MODELING FUNCTIONAL DATA WITH SPATIALLY HETEROGENEOUS SHAPE CHARACTERISTICS

We propose a novel class of models for functional data exhibiting skewness or other shape characteristics that vary with spatial or temporal location. We use copulas so that the marginal distributions and the dependence structure can be modeled independently. Dependence is modeled with a Gaussian or t-copula, so that there is an underlying latent Gaussian process. We model the marginal distributions using the skew t family. The mean, variance, and shape parameters are modeled nonparametrically as functions of location. A computationally tractable inferential framework for estimating heterogeneous asymmetric or heavy-tailed marginal distributions is introduced. This framework provides a new set of tools for increasingly complex data collected in medical and public health studies. Our methods were motivated by and are illustrated with a state-of-the-art study of neuronal tracts in multiple sclerosis patients and healthy controls. Using the tools we have developed, we were able to find those locations along the tract most affected by the disease. However, our methods are general and highly relevant to many functional data sets. In addition to the application to one-dimensional tract profiles illustrated here, higher-dimensional extensions of the methodology could have direct applications to other biological data including functional and structural MRI.

PENALIZED FUNCTIONAL REGRESSION

We develop fast fitting methods for generalized functional linear models. An undersmooth of the functional predictor is obtained by projecting on a large number of smooth eigenvectors and the coefficient function is estimated using penalized spline regression. Our method can be applied to many functional data designs including functions measured with and without error, sparsely or densely sampled. The methods also extend to the case of multiple functional predictors or functional predictors with a natural multilevel structure. Our approach can be implemented using standard mixed effects software and is computationally fast. Our methodology is motivated by a diffusion tensor imaging (DTI) study. The aim of this study is to analyze differences between various cerebral white matter tract property measurements of multiple sclerosis (MS) patients and controls. While the statistical developments proposed here were motivated by the DTI study, the methodology is designed and presented in generality and is applicable to many other areas of scientific research. An online appendix provides R implementations of all simulations.

NONLINEAR TUBE-FITTING FOR THE ANALYSIS OF ANATOMICAL AND FUNCTIONAL STRUCTURES

We are concerned with the estimation of the exterior surface of tube-shaped anatomical structures. This interest is motivated by two distinct scientific goals, one dealing with the distribution of HIV microbicide in the colon and the other with measuring degradation in white-matter tracts in the brain. Our problem is posed as the estimation of the support of a distribution in three dimensions from a sample from that distribution, possibly measured with error. We propose a novel tube-fitting algorithm to construct such estimators. Further, we conduct a simulation study to aid in the choice of a key parameter of the algorithm, and we test our algorithm with validation study tailored to the motivating data sets. Finally, we apply the tube-fitting algorithm to a colon image produced by single photon emission computed tomography (SPECT)and to a white-matter tract image produced using diffusion tensor `imaging (DTI).

Die Wahrheit ist untödlich. Berner Täufer in Geschichte und Gegenwart

Das Buch enthält Vorträge, die im Vorfeld des Täuferjahrs 2007 an der Christkatholischen und Evangelischen Theologischen Fakultät der Universität Bern gehalten wurden. Im geschichtlichen Teil kommt das frühe Berner Täufertum aufgrund neuer Quellen in seinem schweizerischen Umfeld in den Blick. Daneben ist das aktuelle Leben von Mennoniten-gemeinden Gegenstand des Buches. Ein Beitrag befasst sich mit dem modernen Täufertum zwischen Pluralität, Gemeindeautonomie und Tradition bewegt, ein weiterer mit den Mennoniten als einer Friedenskirche in der Ökumene, und in vier Voten wird das Thema «Täufer und Reformierte heute» aus kirchlich und individuell unterschiedlicher Perspektive beleuchtet. Der Band enthält schliesslich zwei Vorträge, die anlässlich des 475-Jahrjubiläums des „Berner Synodus“ von 1532 gehalten wurden. Der reich illustrierte Band knüpft an die seit langem vergriffenen Standardwerke zum Bernischen und Schweizerischen Täufertum von Ernst Müller und Samuel Henri Geiser an. Er beruht auf neuen Quellen und verbindet Wissenschaftlichkeit mit Allgemeinverständlichkeit. Er richtet sich an eine breite Leserschaft sowie an die wissenschaftliche Täuferforschung.

The Amplifier - v. 4, no. 6

In this issue...Washoe Theatre, Fran Reich Orchestra, Mining Symposium, Neil Douglas, Anderson-Carlisle Society, Hockey, Convocation, Coed Club