José L. Vicente-Villardón

Identifying molecular markers associated with classification of genotypes by External Logistic Biplots

UNLABELLED For characterization of genetic diversity in genotypes several molecular techniques, usually resulting in a binary data matrix, have been used. Despite the fact that in Cluster Analysis (CA) and Principal Coordinates Analysis (PCoA) the interpretation of the variables responsible for grouping is not straightforward, these methods are commonly used to classify genotypes using DNA molecular markers. In this article, we present a novel algorithm that uses a combination of PCoA, CA and Logistic Regression (LR), as a better way to interpret the variables (alleles or bands) associated to the classification of genotypes. The combination of three standard techniques with some new ideas about the geometry of the procedures, allows constructing an External Logistic Biplot (ELB) that helps in the interpretation of the variables responsible for the classification or ordination. An application of the method to study the genetic diversity of four populations from Africa, Asia and Europe, using the HapMap data is included. AVAILABILITY The Matlab code for implementing the methods may be obtained from the web site: http://biplot.usal.es.

Comparison and integration of subspaces from a biplot perspective

When one has information about a set of individuals on several variables, in different groups or contexts, and multivariate analysis is applied to each group the following questions arise: which groups show a similar response? how do the groups differ? how do the individuals differ in their responses in the different groups? These issues have led us to address a very interesting question in the practical context; the comparison and integration of the structures resulting from several multivariate analyses. Here we propose a method for the comparison and integration of the results arising from two Biplot analyses applied to the same variables in two different groups of individuals. By extension, we also develop the case of more than two Biplot analyses. Emphasis is placed on the underlying geometry and the interpretation of results, for which we offer indices that allow us to study the integrated structures and perform comparative analyses.

Motor Improvement of Skilled Forelimb Use Induced by Treatment with Growth Hormone and Rehabilitation Is Dependent on the Onset of the Treatment after Cortical Ablation

We previously demonstrated that the administration of GH immediately after severe motor cortex injury, in rats, followed by rehabilitation, improved the functionality of the affected limb and reexpressed nestin in the contralateral motor cortex. Here, we analyze whether these GH effects depend on a time window after the injury and on the reexpression of nestin and actin. Injured animals were treated with GH (0.15 mg/kg/day) or vehicle, at days 7, 14, and 35 after cortical ablation. Rehabilitation was applied at short and long term (LTR) after the lesion and then sacrificed. Nestin and actin were analyzed by immunoblotting in the contralateral motor cortex. Giving GH at days 7 or 35 after the lesion, but not 14 days after it, led to a remarkable improvement in the functionality of the affected paw. Contralateral nestin and actin reexpression was clearly higher in GH-treated animals, probably because compensatory brain plasticity was established. GH and immediate rehabilitation are key for repairing brain injuries, with the exception of a critical time period: GH treatment starting 14 days after the lesion. Our data also indicate that there is not a clear plateau in the recovery from a brain injury in agreement with our data in human patients.

Logistic biplot for nominal data

Classical biplot methods allow for the simultaneous representation of individuals (rows) and variables (columns) of a data matrix. For binary data, logistic biplots have been recently developed. When data are nominal, both classical and binary logistic biplots are not adequate and techniques such as multiple correspondence analysis (MCA), latent trait analysis (LTA) or item response theory (IRT) for nominal items should be used instead. In this paper we extend the binary logistic biplot to nominal data. The resulting method is termed “nominal logistic biplot”(NLB), although the variables are represented as convex prediction regions rather than vectors. Using the methods from computational geometry, the set of prediction regions is converted to a set of points in such a way that the prediction for each individual is established by its closest “category point”. Then interpretation is based on distances rather than on projections. We study the geometry of such a representation and construct computational algorithms for the estimation of parameters and the calculation of prediction regions. Nominal logistic biplots extend both MCA and LTA in the sense that they give a graphical representation for LTA similar to the one obtained in MCA.