Integral points on cubic hypersurfaces

Let g be a cubic polynomial with integer coefficients and n>9 variables, and assume that the congruence g=0 modulo p^k is soluble for all prime powers p^k. We show that the equation g=0 has infinitely many integer solutions when the cubic part of g defines a projective hypersurface with singular locus of dimension <n-10. The proof is based on the Hardy-Littlewood circle method.Comment: 18 page

Control of virtual environments for young people with learning difficulties

Purpose: The objective of this research is to identify the requirements for the selection or development of usable virtual environment (VE) interface devices for young people with learning disabilities. Method: a user-centred design methodology was employed, to produce a design specification for usable VE interface devices. Details of the users' cognitive, physical and perceptual abilities were obtained through observation and normative assessment tests. Conclusions : A review of computer interface technology, including virtual reality and assistive devices, was conducted. As there were no devices identified that met all the requirements of the design specification, it was concluded that there is a need for the design and development of new concepts. Future research will involve concept and prototype development and user-based evaluation of the prototypes

The BHB stars in the Survey Fields of Rodgers et al. (1993): New Observations and Comparisons with other Recent Surveys

We study blue horizontal branch (BHB) and RR Lyrae stars in the Rogers et al. (1993a) fields and compare their velocity and density distributions with other surveys in the same part of the sky. Photometric data are given for 176 early-type stars in the northern field. We identify fourteen BHB stars and four possible BHB stars, and determine the selection efficiency of the Century Survey, the HK Survey, and the SDSS survey for BHB stars. We give light curves and \gamma -radial velocities for three type-ab RR Lyrae stars in the northern field; comparison with the nearby LONEOS Survey shows that there is likely to be an equal number of lower-amplitude type-ab RR Lyrae stars that we do not find. There are therefore at least twice as many BHB stars as type-ab RR Lyrae stars in the northern field--similar to the ratio in the solar neighborhood. The velocity distribution of the southern field shows no evidence for an anomalous thick disk that was found by Gilmore et al. (2002); the halo velocity peaks at a slightly prograde rotational velocity but there is also a significant retrograde halo component in this field. The velocity distribution in the northern field shows no evidence of Galactic rotation for |Z|>4 kpc and a slight prograde motion for |Z|<4 kpc. The space densities of BHB stars in the northern field agree with an extrapolation of the power-law distribution recently derived by de Propris et al. (2010). For |Z|<4 kpc, however, we observe an excess of BHB stars compared with this power-law. We conclude that these BHB stars mostly belong to a spatially flattened, non-rotating inner halo component of the Milky Way in confirmation of the Kinman et al. (2009) analysis of Century Survey BHB stars.Comment: 24 pages, accepted in A

Tensor interaction contributions to single-particle energies

We calculate the contribution of the nucleon-nucleon tensor interaction to single-particle energies with finite-range $G$ matrix potentials and with zero-range Skyrme potentials. The Skx Skyrme parameters including the zero-range tensor terms with strengths calibrated to the finite-range results are refitted to nuclear properties. The fit allows the zero-range proton-neutron tensor interaction as calibrated to the finite-range potential results and that gives the observed change in the single-particle gap $\epsilon$(h$_{11/2}$)-$\epsilon$(g$_{7/2}$) going from $^{114}$Sn to $^{132}$Sn. However, the experimental $\ell$ dependence of the spin-orbit splittings in $^{132}$Sn and $^{208}$Pb is not well described when the tensor is added, due to a change in the radial dependence of the total spin-orbit potential. The gap shift and a good fit to the $\ell$-dependence can be recovered when the like-particle tensor interaction is opposite in sign to that required for the $G$ matrix.Comment: 5 pages, 4 figures, accepted for publication as Rapid Communication in Physical Review

A Template for Implementing Fast Lock-free Trees Using HTM

Algorithms that use hardware transactional memory (HTM) must provide a software-only fallback path to guarantee progress. The design of the fallback path can have a profound impact on performance. If the fallback path is allowed to run concurrently with hardware transactions, then hardware transactions must be instrumented, adding significant overhead. Otherwise, hardware transactions must wait for any processes on the fallback path, causing concurrency bottlenecks, or move to the fallback path. We introduce an approach that combines the best of both worlds. The key idea is to use three execution paths: an HTM fast path, an HTM middle path, and a software fallback path, such that the middle path can run concurrently with each of the other two. The fast path and fallback path do not run concurrently, so the fast path incurs no instrumentation overhead. Furthermore, fast path transactions can move to the middle path instead of waiting or moving to the software path. We demonstrate our approach by producing an accelerated version of the tree update template of Brown et al., which can be used to implement fast lock-free data structures based on down-trees. We used the accelerated template to implement two lock-free trees: a binary search tree (BST), and an (a,b)-tree (a generalization of a B-tree). Experiments show that, with 72 concurrent processes, our accelerated (a,b)-tree performs between 4.0x and 4.2x as many operations per second as an implementation obtained using the original tree update template

Robust nonparametric estimation via wavelet median regression

In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are heavy-tailed, and may not even possess variances or means. Our approach is to first use local medians to turn the problem of nonparametric regression with unknown noise distribution into a standard Gaussian regression problem and then apply a wavelet block thresholding procedure to construct an estimator of the regression function. It is shown that the estimator simultaneously attains the optimal rate of convergence over a wide range of the Besov classes, without prior knowledge of the smoothness of the underlying functions or prior knowledge of the error distribution. The estimator also automatically adapts to the local smoothness of the underlying function, and attains the local adaptive minimax rate for estimating functions at a point. A key technical result in our development is a quantile coupling theorem which gives a tight bound for the quantile coupling between the sample medians and a normal variable. This median coupling inequality may be of independent interest.Comment: Published in at http://dx.doi.org/10.1214/07-AOS513 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Revising old child support orders: The Wisconsin experience

In an effort to make Wisconsin's child support cases more equitable and up-to-date, child support staff reviewed "old" child support orders in thirteen of the state's seventy-two counties. (Reviewing old child support orders is now mandatory under the provisions of the Family Support Act of 1988.) Of the reviewed cases, only 21 percent were revised. Primary reasons for non-revision were the economic circumstances of the noncustodial parent (among welfare cases) and a lack of permission by the custodial parent to proceed (among non-welfare cases). Revised orders increased substantially, an average of $116/month (77 percent). An alternative method of keeping orders current is to express them as a percentage of the noncustodial parent's income; these orders are kept up-to-date automatically and are associated with large increases in collections.

Nonparametric regression in exponential families

Most results in nonparametric regression theory are developed only for the case of additive noise. In such a setting many smoothing techniques including wavelet thresholding methods have been developed and shown to be highly adaptive. In this paper we consider nonparametric regression in exponential families with the main focus on the natural exponential families with a quadratic variance function, which include, for example, Poisson regression, binomial regression and gamma regression. We propose a unified approach of using a mean-matching variance stabilizing transformation to turn the relatively complicated problem of nonparametric regression in exponential families into a standard homoscedastic Gaussian regression problem. Then in principle any good nonparametric Gaussian regression procedure can be applied to the transformed data. To illustrate our general methodology, in this paper we use wavelet block thresholding to construct the final estimators of the regression function. The procedures are easily implementable. Both theoretical and numerical properties of the estimators are investigated. The estimators are shown to enjoy a high degree of adaptivity and spatial adaptivity with near-optimal asymptotic performance over a wide range of Besov spaces. The estimators also perform well numerically.Comment: Published in at http://dx.doi.org/10.1214/09-AOS762 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org