Related papers: On Locality-Sensitive Orderings and their Applicat…
A set of points in d-dimensional Euclidean space is almost equidistant if among any three points of the set, some two are at distance 1. We show that an almost-equidistant set in $\mathbb{R}^d$ has cardinality $O(d^{4/3})$.
Many data analysis problems can be cast as distance geometry problems in \emph{space forms} -- Euclidean, spherical, or hyperbolic spaces. Often, absolute distance measurements are often unreliable or simply unavailable and only proxies to…
We investigate the small-time local controllability of systems in the vicinity of an equilibrium. Given a small time, an initial data and a final data close from the equilibrium, is it possible to find a control (a source term) that guides…
A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices…
We extend the Theory of Computation on real numbers, continuous real functions, and bounded closed Euclidean subsets, to compact metric spaces $(X,d)$: thereby generically including computational and optimization problems over higher types,…
We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The…
This paper reports about the development of two provably correct approximate algorithms which calculate the Euclidean shortest path (ESP) within a given cube-curve with arbitrary accuracy, defined by $\epsilon >0$, and in time complexity…
The indirect estimation of couplings in quantum dynamics relies on the measurement of the spectrum and the overlap of eigenvectors with some reference states. This data can be obtained by local measurements on some sites and eliminates the…
We investigate the complexity of approximately counting stable matchings in the $k$-attribute model, where the preference lists are determined by dot products of "preference vectors" with "attribute vectors", or by Euclidean distances…
We develop algorithms for the optimization of convex objectives that have H\"older continuous $q$-th derivatives by using a $q$-th order oracle, for any $q \geq 1$. Our algorithms work for general norms under mild conditions, including the…
In this paper we describe physical properties arising in the vicinity of two coupled quantum phase transitions. We consider a phenomenological model based on two scalar order parameter fields locally coupled biquadratically and having a…
We study the variance in the number of points contained within a window $\Omega$ of arbitrary size, and to further illuminate our understanding of {\it hyperuniform} systems, i.e., point patterns that do not possess long-wavelength…
We provide an efficient reduction from the problem of querying approximate multiplicatively weighted farthest neighbors in a metric space to the unweighted problem. Combining our techniques with core-sets for approximate unweighted farthest…
In this communication with computer simulation we evaluate simple cubic random-site percolation thresholds for neighbourhoods including the nearest neighbours (NN), the next-nearest neighbours (2NN) and the next-next-nearest neighbours…
We investigate the average minimum cost of a bipartite matching between two samples of n independent random points uniformly distributed on a unit cube in d $\ge$ 3 dimensions, where the matching cost between two points is given by any…
We study the distances, called spacings, between pairs of neighboring energy levels for the quantum harmonic oscillator. Specifically, we consider all energy levels falling between E and E+1, and study how the spacings between these levels…
Higher-order tree-level processes in strong laser fields, i.e. cascades, are in general extremely difficult to calculate, but in some regimes the dominant contribution comes from a sequence of first-order processes, i.e. nonlinear Compton…
We establish that every second countable completely regularly preordered space (E,T,\leq) is quasi-pseudo-metrizable, in the sense that there is a quasi-pseudo-metric p on E for which the pseudo-metric p\veep^-1 induces T and the graph of…
The paper describes the splines $Q_{n,k}(x,a)$, which for an arbitrary point $a\in(0;1)$ and an arbitrary function $y\in\mathring{W}^n_p[0;1]$ set the relations $y^{(k)}(a)=\int_0^1 y^{(n)}(x)Q^{(n)}_{n,k}(x,a)dx$. The relation of the…
The geodesic between two points $a$ and $b$ in the interior of a simple polygon~$P$ is the shortest polygonal path inside $P$ that connects $a$ to $b$. It is thus the natural generalization of straight line segments on unconstrained point…