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SOTorrent: Studying the Origin, Evolution, and Usage of Stack Overflow Code SnippetsSep 08 2018Mar 09 2019Stack Overflow (SO) is the most popular question-and-answer website for software developers, providing a large amount of copyable code snippets. Like other software artifacts, code on SO evolves over time, for example when bugs are fixed or APIs are updated ... More

Contextual Documentation Referencing on Stack OverflowJun 11 2019Software engineering is knowledge-intensive and requires software developers to continually search for knowledge, often on community question answering platforms such as Stack Overflow. Such information sharing platforms do not exist in isolation, and ... More

The Evolution of Stack Overflow Posts: Reconstruction and AnalysisNov 02 2018Stack Overflow (SO) is the most popular question-and-answer website for software developers, providing a large amount of code snippets and free-form text on a wide variety of topics. Like other software artifacts, questions and answers on SO evolve over ... More

Usage and Attribution of Stack Overflow Code Snippets in GitHub ProjectsFeb 08 2018Stack Overflow (SO) is the largest Q&A website for software developers, providing a huge amount of copyable code snippets. Using those snippets raises maintenance and legal issues. SO's license (CC BY-SA 3.0) requires attribution, i.e., referencing the ... More

Constructing Urban Tourism Space Digitally: A Study of Airbnb Listings in Two Berlin NeighborhoodsSep 05 2018Over the past decade, Airbnb has emerged as the most popular platform for renting out single rooms or whole apartments. The impact of Airbnb listings on local neighborhoods has been controversially discussed in many cities around the world. The platform's ... More

Towards a Theory of Software Development ExpertiseJul 16 2018Nov 04 2018Software development includes diverse tasks such as implementing new features, analyzing requirements, and fixing bugs. Being an expert in those tasks requires a certain set of skills, knowledge, and experience. Several studies investigated individual ... More

Empirical Research Plan: Effects of Sketching on Program ComprehensionDec 05 2016Sketching is an important means of communication in software engineering practice. Yet, there is little research investigating the use of sketches. We want to contribute a better understanding of sketching, in particular its use during program comprehension. ... More

Sketches and Diagrams in PracticeJun 28 2017Sketches and diagrams play an important role in the daily work of software developers. In this paper, we investigate the use of sketches and diagrams in software engineering practice. To this end, we used both quantitative and qualitative methods. We ... More

Usage and Attribution of Stack Overflow Code Snippets in GitHub ProjectsFeb 08 2018Sep 21 2018Stack Overflow (SO) is the most popular question-and-answer website for software developers, providing a large amount of copyable code snippets. Using those snippets raises maintenance and legal issues. SO's license (CC BY-SA 3.0) requires attribution, ... More

Worse Than Spam: Issues In Sampling Software DevelopersJul 04 2017Background: Reaching out to professional software developers is a crucial part of empirical software engineering research. One important method to investigate the state of practice is survey research. As drawing a random sample of professional software ... More

Linking Sketches and Diagrams to Source Code ArtifactsJun 29 2017Recent studies have shown that sketches and diagrams play an important role in the daily work of software developers. If these visual artifacts are archived, they are often detached from the source code they document, because there is no adequate tool ... More

Round-Trip Sketches: Supporting the Lifecycle of Software Development Sketches from Analog to Digital and BackAug 05 2017Sketching is an important activity for understanding, designing, and communicating different aspects of software systems such as their requirements or architecture. Often, sketches start on paper or whiteboards, are revised, and may evolve into a digital ... More

Attribution Required: Stack Overflow Code Snippets in GitHub ProjectsJul 03 2017Stack Overflow (SO) is the largest Q&A website for developers, providing a huge amount of copyable code snippets. Using these snippets raises various maintenance and legal issues. The SO license requires attribution, i.e., referencing the original question ... More

SOTorrent: Studying the Origin, Evolution, and Usage of Stack Overflow Code SnippetsSep 08 2018Stack Overflow (SO) is the most popular question-and-answer website for software developers, providing a large amount of copyable code snippets. Like other software artifacts, code on SO evolves over time, for example when bugs are fixed or APIs are updated ... More

