Compositional data analysis of geological variability and process : a case study

Developments in the statistical analysis of compositional data over the last two decades have made possible a much deeper exploration of the nature of variability and the possible processes associated with compositional data sets from many disciplines. In this paper, we concentrate on geochemical data. First, we explain how hypotheses of compositional variability may be formulated within the natural sample space, the unit simplex, including useful hypotheses of sub-compositional discrimination and specific perturbational change. Then we develop through standard methodology, such as generalised likelihood ratio tests, statistical tools to allow the systematic investigation of a lattice of such hypotheses. Some of these tests are simple adaptations of existing multivariate tests but others require special construction. We comment on the use of graphical methods in compositional data analysis and on the ordination of specimens. The recent development of the concept of compositional processes is then explained, together with the necessary tools for a staying-in-the-simplex approach, such as the singular value decomposition of a compositional data set. All these statistical techniques are illustrated for a substantial compositional data set, consisting of 209 major oxide and trace element compositions of metamorphosed limestones from the Grampian Highlands of Scotland. Finally, we discuss some unresolved problems in the statistical analysis of compositional processes

Statistical modelling of compositional problems involving finite probability distributions

Finite probability distributions and compositional data are mathematically similar, consisting of D-dimensional positive vectors with sum 1. Despite this similarity the meaningful forms of analysis in these different areas may require substantially different concepts and statistical modelling. This paper highlights these differences, but also poses the question of how such differences may contribute to understanding in the different areas. At CoDa workshops we have become so accustomed to, even obsessed with, modelling all compositional data problems within a simplex sample space together with its algebraic-geometric Hilbert space structure. The context of this Hilbert sample space is certainly often relevant to the formulation of a number of compositional data problems, but its mathematical elegance should not override appropriate meaningful statistical modelling to resolve the real compositional problem. In this paper I illustrate some relevant modelling by consideration of how a variety of persons differ in their ability to perform inferential tasks particularly in the process of differential diagnosis

Proxies and perplexities: What is the current state of adult (il)literacy in South Africa?

This article provides a detailed analysis of the data from a range of official sources thathave been used to enumerate the number of people who can be described as totally orfunctionally illiterate and estimates whether illiteracy in South Africa can be reduced in theforeseeable future.The study examines the use of years of schooling (conventionally now set at Grade 7) asthe proxy indicator of a person being functionally literate by the main sources, the GeneralPopulation Censuses of 1996, 2001, and 2011 and the annual General Household Surveysand shows that these sources give somewhat contradictory and discordant estimates of therate at which there is gradual decline of illiteracy in South Africa. Other indicators based onself reporting, also used in the Census and General Housing Surveys, show that a largenumber of adult South Africans have difficulty in reading, writing and calculating withnumbers. The study also shows that the data presented by these surveys about participationin literacy and adult basic education and training classes is inaccurate. Note is made thatcurrently South Africa does not make use of any means of direct testing of adult literacy.The article concludes with an exploration on whether South Africa is able to reach the goalof halving illiteracy by 2015. The target of such a reduction is necessarily based on whatthe baseline number of illiterates is as well as decision on whether full function literacymust be obtained or a merely a basic level of alphabetisation. Through a detailed estimationof the results of the Kha Ri Gude adult literacy campaign since 2008 a finding is made thatthe halving of illiteracy will be made, but only at the most basic level, and that attainingfull functional literacy for all South Africans remains a major task

Contributions to parametric statistical theory and practice

In 2 volsSIGLEAvailable from British Library Document Supply Centre- DSC:D34578/81 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Unravelling the Dodecahedral Spaces

The hyperbolic dodecahedral space of Weber and Seifert has a natural non-positively curved cubulation obtained by subdividing the dodecahedron into cubes. We show that the hyperbolic dodecahedral space has a 6-sheeted irregular cover with the property that the canonical hypersurfaces made up of the mid-cubes give a very short hierarchy. Moreover, we describe a 60-sheeted cover in which the associated cubulation is special. We also describe the natural cubulation and covers of the spherical dodecahedral space (aka Poincar\'e homology sphere).Comment: 15 pages + 6 pages appendix, 7 figures, 4 table

The scientific heritage of Richard Henry Dalitz, FRS (1925-2006)

Professor Richard H. Dalitz passed away on January 13, 2006. He was almost 81 years old and his outstanding contributions are intimately connected to some of the major breakthroughs of the 20th century in particle and nuclear physics. These outstanding contributions go beyond the Dalitz Plot, Dalitz Pair and CDD poles that bear his name. He pioneered the theoretical study of strange baryon resonances, of baryon spectroscopy in the quark model, and of hypernuclei, to all of which he made lasting contributions. His formulation of the "$\theta-\tau$ puzzle" led to the discovery that parity is not a symmetry of the weak interactions. A brief scientific evaluation of Dalitz's major contributions to particle and nuclear physics is hereby presented, followed by the first comprehensive list of his scientific publications, as assembled from several sources. The list is divided into two categories: the first, main part comprises Dalitz's research papers and reviews, including topics in the history of particle physics, biographies and reminiscences; the second part lists book reviews, public lectures and obituaries authored by Dalitz, and books edited by him. This provides the first necessary step towards a more systematic research of the Dalitz heritage in modern physics. The present 2016 edition updates the original 2006 edition, published in Nucl. Phys. A 771 (2006) 2-7, doi:10.1016/j.nuclphysa.2006.03.007, and 8-25, doi:10.1016/j.nuclphysa.2006.03.008, by including for the first time a dozen or so of publications, found recently in a list submitted to the Royal Society by Dalitz in 2004, that escaped our attention in the original version.Comment: updates the original edition by including several publications, mostly in category III, that were unknown to us in 200

Secured, not connected: South Africa’s Adult Education system

South Africa has a history of attempts to provide school equivalent education to black adults through night schools. Suppressed in the 1950s and 1960s, they resurfaced after the 1976 Soweto revolt, and in 1996 the Constitution secured adult basic education as a right. Night schools were renamed ‘Public Adult Learning Centres (PALCs)’, and seemed poised to become a powerful delivery mechanism, but continued as inadequate night schools. In 2015 the PALC system was ostensibly transformed into a community college one, but this transformation was based on the weak foundation of inadequate PALCs. A new 2019 plan for the Community Education and Training College System includes long needed major overhauls that must be effected if adults’ right to effective and relevant education is to be finally realised. This paper offers a history of night schools and of policy shifts, and looks at the major shifts promised in the new plan

Inventories to insights

“In the long course of cell life on this earth it remained, for our age, for our generation, to receive the full ownership of our inheritance. We have entered the cell, the Mansion of our birth and started the inventory of our acquired wealth.” (Albert Claude, Nobel lecture, 1974

Correlations Between Oxidase Activity & Dioecism in Phanerograms

Differences in the oxidation potential of tissue fluids of the sexes in dioecious plants have long been known and they appear to be causally related to the contrasts of the staminate and pistillate metabolism (2, 3, 5, 12, 13). Many plant scientists have considered the Manoilev oxidation reaction a valuable test in studies of this type (9, 10, 11). Although its simplicity and wide applicability decommend the Manoilev test, it has not been wholly satisfactory or reliable (8). Color reactions are often unsuitable as quantitative measures of oxidase activity due to the small amount of oxidation necessary to produce marked color change (7). This investigation describes the use of an iodimetric reaction in a study of press sap from staminate and pistillate plants in several dioecious species of flowering plants. Five different dioecious species were investigated comprising asparagus, hemp, Rumex, spinach and Smilax