Density results for automorphic forms on Hilbert modular groups

We give density results for automorphic representations of Hilbert modular groups. In particular, we show that there are infinitely many automorphic representations that have a prescribed discrete series factor at some (but not all) real places.Comment: 35 pages, LaTe

Universality of ac-conduction in anisotropic disordered systems: An effective medium approximation study

Anisotropic disordered system are studied in this work within the random barrier model. In such systems the transition probabilities in different directions have different probability density functions. The frequency-dependent conductivity at low temperatures is obtained using an effective medium approximation. It is shown that the isotropic universal ac-conduction law, $\sigma \ln \sigma=u$, is recovered if properly scaled conductivity ($\sigma$) and frequency ($u$) variables are used.Comment: 5 pages, no figures, final form (with corrected equations

RED-TAILED HAWK TRANSLOCATION FOR REDUCING COLLISIONS WITH AIRCRAFT

Raptor translocation is currently being used by several airports to reduce collisions with aircraft. Changes in red-tailed hawk (Buteo jamaicensis) numbers and hawk/aircraft strikes were studied in relation to translocation of raptors at Eppley Airfield in Omaha, Nebraska from March 1999 through March 2000. The effect of distance on translocation success was also studied. Hawks were captured with pole traps, banded, and released approximately 80, 160, and 240 km from the airport. Two bird surveys were conducted at bimonthly intervals from April 1998 through March 1999, after which surveys were conducted at weekly intervals. These surveys provided an index of hawk numbers on the airfield. Strike data were used to determine if the number of hawk/aircraft strikes had declined. Forty-one red-tailed hawks were translocated from the airfield. No banded birds were recaptured or observed on the airfield. The number of red- tailed hawks on the airfield declined following peak capture periods (\u3e2 hawks per week). There was a 49% decrease in observed hawks in October 1999 through February 2000 relative to the previous year, with the largest decrease in October (82%). Red-tailed hawk numbers remained unchanged in September and March, prior to peak capture periods. No red-tailed hawk strikes were reported and no carcasses were recovered on the airfield from March 1999 to the present. Translocation of red-tailed hawks 80 km or more was effective in reducing the risk of hawk/aircraft strikes. Management efforts must be persistent, however, as the seasonal migration continues to bring new red-tailed hawks into the area

Eigenfunctions of transfer operators and automorphic forms for Hecke triangle groups of infinite covolume

We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume and the dynamics of their geodesic flows

Social Cohesion and Cooperation for Public Goods

A cohesive network keeps groups together and enables members to communicate about and cooperate for public goods. For ongoing cooperation, group members have to know if their group members cooperate or defect, but this information—mostly through gossip—is threatened by noise and biases. If there are redundant information channels, however, errors in monitoring and transmission in one imperfect channel can, to some degree, be corrected by information through another imperfect channel, and may lead to higher levels of cooperation. An influential conceptualization of social cohesion based on redundancy is K-connectivity: the minimum number (K) of node-independent paths connecting pairs of nodes in a group’s network. Ina lab experiment, we tested if higher K-connectivity yields higher levels of cooperation for public goods, controlling for a number of other network effects such as density, size, and average distance. We do not find the hypothesized effect, which might be due to a not-earlier-found shortcoming of the concept, and we propose a solution

Density results for automorphic forms on Hilbert modular groups II

We obtain an asymptotic formula for a weighted sum over cuspidal eigenvalues in a specific region, for \SL_2 over a totally real number field $F$, with discrete subgroup of Hecke type $\Gamma_0(I)$ for a non-zero ideal $I$ in the ring of integers of $F$. The weights are products of Fourier coefficients. This implies in particular the existence of infinitely many cuspidal automorphic representations with multi-eigenvalues in various regions growing to infinity. For instance, in the quadratic case, the regions include floating boxes, floating balls, sectors, slanted strips and products of prescribed small intervals for all but one of the infinite places of $F$. The main tool in the derivation is a sum formula of Kuznetsov type.Comment: Accepted for publication by the Transactions of the American Mathematical Societ

Modelling water-harvesting systems in the arid south of Tunisia using SWAT

In many arid countries, runoff water-harvesting systems support the livelihood of the rural population. Little is known, however, about the effect of these systems on the water balance components of arid watersheds. The objective of this study was to adapt and evaluate the GIS-based watershed model SWAT (Soil Water Assessment Tool) for simulating the main hydrologic processes in arid environments. The model was applied to the 270-km(2) watershed of wadi Koutine in southeast Tunisia, which receives about 200 mm annual rain. The main adjustment for adapting the model to this dry Mediterranean environment was the inclusion of water-harvesting systems, which capture and use surface runoff for crop production in upstream subbasins, and a modification of the crop growth processes. The adjusted version of the model was named SWAT-WH. Model evaluation was performed based on 38 runoff events recorded at the Koutine station between 1973 and 1985. The model predicted that the average annual watershed rainfall of the 12-year evaluation period (209 mm) was split into ET (72%), groundwater recharge (22%) and outflow (6%). The evaluation coefficients for calibration and validation were, respectively, R-2 (coefficient of determination) 0.77 and 0.44; E (Nash-Sutcliffe coefficient) 0.73 and 0.43; and MAE (Mean Absolute Error) 2.6 mm and 3.0 mm, indicating that the model could reproduce the observed events reasonably well. However, the runoff record was dominated by two extreme events, which had a strong effect on the evaluation criteria. Discrepancies remained mainly due to uncertainties in the observed daily rainfall and runoff data. Recommendations for future research include the installation of additional rainfall and runoff gauges with continuous data logging and the collection of more field data to represent the soils and land use. In addition, crop growth and yield monitoring is needed for a proper evaluation of crop production, to allow an economic assessment of the different water uses in the watershed

Spectral Representation for the Effective Macroscopic Response of a Polycrystal: Application to Third-Order Nonlinear Susceptibility

Erratum: In our paper, we show that the spectral representation for isotropic two-component composites also applies to uniaxial polycrystals. We have learned that this result was, in fact, first conjectured by G.W. Milton. While our derivation is more detailed, our result for the spectral function is the same as Milton's. We very much regret not having been aware of this work at the time of writing our paper. Original abstract: We extend the spectral theory used for the calculation of the effective linear response functions of composites to the case of a polycrystalline material with uniaxially anisotropic microscopic symmetry. As an application, we combine these results with a nonlinear decoupling approximation as modified by Ma et al., to calculate the third-order nonlinear optical susceptibility of a uniaxial polycrystal, assuming that the effective dielectric function of the polycrystal can be calculated within the effective-medium approximation.Comment: v2 includes erratum and the original preprin