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

A Multi-Platform Flow Device for Microbial (Co-) Cultivation and Microscopic Analysis

Novel microbial cultivation platforms are of increasing interest to researchers in academia and industry. The development of materials with specialized chemical and geometric properties has opened up new possibilities in the study of previously unculturable microorganisms and has facilitated the design of elegant, high-throughput experimental set-ups. Within the context of the international Genetically Engineered Machine (iGEM) competition, we set out to design, manufacture, and implement a flow device that can accommodate multiple growth platforms, that is, a silicon nitride based microsieve and a porous aluminium oxide based microdish. It provides control over (co-)culturing conditions similar to a chemostat, while allowing organisms to be observed microscopically. The device was designed to be affordable, reusable, and above all, versatile. To test its functionality and general utility, we performed multiple experiments with Escherichia coli cells harboring synthetic gene circuits and were able to quantitatively study emerging expression dynamics in real-time via fluorescence microscopy. Furthermore, we demonstrated that the device provides a unique environment for the cultivation of nematodes, suggesting that the device could also prove useful in microscopy studies of multicellular microorganisms

Hyperresolution information and hyperresolution ignorance in modelling the hydrology of the land surface

There is a strong drive towards hyperresolution earth system models in order to resolve finer scales of motion in the atmosphere. The problem of obtaining more realistic representation of terrestrial fluxes of heat and water, however, is not just a problem of moving to hyperresolution grid scales. It is much more a question of a lack of knowledge about the parameterisation of processes at whatever grid scale is being used for a wider modelling problem. Hyperresolution grid scales cannot alone solve the problem of this hyperresolution ignorance. This paper discusses these issues in more detail with specific reference to land surface parameterisations and flood inundation models. The importance of making local hyperresolution model predictions available for evaluation by local stakeholders is stressed. It is expected that this will be a major driving force for improving model performance in the future. Keith BEVEN, Hannah CLOKE, Florian PAPPENBERGER, Rob LAMB, Neil HUNTE