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How Crossover Speeds Up Building-Block Assembly in Genetic AlgorithmsMar 26 2014Nov 26 2014We re-investigate a fundamental question: how effective is crossover in Genetic Algorithms in combining building blocks of good solutions? Although this has been discussed controversially for decades, we are still lacking a rigorous and intuitive answer. ... More

Memetic Algorithms: Parametrization and Balancing Local and Global SearchSep 29 2011This is a preprint of a book chapter from the Handbook of Memetic Algorithms, Studies in Computational Intelligence, Vol. 379, ISBN 978-3-642-23246-6, Springer, edited by F. Neri, C. Cotta, and P. Moscato. It is devoted to the parametrization of memetic ... More

Analysing the Robustness of Evolutionary Algorithms to Noise: Refined Runtime Bounds and an Example Where Noise is BeneficialDec 03 2018We analyse the performance of well-known evolutionary algorithms (1+1)EA and (1+$\lambda$)EA in the prior noise model, where in each fitness evaluation the search point is altered before evaluation with probability $p$. We present refined results for ... More

A New Method for Lower Bounds on the Running Time of Evolutionary AlgorithmsSep 07 2011Nov 16 2011We present a new method for proving lower bounds on the expected running time of evolutionary algorithms. It is based on fitness-level partitions and an additional condition on transition probabilities between fitness levels. The method is versatile, ... More

On the Impact of the Cutoff Time on the Performance of Algorithm ConfiguratorsApr 12 2019Algorithm configurators are automated methods to optimise the parameters of an algorithm for a class of problems. We evaluate the performance of a simple random local search configurator (ParamRLS) for tuning the neighbourhood size $k$ of the RLS$_k$ ... More

Adaptive Population Models for Offspring Populations and Parallel Evolutionary AlgorithmsFeb 02 2011Mar 02 2011We present two adaptive schemes for dynamically choosing the number of parallel instances in parallel evolutionary algorithms. This includes the choice of the offspring population size in a (1+$\lambda$) EA as a special case. Our schemes are parameterless ... More

Update Strength in EDAs and ACO: How to Avoid Genetic DriftJul 14 2016Jul 15 2016We provide a rigorous runtime analysis concerning the update strength, a vital parameter in probabilistic model-building GAs such as the step size $1/K$ in the compact Genetic Algorithm (cGA) and the evaporation factor $\rho$ in ACO. While a large update ... More

General Upper Bounds on the Running Time of Parallel Evolutionary AlgorithmsJun 15 2012We present a new method for analyzing the running time of parallel evolutionary algorithms with spatially structured populations. Based on the fitness-level method, it yields upper bounds on the expected parallel running time. This allows to rigorously ... More

Analysis of Speedups in Parallel Evolutionary Algorithms for Combinatorial OptimizationSep 08 2011Evolutionary algorithms are popular heuristics for solving various combinatorial problems as they are easy to apply and often produce good results. Island models parallelize evolution by using different populations, called islands, which are connected ... More

Parallel Black-Box Complexity with Tail BoundsJan 31 2019We propose a new black-box complexity model for search algorithms evaluating $\lambda$ search points in parallel. The parallel unary unbiased black-box complexity gives lower bounds on the number of function evaluations every parallel unary unbiased black-box ... More

On the Runtime Analysis of the Clearing Diversity-Preserving MechanismMar 26 2018Clearing is a niching method inspired by the principle of assigning the available resources among a niche to a single individual. The clearing procedure supplies these resources only to the best individual of each niche: the winner. So far, its analysis ... More

Runtime Analysis of Probabilistic Crowding and Restricted Tournament Selection for Bimodal OptimisationMar 26 2018Many real optimisation problems lead to multimodal domains and so require the identification of multiple optima. Niching methods have been developed to maintain the population diversity, to investigate many peaks in parallel and to reduce the effect of ... More

Memetic Algorithms Beat Evolutionary Algorithms on the Class of Hurdle ProblemsApr 17 2018Memetic algorithms are popular hybrid search heuristics that integrate local search into the search process of an evolutionary algorithm in order to combine the advantages of rapid exploitation and global optimisation. However, these algorithms are not ... More

