Jorgensen's inequality for non-Archimedean metric spaces.

Jørgensen’s inequality gives a necessary condition for a non-elementary group of Möbius transformations to be discrete. In this paper we generalise this to the case of groups of Möbius transformations of a non-Archimedean metric space. As an application, we give a version of Jørgensen’s inequality for SL(2, ℚ p )

A hierarchy of bound states in the 1D ferromagnetic Ising chain CoNb2_2O6_6 investigated by high resolution time-domain terahertz spectroscopy

Kink bound states in the one dimensional ferromagnetic Ising chain compound CoNb$_2$O$_6$ have been studied using high resolution time-domain terahertz spectroscopy in zero applied magnetic field. When magnetic order develops at low temperature, nine bound states of kinks become visible. Their energies can be modeled exceedingly well by the Airy function solutions to a 1D Schr\"odinger equation with a linear confining potential. This sequence of bound states terminates at a threshold energy near two times the energy of the lowest bound state. Above this energy scale we observe a broad feature consistent with the onset of the two particle continuum. At energies just below this threshold we observe a prominent excitation that we interpret as a novel bound state of bound states -- two pairs of kinks on neighboring chains

Genotype and diet affect resistance, survival, and fecundity but not fecundity tolerance

Insects are exposed to a variety of potential pathogens in their environment, many of which can severely impact fitness and health. Consequently, hosts have evolved resistance and tolerance strategies to suppress or cope with infections. Hosts utilizing resistance improve fitness by clearing or reducing pathogen loads, and hosts utilizing tolerance reduce harmful fitness effects per pathogen load. To understand variation in, and selective pressures on, resistance and tolerance, we asked to what degree they are shaped by host genetic background, whether plasticity in these responses depends upon dietary environment, and whether there are interactions between these two factors. Females from ten wild‐type Drosophila melanogaster genotypes were kept on high‐ or low‐protein (yeast) diets and infected with one of two opportunistic bacterial pathogens, Lactococcus lactis or Pseudomonas entomophila. We measured host resistance as the inverse of bacterial load in the early infection phase. The relationship (slope) between fly fecundity and individual‐level bacteria load provided our fecundity tolerance measure. Genotype and dietary yeast determined host fecundity and strongly affected survival after infection with pathogenic P. entomophila. There was considerable genetic variation in host resistance, a commonly found phenomenon resulting from for example varying resistance costs or frequency‐dependent selection. Despite this variation and the reproductive cost of higher P. entomophila loads, fecundity tolerance did not vary across genotypes. The absence of genetic variation in tolerance may suggest that at this early infection stage, fecundity tolerance is fixed or that any evolved tolerance mechanisms are not expressed under these infection conditions