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Model-Based Policy Search for Automatic Tuning of Multivariate PID ControllersMar 08 2017PID control architectures are widely used in industrial applications. Despite their low number of open parameters, tuning multiple, coupled PID controllers can become tedious in practice. In this paper, we extend PILCO, a model-based policy search framework, ... More

A Lower Bound for the Discrepancy of a Random Point SetOct 01 2012Oct 05 2013We show that there is a constant $K > 0$ such that for all $N, s \in \N$, $s \le N$, the point set consisting of $N$ points chosen uniformly at random in the $s$-dimensional unit cube $[0,1]^s$ with probability at least $1-\exp(-\Theta(s))$ admits an ... More

Optimal Parameter Choices via Precise Black-Box AnalysisJul 09 2018Oct 17 2018It has been observed that some working principles of evolutionary algorithms, in particular, the influence of the parameters, cannot be understood from results on the asymptotic order of the runtime, but only from more precise results. In this work, we ... More

Asymptotically Optimal Randomized Rumor SpreadingNov 08 2010Nov 17 2010We propose a new protocol solving the fundamental problem of disseminating a piece of information to all members of a group of n players. It builds upon the classical randomized rumor spreading protocol and several extensions. The main achievements are ... More

Learning Gaussian Processes by Minimizing PAC-Bayesian Generalization BoundsOct 29 2018Dec 28 2018Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To this end, ... More

Reversible electric-field-driven magnetization in a columnar nanocomposite filmApr 13 2019Magnetic hysteresis loops show a moderate perpendicular anisotropy of the magnetostrictive CFO pillars, which is related to their vertical compression. The application of an electric field to the electromechanical PMN-PT substrate produced significant ... More

Meta-Learning Acquisition Functions for Bayesian OptimizationApr 04 2019Many practical applications of machine learning require data-efficient black-box function optimization, e.g., to identify hyperparameters or process settings. However, readily available algorithms are typically designed to be universal optimizers and ... More

Meta-Learning Acquisition Functions for Bayesian OptimizationApr 04 2019Apr 09 2019Many practical applications of machine learning require data-efficient black-box function optimization, e.g., to identify hyperparameters or process settings. However, readily available algorithms are typically designed to be universal optimizers and ... More

Trajectory-Based Off-Policy Deep Reinforcement LearningMay 14 2019Policy gradient methods are powerful reinforcement learning algorithms and have been demonstrated to solve many complex tasks. However, these methods are also data-inefficient, afflicted with high variance gradient estimates, and frequently get stuck ... More

Calculation of Discrepancy Measures and ApplicationsMay 07 2014In this book chapter we survey known approaches and algorithms to compute discrepancy measures of point sets. After providing an introduction which puts the calculation of discrepancy measures in a more general context, we focus on the geometric discrepancy ... More

Optimal Parameter Choices Through Self-Adjustment: Applying the 1/5-th Rule in Discrete SettingsApr 13 2015While evolutionary algorithms are known to be very successful for a broad range of applications, the algorithm designer is often left with many algorithmic choices, for example, the size of the population, the mutation rates, and the crossover rates of ... More

Collecting Coupons with Random Initial StakeAug 29 2013Motivated by a problem in the theory of randomized search heuristics, we give a very precise analysis for the coupon collector problem where the collector starts with a random set of coupons (chosen uniformly from all sets). We show that the expected ... More

A Tight Runtime Analysis of the $(1+(λ, λ))$ Genetic Algorithm on OneMaxJun 19 2015Understanding how crossover works is still one of the big challenges in evolutionary computation research, and making our understanding precise and proven by mathematical means might be an even bigger one. As one of few examples where crossover provably ... More

Rumor Spreading in Random Evolving GraphsFeb 15 2013Randomized gossip is one of the most popular way of disseminating information in large scale networks. This method is appreciated for its simplicity, robustness, and efficiency. In the "push" protocol, every informed node selects, at every time step (a.k.a. ... More

An Exponential Lower Bound for the Runtime of the cGA on Jump FunctionsApr 17 2019Jun 25 2019In the first runtime analysis of an estimation-of-distribution algorithm (EDA) on the multi-modal jump function class, Hasen\"ohrl and Sutton (GECCO 2018) proved that the runtime of the compact genetic algorithm with suitable parameter choice on jump ... More

