Abstract involutions of algebraic groups and of Kac-Moody groups

Based on the second author's thesis in this article we provide a uniform treatment of abstract involutions of algebraic groups and of Kac-Moody groups using twin buildings, RGD systems, and twisted involutions of Coxeter groups. Notably we simultaneously generalize the double coset decompositions established by Springer and by Helminck-Wang for algebraic groups and by Kac-Wang for certain Kac-Moody groups, we analyze the filtration studied by Devillers-Muhlherr in the context of arbitrary involutions, and we answer a structural question on the combinatorics of involutions of twin buildings raised by Bennett-Gramlich-Hoffman-Shpectorov

Students’ Perspectives on the First Day of Class: A Replication

Research has shown that first-day practices affect students’ motivation, grades, and end of the semester ratings of the professors. However, research on student preferences of first day practices has been conducted at public, predominantly white institutions and has not investigated if first day preferences differ at a private or historically Black university. Therefore, to investigate consistency in preferences across generations and possible differences in preferences at a private Historically Black College or University (HBCU) we assessed first day preferences and compared our results to the original study (Perlman & McCann, 1999). We sampled 230 predominantly Black students from a small private HBCU. Our findings are similar to Perlman and McCann’s results, indicating that students desire a general overview, details about grading, and getting to know the professor. Students also disliked poor use of class time and beginning course material on the first day. Analyses revealed differences in the preferences of third and fourth year students compared to first and second year students. Analyses also indicated that in our sample a smaller proportion of students cared about first day information being presented in an understandable contest, and that a higher proportion of our sample cared about setting a fun tone and disliked an uncaring or intimidating environment in contrast to Perlman & McCann’s original study

Investor Perceptions of Board Performance: Evidence From Uncontested Director Elections

This paper provides evidence that uncontested director elections provide informative polls of investor perceptions regarding board performance. We find that higher (lower) vote approval is associated with lower (higher) stock price reactions to subsequent announcements of management turnovers. In addition, firms with low vote approval are more likely to experience CEO turnover, greater board turnover, lower CEO compensation, fewer and better-received acquisitions, and more and better-received divestitures in the future. These findings hold after controlling for other variables reflecting or determining investor perceptions, suggesting that elections not only inform as a summary statistic, but incrementally inform as well

Lazy AC-Pattern Matching for Rewriting

We define a lazy pattern-matching mechanism modulo associativity and commutativity. The solutions of a pattern-matching problem are stored in a lazy list composed of a first substitution at the head and a non-evaluated object that encodes the remaining computations. We integrate the lazy AC-matching in a strategy language: rewriting rule and strategy application produce a lazy list of terms.Comment: In Proceedings WRS 2011, arXiv:1204.531

On the distortion of twin building lattices

We show that twin building lattices are undistorted in their ambient group; equivalently, the orbit map of the lattice to the product of the associated twin buildings is a quasi-isometric embedding. As a consequence, we provide an estimate of the quasi-flat rank of these lattices, which implies that there are infinitely many quasi-isometry classes of finitely presented simple groups. In an appendix, we describe how non-distortion of lattices is related to the integrability of the structural cocycle

Supersensitive Multifluorophore RNA‐FISH for Early Virus Detection and Flow‐FISH by Using Click Chemistry

The reliable detection of transcription events through the quantification of the corresponding mRNA is of paramount importance for the diagnostics of infections and diseases. The quantification and localization analysis of the transcripts of a particular gene allows disease states to be characterized more directly compared to an analysis on the transcriptome wide level. This is particularly needed for the early detection of virus infections as now required for emergent viral diseases, e. g. Covid‐19. In situ mRNA analysis, however, is a formidable challenge and currently performed with sets of single‐fluorophore‐containing oligonucleotide probes that hybridize to the mRNA in question. Often a large number of probe strands (>30) are required to get a reliable signal. The more oligonucleotide probes are used, however, the higher the potential off‐target binding effects that create background noise. Here, we used click chemistry and alkyne‐modified DNA oligonucleotides to prepare multiple‐fluorophore‐containing probes. We found that these multiple‐dye probes allow reliable detection and direct visualization of mRNA with only a very small number (5–10) of probe strands. The new method enabled the in situ detection of viral transcripts as early as 4 hours after infection

Quotients of incidence geometries

We develop a theory for quotients of geometries and obtain sufficient conditions for the quotient of a geometry to be a geometry. These conditions are compared with earlier work on quotients, in particular by Pasini and Tits. We also explore geometric properties such as connectivity, firmness and transitivity conditions to determine when they are preserved under the quotienting operation. We show that the class of coset pregeometries, which contains all flag-transitive geometries, is closed under an appropriate quotienting operation.Comment: 26 pages, 5 figure