Related papers: Explicit affine formulas for distances between tup…
This paper concerns the compactness and separability properties of the normed Boolean algebras (N.B.A.) with respect to topology generated by a distance equal to the square root of a measure of symmetric difference between two elements. The…
We present a simplified treatment of stability of filtrations on finite spaces. Interestingly, we can lift the stability result for combinatorial filtrations from [CSEM06] to the case when two filtrations live on different spaces without…
Let $A$ be either a complex or real matrix with all distinct eigenvalues. We propose a new method for the computation of both the unstructured and the real-structured (if the matrix is real) distance $w_{\mathbb K}(A)$ (where ${\mathbb…
For a given Markov chain Monte Carlo algorithm we introduce a distance between two configurations that quantifies the difficulty of transition from one configuration to the other configuration. We argue that the distance takes a universal…
The complete affine structures on abelian Lie algebras in small dimensions are well known. In this paper we are interested by the non complete case. In particular we classify all these structures in dimensions 2 and 3.
The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both…
Categorial methods for generating new local algebras from old ones are presented. A direct proof of the differential structure of the prolongations of a manifold is proposed.
An $(a,b)$-difference necklace of length $n$ is a circular arrangement of the integers $0, 1, 2, \ldots , n-1$ such that any two neighbours have absolute difference $a$ or $b$. We prove that, subject to certain conditions on $a$ and $b$,…
The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact computation of this distance would permit multi-parameter…
The paper describes known and new results about finite difference calculus on configuration spaces. We describe finite difference geometry on configuration spaces, connect finite difference operators with cannonical commutation relations,…
We consider the number of distinct distances between two finite sets of points in ${\bf R}^k$, for any constant dimension $k\ge 2$, where one set $P_1$ consists of $n$ points on a line $l$, and the other set $P_2$ consists of $m$ arbitrary…
We describe a construction of explicit affine extractors over large finite fields with exponentially small error and linear output length. Our construction relies on a deep theorem of Deligne giving tight estimates for exponential sums over…
We consider the discretization q(t+\epsilon)+q(t-\epsilon)-2q(t)=\epsilon^{2}\sin\big(q(t)\big), $\epsilon>0$ a small parameter, of the pendulum equation $ q '' = \sin (q) $; in system form, we have the discretization…
We calculate Sudakov-type form factors for isolated spin-1/2 particles (fermions) entering non-Abelian gauge-field systems. We consider both the on- and the off-mass-shell case using a methodology which rests on a worldline casting of field…
We obtain lower bound for the maximum distance between any three distinct points in an affine lattice which are close to a helix with small curvature and torsion.
For fragments L of first-order logic (FO) with counting quantifiers, we consider the definability problem, which asks whether a given L-formula can be equivalently expressed by a formula in some fragment of L without counting, and the more…
Connections between Lie derivatives and the deviation equation has been investigated in spaces with affine connection. The deviation equations of the geodesics as well as deviation equations of non-geodesics trajectories have been obtained…
We introduce a method for showing that there exist prime numbers which are very close together. The method depends on the level of distribution of primes in arithmetic progressions. Assuming the Elliott-Halberstam conjecture, we prove that…
Let $\cal{P}$ be an affine invariant property of functions $\mathbb{F}_p^n \to [R]$ for fixed $p$ and $R$. We show that if $\cal{P}$ is locally testable with a constant number of queries, then one can estimate the distance of a function $f$…
This paper deals with certain fundamental results about affine hulls and simplices in a real normed linear space. The framework of the paper is Bishop's constructive mathematics, which, with its characteristic interpretation of existence as…