Distributional equivalence and subcompositional coherence in the analysis of contingency tables, ratio-scale measurements and compositional data

We consider two fundamental properties in the analysis of two-way tables of positive data: the principle of distributional equivalence, one of the cornerstones of correspondence analysis of contingency tables, and the principle of subcompositional coherence, which forms the basis of compositional data analysis. For an analysis to be subcompositionally coherent, it suffices to analyse the ratios of the data values. The usual approach to dimension reduction in compositional data analysis is to perform principal component analysis on the logarithms of ratios, but this method does not obey the principle of distributional equivalence. We show that by introducing weights for the rows and columns, the method achieves this desirable property. This weighted log-ratio analysis is theoretically equivalent to spectral mapping , a multivariate method developed almost 30 years ago for displaying ratio-scale data from biological activity spectra. The close relationship between spectral mapping and correspondence analysis is also explained, as well as their connection with association modelling. The weighted log-ratio methodology is applied here to frequency data in linguistics and to chemical compositional data in archaeology.

Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence

Ratio maps and correspondence analysis

We compare two methods for visualising contingency tables and developa method called the ratio map which combines the good properties of both.The first is a biplot based on the logratio approach to compositional dataanalysis. This approach is founded on the principle of subcompositionalcoherence, which assures that results are invariant to considering subsetsof the composition. The second approach, correspondence analysis, isbased on the chi-square approach to contingency table analysis. Acornerstone of correspondence analysis is the principle of distributionalequivalence, which assures invariance in the results when rows or columnswith identical conditional proportions are merged. Both methods may bedescribed as singular value decompositions of appropriately transformedmatrices. Correspondence analysis includes a weighting of the rows andcolumns proportional to the margins of the table. If this idea of row andcolumn weights is introduced into the logratio biplot, we obtain a methodwhich obeys both principles of subcompositional coherence and distributionalequivalence.

Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence

Equivalence between Redfield- and master-equation approaches for a time-dependent quantum system and coherence control

We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-1/2 system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times T(1) and T(2) (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operator-sum representation and the equivalent phenomenological-operator approach. Finally, we present a protocol to circumvent the decoherence processes due to the loss of energy (and thus, associated with T(1)). To this end, we simply associate the time dependence of the quantum system to an easily achieved modulated frequency. A possible implementation of the protocol is also proposed in the context of nuclear magnetic resonance.

Equivalence between hot tensile and creep testing data for Kanthal A1 alloy

Hot tensile and creep tests were carried out on Kanthal A1 alloy in the temperature range from 600 to 800 degrees C. Each of these sets of data were analyzed separately according to their own methodologies, but an attempt was made to find a correlation between them. A new criterion proposed for converting hot tensile data to creep data, makes possible the analysis of the two kinds of results according to usual creep relations like: Norton, Monkman-Grant, Larson-Miller and others. The remarkable compatibility verified between both sets of data by this procedure strongly suggests that hot tensile data can be converted to creep data and vice-versa for Kanthal A1 alloy, as verified previously for other metallic materials.

Factors influencing biodiversity and distributional gradients in mangroves

Numerous factors affect the distribution of mangrove plants. Most mangrove species are typically dispersed by water-buoyant propagules, allowing them to lake advantage of estuarine, coastal and ocean currents both to replenish existing stands and to establish new ones. The direction they travel depends on sea currents and land barriers, but the dispersal distance depends on the time that propagules remain buoyant and viable. This is expected to differ for each species. Similarly, each species will also differ in establishment success and growth development rate, and each has tolerance limits and growth responses which are apparently unique. Such attributes are presumably responsible for the characteristic distributional ranges of each species, as each responds to the environmental, physical and biotic settings they might occupy. In practice, species are often ordered by the interplay of different factors along environmental gradients, and these may conveniently be considered at four geographic scales-global, regional, estuarine and intertidal. We believe these influencing factors act similarly around the world, and to demonstrate this point, we present examples of distributional gradients from the two global biogeographic regions, the Atlantic East Pacific and the Indo-West Pacific.

A test of the hypothesis of ecological equivalence in an Australian subtropical rain forest

We tested the hypothesis that tree species in a subtropical rain forest in south-east Queensland are ecologically equivalent and therefore have identical environmental requirements for their regeneration. We assessed the evidence that juveniles of species differed in their distributions in treefall gap microsites and along gradients of light availability, soil pH, soil PO4-P availability and soil NO3-N availability. Pairwise comparisons were made on a subset of the common species selected on the basis that they showed a relatively high level of positive association, and would therefore, a priori, be expected to have similar regeneration requirements. Detailed comparisons between the species failed to demonstrate evidence for species differentiation with respect to their tolerance of the disturbance associated with gap microsites or to the gradient of NO3-N availability. However, species differed markedly in their distributions along the soil pH gradient and along the gradients of light availability and soil PO4-P availability. The overall level of ecological differentiation between the species is high: seven out of the 10 possible species pairings showed evidence for ecological differentiation. Such niche differentiation amongst the juveniles of tree species may play an important role in maintaining the species richness of rain-forest communities.

