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the *Deutsche* *Forschungsgemeinschaft*.

, 2000

"... This work is a product of the Collaborative Research Center 531, “Computational ..."

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This work is a product of the Collaborative Research Center 531, “Computational

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Supported by the *Deutsche* *Forschungsgemeinschaft*

, 1995

"... We discuss the electroweak phase-transition in the early universe, using nonperturbative flow equations for a computation of the free energy. For a scalar mass above ∼ 70 GeV, high-temperature perturbation theory cannot describe this transition reliably. This is due to the dominance of three-dimensi ..."

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We discuss the electroweak phase-transition in the early universe, using nonperturbative flow equations for a computation of the free energy. For a scalar mass above ∼ 70 GeV, high-temperature perturbation theory cannot describe this transition reliably. This is due to the dominance of three-dimensional physics at high temperatures which implies that the effective gauge coupling grows strong in the symmetric phase. We give an order of magnitude-estimate of non-perturbative effects in reasonable agreement with recent results from electroweak lattice simulations. 1

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Supported by the *Deutsche* *Forschungsgemeinschaft*

, 1994

"... The behavior of the proton magnetic form factor is studied within the modified hard scattering picture, which takes into account gluonic radiative corrections in terms of transverse separations. We parallel the analysis given previously by Li and make apparent a number of serious objections. The app ..."

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The behavior of the proton magnetic form factor is studied within the modified hard scattering picture, which takes into account gluonic radiative corrections in terms of transverse separations. We parallel the analysis given previously by Li and make apparent a number of serious objections. The appropriate cut-off needed to render the form-factor calculation finite is both detailed and analyzed by considering different cut-off prescriptions. The use of the maximum interquark separation as a common infrared cut-off in the Sudakov suppression factor is proposed, since it avoids difficulties with the αs-singularities and yields a proton form factor insensitive to the inclusion of the soft region which therefore can be confidently attributed to perturbative QCD. Results are presented for a variety of proton wave functions including also their intrinsic transverse momentum. It turns out that the perturbative contribution, although theoretically self-consistent for Q2 larger than about 6 GeV 2 to 10 GeV 2, is too small compared to the data.

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Fellow of *Deutsche* *Forschungsgemeinschaft*.

, 1975

"... Data from e ' e- annihilation into hadrons at 4.8 GeV center-of-mass energy were used to search for charmed mesons in the mass range 1.5 to 4.0 GeV/c'. We looked for narrow eaks in the invariant mass distri utions for KT xl, $ %+ XI-, 7 [ P a-, K? K-, KT & $, K ".i K " K &ap ..."

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Data from e ' e- annihilation into hadrons at 4.8 GeV center-of-mass energy were used to search for charmed mesons in the mass range 1.5 to 4.0 GeV/c'. We looked for narrow eaks in the invariant mass distri utions for KT xl, $ %+ XI-, 7 [ P a-, K? K-, KT & $, K ".i K " K ' and n+ nI- X-. We present upper limits for the in&siGe &o&ion cross section times the branching ratio for charmed mesons having these decay modes. (Submitted to Phys. Rev. Lett.) *Work supported by the U.S. Energy Research and Development Administration. Jt-ic

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the *Deutsche* *Forschungsgemeinschaft*. On the Utility of Populations

, 2000

"... Evolutionary algorithms (EAs) are population-based search heuristics often used for function optimization. Typically they use selection, mutation, and crossover as search operators. On many test functions EAs are outperformed by simple hillclimbers. Therefore, it is investigated whether the use of a ..."

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Evolutionary algorithms (EAs) are population-based search heuristics often used for function optimization. Typically they use selection, mutation, and crossover as search operators. On many test functions EAs are outperformed by simple hillclimbers. Therefore, it is investigated whether the use of a population and crossover is at all advantageous. In this paper it is rigorously proven that the use of a population instead of just a single individuum can be an advantage of its own even without making use of crossover. This establishes the advantage of EAs compared to (random) hill-climbers on appropriate objective functions. 1

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Supported by *Deutsche* *Forschungsgemeinschaft*

, 1997

"... An ambiguity inherent in the partial integration procedure leading to the Bern-Kosower rules is fixed in a way which preserves the complete permutation symmetry in the scattering states. This leads to a canonical version of the Bern-Kosower representation for the one-loop N – photon/gluon amplitudes ..."

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An ambiguity inherent in the partial integration procedure leading to the Bern-Kosower rules is fixed in a way which preserves the complete permutation symmetry in the scattering states. This leads to a canonical version of the Bern-Kosower representation for the one-loop N – photon/gluon amplitudes, and to a natural decomposition of those amplitudes into permutation symmetric gauge invariant partial amplitudes. This decomposition exhibits a simple recursive structure.