Navigate, Understand, Communicate: How Developers Locate Performance BugsJun 30 2017Background: Performance bugs can lead to severe issues regarding computation efficiency, power consumption, and user experience. Locating these bugs is a difficult task because developers have to judge for every costly operation whether runtime is consumed ... More

SOTorrent: Reconstructing and Analyzing the Evolution of Stack Overflow PostsMar 20 2018May 07 2018Stack Overflow (SO) is the most popular question-and-answer website for software developers, providing a large amount of code snippets and free-form text on a wide variety of topics. Like other software artifacts, questions and answers on SO evolve over ... More

(No) Influence of Continuous Integration on the Commit Activity in GitHub ProjectsFeb 23 2018Sep 14 2018A core goal of Continuous Integration (CI) is to make small incremental changes to software projects, which are integrated frequently into a mainline repository or branch. This paper presents an empirical study that investigates if developers adjust their ... More

Fast and Tiny Structural Self-Indexes for XMLDec 28 2010XML document markup is highly repetitive and therefore well compressible using dictionary-based methods such as DAGs or grammars. In the context of selectivity estimation, grammar-compressed trees were used before as synopsis for structural XPath queries. ... More

XPath Node Selection over Grammar-Compressed TreesNov 21 2013XML document markup is highly repetitive and therefore well compressible using grammar-based compression. Downward, navigational XPath can be executed over grammar-compressed trees in PTIME: the query is translated into an automaton which is executed ... More

Sorting Discrete i.i.d. Inputs: Quicksort is OptimalAug 17 2016Oct 05 2016We prove the Sedgewick-Bentley conjecture on median-of-$k$ Quicksort on equal keys: The average number of comparisons for Quicksort with fat-pivot (a.k.a. three-way) partitioning is asymptotically only a constant times worse than the information-theoretic ... More

Assessment of Path Reservation in Distributed Real-Time Vehicle GuidanceApr 23 2013In this paper we assess the impact of path reservation as an additional feature in our distributed real-time vehicle guidance protocol BeeJamA. Through our microscopic simulations we show that na\"{\i}ve reservation of links without any further measurements ... More

LiSK - A C++ Library for Evaluating Classical Polylogarithms and $\text{Li}_{22}$May 31 2016I present a lightweight C++ library for the evaluation of classical polylogarithms Li_n and the special function Li_{22} for arbitrary complex arguments. The evaluation is possible in arbitrary precision arithmetic and features also an explicit double ... More

Diffusion and percolation in anisotropic random barrier modelsFeb 02 2004An anisotropic random barrier model is presented, in which the transition probabilities in different directions have different probability density functions. At low temperatures, the anisotropic long--time diffusion coefficients, obtained using an effective ... More

Proceedings Second International Workshop on Trends in Tree Automata and Tree TransducersNov 20 2013This volume contains the papers that were presented at the second international workshop on Trends in Tree Automata and Transducers (TTATT 2013) which took place on October 19th, 2013 in Hanoi/Vietnam. The workshop was colocated with the verification ... More

Relation Variables in Qualitative Spatial ReasoningAug 03 2006We study an alternative to the prevailing approach to modelling qualitative spatial reasoning (QSR) problems as constraint satisfaction problems. In the standard approach, a relation between objects is a constraint whereas in the alternative approach ... More

On complements and the factorization problem for Hopf algebrasDec 12 2010Two new results concerning complements in a semisimple Hopf algebra are proved. They extend some well known results from group theory. The uniqueness of Krull Schmidt Remak type decomposition is proved for semisimple completely reducible Hopf algebras. ... More

On coideal subalgebras of cocentral Kac algebras and a generalization of Wall's conjectureMar 25 2012It shown that any coideal subalgebra of a finite dimensional Hopf algebra is a cyclic module over the dual Hopf algebra. Using this we describe all coideal subalgebras of a cocentral abelian extension of Hopf algebras extending some results from [4].

