News from compositions, the R package

The R-package “compositions”is a tool for advanced compositional analysis. Its basic functionality has seen some conceptual improvement, containing now some facilities to 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 is based 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, or else where the datum shows an erratic or atypical behaviour). Systematic classification schemes are proposed for both outliers and missing values (including zeros) focusing on the nature of irregularities in the datum subcomposition(s). To compute statistics with values missing at random and structural zeros, a projection approach is implemented: a given datum contributes to the estimation of the desired parameters only on the subcompositon where it was observed. For data sets with values below the detection limit, two different approaches are provided: the well-known imputation technique, and also the projection approach. To compute statistics in the presence of outliers, robust statistics are adapted to the characteristics of compositional data, based on the minimum covariance determinant approach. The outlier classification is based on four different models of outlier occur- rence and Monte-Carlo-based tests for their characterization. Furthermore the package provides 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

Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals

A novel test of spatial independence of the distribution of crystals or phases in rocks based on compositional statistics is introduced. It improves and generalizes the common joins-count statistics known from map analysis in geographic information systems. Assigning phases independently to objects in RD is modelled by a single-trial multinomial random function Z(x), where the probabilities of phases add to one and are explicitly modelled as compositions in the K-part simplex SK. Thus, apparent inconsistencies of the tests based on the conventional joins{count statistics and their possibly contradictory interpretations are avoided. In practical applications we assume that the probabilities of phases do not depend on the location but are identical everywhere in the domain of de nition. Thus, the model involves the sum of r independent identical multinomial distributed 1-trial random variables which is an r-trial multinomial distributed random variable. The probabilities of the distribution of the r counts can be considered as a composition in the Q-part simplex SQ. They span the so called Hardy-Weinberg manifold H that is proved to be a K-1-affine subspace of SQ. This is a generalisation of the well-known Hardy-Weinberg law of genetics. If the assignment of phases accounts for some kind of spatial dependence, then the r-trial probabilities do not remain on H. This suggests the use of the Aitchison distance between observed probabilities to H to test dependence. Moreover, when there is a spatial uctuation of the multinomial probabilities, the observed r-trial probabilities move on H. This shift can be used as to check for these uctuations. A practical procedure and an algorithm to perform the test have been developed. Some cases applied to simulated and real data are presented. Key words: Spatial distribution of crystals in rocks, spatial distribution of phases, joins-count statistics, multinomial distribution, Hardy-Weinberg law, Hardy-Weinberg manifold, Aitchison geometry

Procedural Meaning Explicatures in the Development of New Subordination Strategies in Romance

The sociocultural changes that led to the genesis of Romance languages widened the gap between oral and written patterns, which display different discoursive and linguistic devices. In early documents, discoursive implicatures connecting propositions were not generally codified, so that the reader should furnish the correct interpretation according to his own perception of real facts; which can still be attested in current oral utterances. Once Romance languages had undergone several levelling processes which concluded in the first standardizations, implicatures became explicatures and were syntactically codified by means of univocal new complex conjunctions. As a consequence of the emergence of these new subordination strategies, a freer distribution of the information conveyed by the utterances is allowed. The success of complex structural patterns ran alongside of the genesis of new narrative genres and the generalization of a learned rhetoric. Both facts are a spontaneous effect of new approaches to the act of reading. Ancient texts were written to be read to a wide audience, whereas those printed by the end of the XV th century were conceived to be read quietly, in a low voice, by a private reader. The goal of this paper is twofold, since we will show that: a) The development of new complex conjunctions through the history of Romance languages accommodates to four structural patterns that range from parataxis to hypotaxis. b) This development is a reflex of the well known grammaticalization path from discourse to syntax that implies the codification of discoursive strategies (Givón 2 1979, Sperber and Wilson 1986, Carston 1988, Grice 1989, Bach 1994, Blackemore 2002, among others]