Compositional Data Analysis with R

R from http://www.r-project.org/ is ‘GNU S’ – a language and environment for statistical computingand graphics. The environment in which many classical and modern statistical techniques havebeen implemented, but many are supplied as packages. There are 8 standard packages and many moreare available through the cran family of Internet sites http://cran.r-project.org .We started to develop a library of functions in R to support the analysis of mixtures and our goal isa MixeR package for compositional data analysis that provides support foroperations on compositions: perturbation and power multiplication, subcomposition with or withoutresiduals, centering of the data, computing Aitchison’s, Euclidean, Bhattacharyya distances,compositional Kullback-Leibler divergence etc.graphical presentation of compositions in ternary diagrams and tetrahedrons with additional features:barycenter, geometric mean of the data set, the percentiles lines, marking and coloring ofsubsets of the data set, theirs geometric means, notation of individual data in the set . . .dealing with zeros and missing values in compositional data sets with R procedures for simpleand multiplicative replacement strategy,the time series analysis of compositional data.We’ll present the current status of MixeR development and illustrate its use on selected data sets

On the relationship between connections and the asymptotic properties of predictive distributions

In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributions, using the Kullback-Leibler divergence as a loss function. He showed that estimative distributions with asymptotically efficient estimators can be improved by predictive distributions that do not belong to the model. The model is assumed to be a multidimensional curved exponential family. In this paper we generalize the result assuming as a loss function any f divergence. A relationship arises between alpha connections and optimal predictive distributions. In particular, using an alpha divergence to measure the goodness of a predictive distribution, the optimal shift of the estimate distribution is related to alpha-covariant derivatives. The expression that we obtain for the asymptotic risk is also useful to study the higher-order asymptotic properties of an estimator, in the mentioned class of loss functions.

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 Voting Practice of the Fifteen in the UN General Assembly: Convergence and Divergence

The EU has, since the early days of the Community, had the ambition to speak with ‘a single voice’ in international fora, in particular in the United Nations’ General Assembly. This aspiration, which has become more pronounced since the inauguration of the CFSP, has not always been easy to achieve due to domestic or international level factors affecting the EU member states. However, in the last decade there has been a dramatic increase in convergence in the Fifteen’s voting record. This paper contemplates the underlying reasons for such a convergence

Globalization, Divergence and Stagnation

In a world where poor countries provide weak protection for intellectual property rights, market integration shifts technical change in favor of rich nations. Through this channel, free trade may amplify international income differences. At the same time, integration with countries where intellectual property rights are weakly protected can slow down the world growth rate. A crucial implication of these results is that protection of intellectual property is most beneficial in open countries. This prediction, which is novel in the literature, finds support in the data on a panel of 53 countries observed in the years 1965-1990.

Patterns of convergence and divergence in the euro area

We study the extent of macroeconomic convergence/divergence among euro area countries. Our analysis focuses on four variables (unemployment, inflation, relative prices and the current account), and seeks to uncover the role played by monetary union as a convergence factor by using non-euro developed economies and the pre-EMU period as control samples.

Odorant Receptor (Or) genes: polymorphism and divergence in the D. melanogaster and D. pseudoobscura Lineages

Background: In insects, like in most invertebrates, olfaction is the principal sensory modality, which provides animals with essential information for survival and reproduction. Odorant receptors are involved in this response, mediating interactions between an individual and its environment, as well as between individuals of the same or different species. The adaptive importance of odorant receptors renders them good candidates for having their variation shaped by natural selection. Methodology/Principal Findings: We analyzed nucleotide variation in a subset of eight Or genes located on the 3L chromosomal arm of Drosophila melanogaster in a derived population of this species and also in a population of Drosophila pseudoobscura. Some heterogeneity in the silent polymorphism to divergence ratio was detected in the D. melanogaster/D. simulans comparison, with a single gene (Or67b) contributing ~37% to the test statistic. However, no other signals of a very recent selective event were detected at this gene. In contrast, at the speciation timescale, the MK test uncovered the footprint of positive selection driving the evolution of two of the encoded proteins in both D. melanogaster ¿OR65c and OR67a ¿and D. pseudoobscura ¿OR65b1 and OR67c. Conclusions: The powerful polymorphism/divergence approach provided evidence for adaptive evolution at a rather high proportion of the Or genes studied after relatively recent speciation events. It did not provide, however, clear evidence for very recent selective events in either D. melanogaster or D. pseudoobscura.

