When a data set can be considered compositional?

Traditionally, compositional data has been identified with closed data, and the simplex has been considered as the natural sample space of this kind of data. In our opinion, the emphasis on the constrained nature ofcompositional data has contributed to mask its real nature. More crucial than the constraining property of compositional data is the scale-invariant property of this kind of data. Indeed, when we are considering only few parts of a full composition we are not working with constrained data but our data are still compositional. We believe that it is necessary to give a more precisedefinition of composition. This is the aim of this oral contribution

CoDa-dendrogram: A new exploratory too

The use of orthonormal coordinates in the simplex and, particularly, balance coordinates, has suggested the use of a dendrogram for the exploratory analysis of compositional data. The dendrogram is based on a sequential binary partition of a compositional vector into groups of parts. At each step of a partition, one group of parts isdivided into two new groups, and a balancing axis in the simplex between both groupsis defined. The set of balancing axes constitutes an orthonormal basis, and the projections of the sample on them are orthogonal coordinates. They can be represented in adendrogram-like graph showing: (a) the way of grouping parts of the compositional vector; (b) the explanatory role of each subcomposition generated in the partition process;(c) the decomposition of the total variance into balance components associated witheach binary partition; (d) a box-plot of each balance. This representation is useful tohelp the interpretation of balance coordinates; to identify which are the most explanatory coordinates; and to describe the whole sample in a single diagram independentlyof the number of parts of the sample

Compositional data analysis with R

Examples of compositional data. The simplex, a suitable sample space for compositional data and Aitchison's geometry. R, a free language and environment for statistical computing and graphics

Exploration of geological variability and possible processes through the use of compositional data analysis: an example using scottish metamorphosed

Developments in the statistical analysis of compositional data over the last twodecades have made possible a much deeper exploration of the nature of variability,and the possible processes associated with compositional data sets from manydisciplines. In this paper we concentrate on geochemical data sets. First we explainhow hypotheses of compositional variability may be formulated within the naturalsample space, the unit simplex, including useful hypotheses of subcompositionaldiscrimination and specific perturbational change. Then we develop through standardmethodology, such as generalised likelihood ratio tests, statistical tools to allow thesystematic investigation of a complete lattice of such hypotheses. Some of these tests are simple adaptations of existing multivariate tests but others require specialconstruction. We comment on the use of graphical methods in compositional dataanalysis and on the ordination of specimens. The recent development of the conceptof compositional processes is then explained together with the necessary tools for astaying- in-the-simplex approach, namely compositional singular value decompositions. All these statistical techniques are illustrated for a substantial compositional data set, consisting of 209 major-oxide and rare-element compositions of metamorphosed limestones from the Northeast and Central Highlands of Scotland.Finally we point out a number of unresolved problems in the statistical analysis ofcompositional processes

New insights on river water chemistry by using non-centred simplicial principal component analysis: a case study

The use of perturbation and power transformation operations permits the investigation of linear processes in the simplex as in a vectorial space. When the investigated geochemical processes can be constrained by the use of well-known starting point, the eigenvectors of the covariance matrix of a non-centred principalcomponent analysis allow to model compositional changes compared with a reference point.The results obtained for the chemistry of water collected in River Arno (central-northern Italy) have open new perspectives for considering relative changes of the analysed variables and to hypothesise the relative effect of different acting physical-chemical processes, thus posing the basis for a quantitative modelling

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 hasn rows and m columns and all probabilities are non-null. This kind of table can beseen as an element in the simplex of n · m parts. In this context, the marginals areidentified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclideanelements of the Aitchison geometry of the simplex can also be translated into the tableof probabilities: subspaces, orthogonal projections, distances.Two important questions are addressed: a) given a table of probabilities, which isthe nearest independent table to the initial one? b) which is the largest orthogonalprojection of a row onto a column? or, equivalently, which is the information in arow explained by a column, thus explaining the interaction? To answer these questionsthree orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independenttwo-way tables and fully dependent tables representing row-column interaction. Animportant result is that the nearest independent table is the product of the two (rowand column)-wise geometric marginal tables. A corollary is that, in an independenttable, 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

