2023, Saupe, Dietmar

Metabolische Prozesse führen den Stoffwechsel durch, der die für sportliche Belastungen erforderliche Energie zur Verfügung stellt. Eine direkte quantitative Modellierung der Metaboliten als Variablen ist möglich, aber sehr komplex. Einfachere Modelle abstrahieren die zugrunde liegende Physiologie auf elegante Weise und haben sich in der Praxis der Sportinformatik erfolgreich durchgesetzt. Die mathematische Modellierung der messbaren Output-Größen Sauerstoffaufnahme, Lakatkonzentration sowie der Herzfrequenz ergibt eine solide Grundlage mit Anwendungen in der Planung und Steuerung von Leistung im Training und im Wettkampf. Oftmals erscheinen solche Modelle in der Form einfacher linearer Differenzialgleichungen mit exponentiellen, asymptotisch konstanten Lösungen, die gegen ein Äquilibrium konvergieren. Das CP-Modell (critical power) hingegen beschreibt die Beziehung zwischen geleisteter Arbeit und den verbleibenden Energiereserven. Mit diesem physiologischen Modell, kombiniert mit einem mechanischen Modell von physikalischer Leistung beim Radfahren auf einer Strecke mit gegebenem Höhenprofil, lassen sich durch nummerische Verfahren optimale Pacing-Strategien berechnen.

2004, Peitgen, Heinz-Otto, Jürgens, Hartmut, Saupe, Dietmar

For many, chaos theory already belongs to the greatest achievements in the natural sciences in this century. Indeed, it can be claimed that very few developments in natural science have awakened so much public interest. Here and there, we even hear of changing images of reality or of a revolution in the natural sciences.

2002, Hamzaoui, Raouf, Saupe, Dietmar

2004, Peitgen, Heinz-Otto, Jürgens, Hartmut, Saupe, Dietmar

Dyson is referring to mathematicians, like G. Cantor, D. Hilbert, and W. Sierpinski, who have been justly credited with having helped to lead mathematics out of its crisis at the turn of the century by building marvelous abstract foundations on which modern mathematics can now flourish safely. Without question, mathematics has changed during this century. What we see is an ever-increasing dominance of the algebraic approach over the geometric. In their striving for absolute truth, mathematicians have developed new standards for determining the validity of mathematical arguments. In the process, many of the previously accepted methods have been abandoned as inappropriate. Geometric or visual arguments were increasingly forced out. While Newton’s Principia Mathematica, laying the fundamentals of modern mathematics, still made use of the strength of visual arguments, the new objectivity seems to require a dismissal of this approach. From this point of view, it is ironic that some of the constructions which Cantor, Hilbert, Sierpinski and others created to perfect their extremely abstract foundations simultaneously hold the clues to understanding the patterns of nature in a visual sense. The Cantor set, Hilbert curve, and Sierpinski gasket all give testimony to the delicacy and problems of modern set theory and at the same time, as Mandelbrot has taught us, are perfect models for the complexity of nature.

2003, Jürgens, Hartmut, Saupe, Dietmar

SCOUT is a program which implements a series of algorithms based on ideas described in chapter 12 concerning PL continuation methods. The problem to be solved numerically is a nonlinear fixed point or eigenvalue problem, i. e. to find the zeros of F:R^N×R→R^N
(x,λ)↦F(x,λ). More precisely, the following is a list of the various problem areas that are handled by SCOUT.

2002, Müller, Heinrich, Saupe, Dietmar, Straßer, Wolfgang

In den letzten 25 Jahren wuchs in Deutschland das Interesse an Computergraphik, Animation, Kunst, Visualisierung und Graphik-Hardware beständig. War zu Beginn der 80-er Jahre die Entwicklung der ersten Forschergruppen zur Computergraphik an den Universitäten noch langsam, so beschleunigte sie sich in den 90-er Jahren vehement. Seit dieser Zeit ist ein Lehrstuhl für Computergraphik fast flächendeckend Bestandteil von Informatikinstituten. Neben den Lehrstühlen an den Universitäten existieren zahlreiche Forschungseinrichtungen des Bundes oder der Industrie, die eng zusammenarbeiten.

2004, Peitgen, Heinz-Otto, Jürgens, Hartmut, Saupe, Dietmar

Being introduced to the Pascal triangle for the first time, one might think that this mathematical object was a rather innocent one. Surprisingly it has attracted the attention of innumerable scientists and amateur scientists over many centuries. One of the earliest mentions (long before Pascal’s name became associated with it) is in a Chinese document from around 1303.1 Boris A. Bondarenko,2 in his beautiful recently published book, counts several hundred publications which have been devoted to the Pascal triangle and related problems just over the last two hundred years. Prominent mathematicians as well as popular science writers such as Ian Stewart,3 Evgeni B. Dynkin and Wladimir A. Uspenski,4 and Stephen Wolfram5 have devoted articles to the marvelous relationship between elementary number theory and the geometrical patterns found in the Pascal triangle. In chapter 2 we introduced one example: the relation between the Pascal triangle and the Sierpinski gasket.

2003, Saupe, Dietmar, Wagner, Marcel

The goal of this project is the evaluation and development of a new adaptive image sequence coding approach. The codec is based on adaptive vector quantization and has been combined with several video coding techniques like wavelet transform, quad-trees, and rate distortion optimization. In addition we provide a comparison with a state of the art video codec (H.263) and describe new experiments with motion compensation. This project was supported by Micronas Intermetall GmbH.

2001, Hartenstein, Hannes, Ruhl, Matthias, Saupe, Dietmar, Vrscay, Edward R.

The inverse problem of fractal compression amounts to determining a contractive operator such that the corresponding fixed point approximates a given target function. The standard method based on the collage coding strategy is known to represent a suboptimal method. Why does one not search for optimal fractal codes? We will prove that optimal fractal coding, when considered as a discrete optimization problem, constitutes an NP-hard problem, i.e., it cannot be solved in a practical amount of time. Nevertheless, when the fractal code parameters are allowed to vary continuously, we show that one is able to improve on collage coding by fine-tuning some of the fractal code parameters with the help of differential methods. The differentiability of the attractor as a function of its luminance parameters is established. We also comment on the approximating behaviour of collage coding, state a lower bound for the optimal attractor error, and outline an annealing scheme for improved fractal coding.