Superrigid subgroups and syndetic hulls in solvable Lie groups

This is an expository paper. It is not difficult to see that every group homomorphism from the additive group Z of integers to the additive group R of real numbers extends to a homomorphism from R to R. We discuss other examples of discrete subgroups D of connected Lie groups G, such that the homomorphisms defined on D can ("virtually") be extended to homomorphisms defined on all of G. For the case where G is solvable, we give a simple proof that D has this property if it is Zariski dense. The key ingredient is a result on the existence of syndetic hulls.Comment: 17 pages. This is the final version that will appear in the volume "Rigidity in Dynamics and Geometry," edited by M. Burger and A. Iozzi (Springer, 2002

An Empirical Assessment of Alternative Models of Risky Decision Making

In this paper, we assess the degree to which four of the most commonly used models of risky decision making can explain the choices individuals make when faced with risky prospects. To make this assessment, we use experimental evidence for two random samples of young adults. Using a robust, nonlinear least squares procedure, we estimate a model that is general enough to approximate Kahnenman and Tversky's prospect theory and that for certain parametric values will yield the expected utility model, a subjective expected utility model and a probability-transform model. We find that the four models considered explain the decision-making behavior of the majority of our subjects. Surprisingly, we find that the choice behavior of the largest number of subjects is consistent with a probability-transform model. Such models have only been developed recently and have not been used in applied settings. We find least support for the expected utility model -- the most widely used model of risky decision making.

Spectrally resolved single-shot wavefront sensing of broadband high-harmonic sources

Wavefront sensors are an important tool to characterize coherent beams of extreme ultraviolet radiation. However, conventional Hartmann-type sensors do not allow for independent wavefront characterization of different spectral components that may be present in a beam, which limits their applicability for intrinsically broadband high-harmonic generation (HHG) sources. Here we introduce a wavefront sensor that measures the wavefronts of all the harmonics in a HHG beam in a single camera exposure. By replacing the mask apertures with transmission gratings at different orientations, we simultaneously detect harmonic wavefronts and spectra, and obtain sensitivity to spatiotemporal structure such as pulse front tilt as well. We demonstrate the capabilities of the sensor through a parallel measurement of the wavefronts of 9 harmonics in a wavelength range between 25 and 49 nm, with up to lambda/32 precision.Comment: 12 pages, 6 figure

Numerical Investigation of a Mesoscopic Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process

In this paper a spatial homogeneous vehicular traffic flow model based on a stochastic master equation of Boltzmann type in the acceleration variable is solved numerically for a special driver interaction model. The solution is done by a modified direct simulation Monte Carlo method (DSMC) well known in non equilibrium gas kinetic. The velocity and acceleration distribution functions in stochastic equilibrium, mean velocity, traffic density, ACN, velocity scattering and correlations between some of these variables and their car density dependences are discussed.Comment: 23 pages, 10 figure

Magnetism and superconductivity driven by identical 4ff states in a heavy-fermion metal

The apparently inimical relationship between magnetism and superconductivity has come under increasing scrutiny in a wide range of material classes, where the free energy landscape conspires to bring them in close proximity to each other. This is particularly the case when these phases microscopically interpenetrate, though the manner in which this can be accomplished remains to be fully comprehended. Here, we present combined measurements of elastic neutron scattering, magnetotransport, and heat capacity on a prototypical heavy fermion system, in which antiferromagnetism and superconductivity are observed. Monitoring the response of these states to the presence of the other, as well as to external thermal and magnetic perturbations, points to the possibility that they emerge from different parts of the Fermi surface. This enables a single 4$f$ state to be both localized and itinerant, thus accounting for the coexistence of magnetism and superconductivity.Comment: 4 pages, 4 figure

Cost-benefit analysis for commissioning decisions in GEO600

Gravitational wave interferometers are complex instruments, requiring years of commissioning to achieve the required sensitivities for the detection of gravitational waves, of order 10^-21 in dimensionless detector strain, in the tens of Hz to several kHz frequency band. Investigations carried out by the GEO600 detector characterisation group have shown that detector characterisation techniques are useful when planning for commissioning work. At the time of writing, GEO600 is the only large scale laser interferometer currently in operation running with a high duty factor, 70%, limited chiefly by the time spent commissioning the detector. The number of observable gravitational wave sources scales as the product of the volume of space to which the detector is sensitive and the observation time, so the goal of commissioning is to improve the detector sensitivity with the least possible detector down time. We demonstrate a method for increasing the number of sources observable by such a detector, by assessing the severity of non-astrophysical noise contaminations to efficiently guide commissioning. This method will be particularly useful in the early stages and during the initial science runs of the aLIGO and adVirgo detectors, as they are brought up to design performance.Comment: 17 pages, 17 figures, 2 table

Gamification techniques for raising cyber security awareness

Due to the prevalence of online services in modern society, such as internet banking and social media, it is important for users to have an understanding of basic security measures in order to keep themselves safe online. However, users often do not know how to make their online interactions secure, which demonstrates an educational need in this area. Gamification has grown in popularity in recent years and has been used to teach people about a range of subjects. This paper presents an exploratory study investigating the use of gamification techniques to educate average users about password security, with the aim of raising overall security awareness. To explore the impact of such techniques, a role-playing quiz application (RPG) was developed for the Android platform to educate users about password security. Results gained from the work highlightedthat users enjoyed learning via the use of the password application, and felt they benefitted from the inclusion of gamification techniques. Future work seeks to expand the prototype into a full solution, covering a range of security awareness issues