Operator related to a data matrix: a survey

Abstract: The reading of this article will allow the readers to appropriate the data analysis approach which is proposed. The first paragraph gives the basic tools: the triplet (X, Q, D), the operator related to a data matrix and the coefficient RV. The two following paragraphs show how these tools are used for reading out and solving the problems of joint analysis of several data matrices and of principal component analysis with respect to instrumental variables. The conclusion reminds of the construction of this approach along the past thirty five years

Seasonal changes in the biochemical fate of carbon fixed by benthic diatoms in intertidal sediments

Benthic diatoms are important primary producers in intertidal marine sediments and form the basis of the food web in these ecosystems. In order to investigate the carbon flow within diatom mats, we performed in situ 13C pulse-chase labeling experiments and followed in detail the biochemical fate of carbon fixed by the diatoms for five consecutive days. These labeling experiments were done at approximately 2-monthly intervals during 1 yr in order to cover seasonal variations. The fixed carbon was recovered in individual carbohydrates including extracellular polymeric substances (EPS), amino acids, fatty acids, and nucleic acid bases. In addition, we assessed a variety of environmental parameters and photosynthetic characteristics. The fixed carbon was initially mainly stored as carbohydrate (glucose) while nitrogen-rich compounds (e.g., amino acids and RNA/DNA) were produced more slowly. During the year, the diatoms distributed the photosynthetically fixed carbon differently among the various carbon pools that were measured. In summer, the diatoms decreased carbon fixation and accumulated relatively more lipid as a storage compound (27% 6 2% vs. 12% 6 5% in other seasons). The percentage of fixed carbon that was excreted as EPS was lower in summer compared to other seasons, amounting 9% 6 4% and 21% 6 6%, respectively. Hence, it seemed that the physiology of the microphytobenthos was different during summer and caused by higher light intensity and a shift in nitrogen source

Importance of data structure in comparing two dimension reduction methods for classification of microarray gene expression data

BACKGROUND: With the advance of microarray technology, several methods for gene classification and prognosis have been already designed. However, under various denominations, some of these methods have similar approaches. This study evaluates the influence of gene expression variance structure on the performance of methods that describe the relationship between gene expression levels and a given phenotype through projection of data onto discriminant axes. RESULTS: We compared Between-Group Analysis and Discriminant Analysis (with prior dimension reduction through Partial Least Squares or Principal Components Analysis). A geometric approach showed that these two methods are strongly related, but differ in the way they handle data structure. Yet, data structure helps understanding the predictive efficiency of these methods. Three main structure situations may be identified. When the clusters of points are clearly split, both methods perform equally well. When the clusters superpose, both methods fail to give interesting predictions. In intermediate situations, the configuration of the clusters of points has to be handled by the projection to improve prediction. For this, we recommend Discriminant Analysis. Besides, an innovative way of simulation generated the three main structures by modelling different partitions of the whole variance into within-group and between-group variances. These simulated datasets were used in complement to some well-known public datasets to investigate the methods behaviour in a large diversity of structure situations. To examine the structure of a dataset before analysis and preselect an a priori appropriate method for its analysis, we proposed a two-graph preliminary visualization tool: plotting patients on the Between-Group Analysis discriminant axis (x-axis) and on the first and the second within-group Principal Components Analysis component (y-axis), respectively. CONCLUSION: Discriminant Analysis outperformed Between-Group Analysis because it allows for the dataset structure. An a priori knowledge of that structure may guide the choice of the analysis method. Simulated datasets with known properties are valuable to assess and compare the performance of analysis methods, then implementation on real datasets checks and validates the results. Thus, we warn against the use of unchallenging datasets for method comparison, such as the Golub dataset, because their structure is such that any method would be efficient

Shape - but Not Size - Codivergence between Male and Female Copulatory Structures in Onthophagus Beetles

Genitalia are among the fastest evolving morphological traits in arthropods. Among the many hypotheses aimed at explaining this observation, some explicitly or implicitly predict concomitant male and female changes of genital traits that interact during copulation (i.e., lock and key, sexual conflict, cryptic female choice and pleiotropy). Testing these hypotheses requires insights into whether male and female copulatory structures that physically interact during mating also affect each other's evolution and patterns of diversification. Here we compare and contrast size and shape evolution of male and female structures that are known to interact tightly during copulation using two model systems: (a) the sister species O. taurus (1 native, 3 recently established populations) and O. illyricus, and (b) the species-complex O. fracticornis-similis-opacicollis. Partial Least Squares analyses indicated very little to no correlation between size and shape of copulatory structures, both in males and females. Accordingly, comparing shape and size diversification patterns of genitalia within each sex showed that the two components diversify readily - though largely independently of each other - within and between species. Similarly, comparing patterns of divergence across sexes showed that relative sizes of male and female copulatory organs diversify largely independent of each other. However, performing this analysis for genital shape revealed a signature of parallel divergence. Our results therefore suggest that male and female copulatory structures that are linked mechanically during copulation may diverge in concert with respect to their shapes. Furthermore, our results suggest that genital divergence in general, and co-divergence of male and female genital shape in particular, can evolve over an extraordinarily short time frame. Results are discussed in the framework of the hypotheses that assume or predict concomitant evolutionary changes in male and female copulatory organs

Functional correlates of skull shape in Chiroptera: feeding and echolocation adaptations.

Morphological, functional and behavioural adaptations of bats are among the most diverse within mammals. A strong association between bat skull morphology and feeding behaviour has been suggested previously. However, morphological variation related to other drivers of adaptation, in particular echolocation, remains understudied. We assessed variation in skull morphology with respect to ecology (diet and emission type) and function (bite force, masticatory muscles and echolocation characteristics) using geometric morphometrics and comparative methods. Our study suggests that variation in skull shape of 10 bat families is the result of adaptations to broad dietary categories and sound emission types (oral or nasal). Skull shape correlates with echolocation parameters only in a subsample of insectivorous species, possibly because they (almost) entirely rely on this sensory system for locating and capturing prey. Insectivores emitting low frequencies are characterised by a ventrally tilted rostrum, a trait not associated with feeding parameters. This result questions the validity of a trade-off between feeding and echolocation function. Our study advances understanding of the relationship between skull morphology and specific features of echolocation and suggests that evolutionary constraints due to echolocation may differ between different groups within the Chiroptera