Optimizing Monotone Functions Can Be DifficultOct 07 2010Oct 14 2010Extending previous analyses on function classes like linear functions, we analyze how the simple (1+1) evolutionary algorithm optimizes pseudo-Boolean functions that are strictly monotone. Contrary to what one would expect, not all of these functions ... More

Design and Analysis of Diversity-Based Parent Selection Schemes for Speeding Up Evolutionary Multi-objective OptimisationMay 03 2018May 22 2018Parent selection in evolutionary algorithms for multi-objective optimisation is usually performed by dominance mechanisms or indicator functions that prefer non-dominated points. We propose to refine the parent selection on evolutionary multi-objective ... More

First Steps Towards a Runtime Comparison of Natural and Artificial EvolutionApr 23 2015Oct 01 2015Evolutionary algorithms (EAs) form a popular optimisation paradigm inspired by natural evolution. In recent years the field of evolutionary computation has developed a rigorous analytical theory to analyse their runtime on many illustrative problems. ... More

Simple Max-Min Ant Systems and the Optimization of Linear Pseudo-Boolean FunctionsJul 27 2010With this paper, we contribute to the understanding of ant colony optimization (ACO) algorithms by formally analyzing their runtime behavior. We study simple MAX-MIN ant systems on the class of linear pseudo-Boolean functions defined on binary strings ... More

Optimistic and Pessimistic Neural Networks for Scene and Object RecognitionSep 26 2016In this paper the application of uncertainty modeling to convolutional neural networks is evaluated. A novel method for adjusting the network's predictions based on uncertainty information is introduced. This allows the network to be either optimistic ... More

Escaping Local Optima using Crossover with Emergent or Reinforced DiversityAug 10 2016Population diversity is essential for avoiding premature convergence in Genetic Algorithms (GAs) and for the effective use of crossover. Yet the dynamics of how diversity emerges in populations are not well understood. We use rigorous runtime analysis ... More

An elementary approach to the Daugavet equationDec 12 1994Let $T\dopu C(S)\to C(S)$ be a bounded linear operator. We present a necessary and sufficient condition for the so-called Daugavet equation $$ \|\Id+T\| = 1+\|T\| $$ to hold, and we apply it to weakly compact operators and to operators factoring through ... More

Using Search Engine Technology to Improve Library CatalogsNov 18 2015This chapter outlines how search engine technology can be used in online public access library catalogs (OPACs) to help improve users experiences, to identify users intentions, and to indicate how it can be applied in the library context, along with how ... More

Investigating the X-ray Emission from the Galactic TeV Gamma-ray Source MGRO J1908+06Dec 26 2015MGRO J1908+06 is a bright, extended TeV gamma-ray source located near the Galactic plane. The TeV emission has previously been attributed to the pulsar wind nebula of the radio-faint gamma-ray pulsar PSR J1907+0602 discovered with Fermi. However, studies ... More

AR-Components of domestic finite group schemes: McKay-Quivers and RamificationDec 15 2015For a domestic finite group scheme, we give a direct description of the Euclidean components in its Auslander-Reiten quiver via the McKay-quiver of a finite linearly reductive subgroup scheme of $SL(2)$. Moreover, for a normal subgroup scheme $\mathcal{N}$ ... More

The Influence of Commercial Intent of Search Results on Their Perceived RelevanceNov 18 2015We carried out a retrieval effectiveness test on the three major web search engines (i.e., Google, Microsoft and Yahoo). In addition to relevance judgments, we classified the results according to their commercial intent and whether or not they carried ... More

Google Scholar as a tool for discovering journal articles in library and information scienceNov 18 2015Purpose: The purpose of this paper is to measure the coverage of Google Scholar for the Library and Information Science (LIS) journal literature as identified by a list of core LIS journals from a study by Schloegl and Petschnig (2005). Methods: We checked ... More

