The theory and application of penalized methods or Reproducing Kernel Hilbert Spaces made easy

The popular cubic smoothing spline estimate of a regression function arises as the minimizer of the penalized sum of squares $\sum_j(Y_j - {\mu}(t_j))^2 + {\lambda}\int_a^b [{\mu}"(t)]^2 dt$, where the data are $t_j,Y_j$, $j=1,..., n$. The minimization is taken over an infinite-dimensional function space, the space of all functions with square integrable second derivatives. But the calculations can be carried out in a finite-dimensional space. The reduction from minimizing over an infinite dimensional space to minimizing over a finite dimensional space occurs for more general objective functions: the data may be related to the function ${\mu}$ in another way, the sum of squares may be replaced by a more suitable expression, or the penalty, $\int_a^b [{\mu}"(t)]^2 dt$, might take a different form. This paper reviews the Reproducing Kernel Hilbert Space structure that provides a finite-dimensional solution for a general minimization problem. Particular attention is paid to penalties based on linear differential operators. In this case, one can sometimes easily calculate the minimizer explicitly, using Green's functions

Rapid adaptive evolution of colour vision in the threespine stickleback radiation.

Vision is a sensory modality of fundamental importance for many animals, aiding in foraging, detection of predators and mate choice. Adaptation to local ambient light conditions is thought to be commonplace, and a match between spectral sensitivity and light spectrum is predicted. We use opsin gene expression to test for local adaptation and matching of spectral sensitivity in multiple independent lake populations of threespine stickleback populations derived since the last ice age from an ancestral marine form. We show that sensitivity across the visual spectrum is shifted repeatedly towards longer wavelengths in freshwater compared with the ancestral marine form. Laboratory rearing suggests that this shift is largely genetically based. Using a new metric, we found that the magnitude of shift in spectral sensitivity in each population corresponds strongly to the transition in the availability of different wavelengths of light between the marine and lake environments. We also found evidence of local adaptation by sympatric benthic and limnetic ecotypes to different light environments within lakes. Our findings indicate rapid parallel evolution of the visual system to altered light conditions. The changes have not, however, yielded a close matching of spectrum-wide sensitivity to wavelength availability, for reasons we discuss

Cell Edge Features Affected by Microtubule Inhibitor Combinations

The tumor promoter, phorbol 12-myristate 13-acetate (PMA), enhances tumor yield through an epigenetic mechanism. PMA, like another promoter, phosphatase inhibitor okadaic acid, works by maintaining proteins in a phosphorylated state. In order to identify chemicals with promoter and antipromoter effects, this laboratory has developed a standard curve of morphogenetic changes using data from precancerous cell lines that eventually became neoplastic. Using the curve as a basis of comparison, we defined the “signature” phenotype as that adopted when a cell line became neoplastic. The results of solving for signature type disclosed that the microtubule-depolymerizing compound, colchicine, had a promoter-like effect [2]. The opposite effect was found if cells were exposed to paclitaxel (Taxol®) and colchicine [3]. Such findings gave clinicians a rationale to test microtubule inhibitor combinations [4]. Therapy is only effective when agents are administered nearly simultaneously. In the current work, we study the effect of inhibitor combinations on cell features defined by computer-assisted microscopy and classification methods based on latent factors

Visualizing genetic constraints

Principal Components Analysis (PCA) is a common way to study the sources of variation in a high-dimensional data set. Typically, the leading principal components are used to understand the variation in the data or to reduce the dimension of the data for subsequent analysis. The remaining principal components are ignored since they explain little of the variation in the data. However, evolutionary biologists gain important insights from these low variation directions. Specifically, they are interested in directions of low genetic variability that are biologically interpretable. These directions are called genetic constraints and indicate directions in which a trait cannot evolve through selection. Here, we propose studying the subspace spanned by low variance principal components by determining vectors in this subspace that are simplest. Our method and accompanying graphical displays enhance the biologist's ability to visualize the subspace and identify interpretable directions of low genetic variability that align with simple directions.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS603 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Examining the Hospital Elder Life Program in a rehabilitation setting: a pilot feasibility study

Background: The Hospital Elder Life Program (HELP) has been shown to effectively prevent delirium and functional decline in older patients in acute care, but has not been examined in a rehabilitation setting. This pilot study examined potential successes and implementation factors of the HELP in a post-acute rehabilitation hospital setting. Methods: A mixed methods (quantitative and qualitative) evaluation, incorporating a repeated measures design, was used. A total of 100 patients were enrolled; 58 on the pilot intervention unit and 42 on a usual care unit. Group comparisons were made using change scores (pre-post intervention) on outcome measures between pilot unit patients and usual care patients (separate analyses compared usual care patients with pilot unit patients who did or did not receive the HELP). Qualitative data were collected using focus group and individual interviews, and analyzed using emergent coding procedures. Results: Delirium prevalence reduced from 10.9 % (n = 6) to 2.5 % (n = 1) in the intervention group, while remaining the same in the usual care group (2.5 % at both measurement points). Those who received the HELP showed greater improvement on cognitive and functional outcomes, particularly short-term memory and recall, and a shorter average length of stay than patients who did not. Participant groups discussed perceived barriers, benefits, and recommendations for further implementation of the HELP in a rehabilitation setting. Conclusions: This study adds to the limited research on delirium and the effectiveness of the HELP in post-acute rehabilitation settings. The HELP was found to be feasible and have potential benefits for reduced delirium and improved outcomes among rehabilitation patients.Funded in part by an Emerging Team Grant (ETG 92249) from the Canadian Institutes of Health Researc

Unraveling the Determinants of Protrusion Formation

A computerized morphometric classification technique based on latent factors reveals major protrusion classes: factors 4, 5, and 7. Previous work showed that factor 4 represented filopodia, 5 the distribution of lamellar cytoplasm, and 7 a blunt protrusion. We explore the relationship of focal contact (FC) characteristics and their integrated actin cables to factors values. The results show that FC maturation/cytoskeletal integration affects factor 5, because FC elongation/integration was correlated with its values. On the contrary, 7 values decreased with maturation, so cable or FC size or their integration must be restricted to form these protrusions. Where integration did occur, the cables showed distinctive size and orientation, as indicated by correlation of 7 values with FC shape. Results obtained with myosin inhibitors support the interpretation that a central, isometric, contractile network puts constraints on both factor 5 and 7 protrusions. We conclude that cells establish functional domains by rearranging the cytoskeleton