Local functional principal component analysis

Covariance operators of random functions are crucial tools to study the way random elements concentrate over their support. The principal component analysis of a random function X is well-known from a theoretical viewpoint and extensively used in practical situations. In this work we focus on local covariance operators. They provide some pieces of information about the distribution of X around a fixed point of the space x₀. A description of the asymptotic behaviour of the theoretical and empirical counterparts is carried out. Asymptotic developments are given under assumptions on the location of x₀ and on the distributions of projections of the data on the eigenspaces of the (non-local) covariance operator

Power and limitations of electrophoretic separations in proteomics strategies

Proteomics can be defined as the large-scale analysis of proteins. Due to the complexity of biological systems, it is required to concatenate various separation techniques prior to mass spectrometry. These techniques, dealing with proteins or peptides, can rely on chromatography or electrophoresis. In this review, the electrophoretic techniques are under scrutiny. Their principles are recalled, and their applications for peptide and protein separations are presented and critically discussed. In addition, the features that are specific to gel electrophoresis and that interplay with mass spectrometry (i.e., protein detection after electrophoresis, and the process leading from a gel piece to a solution of peptides) are also discussed