4 research outputs found
Algebraic Comparison of Partial Lists in Bioinformatics
The outcome of a functional genomics pipeline is usually a partial list of
genomic features, ranked by their relevance in modelling biological phenotype
in terms of a classification or regression model. Due to resampling protocols
or just within a meta-analysis comparison, instead of one list it is often the
case that sets of alternative feature lists (possibly of different lengths) are
obtained. Here we introduce a method, based on the algebraic theory of
symmetric groups, for studying the variability between lists ("list stability")
in the case of lists of unequal length. We provide algorithms evaluating
stability for lists embedded in the full feature set or just limited to the
features occurring in the partial lists. The method is demonstrated first on
synthetic data in a gene filtering task and then for finding gene profiles on a
recent prostate cancer dataset
A Posteriori Error Estimates for Axisymmetric and Nonlinear Problems.
We propose and examine the primal and dual finite element method for solving an axially symmetric elliptic problem with mixed boundary conditions. We derive an a posteriori error estimate and generalize the method used for a nonlinear elliptic problem. Finally, an a posteriori error estimate for a nonlinear parabolic problem based on the concept of hierarchical finite element basis functions is introduced