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The well-known and popular Savitzky-Golay filter has several disadvantages. A very attractive alternative is a smoother based on penalized least squares, extending ideas presented by Whittaker 80 years ago. This smoother is extremely fast, gives continuous control over smoothness, interpolates automatically, and allows fast leave-one-out cross-validation. It can be programmed in a few lines of Matlab code. Theory, implementation, and applications are presented.

Gliomas are the most common primary brain tumors with heterogeneous morphology and variable prognosis. Treatment decisions in patients rely mainly on histologic classification and clinical parameters. However, differences between histologic subclasses and grades are subtle, and classifying gliomas is subject to a large interobserver variability. To improve current classification standards, we have performed gene expression profiling on a large cohort of glioma samples of all histologic subtypes and grades. We identified seven distinct molecular subgroups that correlate with survival.

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The prediction of future mortality rates is a problem of fundamental importance for the insurance and pensions industry. We show how the method of P-splines can be extended to the smoothing and forecasting of two-dimensional mortality tables. We use a penalized generalized linear model with Poisson errors and show how to construct regression and penalty matrices appropriate for two-dimensional modelling. An important feature of our method is that forecasting is a natural consequence of the smoothing process. We illustrate our methods with two data sets provided by the Continuous Mortality Investigation Bureau, a central body for the collection and processing of UK insurance and pensions data.

A parametric model is proposed for the warping function when aligning chromatograms. A very fast and stable algorithm results that consumes little memory and avoids the artifacts of dynamic time warping. The parameters of the warping function are useful for quality control. They also are easily interpolated, allowing alignment of batches of chromatograms based on warping functions for a limited number of calibration samples.

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Using genome-wide expression profiling of a panel of 27 human mammary cell lines with different mechanisms of E-cadherin inactivation, we evaluated the relationship between E-cadherin status and gene expression levels. Expression profiles of cell lines with E-cadherin (CDH1) promoter methylation were significantly different from those with CDH1 expression or, surprisingly, those with CDH1 truncating mutations. Furthermore, we found no significant differentially expressed genes between cell lines with wild-type and mutated CDH1. The expression profile complied with the fibroblastic morphology of the cell lines with promoter methylation, suggestive of epithelial -mesenchymal transition (EMT). All other lines, also the cases with CDH1 mutations, had epithelial features. Three non-tumorigenic mammary cell lines derived from normal breast epithelium also showed CDH1 promoter methylation, a fibroblastic phenotype and expression profile. We suggest that CDH1 promoter methylation, but not mutational inactivation, is part of an entire programme, resulting in EMT and increased invasiveness in breast cancer. The molecular events that are part of this programme can be inferred from the differentially expressed genes and include genes from the TGFb pathway, transcription factors involved in CDH1 regulation (i.e. ZFHX1B, SNAI2, but not SNAI1, TWIST), annexins, AP1/2 transcription factors and members of the actin and intermediate filament cytoskeleton organisation.