The Runtime of the Compact Genetic Algorithm on Jump FunctionsAug 18 2019In the first and so far only mathematical runtime analysis of an estimation-of-distribution algorithm (EDA) on a multimodal problem, Hasen\"ohrl and Sutton (GECCO 2018) showed for any $k = o(n)$ that the compact genetic algorithm (cGA) with any hypothetical ... More

Probabilistic Recurrent State-Space ModelsJan 31 2018Feb 10 2018State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series data. Fully ... More

Meta-Learning Acquisition Functions for Bayesian OptimizationApr 04 2019May 28 2019Many practical applications of machine learning, such as tuning hyperparameters or process settings, rely on data-efficient black-box function optimization. Readily available algorithms are typically designed to be universal optimizers and, thus, often ... More

An Elementary Analysis of the Probability That a Binomial Random Variable Exceeds Its ExpectationDec 01 2017Jan 04 2018We give an elementary proof of the fact that a binomial random variable $X$ with parameters $n$ and $0.29/n \le p < 1$ with probability at least $1/4$ strictly exceeds its expectation. We also show that for $1/n \le p < 1 - 1/n$, $X$ exceeds its expectation ... More

Better Runtime Guarantees Via Stochastic DominationJan 13 2018Apart from few exceptions, the mathematical runtime analysis of evolutionary algorithms is mostly concerned with expected runtimes. In this work, we argue that stochastic domination is a notion that should be used more frequently in this area. Stochastic ... More

An Exponential Lower Bound for the Runtime of the cGA on Jump FunctionsApr 17 2019In the first runtime analysis of an estimation-of-distribution algorithm (EDA) on the multi-modal jump function class, Hasen\"ohrl and Sutton (GECCO 2018) proved that the runtime of the compact genetic algorithm with suitable parameter choice on jump ... More

Optimal Parameter Settings for the $(1+(λ, λ))$ Genetic AlgorithmApr 04 2016Jul 29 2016The $(1+(\lambda,\lambda))$ genetic algorithm is one of the few algorithms for which a super-constant speed-up through the use of crossover could be proven. So far, this algorithm has been used with parameters based also on intuitive considerations. In ... More

A Tight Runtime Analysis for the cGA on Jump Functions---EDAs Can Cross Fitness Valleys at No Extra CostMar 26 2019We prove that the compact genetic algorithm (cGA) with hypothetical population size $\mu = \Omega(\sqrt n \log n) \cap \text{poly}(n)$ with high probability finds the optimum of any $n$-dimensional jump function with jump size $k < \frac 1 {20} \ln n$ ... More

The Right Mutation Strength for Multi-Valued Decision VariablesApr 12 2016The most common representation in evolutionary computation are bit strings. This is ideal to model binary decision variables, but less useful for variables taking more values. With very little theoretical work existing on how to use evolutionary algorithms ... More

Self-Adjusting Mutation Rates with Provably Optimal Success RulesFeb 07 2019Jul 10 2019The one-fifth success rule is one of the best-known and most widely accepted techniques to control the parameters of evolutionary algorithms. While it is often applied in the literal sense, a common interpretation sees the one-fifth success rule as a ... More

Fast Re-Optimization via Structural DiversityFeb 01 2019When a problem instance is perturbed by a small modification, one would hope to find a good solution for the new instance by building on a known good solution for the previous one. Via a rigorous mathematical analysis, we show that evolutionary algorithms, ... More

Solving Problems with Unknown Solution Length at (Almost) No Extra CostJun 19 2015Most research in the theory of evolutionary computation assumes that the problem at hand has a fixed problem size. This assumption does not always apply to real-world optimization challenges, where the length of an optimal solution may be unknown a priori. ... More

Unbiased Black-Box Complexities of Jump FunctionsMar 30 2014Oct 16 2014We analyze the unbiased black-box complexity of jump functions with small, medium, and large sizes of the fitness plateau surrounding the optimal solution. Among other results, we show that when the jump size is $(1/2 - \varepsilon)n$, that is, only a ... More

Self-Adjusting Mutation Rates with Provably Optimal Success RulesFeb 07 2019The one-fifth success rule is one of the best-known and most widely accepted techniques to control the parameters of evolutionary algorithms. While it is often applied in the literal sense, a common interpretation sees the one-fifth success rule as a ... More

Fast Re-Optimization via Structural DiversityFeb 01 2019Apr 16 2019When a problem instance is perturbed by a small modification, one would hope to find a good solution for the new instance by building on a known good solution for the previous one. Via a rigorous mathematical analysis, we show that evolutionary algorithms, ... More

