GPS and property surveying

In 2010 the Global Positioning System (GPS) developed by the United States military was the best known Global Navigation Satellite System (GNSS). Others included Russia’s GLONASS, China’s COMPASS and Europe’s GALILEO systems. Although military satellite navigation systems can be traced back to the 1960s, their civilian uses emerged in the 1980s, initially limited to navigation positioning, not property surveying. Property surveying methods have varied both between and within nations. However, GPS surveying with some supporting legislation, had, by the early years of the 21st century, sufficiently developed to meet the needs of the property sector. This chapter looks at this development, and its implications with respect to cadastral surveying

Calibrated Tree Priors for Relaxed Phylogenetics and Divergence Time Estimation

The use of fossil evidence to calibrate divergence time estimation has a long history. More recently Bayesian MCMC has become the dominant method of divergence time estimation and fossil evidence has been re-interpreted as the specification of prior distributions on the divergence times of calibration nodes. These so-called "soft calibrations" have become widely used but the statistical properties of calibrated tree priors in a Bayesian setting has not been carefully investigated. Here we clarify that calibration densities, such as those defined in BEAST 1.5, do not represent the marginal prior distribution of the calibration node. We illustrate this with a number of analytical results on small trees. We also describe an alternative construction for a calibrated Yule prior on trees that allows direct specification of the marginal prior distribution of the calibrated divergence time, with or without the restriction of monophyly. This method requires the computation of the Yule prior conditional on the height of the divergence being calibrated. Unfortunately, a practical solution for multiple calibrations remains elusive. Our results suggest that direct estimation of the prior induced by specifying multiple calibration densities should be a prerequisite of any divergence time dating analysis

Why a Catholic Medical School?

Editor\u27s Note: In October 1963, for the observance of Founders Day at St. Louis University, the School of Medicine participated in a panel on the objectives of Catholic medical education. The papers of Reverend E.J. Drummond, S.J., C. Rollins Hanlon, M.D., John V. King, M.D., and Edward T. Auer, M.D. are presented here

Comparison of Low Earth Orbit and Geosynchronous Earth Orbits

The technological, environmental, social, and political ramifications of low Earth orbits as compared to geosynchronous Earth orbits for the solar power satellite (SPS) are assessed. The capital cost of the transmitting facilities is dependent on the areas of the antenna and rectenna relative to the requirement of high efficiency power transmission. The salient features of a low orbit Earth orbits are discussed in terms of cost reduction efforts

The space of ultrametric phylogenetic trees

The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data. Hence the question of statistical consistency of such methods is equivalent to the consistency of the summary of the sample. More generally, statistical consistency is ensured by the tree space used to analyse the sample. In this paper, we consider two standard parameterisations of phylogenetic time-trees used in evolutionary models: inter-coalescent interval lengths and absolute times of divergence events. For each of these parameterisations we introduce a natural metric space on ultrametric phylogenetic trees. We compare the introduced spaces with existing models of tree space and formulate several formal requirements that a metric space on phylogenetic trees must possess in order to be a satisfactory space for statistical analysis, and justify them. We show that only a few known constructions of the space of phylogenetic trees satisfy these requirements. However, our results suggest that these basic requirements are not enough to distinguish between the two metric spaces we introduce and that the choice between metric spaces requires additional properties to be considered. Particularly, that the summary tree minimising the square distance to the trees from the sample might be different for different parameterisations. This suggests that further fundamental insight is needed into the problem of statistical consistency of phylogenetic inference methods.Comment: Minor changes. This version has been published in JTB. 27 pages, 9 figure

Bayesian phylogenetic estimation of fossil ages

Recent advances have allowed for both morphological fossil evidence and molecular sequences to be integrated into a single combined inference of divergence dates under the rule of Bayesian probability. In particular the fossilized birth-death tree prior and the Lewis-Mk model of discrete morphological evolution allow for the estimation of both divergence times and phylogenetic relationships between fossil and extant taxa. We exploit this statistical framework to investigate the internal consistency of these models by producing phylogenetic estimates of the age of each fossil in turn, within two rich and well-characterized data sets of fossil and extant species (penguins and canids). We find that the estimation accuracy of fossil ages is generally high with credible intervals seldom excluding the true age and median relative error in the two data sets of 5.7% and 13.2% respectively. The median relative standard error (RSD) was 9.2% and 7.2% respectively, suggesting good precision, although with some outliers. In fact in the two data sets we analyze the phylogenetic estimates of fossil age is on average < 2 My from the midpoint age of the geological strata from which it was excavated. The high level of internal consistency found in our analyses suggests that the Bayesian statistical model employed is an adequate fit for both the geological and morphological data, and provides evidence from real data that the framework used can accurately model the evolution of discrete morphological traits coded from fossil and extant taxa. We anticipate that this approach will have diverse applications beyond divergence time dating, including dating fossils that are temporally unconstrained, testing of the "morphological clock", and for uncovering potential model misspecification and/or data errors when controversial phylogenetic hypotheses are obtained based on combined divergence dating analyses.Comment: 28 pages, 8 figure

Yangians, Grassmannians and T-duality

We investigate the Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory and show that its formulations in twistor and momentum twistor space can be interchanged. In particular we show that the full symmetry can be thought of as the Yangian of the dual superconformal algebra, annihilating the amplitude with the MHV part factored out. The equivalence of this picture with the one where the ordinary superconformal symmetry is thought of as fundamental is an algebraic expression of T-duality. Motivated by this, we analyse some recently proposed formulas, which reproduce different contributions to amplitudes through a Grassmannian integral. We prove their Yangian invariance by directly applying the generators.Comment: 28 pages, 1 figure; v2: minor correction