Classification of indecomposable modules for finite group schemes of domestic representation typeSep 17 2015Apr 01 2016We investigate the representation theory of domestic group schemes $\mathcal{G}$ over an algebraically closed field of characteristic $p > 2$. We present results about filtrations of induced modules, actions on support varieties, Clifford theory for certain ... More

Existence of localised normal modes in nonlinear latticesJun 25 2015Jul 13 2016We prove the existence of exponentially localised and time-periodic solutions in general nonlinear Hamiltonian lattice systems. Like normal modes, these localised solutions are characterised by collective oscillations at the lattice sites with a uniform ... More

Societal, Economic, Ethical and Legal Challenges of the Digital Revolution: From Big Data to Deep Learning, Artificial Intelligence, and Manipulative TechnologiesApr 15 2015In the wake of the on-going digital revolution, we will see a dramatic transformation of our economy and most of our societal institutions. While the benefits of this transformation can be massive, there are also tremendous risks to our society. After ... More

What can we learn from Knizhnik--Zamolodchikov Equations?Jul 19 2014We discuss structural similarities between Knizhnik--Zamolodchikov equations (in fact, their simplest version needed to introduce the Drinfeld associator) and Dyson--Schwinger equations. We emphasize that the latter allow for a filtration by co-radical ... More

Some mathematical properties of the Bartlett chi ratioOct 17 2013Based on artistic interpretations, art professor Christopher Bartlett (Towson University, USA) suggested introducing a new mathematical constant related to the golden ratio. He called it the chi ratio, as chi follows phi in the Greek alphabet. Without ... More

On the Maxwell Inequalities for Bounded and Convex DomainsNov 09 2013Jul 23 2014For a bounded and convex domain in three dimensions we show that the Maxwell constants are bounded from below and above by Friedrichs' and Poincare's constants.

New Ways to Promote Sustainability and Social Well-Being in a Complex, Strongly Interdependent World: The FuturICT ApproachOct 13 2013FuturICT is one of six proposals currently being considered for support within the European Commission's Flagship Initiative (see Box 1). The vision of the FuturICT project is to develop new science and new information and communication systems that will ... More

A New Kind of Economy is Born - Social Decision-Makers Beat the "Homo Economicus"Sep 28 2013The Internet and Social Media change our way of decision-making. We are no longer the independent decision makers we used to be. Instead, we have become networked minds, social decision-makers, more than ever before. This has several fundamental implications. ... More

Directed transient long-range transport in a slowly driven Hamiltonian system of interacting particlesAug 14 2008We study the Hamiltonian dynamics of a one-dimensional chain of linearly coupled particles in a spatially periodic potential which is subjected to a time-periodic mono-frequency external field. The average over time and space of the related force vanishes ... More

SupersymmetryJun 25 2009The determination of supersymmetric parameters at the LHC in favorable as well as difficult scenarios is presented. If discovered and measured at the LHC and the ILC, supersymmetry may provide a link between collider physics and cosmology.

Extraction of SUSY Parameters from Collider DataAug 26 2008Aug 28 2008The extraction of the parameters of the supersymmetric Lagrangian is discusse d. Particular emphasis is put on the rigorous treatment of experimental and theo retical errors. While the LHC can provide a valuable first estimate of the parameters, the combination ... More

Extracting the fundamental parametersSep 30 2009If supersymmetry is discovered at the LHC, the extraction of the fundamental parameters will be a formidable task. In such a system where measurements depend on different combinations of the parameters in a highly correlated system, the identification ... More

The residues of quantum field theory - numbers we should knowApr 13 2004Apr 23 2004We discuss in an introductory manner structural similarities between the polylogarithm and Green functions in quantum field theory.

New mathematical structures in renormalizable quantum field theoriesNov 14 2002Nov 26 2002Computations in renormalizable perturbative quantum field theories reveal mathematical structures which go way beyond the formal structure which is usually taken as underlying quantum field theory. We review these new structures and the role they can ... More

How useful can knot and number theory be for loop calculations?Jul 17 1998We summarize recent results connecting multiloop Feynman diagram calculations to different parts of mathematics, with special attention given to the Hopf algebra structure of renormalization.