Information Carriers and Identification of Information Objects: An Ontological ApproachJan 01 2012Dec 12 2012Even though library and archival practice, as well as Digital Preservation, have a long tradition in identifying information objects, the question of their precise identity under change of carrier or migration is still a riddle to science. The objective ... More

Control of Large Swarms via Random Finite Set TheoryJan 22 2018Apr 11 2018Controlling large swarms of robotic agents has many challenges including, but not limited to, computational complexity due to the number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's configuration. ... More

On the Effectiveness of Simple Success-Based Parameter Selection Mechanisms for Two Classical Discrete Black-Box Optimization Benchmark ProblemsMar 04 2018Despite significant empirical and theoretically supported evidence that non-static parameter choices can be strongly beneficial in evolutionary computation, the question how to best adjust parameter values plays only a marginal role in contemporary research ... More

A Tight Runtime Analysis for the $(μ+ λ)$ EADec 28 2018Despite significant progress in the theory of evolutionary algorithms, the theoretical understanding of true population-based evolutionary algorithms remains challenging and only few rigorous results exist. Already for the most basic problem, the determination ... More

High resolution magnetostriction measurements in pulsed magnetic fields using Fibre Bragg GratingsFeb 01 2010We report on a new high resolution apparatus for measuring magnetostriction suitable for use at cryogenic temperatures in pulsed high magnetic fields which we have developed at the Hochfeld-Magnetlabor Dresden. Optical fibre strain gauges based on Fibre ... More

Working Principles of Binary Differential EvolutionDec 09 2018We conduct a first fundamental analysis of the working principles of binary differential evolution (BDE), an optimization heuristic for binary decision variables that was derived by Gong and Tuson (2007) from the very successful classic differential evolution ... More

Balanced Partitions of Vector SequencesMay 17 2004Let $d, r \in \N$, $\|\cdot\|$ any norm on $\R^d$ and $B$ denote the unit ball with respect to this norm. We show that any sequence $v_1,v_2,...$ of vectors in $B$ can be partitioned into $r$ subsequences $V_1, ..., V_r$ in a balanced manner with respect ... More

IOHprofiler: A Benchmarking and Profiling Tool for Iterative Optimization HeuristicsOct 11 2018IOHprofiler is a new tool for analyzing and comparing iterative optimization heuristics. Given as input algorithms and problems written in C or Python, it provides as output a statistical evaluation of the algorithms' performance by means of the distribution ... More

The (1+1) Elitist Black-Box Complexity of LeadingOnesApr 08 2016One important goal of black-box complexity theory is the development of complexity models allowing to derive meaningful lower bounds for whole classes of randomized search heuristics. Complementing classical runtime analysis, black-box models help us ... More

Introducing Elitist Black-Box Models: When Does Elitist Selection Weaken the Performance of Evolutionary Algorithms?Aug 27 2015Black-box complexity theory provides lower bounds for the runtime of black-box optimizers like evolutionary algorithms and serves as an inspiration for the design of new genetic algorithms. Several black-box models covering different classes of algorithms ... More

Maximizing Drift is Not Optimal for Solving OneMaxApr 16 2019It seems very intuitive that for the maximization of the OneMax problem $f(x):=\sum_{i=1}^n{x_i}$ the best that an elitist unary unbiased search algorithm can do is to store a best so far solution, and to modify it with the operator that yields the best ... More

Precise Runtime Analysis for PlateausJun 04 2018To gain a better theoretical understanding of how evolutionary algorithms cope with plateaus of constant fitness, we analyze how the $(1 + 1)$~EA optimizes the $n$-dimensional $Plateau_k$ function. This function has a plateau of second-best fitness in ... More

Deterministic Random Walks on the Two-Dimensional GridMar 15 2007Jim Propp's rotor router model is a deterministic analogue of a random walk on a graph. Instead of distributing chips randomly, each vertex serves its neighbors in a fixed order. We analyze the difference between Propp machine and random walk on the infinite ... More

Multiplicative Up-DriftApr 11 2019Drift analysis aims at translating the expected progress of an evolutionary algorithm (or more generally, a random process) into a probabilistic guarantee on its run time (hitting time). So far, drift arguments have been successfully employed in the rigorous ... More