Penguin amplitudes in hadronic B decays: NLO spectator scatteringNov 11 2006We present results on the NLO (alpha_s^2) spectator-scattering corrections to the topological penguin amplitudes for charmless hadronic two-body B-decays in QCD factorization. The corrections can be sizable for the colour-suppressed electroweak penguin ... More

Theory of charmless hadronic B-decaysApr 08 2013I summarize results and performance of the dynamical theory of charmless hadronic B decays, based on QCD factorization in the heavy quark limit. On the theoretical side, a number of NNLO (alpha_s^2) amplitudes are now available, all showing a well-behaved ... More

Space-time constructions for the mean curvature flow in a Ricci flow backgroundJun 13 2012Jul 30 2012Given a solution of the (backwards) Ricci flow one can construct a so called canonical soliton metric on space-time, introduced by E. Cabezas-Rivas and P. Topping. We observe that for a mean curvature flow within a (backwards) Ricci flow background, the ... More

Diffraction at the LHC: a non-technical IntroductionMar 22 2010In diffractive interactions of protons or nuclei a violent collision can occur that leaves the forward going particle completely intact -with probability determined by the structure of the proton or nucleus. At very high energies these collisions also ... More

From Particle Tracks to Velocity and Acceleration Fields Using B-Splines and PenaltiesOct 30 2015In this work a method for reconstructing velocity and acceleration fields is described which uses scattered particle tracking data from flow experiments as input. The goal is to reconstruct these fields faithfully with a limited amount of compute time ... More

First Numerical Implementation of the Loop-Tree Duality MethodOct 14 2015The Loop-Tree Duality (LTD) is a novel perturbative method in QFT that establishes a relation between loop-level and tree-level amplitudes, which gives rise to the idea of treating them simultaneously in a common Monte Carlo. Initially introduced for ... More

Rigidity and Flexibility for Handlebody GroupsAug 10 2016We show that finite index subgroups of the handlebody group are rigid in their ambient mapping class group: any injective map of a finite index subgroup of the genus $g$ handlebody group into the genus $g$ mapping class group is conjugation by a mapping ... More

A non-parametric ensemble transform method for Bayesian inferenceOct 01 2012Jan 14 2013Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). ... More

SLE and spidernetsFeb 12 2018Oct 05 2018We regard SLE from a quantum probability point of view and approximate the underlying quantum process by the growth of a random graph, which arises from the comb product of a certain spidernet and its complement. We obtain a stronger result for the deterministic ... More

Demonstration of entanglement assisted invariance on IBM's Quantum ExperienceSep 23 2016Quantum entanglement is among the most fundamental, yet from classical intuition also most surprising properties of the fully quantum nature of physical reality. We report several experiments performed on IBM's Quantum Experience demonstrating envariance ... More

The Geometrical Description of Feasible Singular Values in the Tensor Train FormatJan 29 2017Tensors have grown in importance and are applied to an increasing number of fields. Crucial in this regard are tensor formats, such as the widespread Tensor Train (TT) decomposition, which represent low rank tensors. This multivariate TT-rank and accordant ... More

Smash nilpotent cycles on products of curvesJul 31 2012Aug 01 2012Voevodsky has conjectured that numerical and smash equivalence coincide on a smooth projective variety. We prove the conjecture for one dimensional cycles on an arbitrary product of curves. As a consequence we get that numerically trivial 1-cycles on ... More

MC3D - 3D Continuum Radiative Transfer, Version 2Jul 18 2002A revised and greatly improved version of the 3D continuum radiative transfer code MC3D is presented. It is based on the Monte-Carlo method and solves the radiative transfer problem self-consistently. It is designed for the simulation of dust temperatures ... More

Limiting Approach to Generalized Gamma Bessel Model via Fractional Calculus and its Applications in Various DisciplinesJul 30 2013The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral one can list out ... More

Interacting growth processes and invariant percolationApr 12 2013Jan 19 2015The aim of this paper is to underline the relation between reversible growth processes and invariant percolation. We present two models of interacting branching random walks (BRWs), truncated BRWs and competing BRWs, where survival of the growth process ... More

Classical basis for quantum spectral fluctuations in hyperbolic systemsMar 23 2003Aug 21 2003We reason in support of the universality of quantum spectral fluctuations in chaotic systems, starting from the pioneering work of Sieber and Richter who expressed the spectral form factor in terms of pairs of periodic orbits with self-crossings and avoided ... More

