November Updates

(1) During 20-21 November, I visited Laurent Clavier at IRCICA in Lille as part of the ARBurst workshop on fundamental limits and statistical modelling for IoT wireless networks.

(2) On the 3rd December, I will be on the PhD committee for Pierre Escamilla supervised by Michele Wigger and Abdellatif Zaidi hosted by Telecom ParisTech and Huawei. Before the defence, I will present a talk:

Title: Tight Frames that are Regular Schemes

Abstract: Finite frames are sequences of vectors in finite dimensional Hilbert spaces that play a key role in signal processing (vector quantisation) and coding theory (spherical codes). In this talk, we focus on the class of tight unit-norm frames for \mathbb{C}^d that also form regular schemes, which we call tight regular schemes (TRS). Many common frames that arise in applications such as equiangular tight frames and frames from mutually unbiased bases fall in this class. We investigate characteristic properties of TRSs and prove that for many constructions, they are intimately connected to weighted 1-designs arising from cubature rules for integrals over spheres in \mathbb{C}^d with weights dependent on the Voronoi regions of each frame element. Aided by additional numerical evidence, we conjecture that all TRSs in fact satisfy this property.

This talk is based on my paper: “Properties of tight frames that are regular schemes,” in Cryptography and Communications – Discrete Structures, Boolean Functions and Sequences available here.

(3) On the 16th December, I will be on the PhD committee for Yasser Mestrah hosted by the University of Reims Champagne-Ardenne and IMT Lille Douai.