Where Has the Old Debate Gone? Realism, Institutionalism, and IR Theory

This paper resorts to the contribution of the science philosopher Gerald Holton to map some of the IR arguments and debates in an unconventional and more insightful way. From this starting point, it is sustained that the formerly all-pervading neorealism-neoinstitutionalism debate has lost its appeal and is attracting less and less interest among scholars. It does not structure the approach of the theoretically-oriented authors any more; at least, not with the habitual intensity. More specifically, we defend that the neo-neo rapprochement, even if it could have demonstrated that international cooperation is possible and relevant in a Realist world, it has also impoverished theoretical debate by hiding some of the most significant issues that preoccupied classical transnationalists. Hence, some authors appear to be trying to rescue some of these arguments in an analytical and systematic fashion, opening up a theoretical querelle that may be the next one to pay attention to.

Mixing compositions and other scales

Theory of compositional data analysis is often focused on the composition only. However in practical applications we often treat a composition together with covariableswith some other scale. This contribution systematically gathers and develop statistical tools for this situation. For instance, for the graphical display of the dependenceof a composition with a categorical variable, a colored set of ternary diagrams mightbe a good idea for a first look at the data, but it will fast hide important aspects ifthe composition has many parts, or it takes extreme values. On the other hand colored scatterplots of ilr components could not be very instructive for the analyst, if theconventional, black-box ilr is used.Thinking on terms of the Euclidean structure of the simplex, we suggest to set upappropriate projections, which on one side show the compositional geometry and on theother side are still comprehensible by a non-expert analyst, readable for all locations andscales of the data. This is e.g. done by defining special balance displays with carefully-selected axes. Following this idea, we need to systematically ask how to display, explore,describe, and test the relation to complementary or explanatory data of categorical, real,ratio or again compositional scales.This contribution shows that it is sufficient to use some basic concepts and very fewadvanced tools from multivariate statistics (principal covariances, multivariate linearmodels, trellis or parallel plots, etc.) to build appropriate procedures for all these combinations of scales. This has some fundamental implications in their software implementation, and how might they be taught to analysts not already experts in multivariateanalysis

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible considerationof densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended theEuclidean structure of the simplex to a Hilbert space structure of the set of densitieswithin a bounded interval, and van den Boogaart (2005) generalized this to the setof densities bounded by an arbitrary reference density. From the many variations ofthe Hilbert structures available, we work with three cases. For bounded variables, abasis derived from Legendre polynomials is used. For variables with a lower bound, westandardize them with respect to an exponential distribution and express their densitiesas coordinates in a basis derived from Laguerre polynomials. Finally, for unboundedvariables, a normal distribution is used as reference, and coordinates are obtained withrespect to a Hermite-polynomials-based basis.To get the coordinates, several approaches can be considered. A numerical accuracyproblem occurs if one estimates the coordinates directly by using discretized scalarproducts. Thus we propose to use a weighted linear regression approach, where all k-order polynomials are used as predictand variables and weights are proportional to thereference density. Finally, for the case of 2-order Hermite polinomials (normal reference)and 1-order Laguerre polinomials (exponential), one can also derive the coordinatesfrom their relationships to the classical mean and variance.Apart of these theoretical issues, this contribution focuses on the application of thistheory to two main problems in sedimentary geology: the comparison of several grainsize distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock orsediment, like their composition

Analyzing shapes as compositions of distances

We propose to analyze shapes as “compositions” of distances in Aitchison geometry asan alternate and complementary tool to classical shape analysis, especially when sizeis non-informative.Shapes are typically described by the location of user-chosen landmarks. Howeverthe shape – considered as invariant under scaling, translation, mirroring and rotation– does not uniquely define the location of landmarks. A simple approach is to usedistances of landmarks instead of the locations of landmarks them self. Distances arepositive numbers defined up to joint scaling, a mathematical structure quite similar tocompositions. The shape fixes only ratios of distances. Perturbations correspond torelative changes of the size of subshapes and of aspect ratios. The power transformincreases the expression of the shape by increasing distance ratios. In analogy to thesubcompositional consistency, results should not depend too much on the choice ofdistances, because different subsets of the pairwise distances of landmarks uniquelydefine the shape.Various compositional analysis tools can be applied to sets of distances directly or afterminor modifications concerning the singularity of the covariance matrix and yield resultswith direct interpretations in terms of shape changes. The remaining problem isthat not all sets of distances correspond to a valid shape. Nevertheless interpolated orpredicted shapes can be backtransformated by multidimensional scaling (when all pairwisedistances are used) or free geodetic adjustment (when sufficiently many distancesare used)

A compositional data analysis package for R providing multiple approaches

”compositions” is a new R-package for the analysis of compositional and positive data.It contains four classes corresponding to the four different types of compositional andpositive geometry (including the Aitchison geometry). It provides means for computation,plotting and high-level multivariate statistical analysis in all four geometries.These geometries are treated in an fully analogous way, based on the principle of workingin coordinates, and the object-oriented programming paradigm of R. In this way,called functions automatically select the most appropriate type of analysis as a functionof the geometry. The graphical capabilities include ternary diagrams and tetrahedrons,various compositional plots (boxplots, barplots, piecharts) and extensive graphical toolsfor principal components. Afterwards, ortion and proportion lines, straight lines andellipses in all geometries can be added to plots. The package is accompanied by ahands-on-introduction, documentation for every function, demos of the graphical capabilitiesand plenty of usage examples. It allows direct and parallel computation inall four vector spaces and provides the beginner with a copy-and-paste style of dataanalysis, while letting advanced users keep the functionality and customizability theydemand of R, as well as all necessary tools to add own analysis routines. A completeexample is included in the appendix