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∗ Research supported by the *Deutsche* *Forschungsgemeinschaft*

"... In index theory and in noncommutative geometry one often associates C∗-algebras with geometric objects. These algebras can for instance arise from pseudodifferential operators, differential forms, convolution algebras etc.. How-ever they are often given a priori as locally convex algebras and one lo ..."

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In index theory and in noncommutative geometry one often associates C∗-algebras with geometric objects. These algebras can for instance arise from pseudodifferential operators, differential forms, convolution algebras etc.. How-ever they are often given a priori as locally convex algebras and one looses a certain amount of information by passing to the C∗-algebra completions. In some cases, for instance for algebras containing unbounded differential oper-ators, there is in fact no C∗-algebra that accommodates them. On the other hand, it seems that nearly all algebraic structures arising from differential geometry can be described very naturally by locally convex algebras (or by the slightly more general concept of bornological algebras). The present note can be seen as part of a program in which we analyze constructions, that are classical in K-theory for C∗-algebras and in index theory, in the framework of locally convex algebras. Since locally convex algebras have, besides their algebraic structure, only very little structure, all arguments in the study of their K-theory or their cyclic homology have to be essentially algebraic (thus in particular they also apply to bornological algebras). This paper is triggered by an analysis of the proof of the Baum-Douglas-Taylor index theorem, [2], in the locally convex setting. Consider the extension EΨ: 0 → K → Ψ(M) → C(S∗M) → 0 determined by the C∗-algebra completion Ψ(M) of the algebra of pseudodif-ferential operators of order 0 on M and the natural extension EB∗M: 0 → C0(T ∗M) → C(B∗M) → C(S∗M) → 0 determined by the evaluation map on the boundary S∗M of the ball bundle B∗M. Both extensions determine elements which we denote by KK(EΨ) and KK(EB∗M), respectively, in the bivariant K-theory of Kasparov.

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27. Supported by *Deutsche* *Forschungsgemeinschaft*

, 2007

"... projects Wo896/4 and Wo896/6 (Priority Program ..."

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the *Deutsche* *Forschungsgemeinschaft*. On Classifications of Fitness Functions

, 1999

"... It is well-known that evolutionary algorithms succeed to optimize some functions efficiently and fail for others. Therefore, one would like to classify fitness functions as more or less hard to optimize for evolu-tionary algorithms. The aim of this paper is to clarify limitations and possibilities f ..."

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It is well-known that evolutionary algorithms succeed to optimize some functions efficiently and fail for others. Therefore, one would like to classify fitness functions as more or less hard to optimize for evolu-tionary algorithms. The aim of this paper is to clarify limitations and possibilities for classifications of fitness functions from a theoretical point of view. We distinguish two different types of classifications, de-scriptive and analytical ones. We shortly discuss three widely known approaches, namely the NK-model, epistasis variance, and fitness dis-tance correlation. Furthermore, we consider another recent measure, bit-wise epistasis introduced by Fonlupt, Robilliard, and Preux (1998). We discuss shortcomings and counter-examples for all four measures and use this to motivate a discussion of possibilities and limitations of classifications of fitness functions in a broader context. and find out its shortcomings. 1

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‘Kognitive Komplexität ’ funded by the *Deutsche* *Forschungsgemeinschaft*.

, 1995

"... Preface This manuscript contains the first part of a larger manuscript of syntax, and replaces the Theory of Syntactic Domains and some versions of a mauscript called Nearness and Syntactic Influence Spheres that circulated during the period from 1992 to 1994. All these versions are now obsolete. Co ..."

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Preface This manuscript contains the first part of a larger manuscript of syntax, and replaces the Theory of Syntactic Domains and some versions of a mauscript called Nearness and Syntactic Influence Spheres that circulated during the period from 1992 to 1994. All these versions are now obsolete. Covering syntax in its entirety is an ambitious goal, and I appreciate any observations that my readers may have concerning the content. The present manuscript is worked out in detail only in the first three chapters. The remaining chapters are assembled from various own sources and therefore rather heterogeneous. I apologize for this. The reason is that I had to prepare the manuscript in time for the workshop, and this time was running out. I also apologize for not giving sufficient credits or references. I have meanwhile learnt that some of the results that I prove have been shown by other people, but a critical assessment would take too much time now. I wish to thank Carsten Grefe and Paul Law for many discussions on this manuscript.