Computation and Homotopical Applications of Induced Crossed Modules

We explain how the computation of induced crossed modules allows the computation of certain homotopy 2-types and, in particular, second homotopy groups. We discuss various issues involved in computing induced crossed modules and give some examples and applications.Comment: 15 pages, xypic, latex2

Detection of Water Ice on the Centaur 1997 CU_(26)

We report the detection of the 1.5 and 2.0 μm absorption bands due to water ice in the near-infrared reflection spectrum of the Centaur 1997 CU_(26), which is currently located just outside the heliocentric distance of Saturn. The water ice bands are weaker than those detected on the surface of any other solar system body; the spectrum is well fit with a model surface consisting predominantly of a neutral dark absorbing substance with only ~3% areal coverage of water ice. The spectrum thus appears very different from that of the Centaur 5140 Pholus, although both objects are of similar brightness and are at similar heliocentric distances

String rewriting for Double Coset Systems

In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not suffer this restriction and we present some examples of infinite double coset systems which can now easily be solved using our approach. Even when both enumerative and rewriting techniques are present, our rewriting methods will be competitive because they i) do not require the preliminary calculation of cosets; and ii) as with single coset problems, there are many examples for which rewriting is more effective than enumeration. Automata provide the means for identifying expressions for normal forms in infinite situations and we show how they may be constructed in this setting. Further, related results on logged string rewriting for monoid presentations are exploited to show how witnesses for the computations can be provided and how information about the subgroups and the relations between them can be extracted. Finally, we discuss how the double coset problem is a special case of the problem of computing induced actions of categories which demonstrates that our rewriting methods are applicable to a much wider class of problems than just the double coset problem.Comment: accepted for publication by the Journal of Symbolic Computatio

Keck Speckle Imaging of the White Dwarf G29-38: No Brown Dwarf Companion Detected

The white dwarf Giclas 29-38 has attracted much attention due to its large infrared excess and the suggestion that excess might be due to a companion brown dwarf. We observed this object using speckle interferometry at the Keck telescope, obtaining diffraction-limited resolution (55 milliarcseconds) at K band, and found it unresolved. Assuming the entire K band excess is due to a single point-like companion, we place an upper limit on the binary separation of 30 milliarcseconds, or 0.42 AU at the star's distance of 14.1 pc. This result, combined with astroseismological data and other images of G29-38, supports the hypothesis that the source of the near-infrared excess is not a cool companion but a dust cloud.Comment: 7 pages, 2 figure

Money and happiness : rank of income, not income, affects life satisfaction

Does money buy happiness, or does happiness come indirectly from the higher rank in society that money brings? Here we test a rank hypothesis, according to which people gain utility from the ranked position of their income within a comparison group. The rank hypothesis contrasts with traditional reference income hypotheses, which suggest utility from income depends on comparison to a social group reference norm. We find that the ranked position of an individual’s income predicts general life satisfaction, while absolute income and reference income have no effect. Furthermore, individuals weight upward comparisons more than downward comparisons. According to the rank hypothesis, income and utility are not directly linked: Increasing an individual’s income will only increase their utility if ranked position also increases and will necessarily reduce the utility of others who will lose rank

Bayesian Spatial Binary Regression for Label Fusion in Structural Neuroimaging

Many analyses of neuroimaging data involve studying one or more regions of interest (ROIs) in a brain image. In order to do so, each ROI must first be identified. Since every brain is unique, the location, size, and shape of each ROI varies across subjects. Thus, each ROI in a brain image must either be manually identified or (semi-) automatically delineated, a task referred to as segmentation. Automatic segmentation often involves mapping a previously manually segmented image to a new brain image and propagating the labels to obtain an estimate of where each ROI is located in the new image. A more recent approach to this problem is to propagate labels from multiple manually segmented atlases and combine the results using a process known as label fusion. To date, most label fusion algorithms either employ voting procedures or impose prior structure and subsequently find the maximum a posteriori estimator (i.e., the posterior mode) through optimization. We propose using a fully Bayesian spatial regression model for label fusion that facilitates direct incorporation of covariate information while making accessible the entire posterior distribution. We discuss the implementation of our model via Markov chain Monte Carlo and illustrate the procedure through both simulation and application to segmentation of the hippocampus, an anatomical structure known to be associated with Alzheimer's disease.Comment: 24 pages, 10 figure

Energy Dependence of Scattering Ground State Polar Molecules

We explore the total cross section of ground state polar molecules in an electric field at various energies, focusing on RbCs and RbK. An external electric field polarizes the molecules and induces strong dipolar interactions leading to non-zero partial waves contributing to the scattering even as the collision energy goes to zero. This results in the need to compute scattering problems with many different values of total M to converge the total cross section. An accurate and efficient approximate total cross section is introduced and used to study the low field temperature dependence. To understand the scattering of the polar molecules we compare a semi-classical cross section with quantum unitarity limit. This comparison leads to the ability to characterize the scattering based on the value of the electric field and the collision energy.Comment: Accepted PRA, 10 pages, 5 figure