Constrained variable clustering and the best basis problem in functional data analysis

International audienceFunctional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained from a fine grid sampling of functional data, all methods benefit from a prior simplification of the functions that reduces the redundancy induced by the regularity. In this paper we propose to use a clustering approach that targets variables rather than individual to design a piecewise constant representation of a set of functions. The contiguity constraint induced by the functional nature of the variables allows a polynomial complexity algorithm to give the optimal solution

GJ 367b: A dense, ultrashort-period sub-Earth planet transiting a nearby red dwarf star

Ultrashort-period (USP) exoplanets have orbital periods shorter than 1 day. Precise masses and radii of USP exoplanets could provide constraints on their unknown formation and evolution processes. We present the work from Lam et al. 2021 (Science, 374, 1271) and report the detection and characterization of the USP planet GJ 367b using high-precision photometry and radial velocity observations. GJ 367b orbits a bright (V-band magnitude of 10.2), nearby, and red (M-type) dwarf star every 7.7 hours. GJ 367b has a radius of 0.718 ± 0.054 Earth-radii and a mass of 0.546 ± 0.078 Earth-masses, making it a sub-Earth planet. The corresponding bulk density is 8.106 ± 2.165 grams per cubic centimeter - close to that of iron. An interior structure model predicts that the planet has an iron core radius fraction of 86 ± 5%, similar to that of Mercury's interior