Cohomological finiteness conditions for a class of metabelian groups

We consider a class of metabelian groups first studied by Baumslag and Stammbach and we show that these groups are consistent with the Bieri-Groves conjecture which relates cohomological finiteness conditions to the Bieri-Neumann-Strebel sigma invariant.Comment: 10 pages Accepted for publication in the Bulletin of the London Mathematical Societ

Geometric and homological finiteness in free abelian covers

We describe some of the connections between the Bieri-Neumann-Strebel-Renz invariants, the Dwyer-Fried invariants, and the cohomology support loci of a space X. Under suitable hypotheses, the geometric and homological finiteness properties of regular, free abelian covers of X can be expressed in terms of the resonance varieties, extracted from the cohomology ring of X. In general, though, translated components in the characteristic varieties affect the answer. We illustrate this theory in the setting of toric complexes, as well as smooth, complex projective and quasi-projective varieties, with special emphasis on configuration spaces of Riemann surfaces and complements of hyperplane arrangements.Comment: 30 pages; to appear in Configuration Spaces: Geometry, Combinatorics and Topology (Centro De Giorgi, 2010), Edizioni della Normale, Pisa, 201

An Optimizing Symbolic Algebra Approach for Generating Fast Multipole Method Operators

We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can generate computer code for any expansion order in multiple languages. The procedure is implemented in the publicly available Python program Mosaic. Optimizations performed at the symbolic level through algebraic manipulations significantly reduce the number of mathematical operations compared with a straightforward implementation of the equations. We find that the optimizer is able to eliminate 20-80% of the floating-point operations and for the expansion orders $p \le 10$ it changes the observed scaling properties. We present our approach using three variants of the operators with the Cartesian basis set for the harmonic potential kernel $1/r$, including the use of totally symmetric and traceless multipole tensors.Comment: Updated to final version submitted to Computer Physics Communications. Accepted on 20 November 201

Haydeeite: a spin-1/2 kagome ferromagnet

The mineral haydeeite, alpha-MgCu3(OD)6Cl2, is a S=1/2 kagome ferromagnet that displays long-range magnetic order below TC=4.2 K with a strongly reduced moment. Our inelastic neutron scattering data show clear spin-wave excitations that are well described by a Heisenberg Hamiltonian with ferromagnetic nearest-neighbor exchange J1=-38 K and antiferromagnetic exchange Jd=+11 K across the hexagons of the kagome lattice. These values place haydeeite very close to the quantum phase transition between ferromagnetic order and non-coplanar twelve-sublattice cuboc2 antiferromagnetic order. Diffuse dynamic short-range ferromagnetic correlations observed above TC persist well into the ferromagnetically ordered phase with a behavior distinct from critical scattering

Effects of age and eccentricity on visual target detection

The aim of this study was to examine the effects of aging and target eccentricity on a visual search task comprising 30 images of everyday life projected into a hemisphere, realizing a ±90° visual field. The task performed binocularly allowed participants to freely move their eyes to scan images for an appearing target or distractor stimulus (presented at 10°; 30°, and 50° eccentricity). The distractor stimulus required no response, while the target stimulus required acknowledgment by pressing the response button. One hundred and seventeen healthy subjects (mean age = 49.63 years, SD = 17.40 years, age range 20–78 years) were studied. The results show that target detection performance decreases with age as well as with increasing eccentricity, especially for older subjects. Reaction time also increases with age and eccentricity, but in contrast to target detection, there is no interaction between age and eccentricity. Eye movement analysis showed that younger subjects exhibited a passive search strategy while older subjects exhibited an active search strategy probably as a compensation for their reduced peripheral detection performance

Aphid genotypes vary in their response to the presence of fungal endosymbionts in host plants

Genetic variation for fitness-relevant traits may be maintained in natural populations by fitness differences that depend on environmental conditions. For herbivores, plant quality and variation in chemical plant defences can maintain genetic variation in performance. Apart from plant secondary compounds, symbiosis between plants and endosymbiotic fungi (endophytes) can produce herbivore-toxic compounds. We show that there is significant variation among aphid genotypes in response to endophytes by comparing life-history traits of 37 clones of the bird cherry-oat aphid Rhopalosiphum padi feeding on endophyte-free and endophyte-infected tall fescue Lolium arundinaceum. Clonal variation for life-history traits was large, and most clones performed better on endophyte-free plants. However, the clones differed in the relative performance across the two environments, resulting in significant genotype · environment interactions for all reproductive traits. These findings suggest that natural variation in prevalence of endophyte infection can contribute to the maintenance of genetic diversity in aphid populations