance of quasi-twisted codes over finite fields are proposed. They are based on spectral analysis and eigenvalues of polynomial matrices. They generalize the Semenov-Trifonov and Zeh-Ling bounds in a…
In this article we show the rough outline of a computer algorithm to generate lower bounds on the exponential function of (in principle) arbitrary precision. We implemented this to generate all necessary analytic terms for the Boltzmann…
Due to their importance in both data analysis and numerical algorithms, low rank approximations have recently been widely studied. They enable the handling of very large matrices. Tight error bounds for the computationally efficient…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
In this thesis we develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive…
We obtain existence and convergence theorems on two variants of the proximal point algorithm for proper lower semicontinuous convex functions in complete geodesic spaces with curvature bounded above.
We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: (1) we improve the Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of…
The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a…
We establish basic information about border rank algorithms for the matrix multiplication tensor and other tensors with symmetry. We prove that border rank algorithms for tensors with symmetry (such as matrix multiplication and the…
We extend Petkov\v{s}ek's algorithm for computing hypergeometric solutions of scalar difference equations to the case of difference systems $\tau(Y) = M Y$, with $M \in {\rm GL}_n(C(x))$, where $\tau$ is the shift operator. Hypergeometric…
We introduce the ``skew apolarity lemma'' and we use it to give algorithms for the skew-symmetric rank and the decompositions of tensors in {$\bigwedge^dV_{\mathbb{C}}$ with $d\leq 3$ and $\dim V_{\mathbb{C}} \leq 8$}. New algorithms to…
We investigate lower bounds for the number of ideal and finite vertices of right-angled hyperbolic polyhedra of finite volume. We use a geometric method of orthogonal gluings to establish new bounds in low dimensions, specifically…
A Petrov-Galerkin finite element method is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary layers. Exponential splines are used…
The geometric constraints of Zhou et al. (2015) are a widely used technique in topology/freeform optimization to impose minimum lengthscales for manufacturability. However, its efficacy degrades as design binarization is increased, and it…