Modelling beyond Regression Functions: an Application of Multimodal Regression to Speed-Flow Data

An enormous amount of publications deals with smoothing in the sense of nonparametric regression. However, nearly all of the literature treats the case where predictors and response are related in the form of a function y=m(x)+noise. In many situations this simple functional model does not capture adequately the essential relation between predictor and response. We show by means of speed-flow diagrams, that a more general setting may be required, allowing for multifunctions instead of only functions. It turns out that in this case the conditional modes are more appropriate for the estimation of the underlying relation than the commonly used mean or the median. Estimation is achieved using a conditional mean-shift procedure, which is adapted to the present situation

How stable are transport model results to changes of resonance parameters? A UrQMD model study

The Ultrarelativistic Quantum Molecular Dynamics [UrQMD] model is widely used to simulate heavy ion collisions in broad energy ranges. It consists of various components to implement the different physical processes underlying the transport approach. A major building block are the shared tables of constants, implementing the baryon masses and widths. Unfortunately, many of these input parameters are not well known experimentally. In view of the upcoming physics program at FAIR, it is therefore of fundamental interest to explore the stability of the model results when these parameters are varied. We perform a systematic variation of particle masses and widths within the limits proposed by the particle data group (or up to 10%). We find that the model results do only weakly depend on the variation of these input parameters. Thus, we conclude that the present implementation is stable with respect to the modification of not yet well specified particle parameters

A simple Hidden Markov Model for midbrain dopaminergic neurons

Poster presentation: Introduction Dopaminergic neurons in the midbrain show a variety of firing patterns, ranging from very regular firing pacemaker cells to bursty and irregular neurons. The effects of different experimental conditions (like pharmacological treatment or genetical manipulations) on these neuronal discharge patterns may be subtle. Applying a stochastic model is a quantitative approach to reveal these changes. ..

The fitting of multifunctions : an approach to nonparametric multimodal regression.

In the last decades a lot of research has been devoted to smoothing in the sense of nonparametric regression. However, this work has nearly exclusively concentrated on fitting regression functions. When the conditional distribution of y|x is multimodal, the assumption of a functional relationship y = m(x) + noise might be too restrictive. We introduce a nonparametric approach to fit multifunctions, allowing to assign a set of output values to a given x. The concept is based on conditional mean shift, which is an easily implemented tool to detect the local maxima of a conditional density function. The methodology is illustrated by environmental data examples

Exploring multivariate data structures with local principal curves.

A new approach to find the underlying structure of a multidimensional data cloud is proposed, which is based on a localized version of principal components analysis. More specifically, we calculate a series of local centers of mass and move through the data in directions given by the first local principal axis. One obtains a smooth ``local principal curve'' passing through the "middle" of a multivariate data cloud. The concept adopts to branched curves by considering the second local principal axis. Since the algorithm is based on a simple eigendecomposition, computation is fast and easy