Métissage au Brésil

Métissage au Brési

On the spectrum of the Thue-Morse quasicrystal and the rarefaction phenomenon

The spectrum of a weighted Dirac comb on the Thue-Morse quasicrystal is investigated, and characterized up to a measure zero set, by means of the Bombieri-Taylor conjecture, for Bragg peaks, and of another conjecture that we call Aubry-Godr\`eche-Luck conjecture, for the singular continuous component. The decomposition of the Fourier transform of the weighted Dirac comb is obtained in terms of tempered distributions. We show that the asymptotic arithmetics of the $p$-rarefied sums of the Thue-Morse sequence (Dumont; Goldstein, Kelly and Speer; Grabner; Drmota and Skalba,...), namely the fractality of sum-of-digits functions, play a fundamental role in the description of the singular continous part of the spectrum, combined with some classical results on Riesz products of Peyri\`ere and M. Queff\'elec. The dominant scaling of the sequences of approximant measures on a part of the singular component is controlled by certain inequalities in which are involved the class number and the regulator of real quadratic fields.Comment: 35 pages In honor of the 60-th birthday of Henri Cohe

Vaccine hesitancy: clarifying a theoretical framework for an ambiguous notion.

Today, according to many public health experts, public confidence in vaccines is waning. The term "vaccine hesitancy" (VH) is increasingly used to describe the spread of such vaccine reluctance. But VH is an ambiguous notion and its theoretical background appears uncertain. To clarify this concept, we first review the current definitions of VH in the public health literature and examine its most prominent characteristics. VH has been defined as a set of beliefs, attitudes, or behaviours, or some combination of them, shared by a large and heterogeneous portion of the population and including people who exhibit reluctant conformism (they may either decline a vaccine, delay it or accept it despite their doubts) and vaccine-specific behaviours. Secondly, we underline some of the ambiguities of this notion and argue that it is more a catchall category than a real concept. We also call into question the usefulness of understanding VH as an intermediate position along a continuum ranging from anti-vaccine to pro-vaccine attitudes, and we discuss its qualification as a belief, attitude or behaviour. Thirdly, we propose a theoretical framework, based on previous literature and taking into account some major structural features of contemporary societies, that considers VH as a kind of decision-making process that depends on people's level of commitment to healthism/risk culture and on their level of confidence in the health authorities and mainstream medicine