Distributional profiles of homologous open reading frames among bacterial phyla: implications for vertical and lateral transmission

If open reading frames (ORFs) have been transmitted primarily by vertical descent, the distributional profile of orthologues of each ORF should be congruent with the organismal tree or a subtree thereof. Distributional patterns not reconciled parsimoniously with tree-like descent and loss are prima facie evidence of lateral gene transfer. Herein, a rigorous criterion for recognizing ORF distributions is described and implemented; it does not require the inference of phylogenetic trees, nor does it assume any specific tree. Because lineage-specific differences in rates of sequence change can also generate unexpected distributional patterns, rate artefacts, were controlled for by requiring pairwise matches between ORFs to exceed a rigorous inclusion threshold, but absence of a match was assessed against a more-permissive exclusion threshold. Applying this dual-threshold criterion to cross-domain and cross-phylum distributional patterns for ORFs in 23 bacterial genomes, a relative abundance of ORFs was observed that find a match in exactly seven other bacterial phyla; 94-99% of these ORFs also find matches among the Archaea and/or Eukarya. In the larger (and some smaller) bacterial genomes, ORFs that find matches in exactly one other bacterial phylum are also relatively abundant, but fewer of these have non-bacterial homologues; most of their matches within the Bacteria are to the Proteobacteria and/or Firmicutes, which cannot be sister lineages to all bacteria. ORFs that are neither distributed universally among the Bacteria, nor necessarily shared with topologically adjacent lineages, are preferentially enriched in large bacterial genomes.

Mid-point for open-ended income category and the effect of equivalence scales on the income-health relationship

To estimate the mid-point of an open-ended income category and to assess the impact of two equivalence scales on income-health associations. Data were obtained from the 2010 Brazilian Oral Health Survey ( Pesquisa Nacional de Saúde Bucal – SBBrasil 2010). Income was converted from categorical to two continuous variables ( per capita and equivalized) for each mid-point. The median mid-point was R$ 14,523.50 and the mean, R$ 24,507.10. When per capita income was applied, 53% of the population were below the poverty line, compared with 15% with equivalized income. The magnitude of income-health associations was similar for continuous income, but categorized equivalized income tended to decrease the strength of association.

Deciding Kleene Algebra Terms Equivalence in Coq

This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.

Distributional and ecological notes on Polygonanthus amazonicus Ducke

Polygonanthus amazonicus Ducke já foi incorporada em oito famílias diferentes, mas era conhecida de apenas uma árvore desde a primeira coletada em 1929. Uma excursão do projeto Flora Amazônica comprovou sua área de ocorrência, que é de pelo menos 17.500 km2 na região compreendida entre Maués e Borba no Estado do Amazonas. Seu habitat e provável meio de dispersão são descritos. o caso desta e de muitas outras espécies com escassa representação nos herbários demonstra a necessidade de se manter um intenso programa de coleta botânica para se manter uma base mais realista da distribuição de muitas espécies.

Approved Drug Products with Theurapeutic Equivalence Evaluation - 34th edition

The publication, Approved Drug Products with Therapeutic Equivalence Evaluations (the List, commonly known as the Orange Book), identifies drug products approved on the basis of safety and effectiveness by the Food and Drug Administration (FDA) under the Federal Food, Drug, and Cosmetic Act (the Act). Drugs on the market approved only on the basis of safety (covered by the ongoing Drug Efficacy Study Implementation [DESI] review [e.g., Donnatal® Tablets and Librax® Capsules] or pre-1938 drugs [e.g., Phenobarbital Tablets]) are not included in this publication. The main criterion for the inclusion of any product is that the product is the subject of an application with an effective approval that has not been withdrawn for safety or efficacy reasons. Inclusion of products on the List is independent of any current regulatory action through administrative or judicial means against a drug product. In addition, the List contains therapeutic equivalence evaluations for approved multisource prescription drug products. These evaluations have been prepared to serve as public information and advice to state health agencies, prescribers, and pharmacists to promote public education in the area of drug product selection and to foster containment of health care costs. Therapeutic equivalence evaluations in this publication are not official FDA actions affecting the legal status of products under the Act.