Stefan Pickl

Bio: Stefan Pickl is an academic researcher from Bundeswehr University Munich. The author has contributed to research in topics: Decision support system & Optimal control. The author has an hindex of 15, co-authored 157 publications receiving 1209 citations. Previous affiliations of Stefan Pickl include University of Twente & Naval Postgraduate School.

How to cope with division problems under interval uncertainty of claims

Abstract: The paper deals with division situations where individual claims can vary within closed intervals. Uncertainty of claims is removed by weighting in a consistent way the upper and lower bounds of the claim intervals. Deterministic division problems with the obtained compromise claims are then considered and classical division rules from the bankruptcy literature are used to generate several procedures leading to efficient and reasonable rules for division problems under interval uncertainty of claims.

How to cope with division problems under interval uncertainty of claims

Abstract: The paper deals with division situations where individual claims can vary within closed intervals.Uncertainty of claims is removed by compromising in a consistent way the upper and lower bounds of the claim intervals.Deterministic division problems with compromise claims are then considered and classical division rules from the bankruptcy literature are used to generate several procedures leading to e .cient and reasonable rules for division problems under interval uncertainty of claims.

Genetic Networks and Anticipation of Gene Expression Patterns

Abstract: An interesting problem for computational biology is the analysis of time‐series expression data Here, the application of modern methods from dynamical systems, optimization theory, numerical algorithms and the utilization of implicit discrete information lead to a deeper understanding In [1], we suggested to represent the behavior of time‐series gene expression patterns by a system of ordinary differential equations, which we analytically and algorithmically investigated under the parametrical aspect of stability or instability Our algorithm strongly exploited combinatorial information In this paper, we deepen, extend and exemplify this study from the viewpoint of underlying mathematical modelling This modelling consists in evaluating DNA‐microarray measurements as the basis of anticipatory prediction, in the choice of a smooth model given by differential equations, in an approach of the right‐hand side with parametric matrices, and in a discrete approximation which is a least squares optimization problem We give a mathematical and biological discussion, and pay attention to the special case of a linear system, where the matrices do not depend on the state of expressions Here, we present first numerical examples

Random graphs

Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Solving Ordinary Differential Equations

Abstract: Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.