News from compositions, the R package

The R-package “compositions”is a tool for advanced compositional analysis. Its basicfunctionality has seen some conceptual improvement, containing now some facilitiesto work with and represent ilr bases built from balances, and an elaborated subsys-tem for dealing with several kinds of irregular data: (rounded or structural) zeroes,incomplete observations and outliers. The general approach to these irregularities isbased on subcompositions: for an irregular datum, one can distinguish a “regular” sub-composition (where all parts are actually observed and the datum behaves typically)and a “problematic” subcomposition (with those unobserved, zero or rounded parts, orelse where the datum shows an erratic or atypical behaviour). Systematic classificationschemes are proposed for both outliers and missing values (including zeros) focusing onthe nature of irregularities in the datum subcomposition(s).To compute statistics with values missing at random and structural zeros, a projectionapproach is implemented: a given datum contributes to the estimation of the desiredparameters only on the subcompositon where it was observed. For data sets withvalues below the detection limit, two different approaches are provided: the well-knownimputation technique, and also the projection approach.To compute statistics in the presence of outliers, robust statistics are adapted to thecharacteristics of compositional data, based on the minimum covariance determinantapproach. The outlier classification is based on four different models of outlier occur-rence and Monte-Carlo-based tests for their characterization. Furthermore the packageprovides special plots helping to understand the nature of outliers in the dataset.Keywords: coda-dendrogram, lost values, MAR, missing data, MCD estimator,robustness, rounded zeros

Runaway Greenhouse Effect in a Semigray Radiative-Convective Model

The effects of the nongray absorption (i.e., atmospheric opacity varying with wavelength) on the possible upper bound of the outgoing longwave radiation (OLR) emitted by a planetary atmosphere have been examined. This analysis is based on the semigray approach, which appears to be a reasonable compromise between the complexity of nongray models and the simplicity of the gray assumption (i.e., atmospheric absorption independent of wavelength). Atmospheric gases in semigray atmospheres make use of constant absorption coefficients in finite-width spectral bands. Here, such a semigray absorption is introduced in a one-dimensional (1D) radiative– convective model with a stratosphere in radiative equilibrium and a troposphere fully saturated with water vapor, which is the semigray gas. A single atmospheric window in the infrared spectrum has been assumed. In contrast to the single absolute limit of OLR found in gray atmospheres, semigray ones may also show a relative limit. This means that both finite and infinite runaway effects may arise in some semigray cases. Of particular importance is the finding of an entirely new branch of stable steady states that does not appear in gray atmospheres. This new multiple equilibrium is a consequence of the nongray absorption only. It is suspected that this new set of stable solutions has not been previously revealed in analyses of radiative–convective models since it does not appear for an atmosphere with nongray parameters similar to those for the earth’s current state

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Centralnotations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform.In this way very elaborated aspects of mathematical statistics can be understoodeasily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating,combination of likelihood and robust M-estimation functions are simple additions/perturbations in A2(Pprior). Weighting observations corresponds to a weightedaddition of the corresponding evidence.Likelihood based statistics for general exponential families turns out to have aparticularly easy interpretation in terms of A2(P). Regular exponential families formfinite dimensional linear subspaces of A2(P) and they correspond to finite dimensionalsubspaces formed by their posterior in the dual information space A2(Pprior).The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P.The discussion of A2(P) valued random variables, such as estimation functionsor likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

The Brauer group and the second Abel-Jacobi map for 0-cycles on algebraic varieties

This paper focuses on the connection between the Brauer group and the 0-cycles of an algebraic variety. We give an alternative construction of the second l-adic Abel-Jacobi map for such cycles, linked to the algebraic geometry of Severi-Brauer varieties on X. This allows us then to relate this Abel-Jacobi map to the standard pairing between 0-cycles and Brauer groups (see [M], [L]), completing results from [M] in this direction. Second, for surfaces, it allows us to present this map according to the more geometrical approach devised by M. Green in the framework of (arithmetic) mixed Hodge structures (see [G]). Needless to say, this paper owes much to the work of U. Jannsen and, especially, to his recently published older letter [J4] to B. Gross.

Bayes linear spaces

Linear spaces consisting of σ-finite probability measures and infinite measures (improper priors and likelihood functions) are defined. The commutative group operation, called perturbation, is the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative. Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. For example, exponential families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in particular some well-known properties of conjugated priors and likelihood functions, are revisited and slightly extended

Determination of the components of the gyration tensor of quartz by oblique incidence transmission two-modulator generalized ellipsometry

The two independent components of the gyration tensor of quartz, g11 and g33, have been spectroscopically measured using a transmission two-modulator generalized ellipsometer. The method is used to determine the optical activity in crystals in directions other than the optic axis, where the linear birefringence is much larger than the optical activity.

Analytical investigation of the atmospheric radiation limits in semigray atmospheres in radiative equilibrium

We model the wavelength-dependent absorption of atmospheric gases by assuming constant mass absorption coefficients in finite-width spectral bands. Such a semigray atmosphere is analytically solved by a discrete ordinate method. The general solution is analyzed for a water vapor saturated atmosphere that also contains a carbon dioxide-like absorbing gas in the infrared. A multiple stable equilibrium with a relative upper limit in the outgoing long-wave radiation is found. Differing from previous radiative–convective models, we find that the amount of carbon dioxide strongly modifies the value of this relative upper limit. This result is also obtained in a gray (i.e., equal absorption of radiation at all infrared wavelengths) water vapor saturated atmosphere. The destabilizing effect of carbon dioxide implies that massive carbon dioxide atmospheres are more likely to reach a runaway greenhouse state than thin carbon dioxide ones