In this paper, we revisit the origins of Emile Borel's developing interest in probability around 1905. This resulted from new findings in his research on continued fraction, but it also cannot be separated from the discovery of new applications for the mathematics of randomness (such as biology or economics) and of their importance as a life‐changing tool for the citizen. In particular, we underline the role of a paper published by Vito Volterra in Borel's Revue du Mois.
Nous examinons dans cet article la manière singulière dont Émile Borel, à partir de ses études sur la structure des nombres réels et un certain rejet de la vision abstraite de Georg Cantor, a trouvé dans le calcul des probabilités un outil adéquat pour formuler une nouvelle approche des problèmes, dans le même temps où il prenait conscience de son utilité pour l’approche des phénomènes de la physique et de la société.
Taking the specific case of coagulation factor VIII assay, we determined the characteristics of an internal quality control panel assuring control of the assay method for all of the critical factor VIII concentrations. The precision of the assay method was determined on six control materials C1-C6, with expected factor VIII levels of 1, 5, 30, 50, 80 and 150 U/dl, respectively. Given that, when two control levels correlate statistically, the information provided by one of them is redundant, we used correlation and principal components analysis to define a priori adequate and inadequate control panels. For each of these panels, we calculated the number of runs required, using Hotelling's method, to detect a shift expressed on C1 and impacted on C2, C3, C4, C5 and C6 in relation to the correlation phenomena among the six levels. The C1/C6 panel proved to be as informative in this regard as the complete panel for a 1 U/dl shift simulated on C1 and impacted on other levels too. These correlation phenomena allow the biologist to implement fewer control levels than there are critical concentrations needing to be explored in the internal quality control plan.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.