OneMax in Black-Box Models with Several RestrictionsApr 10 2015Sep 10 2015Black-box complexity studies lower bounds for the efficiency of general-purpose black-box optimization algorithms such as evolutionary algorithms and other search heuristics. Different models exist, each one being designed to analyze a different aspect ... More

Significance-based Estimation-of-Distribution AlgorithmsJul 10 2018Oct 11 2018Estimation-of-distribution algorithms (EDAs) are randomized search heuristics that maintain a probabilistic model of the solution space. This model is updated from iteration to iteration, based on the quality of the solutions sampled according to the ... More

Hyper-Parameter Tuning for the (1+(λ,λ)) GAApr 09 2019It is known that the $(1+(\lambda,\lambda))$~Genetic Algorithm (GA) with self-adjusting parameter choices achieves a linear expected optimization time on OneMax if its hyper-parameters are suitably chosen. However, it is not very well understood how the ... More

A new code for Fourier-Legendre analysis of large datasets: first results and a comparison with ring-diagram analysisNov 18 2010Fourier-Legendre decomposition (FLD) of solar Doppler imaging data is a promising method to estimate the sub-surface solar meridional flow. FLD is sensible to low-degree oscillation modes and thus has the potential to probe the deep meridional flow. We ... More

Observation of minority spin character of the new electron doped manganite La_0.7Ce_0.3MnO_3 from tunneling magnetoresistanceMay 15 2002Oct 11 2002We report the magnetotransport characteristics of a trilayer ferromagnetic tunnel junction build of an electron doped manganite (La_0.7Ce_0.3MnO_3) and a hole doped manganite (La_0.7Ca_0.3MnO_3). At low temperatures the junction exhibits a large positive ... More

Hereditary Discrepancies in Different Numbers of Colors IINov 24 2006We bound the hereditary discrepancy of a hypergraph $\HH$ in two colors in terms of its hereditary discrepancy in $c$ colors. We show that $\herdisc(\HH,2) \le K c \herdisc(\HH,c)$, where $K$ is some absolute constant. This bound is sharp.

The recovery of ridge functions on the hypercube suffers from the curse of dimensionalityMar 25 2019A multivariate ridge function is a function of the form $f(x) = g(a^{\scriptscriptstyle T} x)$, where $g$ is univariate and $a \in \mathbb{R}^d$. We show that the recovery of an unknown ridge function defined on the hypercube $[-1,1]^d$ with Lipschitz-regular ... More

Improved Protocols and Hardness Results for the Two-Player Cryptogenography ProblemMar 19 2016The cryptogenography problem, introduced by Brody, Jakobsen, Scheder, and Winkler (ITCS 2014), is to collaboratively leak a piece of information known to only one member of a group (i)~without revealing who was the origin of this information and (ii)~without ... More

Quasi-Random Rumor Spreading: Reducing Randomness Can Be CostlyAug 03 2010We give a time-randomness tradeoff for the quasi-random rumor spreading protocol proposed by Doerr, Friedrich and Sauerwald [SODA 2008] on complete graphs. In this protocol, the goal is to spread a piece of information originating from one vertex throughout ... More

Comment on "Linear and passive silicon optical isolator" in Scientific Reports 2, 674Jan 30 2013Wang et al. [1] demonstrated different power transmission coefficients for forward and backward propagation in simulation and experiment. From such a demonstration, the central claim of their paper is that "the spatial inversion symmetry breaking diode ... More

Adaptive Drift AnalysisAug 01 2011Sep 27 2011We show that, for any c>0, the (1+1) evolutionary algorithm using an arbitrary mutation rate p_n = c/n finds the optimum of a linear objective function over bit strings of length n in expected time Theta(n log n). Previously, this was only known for c ... More

Towards a More Practice-Aware Runtime Analysis of Evolutionary AlgorithmsDec 03 2018Theory of evolutionary computation (EC) aims at providing mathematically founded statements about the performance of evolutionary algorithms (EAs). The predominant topic in this research domain is runtime analysis, which studies the time it takes a given ... More

Deep Learning architectures for generalized immunofluorescence based nuclear image segmentationJul 30 2019Separating and labeling each instance of a nucleus (instance-aware segmentation) is the key challenge in segmenting single cell nuclei on fluorescence microscopy images. Deep Neural Networks can learn the implicit transformation of a nuclear image into ... More