Factorization in quantum field theory: an exercise in Hopf algebras and local singularitiesJun 03 2003Jun 10 2003I discuss the role of Hochschild cohomology in Quantum Field Theory with particular emphasis on Dyson--Schwinger equations.

On knots in subdivergent diagramsOct 17 1996Jul 14 1997We investigate Feynman diagrams which are calculable in terms of generalized one-loop functions, and explore how the presence or absence of transcendentals in their counterterms reflects the entanglement of link diagram constructed from them and explains ... More

The Earth's Gamma-ray Albedo as observed by EGRETOct 20 2004The Earth's high energy gamma-ray emission is caused by cosmic ray interactions with the atmosphere. The EGRET detector on-board the CGRO satellite is only the second experiment (after SAS-2) to provide a suitable dataset for the comprehensive study of ... More

Faster Background Determination - a method for gaining time coverage and flux measurement accuracy with Cherenkov telescopesApr 28 2003An improved way of taking off-source data for background determination in Cherenkov telescope observations is proposed. Generalizing the traditional concept of taking on-source/off-source observations of equal duration (e.g. 30 minutes ON followed by ... More

Validation of internal rating systems and PD estimatesJun 07 2006This paper elaborates on the validation requirements for rating systems and probabilities of default (PDs) which were introduced with the New Capital Standards (Basel II). We start in Section 2 with some introductory remarks on the topics and approaches ... More

Modeling and Simulation of Multi-Lane Traffic FlowJun 09 1998A most important aspect in the field of traffic modeling is the simulation of bottleneck situations. For their realistic description a macroscopic multi-lane model for uni-directional freeways including acceleration, deceleration, velocity fluctuations, ... More

Empirical Traffic Data and Their Implications for Traffic ModelingJun 04 1998From single vehicle data a number of new empirical results about the temporal evolution, correlation, and density-dependence of macroscopic traffic quantities have been determined. These have relevant implications for traffic modeling and allow to test ... More

Derivation of a Fundamental Diagram for Urban Traffic FlowJul 11 2008Feb 04 2009Despite the importance of urban traffic flows, there are only a few theoretical approaches to determine fundamental relationships between macroscopic traffic variables such as the traffic density, the utilization, the average velocity, and the travel ... More

Production, Supply, and Traffic Systems: A Unified DescriptionJan 23 2004The transport of products between different suppliers or production units can be described similarly to driven many-particle and traffic systems. We introduce equations for the flow of goods in supply networks and the adaptation of production speeds. ... More

A Section-Based Queueing-Theoretical Traffic Model for Congestion and Travel Time Analysis in NetworksJul 01 2003Dec 14 2003While many classical traffic models treat the spatial extension of streets continuously or by discretization into cells of a certain length, we will subdivide roads into comparatively long homogeneous road sections of constant capacity with an inhomogeneity ... More

Modeling Supply Chains and Business Cycles as Unstable Transport PhenomenaJan 13 2003Physical concepts developed to describe instabilities in traffic flows can be generalized in a way that allows one to understand the well-known instability of supply chains (the so-called ``bullwhip effect''). That is, small variations in the consumption ... More

Structure and Instability of High-Density Equations for Traffic FlowJun 10 1998Similar to the treatment of dense gases, fluid-dynamic equations for the dynamics of congested vehicular traffic are derived from Enskog-like kinetic equations. These contain additional terms due to the anisotropic vehicle interactions. The calculations ... More

A stochastic behavioral model and a `microscopic' foundation of evolutionary game theoryMay 26 1998A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations. That means, the ... More

Injective Spaces via AdjunctionApr 02 2008Our work over the past years shows that not only the collection of (for instance) all topological spaces gives rise to a category, but also each topological space can be seen individually as a category by interpreting the convergence relation $\mathfrak{x}\to ... More

Chen's Iterated Integral represents the Operator Product ExpansionJan 21 1999Sep 18 1999The recently discovered formalism underlying renormalization theory, the Hopf algebra of rooted trees, allows to generalize Chen's lemma. In its generalized form it describes the change of a scale in Green functions, and hence relates to the operator ... More