The genomic distribution of intraspecific and interspecific sequence divergence of human segmental duplications relative to human/chimpanzee chromosomal rearrangements

Background: It has been suggested that chromosomal rearrangements harbor the molecular footprint of the biological phenomena which they induce, in the form, for instance, of changes in the sequence divergence rates of linked genes. So far, all the studies of these potential associations have focused on the relationship between structural changes and the rates of evolution of single-copy DNA and have tried to exclude segmental duplications (SDs). This is paradoxical, since SDs are one of the primary forces driving the evolution of structure and function in our genomes and have been linked not only with novel genes acquiring new functions, but also with overall higher DNA sequence divergence and major chromosomal rearrangements.Results: Here we take the opposite view and focus on SDs. We analyze several of the features of SDs, including the rates of intraspecific divergence between paralogous copies of human SDs and of interspecific divergence between human SDs and chimpanzee DNA. We study how divergence measures relate to chromosomal rearrangements, while considering other factors that affect evolutionary rates in single copy DNA. Conclusion: We find that interspecific SD divergence behaves similarly to divergence of single-copy DNA. In contrast, old and recent paralogous copies of SDs do present different patterns of intraspecific divergence. Also, we show that some relatively recent SDs accumulate in regions that carry inversions in sister lineages.

The null divergence factor

Let (P, Q) be a C 1 vector field defined in a open subset U ⊂ R2 . We call a null divergence factor a C 1 solution V (x, y) of the equation P ∂V + Q ∂V = ∂P + ∂Q V . In previous works ∂x ∂y ∂x ∂y it has been shown that this function plays a fundamental role in the problem of the center and in the determination of the limit cycles. In this paper we show how to construct systems with a given null divergence factor. The method presented in this paper is a generalization of the classical Darboux method to generate integrable systems.

Genetic variation in the European hake, Merluccius merluccius. Description of protein loci and genetic divergence between Atlantic and Mediterranean populations = Anàlisi de la variabilitat genètica en el lluç europeu, Merluccius merluccius. Descripció dels loci electroforètics i divergència genètica entre les poblacions atlàntica i mediterrània

We examined the genetic population structure of the european hake (Merluccius merluccius) using electrophoretically detectable population markers in 35 protein loci. Samples were collected from 7 locations in the Atlantic Ocean and Mediterranean Sea. Six loci were polymorphic using the 0.05 criterion of polymorphism. Sample heterozigosities ranged from 0.052 to 0.072 and averaged 0.0625. In this study, significant allele frequency differences were detected between Atlantic and Mediterranean populations in three polymorphic loci: GAPDH-1*, GPI-2* and SOD-1*. Two major genetic groups were considered: a North-Atlantic stock and the Mediterranean stock. The Nei genetic distance, D, (based on 33 loci) between samples from these two groups ranged from 0.002 to 0.006. Genetic differenciation between these areas appears to reflect the barrier effect of Strait of Gibraltar. On average over loci, 96.92 % of the total gene diversity was contained within samples, 0.23 % expressed differences among locations within areas, and 2.64 % differences between regions. A review of morphological variation together with the genetic data presented here suggest that the populations of hake from these areas are subdivided into two different stocks: the North-Atlantic stock and the Mediterranean stock. The most conservative approach to the management of these stocks is to consider the Atlantic and Mediterranean stocks independently from oneanother

Convergence across countries and regions: theory and empirics

This paper surveys the recent literature on convergence across countries and regions. I discuss the main convergence and divergence mechanisms identified in the literature and develop a simple model that illustrates their implications for income dynamics. I then review the existing empirical evidence and discuss its theoretical implications. Early optimism concerning the ability of a human capital-augmented neoclassical model to explain productivity differences across economies has been questioned on the basis of more recent contributions that make use of panel data techniques and obtain theoretically implausible results. Some recent research in this area tries to reconcile these findings with sensible theoretical models by exploring the role of alternative convergence mechanisms and the possible shortcomings of panel data techniques for convergence analysis.

