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#### Faculty / Organisational entity

Algebraic Systems Theory
(2004)

Control systems are usually described by differential equations, but their properties of interest are most naturally expressed in terms of the system trajectories, i.e., the set of all solutions to the equations. This is the central idea behind the so-called "behavioral approach" to systems and control theory. On the other hand, the manipulation of linear systems of differential equations can be formalized using algebra, more precisely, module theory and homological methods ("algebraic analysis"). The relationship between modules and systems is very rich, in fact, it is a categorical duality in many cases of practical interest. This leads to algebraic characterizations of structural systems properties such as autonomy, controllability, and observability. The aim of these lecture notes is to investigate this module-system correspondence. Particular emphasis is put on the application areas of one-dimensional rational systems (linear ODE with rational coefficients), and multi-dimensional constant systems (linear PDE with constant coefficients).

Today, test methods for communication protocols assume, among other things, that the protocol design is specified as a single, monolithic finite state machine (FSM). From this specification, test suites that are capable of detecting output and/or transfer faults in the protocol implementation are derived. Limited applicability ofthese methods is mainly because oftheir specific assumptions, and due to the size of the derived test suite and the resulting test effort for realistic protocols. In this work, the compositional test method (C-method), which exploits the available structure of a communication protocol, is proposed. The C-method first tests each protocol component separately for output and/or transfer faults, using one of the traditional test methods, then checks for composability, and finally tests the composite system for composition faults. To check for composability and to derive the test suite for the detection of composition faults, it is not required to construct the global state machine. Instead, all information is derived from the component state machines, which avoids a potential state explosion and lengthy test cases. Furthermore, the test suite checks for composition faults only. This substantially reduces the size of the test suite and thus the overall test effort.

A spectral theory for constituents of macroscopically homogeneous random microstructures modeled as homogeneous random closed sets is developed and provided with a sound mathematical basis, where the spectrum obtained by Fourier methods corresponds to the angular intensity distribution of x-rays scattered by this constituent. It is shown that the fast Fourier transform applied to three-dimensional images of microstructures obtained by micro-tomography is a powerful tool of image processing. The applicability of this technique is is demonstrated in the analysis of images of porous media.

Ein maßgeschneidertes Kommunikationssystem für eine mobile Applikation mit Dienstgüteanforderungen
(2004)

In diesem Beitrag wird die Maßschneiderung eines Ad-Hoc-Kommunikationssystems zur Fernsteuerung eines Luftschiffs über WLAN vorgestellt. Dabei steht die Dienstunterstützung bei der Übertragung mehrerer Datenströme im Vordergrund. Es werden verschiedene Dienstgütemechanismen erklärt und deren Entwicklung und Integration in ein Kommunikationsprotokoll mit Hilfe eines komponentenbasierten Ansatzes genauer erläutert.

The Chained Lin-Kernighan algorithm (CLK) is one of the best heuristics to solve Traveling Salesman Problems (TSP). In this paper a distributed algorithm is proposed, were nodes in a network locally optimize TSP instances by using the CLK algorithm. Within an Evolutionary Algorithm (EA) network-based framework the resulting tours are modified and exchanged with neighboring nodes. We show that the distributed variant finds better tours compared to the original CLK given the same amount of computation time. For instance fl3795, the original CLK got stuck in local optima in each of 10 runs, whereas the distributed algorithm found optimal tours in each run requiring less than 10 CPU minutes per node on average in an 8 node setup. For instance sw24978, the distributed algorithm had an average solution quality of 0.050% above the optimum, compared to CLK's average solution of 0.119% above the optimum given the same total CPU time (104 seconds). Considering the best tours of both variants for this instance, the distributed algorithm is 0.033% above the optimum and the CLK algorithm 0.099%.

In this work the problem of fluid flow in deformable porous media is studied. First, the stationary fluid-structure interaction (FSI) problem is formulated in terms of incompressible Newtonian fluid and a linearized elastic solid. The flow is assumed to be characterized by very low Reynolds number and is described by the Stokes equations. The strains in the solid are small allowing for the solid to be described by the Lame equations, but no restrictions are applied on the magnitude of the displacements leading to strongly coupled, nonlinear fluid-structure problem. The FSI problem is then solved numerically by an iterative procedure which solves sequentially fluid and solid subproblems. Each of the two subproblems is discretized by finite elements and the fluid-structure coupling is reduced to an interface boundary condition. Several numerical examples are presented and the results from the numerical computations are used to perform permeability computations for different geometries.

Piezoelectric filters are used in telecommunication to filter electrical signals. This report deals with the problem of calculating passing and damped frequency intervals for a filter with given geometrical configurations and materials. Only periodic filters, which are widely used in practice, were considered. These filters consist of periodically arranged cells. For a small amount of cells a numerical procedure to visualise the wave propagation in the filter was developed. For a big number of cells another model of the filter was obtained. In this model it is assumed that the filter occupies an infinite domain. This leads to a differential equation, with periodic coefficients, that describes propagation of the wave with a given frequency in the filter. To analyse this equation the Spectral Theory for Periodic Operators had to be employed. Different ways -- analytical and numerical -- to apply the theory were proposed and analysed.

We consider the contact of two elastic bodies with rough surfaces at the interface. The size of the micropeaks and valleys is very small compared with the macrosize of the bodies’ domains. This makes the direct application of the FEM for the calculation of the contact problem prohibitively costly. A method is developed that allows deriving a macrocontact condition on the interface. The method involves the twoscale asymptotic homogenization procedure that takes into account the microgeometry of the interface layer and the stiffnesses of materials of both domains. The macrocontact condition can then be used in a FEM model for the contact problem on the macrolevel. The averaged contact stiffness obtained allows the replacement of the interface layer in the macromodel by the macrocontact condition.

IMRT planning on adaptive volume structures – a significant advance of computational complexity
(2004)

In intensity-modulated radiotherapy (IMRT) planning the oncologist faces the challenging task of finding a treatment plan that he considers to be an ideal compromise of the inherently contradictive goals of delivering a sufficiently high dose to the target while widely sparing critical structures. The search for this a priori unknown compromise typically requires the computation of several plans, i.e. the solution of several optimization problems. This accumulates to a high computational expense due to the large scale of these problems - a consequence of the discrete problem formulation. This paper presents the adaptive clustering method as a new algorithmic concept to overcome these difficulties. The computations are performed on an individually adapted structure of voxel clusters rather than on the original voxels leading to a decisively reduced computational complexity as numerical examples on real clinical data demonstrate. In contrast to many other similar concepts, the typical trade-off between a reduction in computational complexity and a loss in exactness can be avoided: the adaptive clustering method produces the optimum of the original problem. This flexible method can be applied to both single- and multi-criteria optimization methods based on most of the convex evaluation functions used in practice

We propose a framework for the synthesis of temporal logic programs which are formulated in a simple temporal logic programming language from both positive and negative examples. First we will prove that results from the theory of first order inductive logic programming carry over to the domain of temporal logic. After this we will show how programs formulated in the presented language can be generalized or specialized in order to satisfy the specification induced by the sets of examples.