On commensurable hyperbolic Coxeter groups

For Coxeter groups acting non-cocompactly but with finite covolume on real hyperbolic space Hn, new methods are presented to distinguish them up to (wide) commensurability. We exploit these ideas and determine the commensurability classes of all hyperbolic Coxeter groups whose fundamental polyhedra are pyramids over a product of two simplices of positive dimensions

All-mass n-gon integrals in n dimensions

We explore the correspondence between one-loop Feynman integrals and (hyperbolic) simplicial geometry to describe the "all-mass" case: integrals with generic external and internal masses. Specifically, we focus on $n$-particle integrals in exactly $n$ space-time dimensions, as these integrals have particularly nice geometric properties and respect a dual conformal symmetry. In four dimensions, we leverage this geometric connection to give a concise dilogarithmic expression for the all-mass box in terms of the Murakami-Yano formula. In five dimensions, we use a generalized Gauss-Bonnet theorem to derive a similar dilogarithmic expression for the all-mass pentagon. We also use the Schl\"afli formula to write down the symbol of these integrals for all $n$. Finally, we discuss how the geometry behind these formulas depends on space-time signature, and we gather together many results related to these integrals from the mathematics and physics literature.Comment: 49 pages, 8 figure

Habitat Assessment of Non-Wadeable Rivers in Michigan

Habitat evaluation of wadeable streams based on accepted protocols provides a rapid and widely used adjunct to biological assessment. However, little effort has been devoted to habitat evaluation in non-wadeable rivers, where it is likely that protocols will differ and field logistics will be more challenging. We developed and tested a non-wadeable habitat index (NWHI) for rivers of Michigan, where non-wadeable rivers were defined as those of order ≥5, drainage area ≥1600 km 2 , mainstem lengths ≥100 km, and mean annual discharge ≥15 m 3 /s. This identified 22 candidate rivers that ranged in length from 103 to 825 km and in drainage area from 1620 to 16,860 km 2 . We measured 171 individual habitat variables over 2-km reaches at 35 locations on 14 rivers during 2000–2002, where mean wetted width was found to range from 32 to 185 m and mean thalweg depth from 0.8 to 8.3 m. We used correlation and principal components analysis to reduce the number of variables, and examined the spatial pattern of retained variables to exclude any that appeared to reflect spatial location rather than reach condition, resulting in 12 variables to be considered in the habitat index. The proposed NWHI included seven variables: riparian width, large woody debris, aquatic vegetation, bottom deposition, bank stability, thalweg substrate, and off-channel habitat. These variables were included because of their statistical association with independently derived measures of human disturbance in the riparian zone and the catchment, and because they are considered important in other habitat protocols or to the ecology of large rivers. Five variables were excluded because they were primarily related to river size rather than anthropogenic disturbance. This index correlated strongly with indices of disturbance based on the riparian (adjusted R 2 = 0.62) and the catchment (adjusted R 2 = 0.50), and distinguished the 35 river reaches into the categories of poor (2), fair (19), good (13), and excellent (1). Habitat variables retained in the NWHI differ from several used in wadeable streams, and place greater emphasis on known characteristic features of larger rivers.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41269/1/267_2004_Article_141.pd

Development of SNP-based assays for disease resistance and fruit quality traits in apple (Malus × domestica Borkh.) and validation in breeding pilot studies

The development of molecular markers linked to specific traits is now routine practice, but the gap between genomics and breeding often delays their application. In the frame of the FP7 European project FruitBreedomics, apple pilot studies were designed to exploit the project\u2019s outcomes towards the practical application of marker-assisted breeding (MAB) programs. The aim of this pilot study was to develop an outsourcing genotyping pipeline, which will provide access to the single nucleotide polymorphism (SNP) markers analysis for breeding companies without an internal DNA lab. The process from seed sowing to genotypic and phenotypic seedling selection was optimized. KASP\u2122 (competitive allele-specific PCR) genotyping assays were developed for a number of major resistance genes for apple scab (Rvi2, Rvi4, Rvi6, and Rvi15); powdery mildew (Pl2); and rosy apple aphid (Dp-fl). In addition, KASP\u2122 assays for the genes Md-ACS1, Md-ACO1, and Md-PG1 involved in fruit quality (firmness, texture, and storability) were also developed. The pilot study demonstrated the efficacy of the SNP-based selection strategy, especially for those programs dealing with traits not easily assessable in vivo, such as pyramided resistances and fruit quality traits