Localisation of directional scale-discretised wavelets on the sphere

Scale-discretised wavelets yield a directional wavelet framework on the sphere where a signal can be probed not only in scale and position but also in orientation. Furthermore, a signal can be synthesised from its wavelet coefficients exactly, in theory and practice (to machine precision). Scale-discretised wavelets are closely related to spherical needlets (both were developed independently at about the same time) but relax the axisymmetric property of needlets so that directional signal content can be probed. Needlets have been shown to satisfy important quasi-exponential localisation and asymptotic uncorrelation properties. We show that these properties also hold for directional scale-discretised wavelets on the sphere and derive similar localisation and uncorrelation bounds in both the scalar and spin settings. Scale-discretised wavelets can thus be considered as directional needlets.Comment: 28 pages, 8 figures, minor changes to match version accepted for publication by ACH

Counterexample Guided Inductive Optimization Applied to Mobile Robots Path Planning (Extended Version)

We describe and evaluate a novel optimization-based off-line path planning algorithm for mobile robots based on the Counterexample-Guided Inductive Optimization (CEGIO) technique. CEGIO iteratively employs counterexamples generated from Boolean Satisfiability (SAT) and Satisfiability Modulo Theories (SMT) solvers, in order to guide the optimization process and to ensure global optimization. This paper marks the first application of CEGIO for planning mobile robot path. In particular, CEGIO has been successfully applied to obtain optimal two-dimensional paths for autonomous mobile robots using off-the-shelf SAT and SMT solvers.Comment: 7 pages, 14rd Latin American Robotics Symposium (LARS'2017

A worldwide correlation of lactase persistence phenotype and genotypes

Background: The ability of adult humans to digest the milk sugar lactose - lactase persistence - is a dominant Mendelian trait that has been a subject of extensive genetic, medical and evolutionary research. Lactase persistence is common in people of European ancestry as well as some African, Middle Eastern and Southern Asian groups, but is rare or absent elsewhere in the world. The recent identification of independent nucleotide changes that are strongly associated with lactase persistence in different populations worldwide has led to the possibility of genetic tests for the trait. However, it is highly unlikely that all lactase persistence-associated variants are known. Using an extensive database of lactase persistence phenotype frequencies, together with information on how those data were collected and data on the frequencies of lactase persistence variants, we present a global summary of the extent to which current genetic knowledge can explain lactase persistence phenotype frequency. Results: We used surface interpolation of Old World lactase persistence genotype and phenotype frequency estimates obtained from all available literature and perform a comparison between predicted and observed trait frequencies in continuous space. By accommodating additional data on sample numbers and known false negative and false positive rates for the various lactase persistence phenotype tests (blood glucose and breath hydrogen), we also apply a Monte Carlo method to estimate the probability that known lactase persistence-associated allele frequencies can explain observed trait frequencies in different regions. Conclusion: Lactase persistence genotype data is currently insufficient to explain lactase persistence phenotype frequency in much of western and southern Africa, southeastern Europe, the Middle East and parts of central and southern Asia. We suggest that further studies of genetic variation in these regions should reveal additional nucleotide variants that are associated with lactase persistence

High-Density Genotypes of Inbred Mouse Strains: Improved Power and Precision of Association Mapping.

Human genome-wide association studies have identified thousands of loci associated with disease phenotypes. Genome-wide association studies also have become feasible using rodent models and these have some important advantages over human studies, including controlled environment, access to tissues for molecular profiling, reproducible genotypes, and a wide array of techniques for experimental validation. Association mapping with common mouse inbred strains generally requires 100 or more strains to achieve sufficient power and mapping resolution; in contrast, sample sizes for human studies typically are one or more orders of magnitude greater than this. To enable well-powered studies in mice, we have generated high-density genotypes for ∼175 inbred strains of mice using the Mouse Diversity Array. These new data increase marker density by 1.9-fold, have reduced missing data rates, and provide more accurate identification of heterozygous regions compared with previous genotype data. We report the discovery of new loci from previously reported association mapping studies using the new genotype data. The data are freely available for download, and Web-based tools provide easy access for association mapping and viewing of the underlying intensity data for individual loci