Weyl group multiple Dirichlet series constructed from quadratic characters

We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain group of functional equations. These are the first examples of an infinite collection of unstable Weyl group multiple Dirichlet series in greater than two variables.Comment: incorporated referee's comment

The Forest City Landslide

A large and complex landslide in marine shales is impacting the approach roadway and a 4600-ft long bridge carrying U.S. Route 212 over the Oahe Reservoir at Forest City, South Dakota. After extensive investigation and analyses it was determined that the main landslide could be remediated by unloading the slide using a large cut through the escarpment located upslope from the bridge. Although moving with the main slide, the 900- foot long approach embankment is failing in directions differing from the main slide. Preliminary study indicates that the independent slides within the approach embankment can be stabilized by stone columns or reinforced concrete dowels. Partial remediation has been achieved by the installation of stone columns around the embankment toe

Arithmetical properties of Multiple Ramanujan sums

In the present paper, we introduce a multiple Ramanujan sum for arithmetic functions, which gives a multivariable extension of the generalized Ramanujan sum studied by D. R. Anderson and T. M. Apostol. We then find fundamental arithmetic properties of the multiple Ramanujan sum and study several types of Dirichlet series involving the multiple Ramanujan sum. As an application, we evaluate higher-dimensional determinants of higher-dimensional matrices, the entries of which are given by values of the multiple Ramanujan sum.Comment: 19 page

Territorial landscapes: incorporating density-dependence into wolf habitat selection studies.

Habitat selection is a process that spans space, time and individual life histories. Ecological analyses of animal distributions and preferences are most accurate when they account for inherent dynamics of the habitat selection process. Strong territoriality can constrain perception of habitat availability by individual animals or groups attempting to colonize or establish new territory. Because habitat selection is a function of habitat availability, broad-scale changes in habitat availability or occupancy can drive density-dependent habitat functional responses. We investigated density-dependent habitat selection over a 19-year period of grey wolf

SL(2,Z) Multiplets in N=4 SYM Theory

We discuss the action of SL(2,Z) on local operators in D=4, N=4 SYM theory in the superconformal phase. The modular property of the operator's scaling dimension determines whether the operator transforms as a singlet, or covariantly, as part of a finite or infinite dimensional multiplet under the SL(2,Z) action. As an example, we argue that operators in the Konishi multiplet transform as part of a (p,q) PSL(2,Z) multiplet. We also comment on the non-perturbative local operators dual to the Konishi multiplet.Comment: 14 pages, harvmac; v2: published version with minor change

Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems

The Hall viscosity, a non-dissipative transport coefficient analogous to Hall conductivity, is considered for quantum fluids in gapped or topological phases. The relation to mean orbital spin per particle discovered in previous work by one of us is elucidated with the help of examples, using the geometry of shear transformations and rotations. For non-interacting particles in a magnetic field, there are several ways to derive the result (even at non-zero temperature), including standard linear response theory. Arguments for the quantization, and the robustness of Hall viscosity to small changes in the Hamiltonian that preserve rotational invariance, are given. Numerical calculations of adiabatic transport are performed to check the predictions for quantum Hall systems, with excellent agreement for trial states. The coefficient of k^4 in the static structure factor is also considered, and shown to be exactly related to the orbital spin and robust to perturbations in rotation invariant systems also.Comment: v2: Now 30 pages, 10 figures; new calculation using disk geometry; some other improvements; no change in result

Vaginal Flora in Postmenopausal Women: The Effect of Estrogen Replacement

Objective:To determine the effect of estrogen replacement therapy (ERT) on the vaginal flora of postmenopausal women

Modeling Marine Protected Areas for Threatened Eiders in a Climatically Changing Bering Sea

Delineating protected areas for sensitive species is a growing challenge as changing climate alters the geographic pattern of habitats as well as human responses to those shifts. When human impacts are expected within projected ranges of threatened species, there is often demand to demarcate the minimum habitat required to ensure the species\u27 persistence. Because diminished or wide-ranging populations may not occupy all viable (and needed) habitat at once, one must identify thresholds of resources that will support the species even in unoccupied areas. Long-term data on the shifting mosaic of critical resources may indicate ranges of future variability. We addressed these issues for the Spectacled Eider (Somateria fischeri), a federally threatened species that winters in pack ice of the Bering Sea. Changing climate has decreased ice cover and severely reduced the eiders\u27 benthic prey and has increased prospects for expansion of bottom trawling that may further affect prey communities. To assess long-term changes in habitats that will support eiders, we linked data on benthic prey, sea ice, and weather from 1970 to 2001 with a spatially explicit simulation model of eider energy balance that integrated field, laboratory, and remote-sensing studies. Areas estimated to have prey densities adequate for eiders in 1970–1974 did not include most areas that were viable 20 years later (1993–1994). Unless the entire area with adequate prey in 1993–1994 had been protected, the much reduced viable area in 1999–2001 might well have been excluded. During long non-foraging periods (as at night), eiders can save much energy by resting on ice vs. floating on water; thus, loss of ice cover in the future might substantially decrease the area in which prey densities are adequate to offset the eiders\u27 energy needs. For wide-ranging benthivores such as eiders, our results emphasize that fixed protected areas based on current conditions can be too small or inflexible to subsume long-term shifts in habitat conditions. Better knowledge of patterns of natural disturbance experienced by prey communities, and appropriate allocation of human disturbance over seasons or years, may yield alternative strategies to large-scale closures that may be politically and economically problemati

Central limit theorem for multiplicative class functions on the symmetric group

Hambly, Keevash, O'Connell and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We prove here a central limit theorem for multiplicative class functions on symmetric group with respect to the Ewens measure and compute the covariance of the real and the imaginary part in the limit. We also estimate the rate of convergence with the Wasserstein distance.Comment: 23 pages; the mathematics is the same as in the previous version, but there are several improvments in the presentation, including a more intuitve name for the considered function