Betatron modulation of microwave instability in small isochronous ring

A novel coupling of the transverse betatron motion to the longitudinal microwave instability is studied. Besides the radial coherent dipole mode space charge field, simulation and theoretical studies in this paper show that the longitudinal coherent dipole mode space charge field due to centroid wiggles also plays an important role in the isochronous regime, it induces betatron oscillation frequencies in temporal evolutions of spectra of longitudinal charge densities, radial centroid offsets and coherent energy deviations of local centroids.Comment: 13 page

Constrained ordination analysis with enrichment of bell-shaped response functions

Constrained ordination methods aims at finding an environmental gradient along which the species abundances are maximally separated. The species response functions, which describe the expected abundance as a function of the environmental score, are according to the ecological fundamental niche theory only meaningful if they are bell-shaped. Many classical model-based ordination methods, however, use quadratic regression models without imposing the bell-shape and thus allowing for meaningless U-shaped response functions. The analysis output (e.g. a biplot) may therefore be potentially misleading and the conclusions are prone to errors. In this paper we present a log-likelihood ratio criterion with a penalisation term to enforce more bell-shaped response shapes. We report the results of a simulation study and apply our method to metagenomics data from microbial ecology