Analytic Description of Cross Sections for Regular Forms of Zincblende- and Diamond-Lattice NanowiresJan 03 2019Jan 10 2019Semiconductor nanowires (NWires) experience stress and charge transfer by their environment and impurity atoms. In return, the environment of NWires experiences a NWire stress response which may lead to propagated strain and change in shape and size of ... More

On the Polynomial and Exponential Decay of Eigen-Forms of Generalized Time-Harmonic Maxwell ProblemsMay 20 2011We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain with non-smooth inhomogeneous, anisotropic coefficients ... More

The art of probability-of-default curve calibrationDec 15 2012Nov 26 2013PD curve calibration refers to the transformation of a set of rating grade level probabilities of default (PDs) to another average PD level that is determined by a change of the underlying portfolio-wide PD. This paper presents a framework that allows ... More

Capital allocation for credit portfolios with kernel estimatorsDec 16 2006May 11 2008Determining contributions by sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often economic capital is measured as Value-at-Risk (VaR) of the portfolio loss distribution. For ... More

Algebraic Structures in local QFTJul 02 2010A review of the Hodge and Hopf-algebraic approach to QFT.

Nigel Kalton's work in isometrical Banach space theoryMar 16 2011This paper surveys some of the late Nigel Kalton's contributions to Banach space theory. The paper is written for the Nigel Kalton Memorial Website http://mathematics.missouri.edu/kalton/, which is scheduled to go online in summer 2011.

Conditional Expectation as Quantile DerivativeApr 19 2001For a linear combination of random variables, fix some confidence level and consider the quantile of the combination at this level. We are interested in the partial derivatives of the quantile with respect to the weights of the random variables in the ... More

Parallel Focal Structure and Singular Riemannian FoliationsMar 02 2004Jun 15 2004We prove that a submanifold with parallel focal structure, which is a generalization of isoparametric and equifocal submanifolds, induces a singular Riemannian foliation of the ambient space by its parallel and focal manifolds.

Bounded solutions to backward SDE's with jumps for utility optimization and indifference hedgingFeb 14 2007We prove results on bounded solutions to backward stochastic equations driven by random measures. Those bounded BSDE solutions are then applied to solve different stochastic optimization problems with exponential utility in models where the underlying ... More

Parameter curves for the regular representations of tame bimodulesDec 19 2007Jun 16 2008We present results and examples which show that the consideration of a certain tubular mutation is advantageous in the study of noncommutative curves which parametrize the simple regular representations of a tame bimodule. We classify all tame bimodules ... More

Some integral representations and limits for (products of) the parabolic cylinder functionMay 08 2015May 26 2015Veestraeten [1] recently derived inverse Laplace transforms for Laplace transforms that contain products of two parabolic cylinder functions by exploiting the link between the parabolic cylinder function and the transition density and distribution functions ... More

The dissipation distance for a 2D single crystal with two symmetric slip systemsJul 22 2002We solve a model problem from single crystal plasticity.We consider 4 slip systems in the plane with orthogonal slip-directions and equal slip rates, forward as well as backwards. We compute the associated dissipation distance by solving an optimal control ... More

Feynman diagrams and polylogarithms: shuffles and pentagonsMay 30 2000We summarize the Hopf algebra structure on Feynman diagrams and emphasize the interest in further algebraic structures hidden in Feynman graphs.

Knots and DivergencesMar 10 1995We give empirical evidence that the UV-divergences of a renormalizable field theory are knot invariants.

An algebraic approach to Z-FactorsMay 31 1994We sketch a systematic approach to multiloop calculations. We focus on the Z-factors of a renormalizable theory and show that they can be obtained by purely algebraic methods based on power-counting and the forest structure of the divergent graphs. (submitted ... More

Tensor Integrals for Two Loop Standard Model CalculationsDec 06 1993Jan 08 1994We give a new method for the reduction of tensor integrals to finite integral representations and UV divergent analytic expressions. This includes a new method for the handling of the gamma-algebra. TYPO IN EQUATION (5) CORRECTED, MACROS REORDERED.

