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

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

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. ..

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

Refactoring the UrQMD model for many-core architectures

Ultrarelativistic Quantum Molecular Dynamics is a physics model to describe the transport, collision, scattering, and decay of nuclear particles. The UrQMD framework has been in use for nearly 20 years since its first development. In this period computing aspects, the design of code, and the efficiency of computation have been minor points of interest. Nowadays an additional issue arises due to the fact that the run time of the framework does not diminish any more with new hardware generations. The current development in computing hardware is mainly focused on parallelism. Especially in scientific applications a high order of parallelisation can be achieved due to the superposition principle. In this thesis it is shown how modern design criteria and algorithm redesign are applied to physics frameworks. The redesign with a special emphasise on many-core architectures allows for significant improvements of the execution speed. The most time consuming part of UrQMD is a newly introduced relativistic hydrodynamic phase. The algorithm used to simulate the hydrodynamic evolution is the SHASTA. As the sequential form of SHASTA is successfully applied in various simulation frameworks for heavy ion collisions its possible parallelisation is analysed. Two different implementations of SHASTA are presented. The first one is an improved sequential implementation. By applying a more concise design and evading unnecessary memory copies, the execution time could be reduced to the half of the FORTRAN version’s execution time. The usage of memory could be reduced by 80% compared to the memory needed in the original version. The second implementation concentrates fully on the usage of many-core architectures and deviates significantly from the classical implementation. Contrary to the sequential implementation, it follows the recalculate instead of memory look-up paradigm. By this means the execution speed could be accelerated up to a factor of 460 on GPUs. Additionally a stability analysis of the UrQMD model is presented. Applying metapro- gramming UrQMD is compiled and executed in a massively parallel setup. The resulting simulation data of all parallel UrQMD instances were hereafter gathered and analysed. Hence UrQMD could be proven of high stability to the uncertainty of experimental data. As a further application of modern programming paradigms a prototypical implementa- tion of the worldline formalism is presented. This formalism allows for a direct calculation of Feynman integrals and constitutes therefore an interesting enhancement for the UrQMD model. Its massively parallel implementation on GPUs is examined