Computing the Arithmetic Genus of Hilbert Modular Fourfolds

The Hilbert modular fourfold determined by the totally real quartic number field k is a desingularization of a natural compactification of the quotient space Gamma(k)\H-4, where Gamma(k) = PSL2(O-k) acts on H-4 by fractional linear transformations via the four embeddings of k into R. The arithmetic genus, equal to one plus the dimension of the space of Hilbert modular cusp forms of weight (2, 2, 2, 2), is a birational invariant useful in the classification of these varieties. In this work, we describe an algorithm allowing for the automated computation of the arithmetic genus and give sample results

Computing the Arithmetic Genus of Hilbert Modular Fourfolds

The Hilbert modular fourfold determined by the totally real quartic number field k is a desingularization of a natural compactification of the quotient space Gamma(k)\H-4, where Gamma(k) = PSL2(O-k) acts on H-4 by fractional linear transformations via the four embeddings of k into R. The arithmetic genus, equal to one plus the dimension of the space of Hilbert modular cusp forms of weight (2, 2, 2, 2), is a birational invariant useful in the classification of these varieties. In this work, we describe an algorithm allowing for the automated computation of the arithmetic genus and give sample results

Click Here Now: The Impact of Color and Size on Advertisements

Businesses and companies are always trying to find the most effective way to advertise their products to create higher click-through rates, increasing the intent to purchase, and consequently raising sales and revenue. This research examines the effect that several different design elements of an online advertisement have on the attitudes or behaviors of consumers. An online survey was sent out to students at Gettysburg College, consisting of pairs of advertisements differing either in color, hue, or size. Participants in the online survey were asked to click on the image that they preferred. All three of these categories had a significant effect on click-through rates on advertisements. Highly-saturated advertisements were significantly preferred over the low-saturated advertisements. There was a significant difference in size preference, but the average preference was evenly split between square and vertical rectangle sizes in the shape category. Warm colors were marginally preferred over cool colors in the images that were used. These findings are important for businesses in order for them to receive the greatest number of clicks on products advertised because those clicks lead to purchases of the product. Further research could also include the examination of other characteristics of advertisements

Calibration of liquid argon and neon detectors with 83Krm^{83}Kr^m

We report results from tests of $^{83}$Kr$^{\mathrm{m}}$, as a calibration source in liquid argon and liquid neon. $^{83}$Kr$^{\mathrm{m}}$ atoms are produced in the decay of $^{83}$Rb, and a clear $^{83}$Kr$^{\mathrm{m}}$ scintillation peak at 41.5 keV appears in both liquids when filling our detector through a piece of zeolite coated with $^{83}$Rb. Based on this scintillation peak, we observe 6.0 photoelectrons/keV in liquid argon with a resolution of 6% ($\sigma$/E) and 3.0 photoelectrons/keV in liquid neon with a resolution of 19% ($\sigma$/E). The observed peak intensity subsequently decays with the $^{83}$Kr$^{\mathrm{m}}$ half-life after stopping the fill, and we find evidence that the spatial location of $^{83}$Kr$^{\mathrm{m}}$ atoms in the chamber can be resolved. $^{83}$Kr$^{\mathrm{m}}$ will be a useful calibration source for liquid argon and neon dark matter and solar neutrino detectors.Comment: 7 pages, 12 figure

Study of nuclear recoils in liquid argon with monoenergetic neutrons

For the development of liquid argon dark matter detectors we assembled a setup in the laboratory to scatter neutrons on a small liquid argon target. The neutrons are produced mono-energetically (E_kin=2.45 MeV) by nuclear fusion in a deuterium plasma and are collimated onto a 3" liquid argon cell operating in single-phase mode (zero electric field). Organic liquid scintillators are used to tag scattered neutrons and to provide a time-of-flight measurement. The setup is designed to study light pulse shapes and scintillation yields from nuclear and electronic recoils as well as from {\alpha}-particles at working points relevant to dark matter searches. Liquid argon offers the possibility to scrutinise scintillation yields in noble liquids with respect to the populations of the two fundamental excimer states. Here we present experimental methods and first results from recent data towards such studies.Comment: 9 pages, 8 figures, proceedings of TAUP 2011, to be published in Journal of Physics: Conference Series (JCPS

Curvature-coupling dependence of membrane protein diffusion coefficients

We consider the lateral diffusion of a protein interacting with the curvature of the membrane. The interaction energy is minimized if the particle is at a membrane position with a certain curvature that agrees with the spontaneous curvature of the particle. We employ stochastic simulations that take into account both the thermal fluctuations of the membrane and the diffusive behavior of the particle. In this study we neglect the influence of the particle on the membrane dynamics, thus the membrane dynamics agrees with that of a freely fluctuating membrane. Overall, we find that this curvature-coupling substantially enhances the diffusion coefficient. We compare the ratio of the projected or measured diffusion coefficient and the free intramembrane diffusion coefficient, which is a parameter of the simulations, with analytical results that rely on several approximations. We find that the simulations always lead to a somewhat smaller diffusion coefficient than our analytical approach. A detailed study of the correlations of the forces acting on the particle indicates that the diffusing inclusion tries to follow favorable positions on the membrane, such that forces along the trajectory are on average smaller than they would be for random particle positions.Comment: 16 pages, 8 figure