2-loop Integrals in the Standard ModelDec 12 1992Dec 14 1992We introduce in typical examples new methods for the calculation of massive loop integrals appearing in the radiative correction calculations of the Standard Model.

A Short Note on Two-Loop Box FunctionsJul 06 1994Jul 06 1994It is shown that the two-loop four-point functions are similar in structure to the three-point two-loop functions for all mass cases and topologies. The result is derived by using a rotation to a (+,-,-,+) signature without spoiling analyticity properties. ... More

The Role of $γ_5$ in Dimensional RegularizationJan 31 1994We discuss the consistency of a new \gf -scheme with renormalization. In particular we study the power-counting behaviour of multiloop graphs to prove its consistency. As a side effect we obtain a short proof of the Adler-Bardeen theorem. Further we show ... More

Generic growth instabilities in one-layered tissue sheetsJul 14 1999Jul 22 1999Growth and folding in one-layered model tissue sheets are studied in a stochastic, lattice-free single cell model which considers the discrete cellular structure of the tissue, and a coarse grained analytical approach. The polarity of the tissue sheet ... More

On the Hopf algebra structure of perturbative quantum field theoriesJul 23 1997Jan 15 1998We show that the process of renormalization encapsules a Hopf algebra structure in a natural manner. This sheds light on the recently proposed connection between knots and renormalization theory.

A traffic lights approach to PD validationMay 02 2003As a consequence of the dependence experienced in loan portfolios, the standard binomial test which is based on the assumption of independence does not appear appropriate for validating probabilities of default (PDs). The model underlying the new rules ... More

Traffic and Related Self-Driven Many-Particle SystemsDec 13 2000Apr 23 2001Since the subject of traffic dynamics has captured the interest of physicists, many astonishing effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by so-called ``phantom ... More

Which are the youngest protostars? Determining properties of confirmed and candidate Class0 sources by broad-band photometryOct 02 2004We searched the literature to obtain a complete list of known Class0 sources. A list of 95 confirmed or candidate objects was compiled. To the best of our knowledge, all published broad-band observations from 1mu to 3.5mm have been collected and are assembled ... More

Counting perfect colourings of plane regular tilingsJul 29 2008A first step in investigating colour symmetries of periodic and nonperiodic patterns is determining the number of colours which allow perfect colourings of the pattern under consideration. A perfect colouring is one where each symmetry of the uncoloured ... More

Quantum fields, periods and algebraic geometryMay 20 2014We discuss how basic notions of graph theory and associated graph polynomials define questions for algebraic geometry, with an emphasis given to an analysis of the structure of Feynman rules as determined by those graph polynomials as well as algebraic ... More

Homology of moduli spaces of linkages in high-dimensional Euclidean spaceJan 02 2013We study the topology of moduli spaces of closed linkages in \R^d depending on a length vector \ell\in \R^n. In particular, we use equivariant Morse theory to obtain information on the homology groups of these spaces, which works best for odd d. In the ... More

Capital Allocation to Business Units and Sub-Portfolios: the Euler PrincipleAug 19 2007Jun 22 2008Despite the fact that the Euler allocation principle has been adopted by many financial institutions for their internal capital allocation process, a comprehensive description of Euler allocation seems still to be missing. We try to fill this gap by presenting ... More

About Substitution Tilings with Statistical Circular SymmetryMar 14 2008Two results about equidistribution of tile orientations in primitive substitution tilings are stated, one for finitely many, one for infinitely many orientations. Furthermore, consequences for the associated diffraction spectra and the dynamical systems ... More

Self-dual tilings with respect to star-dualityApr 19 2007The concept of star-duality is described for self-similar cut-and-project tilings in arbitrary dimensions. This generalises Thurston's concept of a Galois-dual tiling. The dual tilings of the Penrose tilings as well as the Ammann-Beenker tilings are calculated. ... More

