Statistical-mechanical description of classical test-particle dynamics in the presence of an external force field: modelling noise and damping from first principles

Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly coupled to a large heat-bath in thermal equilibrium. Both subsystems are subject to an external force field. From the (time-non-local) generalized master equation a Fokker-Planck-type equation follows as a "quasi-Markovian" approximation. The kinetic operator thus defined is shown to be ill-defined; in specific, it does not preserve the positivity of the test-particle distribution function f(x, v; t). Adopting an alternative approach, previously introduced for quantum open systems, is proposed to lead to a correct kinetic operator, which yields all the expected properties. A set of explicit expressions for the diffusion and drift coefficients are obtained, allowing for modelling macroscopic diffusion and dynamical friction phenomena, in terms of an external field and intrinsic physical parameters.

Ensuring the statistical soundness of competitive gene set approaches: gene filtering and genome-scale coverage are essential

In this article, we focus on the analysis of competitive gene set methods for detecting the statistical significance of pathways from gene expression data. Our main result is to demonstrate that some of the most frequently used gene set methods, GSEA, GSEArot and GAGE, are severely influenced by the filtering of the data in a way that such an analysis is no longer reconcilable with the principles of statistical inference, rendering the obtained results in the worst case inexpressive. A possible consequence of this is that these methods can increase their power by the addition of unrelated data and noise. Our results are obtained within a bootstrapping framework that allows a rigorous assessment of the robustness of results and enables power estimates. Our results indicate that when using competitive gene set methods, it is imperative to apply a stringent gene filtering criterion. However, even when genes are filtered appropriately, for gene expression data from chips that do not provide a genome-scale coverage of the expression values of all mRNAs, this is not enough for GSEA, GSEArot and GAGE to ensure the statistical soundness of the applied procedure. For this reason, for biomedical and clinical studies, we strongly advice not to use GSEA, GSEArot and GAGE for such data sets.

Chemometric techniques in multivariate statistical modelling of process plant

The techniques of principal component analysis (PCA) and partial least squares (PLS) are introduced from the point of view of providing a multivariate statistical method for modelling process plants. The advantages and limitations of PCA and PLS are discussed from the perspective of the type of data and problems that might be encountered in this application area. These concepts are exemplified by two case studies dealing first with data from a continuous stirred tank reactor (CSTR) simulation and second a literature source describing a low-density polyethylene (LDPE) reactor simulation.