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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

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

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

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

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

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

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

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

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

On the Impact of the Cutoff Time on the Performance of Algorithm ConfiguratorsApr 12 2019May 21 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

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

Learning Deep Representations for Word Spotting Under Weak SupervisionDec 01 2017Jan 26 2018Convolutional Neural Networks have made their mark in various fields of computer vision in recent years. They have achieved state-of-the-art performance in the field of document analysis as well. However, CNNs require a large amount of annotated training ... More

Optimistic and Pessimistic Neural Networks for Scene and Object RecognitionSep 26 2016Dec 22 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

Attribute CNNs for Word Spotting in Handwritten DocumentsDec 20 2017Word spotting has become a field of strong research interest in document image analysis over the last years. Recently, AttributeSVMs were proposed which predict a binary attribute representation. At their time, this influential method defined the state-of-the-art ... 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

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

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.

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

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

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

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

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

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

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

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.

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

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

A remark on quantum gravityMay 26 2007We discuss the structure of Dyson--Schwinger equations in quantum gravity and conclude in particular that all relevant skeletons are of first order in the loop number. There is an accompanying sub Hopf algebra on gravity amplitudes equivalent to identities ... More

Combinatorics of (perturbative) quantum field theoryOct 09 2000We review the structures imposed on perturbative QFT by the fact that its Feynman diagrams provide Hopf and Lie algebras. We emphasize the role which the Hopf algebra plays in renormalization by providing the forest formulas. We exhibit how the associated ... More

Renormalization and Knot TheoryDec 06 1994Dec 08 1994We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory.

Not so non-renormalizable gravityMay 29 2008We review recent progress with the understanding of quantum fields, including ideas how gravity might turn out to be a renormalizable theory after all.

Dyson Schwinger Equations: From Hopf algebras to Number TheorySep 01 2006Sep 13 2006We consider the structure of renormalizable quantum field theories from the viewpoint of their underlying Hopf algebra structure. We review how to use this Hopf algebra and the ensuing Hochschild cohomology to derive non-perturbative results for the short-distance ... More

On Overlapping DivergencesOct 03 1998Feb 12 1999Using set-theoretic considerations, we show that the forest formula for overlapping divergences comes from the Hopf algebra of rooted trees.

Habilitationsschrift: Renormalization and Knot TheoryJul 17 1996Jul 28 1997We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory as well as number theory and report on recent ... More

The Daugavet equation for operators on function spacesJul 28 1995We prove the norm identity $\|\Id+T\| =1+\|T\|$, which is known as the Daugavet equation, for weakly compact operators $T$ on natural function spaces such as function algebras and $L^{1}$-predual spaces, provided a non-discreteness assumption is met. ... More

A Flexible Primal-Dual ToolboxMar 18 2016Jul 20 2016\textbf{FlexBox} is a flexible MATLAB toolbox for finite dimensional convex variational problems in image processing and beyond. Such problems often consist of non-differentiable parts and involve linear operators. The toolbox uses a primal-dual scheme ... More

The single risk factor approach to capital charges in case of correlated loss given default ratesFeb 14 2004Feb 18 2004A new methodology for incorporating LGD correlation effects into the Basel II risk weight functions is introduced. This methodology is based on modelling of LGD and default event with a single loss variable. The resulting formulas for capital charges ... More

Remarks on the monotonicity of default probabilitiesJul 23 2002The consultative papers for the Basel II Accord require rating systems to provide a ranking of obligors in the sense that the rating categories indicate the creditworthiness in terms of default probabilities. As a consequence, the default probabilities ... More

Reply to "What Faster-than-traffic Characteristic Speeds Mean for Vehicular Traffic Flow"Jun 14 2009This contribution replies to H. M. Zhang's paper "What Faster-than-traffic Characteristic Speeds Mean for Vehicular Traffic Flow", which comments on the manuscript "On the Controversy around Daganzo's Requiem for and Aw-Rascle's Resurrection of Second-Order ... More

Modeling Multi-Lane Traffic Flow with Queuing EffectsJun 03 1998On the basis of assumptions about the behavior of driver-vehicle units concerning acceleration, deceleration, overtaking, and lane-changing maneuvers, a gas-kinetic traffic model for uni-directional multi-lane freeways is constructed. Queuing effects ... More

Survival Analysis, Master Equation, Efficient Simulation of Path-Related Quantities, and Hidden State Concept of TransitionsMay 27 1998This paper presents and derives the interrelations between survival analysis and master equation. Survival analysis deals with modeling the transitions between succeeding states of a system in terms of hazard rates. Questions related with this are the ... More