Substitution tilings with statistical circular symmetryApr 19 2007Two new series of substitution tilings are introduced in which the tiles appear in infinitely many orientations. It is shown that several properties of the well-known pinwheel tiling do also hold for these new examples, and, in fact, for all substitution ... More

Hodge-Helmholtz Decompositions of Weighted Sobolev Spaces in Irregular Exterior Domains with Inhomogeneous and Anisotropic MediaMay 20 2011We study in detail Hodge-Helmholtz decompositions in non-smooth exterior domains filled with inhomogeneous and anisotropic media. We show decompositions of alternating differential forms belonging to weighted Sobolev spaces into irrotational and solenoidal ... More

On the smallest poles of Igusa's p-adic zeta functionsSep 02 2005Let K be a p-adic field. We explore Igusa's p-adic zeta function, which is associated to a K-analytic function on an open and compact subset of K^n. First we deduce a formula for an important coefficient in the Laurent series of this meromorphic function ... More

A four for the price of one duality principle for distributive spacesFeb 13 2011In this paper we consider topological spaces as generalised orders and characterise those spaces which satisfy a (suitably defined) topological distributive law. Furthermore, we show that the category of these spaces is dually equivalent to a certain ... More

Solution Theory, Variational Formulations, and Functional A Posteriori Error Estimates for General First Order Systems with Applications to Electro-Magneto-Statics and MoreNov 09 2016May 21 2018We prove a comprehensive solution theory using tools from functional analysis, show corresponding variational formulations, and present functional a posteriori error estimates for general linear first order systems. As a prototypical application we will ... More

Variational approach to contact line dynamics for thin filmsJan 31 2018This paper investigates a variational approach to viscous flows with contact line dynamics based on energy-dissipation modeling. The corresponding model is reduced to a thin-film equation and its variational structure is also constructed and discussed. ... More

Inhomogeneous Field Configurations and the Electroweak Phase TransitionSep 24 1993We investigate the effects of inhomogeneous scalar field configurations on the electroweak phase transition. For this purpose we calculate the leading perturbative correction to the wave function correction term $Z(\vph,T)$, i.e., the kinetic term in ... More

Locality, QED and Classical ElectrodynamicsOct 05 1998We report on some conceptual changes in our present understanding of Quantum Field Theory and muse about possible consequences for the understanding of $v>c$ signals.

Three Etudes in QFTSep 24 2009We review QFT from the algebraic structure of its perturbative expansion and point out three new results.

The core Hopf algebraFeb 07 2009We study the core Hopf algebra underlying the renormalization Hopf algebra.

Anatomy of a gauge theorySep 17 2005Feb 08 2006We exhibit the role of Hochschild cohomology in quantum field theory with particular emphasis on gauge theory and Dyson--Schwinger equations, the quantum equations of motion. These equations emerge from Hopf- and Lie algebra theory and free quantum field ... More

What is the trouble with Dyson--Schwinger equations?Jul 02 2004We discuss similarities and differences between Green Functions in Quantum Field Theory and polylogarithms. Both can be obtained as solutions of fixpoint equations which originate from an underlying Hopf algebra structure. Typically, the equation is linear ... More

Feynman Diagram Calculations - From finite Integral Representations to knotted InfinitiesMay 05 1995May 07 1995Work is reported on finite integral representations for 2-loop massive 2-, 3- and 4-point functions, using orthogonal and parallel space variables. It is shown that this can be utilized to cover particles with arbitrary spin (tensor integrals), and that ... More

Threshold corrections to the gamma t anti-t vertex at O(alpha alpha(s))Feb 18 2009In these proceedings a recent calculation of the last missing piece of the two-loop O(alpha alpha(s)) corrections to gamma t anti-t vertex at the t anti-t threshold due to the exchange of a W boson and a gluon is summarised. The calculation constitutes ... More

Statistical Properties of Narrow-Line Seyfert 1 galaxiesMay 08 2000The number of publications considering Narrow-Line Seyfert 1 galaxies has increased dramatically in recent years. Especially after the launch of the X-ray missions ROSAT and ASCA, Narrow-Line Seyfert 1s have become very popular. In these proceedings I ... More