Compositional data and Simpson's paradox

Simpson's paradox, also known as amalgamation or aggregation paradox, appears whendealing with proportions. Proportions are by construction parts of a whole, which canbe interpreted as compositions assuming they only carry relative information. TheAitchison inner product space structure of the simplex, the sample space of compositions, explains the appearance of the paradox, given that amalgamation is a nonlinearoperation within that structure. Here we propose to use balances, which are specificelements of this structure, to analyse situations where the paradox might appear. Withthe proposed approach we obtain that the centre of the tables analysed is a naturalway to compare them, which avoids by construction the possibility of a paradox.Key words: Aitchison geometry, geometric mean, orthogonal projection

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Some biological data on cetaceans populations present in the western coasts of Ireland

Ireland’s waters constitute one of the richest habitats for cetaceans in Europe. Marine mammals, particularly cetaceans, are known to be definitive hosts of digestive parasites from the Fm.Anisakidae. The main aim of this study is to collect and compile all the information available out there regarding parasites of the Fm. Anisakidae and their definitive hosts. Secondary objectives are to relate the presence of cetacean species with the presence of parasites of the Fm. Anisakidae and to determine whether this greater number of cetaceans relates to a greater level of parasitism. Prevalence and burdens of anisakids in definitive hosts vary widely with host species, geographic location, and season. Results from several post-mortem exams are given. However, they cannot be compared due to differences in collecting techniques. Anisakis simplex is the most commonly and widespread parasite found in the majority of the samples and in a majornumber of hosts, which include harbour porpoise, short-beaked common dolphin and bottlenose dolphin. Studies on harbour porpoise obtained prevalences of Anisakis spp. of 46% (n=26) and of 100% (n= 12). Another study in common dolphin reported a prevalence of 68% (n=25). Several reasons could influence the variations in the presence of Anisakis. Studies on commerciallyexploited fish have reported prevalences of Anisakis simplex ranging from 65-100% in wildAtlantic salmon and from 42-53.4% in Atlantic cod

ALDH1A3 loss of function causes bilateral anophthalmia/microphthalmia and hypoplasia of the optic nerve and optic chiasm.

The major active retinoid, all-trans retinoic acid, has long been recognized as critical for the development of several organs, including the eye. Mutations in STRA6, the gene encoding the cellular receptor for vitamin A, in patients with Matthew-Wood syndrome and anophthalmia/microphthalmia (A/M), have previously demonstrated the importance of retinol metabolism in human eye disease. We used homozygosity mapping combined with next-generation sequencing to interrogate patients with anophthalmia and microphthalmia for new causative genes. We used whole-exome and whole-genome sequencing to study a family with two affected brothers with bilateral A/M and a simplex case with bilateral anophthalmia and hypoplasia of the optic nerve and optic chiasm. Analysis of novel sequence variants revealed homozygosity for two nonsense mutations in ALDH1A3, c.568A>G, predicting p.Lys190*, in the familial cases, and c.1165A>T, predicting p.Lys389*, in the simplex case. Both mutations predict nonsense-mediated decay and complete loss of function. We performed antisense morpholino (MO) studies in Danio rerio to characterize the developmental effects of loss of Aldh1a3 function. MO-injected larvae showed a significant reduction in eye size, and aberrant axonal projections to the tectum were noted. We conclude that ALDH1A3 loss of function causes anophthalmia and aberrant eye development in humans and in animal model systems.

