Interactions between grain size and composition of sediments: two examples

Two contrasting case studies of sediment and detrital mineral composition are investigated in order to outline interactions between chemical composition and grain size. Modern glacial sediments exhibit a strong dependence of the two parameters due to the preferential enrichment of mafic minerals, especially biotite, in the fine-grained fractions. On the other hand, the composition of detrital heavy minerals (here: rutile) appears to be not systematically related to grain-size, but is strongly controlled by location, i.e. the petrology of the source rocks of detrital grains. This supports the use of rutile as a well-suited tracer mineral for provenance studies. The results further suggest that (i) interpretations derived from whole-rock sediment geochemistry should be flanked by grain-size observations, and (ii) a more sound statistical evaluation of these interactions require the development of new tailor-made statistical tools to deal with such so-called two-way compositions

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

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table has n rows and m columns and all probabilities are non-null. This kind of table can be seen as an element in the simplex of n · m parts. In this context, the marginals are identified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclidean elements of the Aitchison geometry of the simplex can also be translated into the table of probabilities: subspaces, orthogonal projections, distances. Two important questions are addressed: a) given a table of probabilities, which is the nearest independent table to the initial one? b) which is the largest orthogonal projection of a row onto a column? or, equivalently, which is the information in a row explained by a column, thus explaining the interaction? To answer these questions three orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independent two-way tables and fully dependent tables representing row-column interaction. An important result is that the nearest independent table is the product of the two (row and column)-wise geometric marginal tables. A corollary is that, in an independent table, the geometric marginals conform with the traditional (arithmetic) marginals. These decompositions can be compared with standard log-linear models. Key words: balance, compositional data, simplex, Aitchison geometry, composition, orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure, contingency table

G+: Enhanced Traffic Grooming in WDM Mesh Networks using Lighttours

In this article, a new technique for grooming low-speed traffic demands into high-speed optical routes is proposed. This enhancement allows a transparent wavelength-routing switch (WRS) to aggregate traffic en route over existing optical routes without incurring expensive optical-electrical-optical (OEO) conversions. This implies that: a) an optical route may be considered as having more than one ingress node (all inline) and, b) traffic demands can partially use optical routes to reach their destination. The proposed optical routes are named "lighttours" since the traffic originating from different sources can be forwarded together in a single optical route, i.e., as taking a "tour" over different sources towards the same destination. The possibility of creating lighttours is the consequence of a novel WRS architecture proposed in this article, named "enhanced grooming" (G+). The ability to groom more traffic in the middle of a lighttour is achieved with the support of a simple optical device named lambda-monitor (previously introduced in the RingO project). In this article, we present the new WRS architecture and its advantages. To compare the advantages of lighttours with respect to classical lightpaths, an integer linear programming (ILP) model is proposed for the well-known multilayer problem: traffic grooming, routing and wavelength assignment The ILP model may be used for several objectives. However, this article focuses on two objectives: maximizing the network throughput, and minimizing the number of optical-electro-optical conversions used. Experiments show that G+ can route all the traffic using only half of the total OEO conversions needed by classical grooming. An heuristic is also proposed, aiming at achieving near optimal results in polynomial time