Allocative and productive efficiency in REE with asymetric information

We characterize the divergence between informational and economic efficiency in a rational expectations competitive market with asymmetric information about the costs of production. We find that prices may contain too much or too little information with respect to incentive efficient allocations depending on whether the main role of the price is, respectively, the traditional as index of scarcity or informational. Only when REE degenerate to Cournot equilibria the market solution does not show llocative inefficiency. With multidimensional uncertainty we find that the REE price does not have in general the incentive efficient information mix: It pays to sacrifice allocative efficiency at the REE to improve productive efficiency.

Environmental management problems, future generations and social decisions

The decisions of many individuals and social groups, taking according to well-defined objectives, are causing serious social and environmental problems, in spite of following the dictates of economic rationality. There are many examples of serious problems for which there are not yet appropriate solutions, such as management of scarce natural resources including aquifer water or the distribution of space among incompatible uses. In order to solve these problems, the paper first characterizes the resources and goods involved from an economic perspective. Then, for each case, the paper notes that there is a serious divergence between individual and collective interests and, where possible, it designs the procedure for solving the conflict of interests. With this procedure, the real opportunities for the application of economic theory are shown, and especially the theory on collective goods and externalities. The limitations of conventional economic analysis are shown and the opportunity to correct the shortfalls is examined. Many environmental problems, such as climate change, have an impact on different generations that do not participate in present decisions. The paper shows that for these cases, the solutions suggested by economic theory are not valid. Furthermore, conventional methods of economic valuation (which usually help decision-makers) are unable to account for the existence of different generations and tend to obviate long-term impacts. The paper analyzes how economic valuation methods could account for the costs and benefits enjoyed by present and future generations. The paper studies an appropriate consideration of preferences for future consumption and the incorporation of sustainability as a requirement in social decisions, which implies not only more efficiency but also a fairer distribution between generations than the one implied by conventional economic analysis.

Business-science research collaboration under moral hazard

I analyze, in the context of business and science research collaboration, how the characteristics of partnership agreements are the result of an optimal contract between partners. The final outcome depends on the structure governing the partnership, and on the informational problems towards the efforts involved. The positive effect that the effort of each party has on the success of the other party, makes collaboration a preferred solution. Divergence in research goals may, however, create conflicts between partners. This paper shows how two different structures of partnership governance (a centralized, and a decentralized ones) may optimally use the type of project to motivate the supply of non-contractible efforts. Decentralized structure, however, always choose a project closer to its own preferences. Incentives may also come from monetary transfers, either from partners sharing each other benefits, or from public funds. I derive conditions under which public interventio

Anàlisi i tècniques de processat del senyal per a la generació de mapes eòlics

L’emplaçament del projecte es situa a un parc eòlic marítim, on es vol observar el vent a través del radar VAD, Velocity Azimuth Display, per poder controlar la velocitat de rotació dels aerogeneradors, i poder substituir els actuals anemòmetres. No ens centrarem en el control d’aquest, sinó que l’objectiu principal d’aquest projecte és analitzar el funcionament i processat de dades del VAD. Es proposaran, simularan i estudiaran noves tècniques d’estimació espectral per obtenir una millora important amb les mesures de velocitat, direcció i divergència del vent, per tal de construir un radar més robust a pertorbacions. A més a més, també il·lustrarem mapes eòlics obtinguts a partir de tot el processat.