Efficient Finite Groups Arising in the Study of Relative Asphericity

We study a class of two-generator two-relator groups, denoted Jn(m, k), that arise in the study of relative asphericity as groups satisfying a transitional curvature condition. Particular instances of these groups occur in the literature as finite groups of intriguing orders. Here we find infinite families of non-elementary virtually free groups and of finite metabelian non-nilpotent groups, for which we determine the orders. All Mersenne primes arise as factors of the orders of the non-metacyclic groups in the class, as do all primes from other conjecturally infinite families of primes. We classify the finite groups up to isomorphism and show that our class overlaps and extends a class of groups Fa,b,c with trivalent Cayley graphs that was introduced by C.M.Campbell, H.S.M.Coxeter, and E.F.Robertson. The theory of cyclically presented groups informs our methods and we extend part of this theory (namely, on connections with polynomial resultants) to ?bicyclically presented groups? that arise naturally in our analysis. As a corollary to our main results we obtain new infinite families of finite metacyclic generalized Fibonacci groups

Nephila clavipes spiders (Araneae: Nephilidae) keep track of captured prey counts: testing for a sense of numerosity in an orb-weaver

artículo (arbitrado) -- Universidad de Costa Rica. Escuela de Biología, 2014. Este documento es privado debido a limitaciones de derechos de autor.Nephila clavipes golden orb-web spiders accumulate prey larders on their webs and search for them if they are removed from their web. Spiders that lose larger larders (i.e., spiders that lose larders consisting of more prey items) search for longer intervals, indicating that the spiders form memories of the size of the prey larders they have accumulated, and use those memories to regulate recovery efforts when the larders are pilfered. Here, we ask whether the spiders represent prey counts (i.e., numerosity) or a continuous integration of prey quantity (mass) in their memories. We manipulated larder sizes in treatments that varied in either prey size or prey numbers but were equivalent in total prey quantity (mass). We then removed the larders to elicit searching and used the spiders’ searching behavior as an assay of their representations in memory. Searching increased with prey quantity (larder size) and did so more steeply with higher prey counts than with single prey of larger sizes. Thus, Nephila spiders seem to track prey quantity in two ways, but to attend more to prey numerosity. We discuss alternatives for continuous accumulator mechanisms that remain to be tested against the numerosity hypothesis, and the evolutionary and adaptive significance of evidence suggestive of numerosity in a sit-and-wait invertebrate predator.Universidad de Costa Rica, Escuela de Biologia UWM Graduate School Committee AwardUCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Biologí

The Double Limit Theorem and Its Legacy

International audienceThis chapter surveys recent and less recent results on convergence of Kleinian representations, following Thurston's Double Limit and "AH(acylindrical) is compact" Theorems