Two-term spectral asymptotics for the Dirichlet pseudo-relativistic kinetic energy operator on a bounded domainJun 27 2017Aug 06 2018Continuing the series of works following Weyl's one-term asymptotic formula for the counting function $N(\lambda)=\sum_{n=1}^\infty(\lambda_n{-}\lambda)_-$ of the eigenvalues of the Dirichlet Laplacian and the much later found two-term expansion on domains ... More

Totally geodesic submanifolds in Riemannian symmetric spacesOct 24 2008In the first part of this expository article, the most important constructions and classification results concerning totally geodesic submanifolds in Riemannian symmetric spaces are summarized. In the second part, I describe the results of my classification ... More

Harmonic morphisms on conformally flat 3-spheresFeb 26 2009We show that under some non-degeneracy assumption the only submersive harmonic morphism on a conformally flat $3-$sphere is the Hopf fibration. The proof involves an appropriate use the Chern-Simons functional.

On hypersurfaces of positive reach, alternating Steiner formulae and Hadwiger's ProblemApr 15 2013We give new characterisations of sets of positive reach and show that a closed hypersurface has positive reach if and only if it is of class $C^{1,1}$. These results are then used to prove new alternating Steiner formul{\ae} for hypersurfaces of positive ... More

Quasinormal modes of magnetic black branes at finite 't Hooft couplingNov 09 2018Nov 29 2018The aim of this work is to extend the knowledge about Quasinormal Modes (QNMs) and the equilibration of strongly coupled systems, specifically of a quark gluon plasma (which we consider to be in a strong magnetic background field) by using the duality ... More

Aspects of Calabi-Yau Fourfold CompactificationsSep 25 2018The study of the geometry of Calabi-Yau fourfolds is relevant for compactifications of string theory, M-theory, and F-theory to various dimensions. In the first part of this thesis, we study the action of mirror symmetry on two-dimensional $\cN=(2,2)$ ... More

Stability and uniqueness of self-similar profiles in $L^1$ spaces for perturbations of the constant kernel in Smoluchowski's coagulation equationFeb 26 2019In this work, we consider self-similar profiles for Smoluchowski's coagulation equation for kernels which are possibly unbounded perturbations of the constant one. For this model, we show that the self-similar solutions for the perturbed kernel are close ... More

Rational cohomology of \bar R_2 (and \bar S_2)Dec 23 2010We compute the rational cohomology ring of \bar R_2, the (compactified) moduli space of Prym curves of genus 2. We also recompute the rational cohomology ring of \bar S_2, the moduli space of spin curves of genus 2, thereby correcting some errors made ... More

Superconvergence Using Pointwise Interpolation in Convection-Diffusion ProblemsApr 28 2013Considering a singularly perturbed convection-diffusion problem, we present an analysis for a superconvergence result using pointwise interpolation of Gau{\ss}-Lobatto type for higher-order streamline diffusion FEM. We show a useful connection between ... More

Computations and Applications of eta invariantsNov 22 2010Apr 27 2011We give a survey on eta invariants including methods of computation and applications in differential topology.

Categoricity of Shimura VarietiesMar 18 2018Dec 15 2018We propose a model-theoretic structure for Shimura varieties and give necessary and sufficient conditions to obtain categoricity. We show that these conditions are directly related to important conjectures in number theory coming from Galois representations ... More

Torsion Invariants for FamiliesApr 18 2008May 09 2009We give an overview over the higher torsion invariants of Bismut-Lott, Igusa-Klein and Dwyer-Weiss-Williams, including some more or less recent developments.

Tame hereditary path algebras and amenabilityAug 06 2018In this note we are concerned with the notion of amenable representation type as defined in a recent paper by G\'abor Elek. Roughly speaking, an algebra is of amenable type if for all $\varepsilon > 0$, every finite-dimensional module has a submodule ... More

Asymptotic link invariants for ergodic vector fieldsMar 06 2008We study the asymptotics of a family of link invariants on the orbits of a smooth volume-preserving ergodic vector field on a compact domain of the 3-space. These invariants, called linear saddle invariants, include many concordance invariants and generate ... More

Linear systems over localizations of ringsSep 24 2017Dec 18 2017We describe a method for solving linear systems over the localization of a commutative ring $R$ at a multiplicatively closed subset $S$ that works under the following hypotheses: the ring $R$ is coherent, i.e., we can compute finite generating sets of ... More