A Fluid Dynamic Model for the Movement of PedestriansMay 18 1998A kind of fluid dynamic description for the collective movement of pedestrians is developed on the basis of a Boltzmann-like gaskinetic model. The differences between these pedestrian specific equations and those for ordinary fluids are worked out, for ... More

A Contracted Path Integral Solution of the Discrete Master EquationMay 14 1998A new representation of the exact time dependent solution of the discrete master equation is derived. This representation can be considered as contraction of the path integral solution of Haken. It allows the calculation of the probability distribution ... More

Derivation of Non-Local Macroscopic Traffic Equations and Consistent Traffic Pressures from Microscopic Car-Following ModelsMay 22 2008This contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic car-following models. While it is shown that some conventional approaches lead to theoretical problems, it is proposed ... More

Traffic Data and Their Implications for Consistent Traffic Flow ModelingJun 18 1998The paper analyzes traffic data of the Dutch freeway A9 with respect to certain aspects which are relevant for traffic flow modeling as well as the calibration of model parameters and functions. Apart from the dynamic velocity distribution, the density-dependence ... More

Interrelations between Stochastic Equations for Systems with Pair InteractionsMay 20 1998Several types of stochastic equations are important in thermodynamics, chemistry, evolutionary biology, population dynamics and quantitative social science. For systems with pair interactions four different types of equations are derived, starting from ... More

Models for Pedestrian BehaviorMay 07 1998May 13 1998The behavior of pedestrians shows certain regularities, which can be described by quantitative (partly stochastic) models. The models are based on the behavior of individual pedestrians, which depends on the pedestrian intentions and on the aspects of ... More

Solution Theory and Functional A Posteriori Error Estimates for General First Order Systems with Applications to Electro-Magneto-StaticsNov 09 2016We prove a solution theory and functional a posteriori error estimates for general linear first order systems. As a prototypical application we will discuss the system of electro-magneto statics with mixed tangential and normal boundary conditions. Second ... More

Does quantification without adjustments work?Feb 28 2016Aug 12 2016Classification is the task of predicting the class labels of objects based on the observation of their features. In contrast, quantification has been defined as the task of determining the prevalences of the different sorts of class labels in a target ... More

The Web is missing an essential part of infrastructure: an Open Web IndexMar 09 2019A proposal for building an index of the Web that separates the infrastructure part of the search engine - the index - from the services part that will form the basis for myriad search engines and other services utilizing Web data on top of a public infrastructure ... More

Permutation Matrices and the Moments of their Characteristic PolynomialsOct 27 2009Jul 13 2010In this paper, we are interested in the moments of the characteristic polynomial $Z_n(x)$ of the $n\times n$ permutation matrices with respect to the uniform measure. We use a combinatorial argument to write down the generating function of $\E{\prod_{k=1}^p ... More

Bayesian estimation of probabilities of default for low default portfoliosDec 23 2011Aug 04 2013The estimation of probabilities of default (PDs) for low default portfolios by means of upper confidence bounds is a well established procedure in many financial institutions. However, there are often discussions within the institutions or between institutions ... More

The two defaults scenario for stressing credit portfolio loss distributionsFeb 12 2010Oct 25 2015The impact of a stress scenario of default events on the loss distribution of a credit portfolio can be assessed by determining the loss distribution conditional on these events. While it is conceptually easy to estimate loss distributions conditional ... More

Integral representations for products of two parabolic cylinder functions with different arguments and ordersAug 25 2015This paper derives new integral representations for products of two parabolic cylinder functions. In particular, expressions are obtained for D_{nu}(x)D_{mu}(y), with x>0 and y>0, that allow for different orders and arguments in the two parabolic cylinder ... More

Fitting a distribution to Value-at-Risk and Expected Shortfall, with an application to covered bondsMay 27 2015Nov 12 2015Covered bonds are a specific example of senior secured debt. If the issuer of the bonds defaults the proceeds of the assets in the cover pool are used for their debt service. If in this situation the cover pool proceeds do not suffice for the debt service, ... More

Low Frequency Asymptotics for Time-Harmonic Generalized Maxwell Equations in Nonsmooth Exterior DomainsMay 20 2011We discuss the radiation problem of total reflection for a time-harmonic generalized Maxwell system in a non-smooth exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the identity. ... More

A Global div-curl-Lemma for Mixed Boundary Conditions in Weak Lipschitz Domains and a Corresponding Generalized $\mathrm{A}_{0}^{*}$-$\mathrm{A}_{1}$-Lemma in Hilbert SpacesJun 30 2017Dec 11 2018We prove global and local versions of the so-called div-curl-lemma, a crucial result in the homogenization theory of partial differential equations, for mixed boundary conditions on bounded weak Lipschitz domains in 3D with weak Lipschitz interfaces. ... More