Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

Synthesis and evaluation of cyclic cationic peptides as antimicrobial agents for use in plant protection

Aquesta tesi doctoral se centra en l'estudi de l'aplicació de pèptids antimicrobians en la lluita contra agents patògens de cultius de plantes d'interès econòmic.L'estratègia sintètica s'ha portat a terme utilitzant metodologies convencionals de síntesi de pèptids en fase sòlida com l'estratègia tridimensional ortogonal Fmoc/tBut/Allyl. Ha calgut fer la recerca de les condicions òptimes per a l'eliminació del grup Allyl i la ciclació. D'entre els pèptids cíclics de 4-10 aminoacids sintetitzats, el decapèptid c(Lys-Leu-Lys-Leu-Lys-Phe-Lys-Lys-Leu-Gln) ha resultat ésser el més efectiu i s'ha pres com a base per al disseny d'una quimioteca de 56 pèptids. Dels resultats obtinguts s'ha sintetitzat una segona quimioteca basada en l'estructura general c(X1-X2-X3-X4-Lys-Phe-Lys-Lys-Leu-Gln) determinada com la que posseix el millor perfil d'activitat. Els pèptids més efectius obtinguts constituixen els primers exemples de pèptids cíclics actius contra E. amylovora i poden ser considerats com a bons candidats pel desenvolupament d'agents antimicrobians efectius en protecció vegetal.