Playing Mastermind with Many ColorsJul 03 2012Jan 17 2013We analyze the general version of the classic guessing game Mastermind with $n$ positions and $k$ colors. Since the case $k \le n^{1-\varepsilon}$, $\varepsilon>0$ a constant, is well understood, we concentrate on larger numbers of colors. For the most ... More

Simple and Optimal Randomized Fault-Tolerant Rumor SpreadingSep 27 2012Jan 05 2015We revisit the classic problem of spreading a piece of information in a group of $n$ fully connected processors. By suitably adding a small dose of randomness to the protocol of Gasienic and Pelc (1996), we derive for the first time protocols that (i) ... More

Constructing Low Star Discrepancy Point Sets with Genetic AlgorithmsApr 07 2013Oct 07 2013Geometric discrepancies are standard measures to quantify the irregularity of distributions. They are an important notion in numerical integration. One of the most important discrepancy notions is the so-called \emph{star discrepancy}. Roughly speaking, ... More

A simple electrostatic model applicable to biomolecular recognitionSep 30 2009An exact, analytic solution for a simple electrostatic model applicable to biomolecular recognition is presented. In the model, a layer of high dielectric constant material (representative of the solvent, water) whose thickness may vary separates two ... More

Discrepancy of Symmetric Products of HypergraphsApr 20 2006For a hypergraph ${\mathcal H} = (V,{\mathcal E})$, its $d$--fold symmetric product is $\Delta^d {\mathcal H} = (V^d,\{E^d |E \in {\mathcal E}\})$. We give several upper and lower bounds for the $c$-color discrepancy of such products. In particular, we ... More

The antiferromagnetic spin-1/2 Heisenberg model on the square lattice in a magnetic fieldDec 17 2008Mar 16 2009We study the field dependence of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice by means of exact diagonalizations. In a first part, we calculate the spin-wave velocity, the spin-stiffness, and the magnetic susceptibility and thus ... More

Solving DC programs with polyhedral component utilizing a multiple objective linear programming solverOct 18 2016A class of non-convex optimization problems with DC objective function and linear constraints is studied, where DC stands for being representable as the difference $f=g-h$ of two convex functions $g$ and $h$. In particular, we deal with the special case ... More

Formality of $\mathbb{P}$-objectsSep 19 2017We show that a $\mathbb{P}$-object and simple configurations of $\mathbb{P}$-objects have a formal derived endomorphism algebra. Hence the triangulated category (classically) generated by such objects is independent of the ambient triangulated category. ... More

Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solverOct 18 2016Mar 15 2017A class of non-convex optimization problems with DC objective function is studied, where DC stands for being representable as the difference $f=g-h$ of two convex functions $g$ and $h$. In particular, we deal with the special case where one of the two ... More

Computing Minimum Cycle Bases in Weighted Partial 2-Trees in Linear TimeMar 04 2013Jan 10 2014We present a linear time algorithm for computing an implicit linear space representation of a minimum cycle basis (MCB) in weighted partial 2-trees, i.e., graphs of treewidth two. The implicit representation can be made explicit in a running time that ... More

Randomized Rounding for Routing and Covering Problems: Experiments and ImprovementsJul 02 2010Following previous theoretical work by Srinivasan (FOCS 2001) and the first author (STACS 2006) and a first experimental evaluation on random instances (ALENEX 2009), we investigate how the recently developed different approaches to generate randomized ... More

How different are the Liège and Hamburg atlases of the solar spectrum?Apr 13 2016Context: The high-fidelity solar spectral atlas prepared by Delbouille and co-workers (Li\`ege atlas), and the one by Neckel and co-workers (Hamburg atlas), are widely recognised as the most important reference spectra of the Sun at disc-centre in the ... More

Evolving Boolean Functions with Conjunctions and Disjunctions via Genetic ProgrammingMar 28 2019Recently it has been proved that simple GP systems can efficiently evolve the conjunction of $n$ variables if they are equipped with the minimal required components. In this paper, we make a considerable step forward by analysing the behaviour and performance ... More

The Efficiency Threshold for the Offspring Population Size of the ($μ$, $λ$) EAApr 15 2019Understanding when evolutionary algorithms are efficient or not, and how they efficiently solve problems, is one of the central research tasks in evolutionary computation. In this work, we make progress in understanding the interplay between parent and ... More

