Euclidean minima and central division algebras

The notion of Euclidean minimum of a number field is a classical one. In this paper we generalize it to central division algebras and establish some general results in this new context

Euclidean minima and central division algebras

A paraître dans International Journal of Number TheoryInternational audienceNous étudions la notion de minimum euclidien dans le cadre des algèbres centrales à division. Ceci nous permet d'étendre à ces nouveaux objets de récents résultats obtenus sur les corps de nombres

Lessons Learned During the Implementation of a Cold Gas Propulsion System for the SunRISE Mission

The SunRISE mission utilizes a two-phase cold gas propulsion system, which provides several advantages over other cold gas systems but experienced challenges during assembly and testing. Since 2020, Georgia Tech Research Corporation (GTRC), Utah State University Space Dynamics Laboratory (SDL), and the Jet Propulsion Laboratory (FPL) have implemented several improvements to the SunRISE propulsion system. The SunRISE propulsion system leverages an additively manufactured monolithic structure, commercial off-the-shelf (COTS) valves and transducers, and the benign working fluid R-236fa to provide a suitable propulsion system for the SunRise mission. While the GTRC propulsion system had been developed for other missions, the multi-organizational team found and corrected several previously undetected design issues, including filters with highly variable flow performance, solenoid valve drive circuit issues, and inconsistencies in the tank additive manufacturing process that impacted manufacturing yield, thrust consistency, and quality of seals. Leaks in metallic fittings were also identified, and process improvements were put in place to mitigate them. Solenoid valve stiction was the last issue which was mitigated through valve screening and drive circuit adjustments. In this paper, we present lessons learned from the SunRISE propulsion system effort to aid future teams in identifying and addressing similar issues

On Various Ways of Measuring Unemployment, with Applications to Switzerland

This paper discusses first various ways of measuring unemployment and, borrowing ideas from the poverty measurement literature, proposes four more general unemployment indices which are parallel to Sen poverty index, to its generalization by Shorrocks, to the FGT, and to the Watts poverty indices. It then presents an empirical illustration based on Swiss data at the level of the “canton.” More precisely, using the so-called Shapley decomposition, it computes the contribution to the difference between the value of each of these four unemployment indices in a given “canton” and in Switzerland as a whole, of three components measuring, respectively, the impact of differences in the traditional unemployment rate, in the average unemployment duration, and in the inequality in the unemployment durations. The paper ends by discussing the impact on the results obtained of assumptions made concerning the maximum unemployment duration

Euclidean minima and central division algebras

Nous étudions la notion de minimum euclidien dans le cadre des algèbres centrales à division. Ceci nous permet d'étendre à ces nouveaux objets de récents résultats obtenus sur les corps de nombres

Native Architecture of the Centriole Proximal Region Reveals Features Underlying Its 9-Fold Radial Symmetry

Centrioles are cylindrical microtubule-based structures whose assembly is critical for the formation of cilia, flagella, and centrosomes. The centriole proximal region harbors a cartwheel that dictates the 9-fold symmetry of centrioles. Although the cartwheel architecture has been recently analyzed, how it connects to the peripheral microtubules is not understood. More generally, a high-resolution view of the proximal region of the centriole is lacking, thus limiting understanding of the underlying assembly mechanisms

Fluorescence-Based Reporters for Detection of Mutagenesis in E. coli.

Mutagenesis in model organisms following exposure to chemicals is used as an indicator of genotoxicity. Mutagenesis assays are also used to study mechanisms of DNA homeostasis. This chapter focuses on detection of mutagenesis in prokaryotes, which boils down to two approaches: reporter inactivation (forward mutation assay) and reversion of an inactivating mutation (reversion mutation assay). Both methods are labor intensive, involving visual screening, quantification of colonies on solid media, or determining a Poisson distribution in liquid culture. Here, we present two reversion reporters for in vivo mutagenesis that produce a quantitative output, and thus have the potential to greatly reduce the amount of test chemical and labor involved in these assays. This output is obtained by coupling a TEM β lactamase-based reversion assay with GFP fluorescence, either by placing the two genes on the same plasmid or by fusing them translationally and interrupting the N-terminus of the chimeric ORF with a stop codon. We also describe a reporter aimed at facilitating the monitoring of continuous mutagenesis in mutator strains. This reporter couples two reversion markers, allowing the temporal separation of mutation events in time, thus providing information about the dynamics of mutagenesis in mutator strains. Here, we describe these reporter systems, provide protocols for use, and demonstrate their key functional features using error-prone Pol I mutagenesis as a source of mutations