Planteamiento y optimización de experimentos analíticos

En el prosent projecte s'introduirà la teoria del disseny estadístic d'experiments i ens endinsarem amb més profunditat en els dissenys factorials complerts. Aquest tipus de dissenys, són d'aplicació en sistemes en els que es desitja estudiar la influència que tenen els k factors sobre una variable resposta. Els dissenys factorials complerts, són aquells en els que els k factors poden prendre diversos nivells, i es contemplen totes les posibles combinacions entre ells. Aquest projecte es centrarà més concretament en els dissenys factorials complerts 2, on el número 2 indica que cadascun els factors pren 2 nivells diferents. S'explicarà la teoria corresponent a aquests dissenys amb l'ajuda de diversos exemples, explicant des de un disseny factorial en el que s'estudia la influència de 2 factros (2), fins a un en el que s'estudia la influència de 4 factors (2). També s'ha introduït alguns mètodes que ens ajudaran a trobar models matemàtics que s'ajustin al sistema, i algunes metodologies d'optimització com la metodologia de superficie de resposta o el mètode simplex, per poder treure el màxim partit als nostres recursos. Una vegada introduïts tots aquests conceptes, es procedirà a realitzar un estudi i optimització d'una reacció química que consisteix en l'eliminació del coure d'una dissolució per a la posterior utilització d'aquesta dissolució en la industria per a l'extracció d'or i plata. El segon cas d'aplicació serà la realització de l'estudi i optimització del procés d'obtenció de biodièsel. En ambdós casos s'aplicarà un disseny factorial complet 2, però en cada un s'aplicarà una metodologia diferent per realitzar la optimització. Donat que aquest és un projecte purament centrat en el disseny d'experiments i en el tractament de les dades obtingudes, l'experimentació no ha sigut realitzada per nosaltres, sinó que la informació referent a la mateixa s'ha obtingut d'articles acadèmics realitzats per diferents universitats que han realitzat els estudis corresponents.

CpG-ODN-induced sustained expression of BTLA mediating selective inhibition of human B cells.

BTLA (B- and T-lymphocyte attenuator) is a prominent co-receptor that is structurally and functionally related to CTLA-4 and PD-1. In T cells, BTLA inhibits TCR-mediated activation. In B cells, roles and functions of BTLA are still poorly understood and have never been studied in the context of B cells activated by CpG via TLR9. In this study, we evaluated the expression of BTLA depending on activation and differentiation of human B cell subsets in peripheral blood and lymph nodes. Stimulation with CpG upregulated BTLA, but not its ligand: herpes virus entry mediator (HVEM), on B cells in vitro and sustained its expression in vivo in melanoma patients after vaccination. Upon ligation with HVEM, BTLA inhibited CpG-mediated B cell functions (proliferation, cytokine production, and upregulation of co-stimulatory molecules), which was reversed by blocking BTLA/HVEM interactions. Interestingly, chemokine secretion (IL-8 and MIP1β) was not affected by BTLA/HVEM ligation, suggesting that BTLA-mediated inhibition is selective for some but not all B cell functions. We conclude that BTLA is an important immune checkpoint for B cells, as similarly known for T cells.

Varicella zoster virus reactivation during or immediately following treatment of tegumentary leishmaniasis with antimony compounds

Antimony compounds are the cornerstone treatments for tegumentary leishmaniasis. The reactivation of herpes virus is a side effect described in few reports. We conducted an observational study to describe the incidence of herpes zoster reactivation during treatment with antimony compounds. The global incidence of herpes zoster is approximately 2.5 cases per 1,000 persons per month (or 30 cases per 1,000 persons per year). The estimated incidence of herpes zoster in patients undergoing antimony therapy is higher than previously reported.

Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completelyabsent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and byMartín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involvedparts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method isintroduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that thetheoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approachhas reasonable properties from a compositional point of view. In particular, it is “natural” in the sense thatit recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in thesame paper a substitution method for missing values on compositional data sets is introduced

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel densityestimation techniques in the context of compositional data analysis. Indeed, they gavetwo options for the choice of the kernel to be used in the kernel estimator. One ofthese kernels is based on the use the alr transformation on the simplex SD jointly withthe normal distribution on RD-1. However, these authors themselves recognized thatthis method has some deficiencies. A method for overcoming these dificulties based onrecent developments for compositional data analysis and multivariate kernel estimationtheory, combining the ilr transformation with the use of the normal density with a fullbandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu-Figueras (2006). Here we present an extensive simulation study that compares bothmethods in practice, thus exploring the finite-sample behaviour of both estimators