Gauge Deformations and Embedding Theorems for Special GeometriesSep 30 2009Jul 30 2010We reduce the embedding problem for hypo SU(2) and SU(3)-structures to the embedding problem for hypo G2-structures into parallel Spin(7)-manifolds. The latter will be described in terms of gauge deformations. This description involves the intrinsic torsion ... More

Time reversal for radiative transport with applications to inverse and control problemsApr 10 2013Aug 03 2013In this paper we develop a time reversal method for the radiative transport equation to solve two problems: an inverse problem for the recovery of an initial condition from boundary measurements, and the exact boundary controllability of the transport ... More

Transportation-cost inequalities for diffusions driven by Gaussian processesMar 11 2014Sep 21 2016We prove transportation-cost inequalities for the law of SDE solutions driven by general Gaussian processes. Examples include the fractional Brownian motion, but also more general processes like bifractional Brownian motion. In case of multiplicative ... More

On the second cohomology group of a simplicial groupNov 15 2009Sep 29 2010We give an algebraic proof for the result of Eilenberg and Mac Lane that the second cohomology group of a simplicial group G can be computed as a quotient of a fibre product involving the first two homotopy groups and the first Postnikov invariant of ... More

On the irreducible representations of generalized quantum doublesFeb 20 2012A description of all the irreducible representations of generalized quantum doubles associated to skew pairings of semisimple Hopf algebras is given. In particular a description of the irreducible representations of semisimple Drinfeld doubles is obtained. ... More

Backward-Backward Splitting in Hadamard SpacesSep 23 2013Sep 30 2013The backward-backward algorithm is a tool for finding minima of a regularization of the sum of two convex functions in Hilbert spaces. We generalize this setting to Hadamard spaces and prove the convergence of an error-tolerant version of the backward-backward ... More

Mellin moments of heavy flavor contributions to F_2(x,Q^2) at NNLOOct 16 2009This thesis is concerned with the calculation of fixed moments of the O(a_s^3) heavy flavor contributions to the Wilson coefficients of the structure function F_2(x,Q^2) in the limit Q^2 >> m^2, neglecting power corrections. The massive Wilson coefficients ... More

Accurate variational electronic structure calculations with the density matrix renormalization groupMay 06 2014During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. The underlying matrix product state (MPS) ansatz is a low-rank decomposition of the full configuration interaction ... More

Turbulent spectra in real-time gauge field evolutionDec 12 2008We investigate ultraviolet fixed points in the real-time evolution of non-Abelian gauge fields. Classical-statistical lattice simulations reveal equal-time correlation functions with a spectral index 3/2. Analytical understanding of this result is achieved ... More

Supersymmetry beyond minimal flavour violationAug 14 2008Nov 18 2008We review the sources and phenomenology of non-minimal flavour violation in the MSSM. We discuss in some detail the most important theoretical and experimental constraints, as well as promising observables to look for supersymmetric effects at the LHC ... More

On strategies for determination and characterization of the underlying eventSep 04 2010Sep 22 2010We discuss the problem of the separation and description of the underlying event (UE) within two existing approaches to UE measurement: the "traditional" method, widely used at Tevatron, and a recently proposed jet-area/median method. A simple toy model ... More

Wilson Loops, Bianchi Constraints and Duality in Abelian Lattice ModelsAug 05 1998Nov 18 1998We introduce new modified Abelian lattice models, with inhomogeneous local interactions, in which a sum over topological sectors are included in the defining partition function. The dual models, on lattices with arbitrary topology, are constructed and ... More

Bipartite Field Theories: from D-Brane Probes to Scattering AmplitudesJul 03 2012Dec 20 2012We introduce and initiate the investigation of a general class of 4d, N=1 quiver gauge theories whose Lagrangian is defined by a bipartite graph on a Riemann surface, with or without boundaries. We refer to such class of theories as Bipartite Field Theories ... More

The Chordal Loewner Equation and Monotone Probability TheoryMay 21 2016Jun 21 2016In [5], O. Bauer interpreted the chordal Loewner equation in terms of non-commutative probability theory. We follow this perspective and identify the chordal Loewner equations as the non-autonomous versions of evolution equations for semigroups in monotone ... More

