Related papers: 25 years ago: the official farewell to the meter
We study the problem of representing all distances between $n$ points in $\mathbb R^d$, with arbitrarily small distortion, using as few bits as possible. We give asymptotically tight bounds for this problem, for Euclidean metrics, for…
Several group in the World followed the solar diameter with dedicated instruments, namely solar astrolabes, since 1974. Their data have been gathered in several observing stations connected in the R2S3 (Reseau de Suivi au Sol du Rayon…
In the early 80's, Alain Quilliot presented an approach of ordered sets and graphs in terms of metric spaces, where instead of positive real numbers, the values of the distance are elements of an ordered monoid equipped with an involution.…
Invited presentation on issues at the intersection of science and politics in the United States, delivered at the 150 year anniversary of the French Physical Society on the 6th of July 2023 in Paris.
In this survey we present a generalization of the notion of metric space and some applications to discrete structures as graphs, ordered sets and transition systems. Results in that direction started in the middle eighties based on the…
While the completion of the Pierre Auger Observatory (or simply ``Auger'') is still underway, the 5165 km^2.sr.yr integrated acceptance accumulated since the January 1st, 2004 is now significantly larger than what was gathered by the…
The traditional measurement theory interprets the variance as the dispersion of a measured value, which is actually contrary to a general mathematical concept that the variance of a constant is 0. This paper will fully demonstrate that the…
The use of time--like geodesics to measure temporal distances is better justified than the use of space--like geodesics for a measurement of spatial distances. We give examples where a ''spatial distance'' cannot be appropriately determined…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
A new Kerr-like metric with quadrupole moment is obtained by means of perturbing the Kerr spacetime. The form of this new metric is simple as the Kerr metric. By comparison with the exterior Hartle-Thorne metric, it is shown that it could…
Given a probability measure with density, Fermat distances and density-driven metrics are conformal transformations of the Euclidean metric that shrink distances in high density areas and enlarge distances in low density areas. Although…
The Fr\'echet distance is a popular metric for curves; however, its bottleneck character is a disadvantage in many applications. Here we introduce two variants of the Fr\'echet distance to cope with this problem and expand the work on…
In the past six years, Betelgeuse has been in the news and drawn significant public interest. Starting in October 2019, Betelgeuse underwent a striking dimming event, fading from magnitude 0.5 to 1.7 by mid February 2020 a threefold…
In this paper, we review the basic properties of measures vanishing at infinity and prove a version of the Riemann--Lebesgue lemma for Fourier transformable measures.
Georges Lemaitre gave a theoretical proof for his 1927 doctoral thesis in astronomy that the maximum spherical radius of our Universe can be computed from first principles to be 14.2 billion light-years (Lemaitre 1927a). That estimate,…
Attempts to measure extragalactic distances over the last 90 years are briefly described. It follows a short history of the discovery of the expansion of space. Reasons are discussed for the decrease of the Hubble constant from Ho~500…
The article is dedicated to recalling the life and mathematics of Louis Nirenberg, a distinguished Canadian mathematician who recently died in New York, where he lived. An emblematic figure of Analysis and Partial Differential Equations in…
The dynamic time warping (dtw) distance fails to satisfy the triangle inequality and the identity of indiscernibles. As a consequence, the dtw-distance is not warping-invariant, which in turn results in peculiarities in data mining…
This article is an extended version of the article published by EDP Sciences at the occasion of the 150 years of the ``Soci\'et\'e Fran\c{c}aise de Physique'' (in French)
We present in this article experimental results obtained with the "dispositif de Lenay" : for a localization task (distal perception) and an orientation estimation task (proximal perception of the orientation of a cylinder in a plane). In…