Gauge-invariant Green's functions for the bosonic sector of the standard modelDec 18 1998Jun 21 2000There are many applications in gauge theories where the usually employed framework involving gauge-dependent Green's functions leads to considerable problems. In order to overcome the difficulties invariably tied to gauge dependence, we present a manifestly ... More

Equivariant Differential CohomologyOct 21 2015Nov 10 2015The construction of characteristic classes via the curvature form of a connection is one motivation for the refinement of integral cohomology by de Rham cocycles -- known as differential cohomology. We will discuss the analog in the case of a group action ... More

Special Drawing Rights in a New Decentralized CenturyJun 25 2019Unfulfilled expectations from macro-economic initiatives during the Great Recession and the massive shift into globalization echo today with political upheaval, anti-establishment propaganda, and looming trade/currency wars that threaten domestic and ... More

Quasirandom Rumor SpreadingDec 24 2010Aug 07 2013We propose and analyze a quasirandom analogue of the classical push model for disseminating information in networks ("randomized rumor spreading"). In the classical model, in each round each informed vertex chooses a neighbor at random and informs it, ... More

Strong Robustness of Randomized Rumor Spreading ProtocolsJan 18 2010Oct 03 2012Randomized rumor spreading is a classical protocol to disseminate information across a network. At SODA 2008, a quasirandom version of this protocol was proposed and competitive bounds for its run-time were proven. This prompts the question: to what extent ... More

Verification of the helioseismic Fourier-Legendre analysis for meridional flow measurementsJun 16 2016Measuring the Sun's internal meridional flow is one of the key issues of helioseismology. Using the Fourier-Legendre analysis is a technique for addressing this problem. We validate this technique with the help of artificial helioseismic data. The analysed ... More

Status of sub-GeV Hidden Particle SearchesAug 26 2010Hidden sector particles with sub-GeV masses like hidden U(1) gauge bosons, the NMSSM CP-odd Higgs, and other axion-like particles are experimentally little constrained as they interact only very weakly with the visible sector. For masses below the muon ... More

The electroweak chiral Lagrangian reanalyzedJul 09 1999Oct 26 2000In this paper we reanalyze the electroweak chiral Lagrangian with particular focus on two issues related to gauge invariance. Our analysis is based on a manifestly gauge-invariant approach that we introduced recently. It deals with gauge-invariant Green's ... More

A universal ionization threshold for strongly driven Rydberg statesApr 21 2004We observe a universal ionization threshold for microwave driven one-electron Rydberg states of H, Li, Na, and Rb, in an {\em ab initio} numerical treatment without adjustable parameters. This sheds new light on old experimental data, and widens the scene ... More

Residual Symmetries in the Spectrum of Periodically Driven Alkali Rydberg StatesNov 25 1999We identify a fundamental structure in the spectrum of microwave driven alkali Rydberg states, which highlights the remnants of the Coulomb symmetry in the presence of a non-hydrogenic core. Core-induced corrections with respect to the hydrogen spectrum ... More

Particle-particle ladder based basis-set corrections applied to atoms and molecules using coupled-cluster theoryMar 13 2019We investigate the basis-set convergence of coupled cluster electronic correlation energies using a recently proposed finite basis-set correction technique. The correction is applied to atomic and molecular systems and is based on a diagrammatically decomposed ... More

A Multilevel Monte Carlo Algorithm for Parabolic Advection-Diffusion Problems with Discontinuous CoefficientsFeb 06 2019The Richards' equation is a model for flow of water in unsaturated soils. The coefficients of this (nonlinear) partial differential equation describe the permeability of the medium. Insufficient or uncertain measurements are commonly modeled by random ... More

Particle-particle ladder based basis-set corrections applied to atoms and molecules using coupled-cluster theoryMar 13 2019Mar 14 2019We investigate the basis-set convergence of coupled cluster electronic correlation energies using a recently proposed finite basis-set correction technique. The correction is applied to atomic and molecular systems and is based on a diagrammatically decomposed ... More

Inverse Scattering for the Laplace operator with boundary conditions on Lipschitz surfacesJan 26 2019Feb 17 2019We provide a general scheme, in the combined frameworks of Mathematical Scattering Theory and Factorization Method, for inverse scattering for the couple of self-adjoint operators $(\widetilde\Delta,\Delta)$, where $\Delta$ is the free Laplacian in $L^{2}({\mathbb ... More