Second-order perturbation theory for 3He and pd scattering in pionless EFTSep 11 2016This work implements pionless effective field theory with the two-nucleon system expanded around the unitarity limit at second order perturbation theory. The expansion is found to converge well. All Coulomb effects are treated in perturbation theory, ... More

A Projection to the Pure Spinor SpaceFeb 02 2012This article is based on a talk given at the Memorial Conference for Maximilian Kreuzer at the ESI in Vienna and contains a compact summary of a recent collaboration with P.A. Grassi. A non-linear projection from the space of SO(10) Weyl spinors to the ... More

The burnside problem for $\text{Diff}_{\text{Vol}}(\mathbb{S}^2)$Jul 15 2016Let $S$ be a closed surface and $\text{Diff}_{\text{Vol}}(S)$ be the group of volume preserving diffeomorphisms of $S$. A finitely generated group $G$ is periodic of bounded exponent if there exists $k \in \mathbb{N}$ such that every element of $G$ has ... More

Distributed Event-based State EstimationNov 16 2015An event-based state estimation approach for reducing communication in a networked control system is proposed. Multiple distributed sensor-actuator-agents observe a dynamic process and sporadically exchange their measurements and inputs over a bus network. ... More

Composition, collimation, contamination: the jet of Cygnus X-1Sep 26 2005We model the observed size and brightness of the VLBA radio core of the jet in Cygnus X-1 to derive an expression for the jet power as a function of basic jet parameters. We apply this expression to recent constraints on the jet power from observations ... More

Self-exciting Point Processes: Infections and ImplementationsFeb 12 2018This is a comment on Reinhart's "Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications" (arXiv:1708.02647v1). I contribute some experiences from modelling the spread of infectious diseases. Furthermore, I try to complement the ... More

Average Cost of QuickXsort with Pivot SamplingMar 15 2018May 17 2018QuickXsort is a strategy to combine Quicksort with another sorting method X, so that the result has essentially the same comparison cost as X in isolation, but sorts in place even when X requires a linear-size buffer. We solve the recurrence for QuickXsort ... More

H1 Diffractive Structure Function Measurements and QCD FitsDec 15 2004Measurements of diffractive structure functions in ep collisions and diffractive parton densities extracted from QCD fits are presented.

One-dimensional quantum wires: A pedestrian approach to bosonizationAug 01 2007Sep 08 2009In these lecture notes we will consider systems in which the motion of electrons is confined to one dimension (1D). In these so-called quantum wires electron-electron interaction effects play an important role because the restricted dimensions enhance ... More

Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal OperatorsFeb 06 1996May 28 1996Field theory calculations predict multiplicative logarithmic corrections to correlation functions from marginally irrelevant operators. However, for the numerically most suitable model - the spin-1/2 chain - these corrections have been controversial. ... More

An Accurate Determination of the Exchange Constant in Sr_2CuO_3 from Recent Theoretical ResultsAug 10 1995Feb 08 1996Data from susceptibility measurements on Sr_2CuO_3 are compared with recent theoretical predictions for the magnetic susceptibility of the antiferromagnetic spin-1/2 Heisenberg chain. The experimental data fully confirms the theoretical predictions and ... More

Polylogarithmic Cuts in Models of V^0Mar 25 2013Mar 29 2013We study initial cuts of models of weak two-sorted Bounded Arithmetics with respect to the strength of their theories and show that these theories are stronger than the original one. More explicitly we will see that polylogarithmic cuts of models of $\mathbf{V}^0$ ... More

Graphs with degree complete labelingJun 14 2017In 2006 Qian [J. Qian, Degree complete graphs; Discrete Mathematics 306 (2006), 533--537] introduced the concept of degree complete graphs for labeled graphs. He also gave a characterization of these graphs in terms of two forbidden subgraphs. Furthermore, ... More

Considerations about Chopper Configuration at a time-of-flight SANS Instrument at a Spallation SourceJun 14 2016In any neutron scattering experiment the measurement of the position of the scattered neutrons and their respective velocities is necessary. In order to do so, a position sensitive detector as well as a way to determine the velocities is needed. Measuring ... More

Equivariant Quantizations of Symmetric AlgebrasOct 12 2008Dec 09 2008Let g be a Lie bialgebra and let V be a finite-dimensional g-module. We study deformations of the symmetric algebra of V which are equivariant with respect to an action of the quantized enveloping algebra of g. In particular we investigate such quantizations ... More

R-Matrix Poisson Algebras and Their DeformationsJun 03 2007We classify in this paper Poisson structures on modules over semisimple Lie algebras arising from classical r-matrices. We then study their quantizations and the relation to classical invariant theory.

