The mass of the Milky Way and M31 using the method of least action

We constrain the most likely range of masses for the Milky Way and M31 using an application of the Numerical Action Method (NAM) that optimizes the fit to observed parameters over a large ensemble of NAM-generated solutions. Our 95% confidence level mass ranges, 1.5-4.5 x 10^12 m_sun for MW and 1.5-5.5 x 10^12 m_sun for M31, are consistent with the upper range of estimates from other methods and suggests that a larger proportion of the total mass becomes detectable when the peculiar motions of many nearby satellites are taken into account in the dynamical analysis. We test the method against simulated Local Group catalogs extracted from the Millennium Run to confirm that mass predictions are consistent with actual galaxy halo masses.Comment: 2 figure

Obstructions to weak decomposability for simplicial polytopes

Provan and Billera introduced notions of (weak) decomposability of simplicial complexes as a means of attempting to prove polynomial upper bounds on the diameter of the facet-ridge graph of a simplicial polytope. Recently, De Loera and Klee provided the first examples of simplicial polytopes that are not weakly vertex-decomposable. These polytopes are polar to certain simple transportation polytopes. In this paper, we refine their analysis to prove that these $d$-dimensional polytopes are not even weakly $O(\sqrt{d})$-decomposable. As a consequence, (weak) decomposability cannot be used to prove a polynomial version of the Hirsch conjecture

Salem numbers and arithmetic hyperbolic groups

In this paper we prove that there is a direct relationship between Salem numbers and translation lengths of hyperbolic elements of arithmetic hyperbolic groups that are determined by a quadratic form over a totally real number field. As an application we determine a sharp lower bound for the length of a closed geodesic in a noncompact arithmetic hyperbolic n-orbifold for each dimension n. We also discuss a "short geodesic conjecture", and prove its equivalence with "Lehmer's conjecture" for Salem numbers.Comment: The exposition in version 3 is more compact; this shortens the paper: 26 pages now instead of 37. A discussion on Lehmer's problem has been added in Section 1.2. Final version, to appear is Trans. AM

Hedonic Prices and House Numbers: The Influence of Feng Shui

In contemporary practice, feng shui incorporates a wide range of concepts considered to affect a person’s luck. These include traditional ideas about site selection and building design, as well as newer beliefs about the “luckiness” of certain numbers. Focusing on an area with a relatively high percentage of Chinese households in Auckland, New Zealand, this paper uses hedonic price analysis to investigate whether house values are affected by lucky and unlucky numbers. Sales transactions for 1989 to 1996 are used in this analysis. The results demonstrate that lucky house numbers are capitalised into house values.Feng shui, hedonic price model, lucky, New Zealand

Do Housing Submarkets Really Matter?

We maintain that the appropriate definition of submarkets depends on the use to which they will be put. For mass appraisal purposes, submarkets should be defined so that the accuracy of hedonic predictions will be optimized. Thus we test whether out-of-sample hedonic value predictions can be improved when a large urban housing market is divided into submarkets and we explore the effects of alternative definitions of submarkets on the accuracy of predictions. We compare a set of submarkets based on small geographical areas defined by real estate appraisers with a set of statistically generated submarkets consisting of dwellings that are similar but not necessarily contiguous. The empirical analysis uses a transactions database from Auckland, New Zealand. Price predictions are found to be most accurate when based on the housing market segmentation used by appraisers. We conclude that housing submarkets matter, and location plays the major role in explaining why they matter.Housing; Submarkets; Price Predictions; Mass Appraisal; Hedonic Method