Tanaka structures modeled on extended Poincaré algebrasJan 03 2012Oct 04 2012Let (V,(.,.)) be a pseudo-Euclidean vector space and S an irreducible Cl(V)-module. An extended translation algebra is a graded Lie algebra m = m_{-2}+m_{-1} = V+S with bracket given by ([s,t],v) = b(v.s,t) for some nondegenerate so(V)-invariant reflexive ... More

Formality of $\mathbb{P}$-objectsSep 19 2017May 06 2019We show that a $\mathbb{P}$-object and simple configurations of $\mathbb{P}$-objects have a formal derived endomorphism algebra. Hence the triangulated category (classically) generated by such objects is independent of the ambient triangulated category. ... More

PT-symmetrically deformed shock wavesJan 27 2012We investigate for a large class of nonlinear wave equations, which allow for shock wave formations, how these solutions behave when they are PT-symmetrically deformed. For real solutions we find that they are transformed into peaked solutions with a ... More

Numerical analysis of detection-mechanism models of SNSPDAug 27 2013Nov 12 2013The microscopic mechanism of photon detection in superconducting nanowire single-photon detectors is still under debate. We present a simple, but powerful theoretical model that allows us to identify essential differences between competing detection mechanisms. ... More

A Multilevel Monte Carlo Algorithm for Parabolic Advection-Diffusion Problems with Discontinuous CoefficientsFeb 06 2019Apr 18 2019The Richards' equation is a model for flow of water in unsaturated soils. The coefficients of this (nonlinear) partial differential equation describe the permeability of the medium. Insufficient or uncertain measurements are commonly modeled by random ... More

Improved Bounds and Schemes for the Declustering ProblemMar 02 2006The declustering problem is to allocate given data on parallel working storage devices in such a manner that typical requests find their data evenly distributed on the devices. Using deep results from discrepancy theory, we improve previous work of several ... More

Interpolating Local and Global Search by Controlling the Variance of Standard Bit MutationJan 17 2019A key property underlying the success of evolutionary algorithms (EAs) is their global search behavior, which allows the algorithms to `jump' from a current state to other parts of the search space, thereby avoiding to get stuck in local optima. This ... More

Lognormal Infection Times of Online Information SpreadMay 22 2013The infection times of individuals in online information spread such as the inter-arrival time of Twitter messages or the propagation time of news stories on a social media site can be explained through a convolution of lognormally distributed observation ... More

Evolving Boolean Functions with Conjunctions and Disjunctions via Genetic ProgrammingMar 28 2019May 01 2019Recently it has been proved that simple GP systems can efficiently evolve the conjunction of $n$ variables if they are equipped with the minimal required components. In this paper, we make a considerable step forward by analysing the behaviour and performance ... More

Runtime Analysis for Self-adaptive Mutation RatesNov 30 2018We propose and analyze a self-adaptive version of the $(1,\lambda)$ evolutionary algorithm in which the current mutation rate is part of the individual and thus also subject to mutation. A rigorous runtime analysis on the OneMax benchmark function reveals ... More

Equivariant characteristic forms in the Cartan model and Borel equivariant cohomologyAug 31 2015Nov 10 2015We show the compatibility of the differential geometric and the topological construction of equivariant characteristic classes for compact Lie groups. Our analysis motivates a differential geometric construction for equivariant characteristic classes ... More

Band-edge BCS-BEC crossover in a two-band superconductor: physical properties and detection parametersJul 11 2014Superconductivity in iron-based, magnesium diborides, and other novel superconducting materials has a strong multi-band and multi-gap character. Recent experiments support the possibillity for a BCS-BEC crossover induced by strong-coupling and proximity ... More

Ethemba Trusted Host EnvironmentMainly Based on AttestationJan 28 2009Ethemba provides a framework and demonstrator for TPM applications.

Thermodynamic properties and thermal correlation lengths of a Hubbard model with bond-charge interactionFeb 27 2004We investigate the thermodynamics of a one-dimensional Hubbard model with bond-charge interaction X using the transfer matrix renormalization group method (TMRG). Numerical results for various quantities like spin and charge susceptibilities, particle ... More

Imbalanced thee-component Fermi gas with attractive interactions: Multiple FFLO-pairing, Bose-Fermi and Fermi-Fermi mixtures versus collapse and phase separationJun 04 2009We present a detailed study of the population imbalanced three-component Hubbard chain with attractive interactions. Such a system can be realized experimentally with three different hyperfine states of ultra cold $^6$Li atoms in an optical lattice. We ... More