Quadratic-time Algorithm for the String Constrained LCS ProblemJun 30 2011The problem of finding a longest common subsequence of two main sequences with some constraint that must be a substring of the result (STR-IC-LCS) was formulated recently. It is a variant of the constrained longest common subsequence problem. As the known ... More

Morse theory and higher torsion invariants IIMay 20 2003Let p: M -> B be a family of compact manifolds equipped with a unitarily flat vector bundle F -> M. We generalize Igusa's higher Franz-Reidemeister torsion \tau(M/B;F) to the case that the fibre-wise cohomology H^*(M/B;F) -> B carries a parallel metric. ... More

Global instability of wing shock buffetJun 19 2018Shock buffet on wings encountered in edge-of-the-envelope transonic flight remains an unresolved and disputed flow phenomenon, challenging both fundamental fluid mechanics and applied aircraft aerodynamics. The question of global instability leading to ... More

Higher genus minimal surfaces in $S^3$ and stable bundlesMar 27 2009Aug 06 2010We consider compact minimal surfaces $f\colon M\to S^3$ of genus 2 which are homotopic to an embedding. We assume that the associated holomorphic bundle is stable. We prove that these surfaces can be constructed from a globally defined family of meromorphic ... More

Categorical Hopf kernels and representations of semisimple Hopf algebrasOct 11 2010In the category of semisimple Hopf algebras the Hopf kernels introduced by Andruskiewitsch and Devoto in \cite{AD} coincide with kernels of representation as introduced in \cite{Bker}. Some new results concerning the normality of kernels are also presented. ... More

Depth Two Hopf Subalgebras of Semisimple Hopf algebrasJul 18 2008Let H be a finite dimensional semisimple Hopf algebra over an algebraically closed field of characteristic zero. In this note we give a short proof of the fact that a Hopf subalgebra of H is a depth two subalgebra if and only if it is normal Hopf subalgebra. ... More

A Schanuel Property for $j$Jan 20 2017Oct 01 2017I give a model-theoretic setting for the modular $j$ function and its derivatives. These structures, here called $j$-fields, provide an adequate setting for interpreting the Ax-Schanuel theorem for $j$ (Pila-Tsimerman 2015). Following the ideas of M. ... More

Validation of credit default probabilities via multiple testing proceduresJun 25 2010We apply multiple testing procedures to the validation of estimated default probabilities in credit rating systems. The goal is to identify rating classes for which the probability of default is estimated inaccurately, while still maintaining a predefined ... More

A Geometric Description of Feasible Singular Values in the Tensor Train FormatJan 29 2017Apr 09 2019Tree tensor networks such as the tensor train format are a common tool for high dimensional problems. The associated multivariate rank and accordant tuples of singular values are based on different matricizations of the same tensor. While the behavior ... More

Non-Coexistence of Infinite Clusters in Two-Dimensional Dependent Site PercolationMar 04 2011Jul 20 2011This paper presents three results on dependent site percolation on the square lattice. First, there exists no positively associated probability measure on {0,1}^{Z^2} with the following properties: a) a single infinite 0cluster exists almost surely, b) ... More

Asymptotic Rasmussen InvariantFeb 12 2007We use simple properties of the Rasmussen invariant of knots to study its asymptotic behaviour on the orbits of a smooth volume preserving vector field on a compact domain in the 3-space. A comparison with the asymptotic signature allows us to prove that ... More

Invariance Principle for the Random Conductance Model with dynamic bounded ConductancesFeb 03 2012Oct 11 2012We study a continuous time random walk X in an environment of dynamic random conductances. We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We prove a quenched ... More