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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

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 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

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

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

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

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

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

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

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

(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

On an analogue of a Brauer theorem for fusion categoriesMar 16 2015In this paper we prove an analogue of Brauer's theorem for faithful objects in fusion categories. Other notions, such as the order and the index associated to faithful objects of fusion categories are also discussed. We show that the index of a faithful ... More

Resolutions for unit groups of ordersSep 28 2016We present a general algorithm for constructing a free resolution for unit groups of orders in semisimple rational algebras. The approach is based on computing a contractible $G$-complex employing the theory of minimal classes of quadratic forms and Opgenorth's ... More

Equivalence Problems for Tree Transducers: A Brief SurveyMay 22 2014The decidability of equivalence for three important classes of tree transducers is discussed. Each class can be obtained as a natural restriction of deterministic macro tree transducers (MTTs): (1) no context parameters, i.e., top-down tree transducers, ... More

Continuity of discrete homomorphisms of diffeomorphism groupsJul 16 2013Jul 15 2016Let $M$ and $N$ be two closed $C^{\infty}$ manifolds and let $\text{Diff}_c(M)$ denote the group of $C^{\infty}$ diffeomorphisms isotopic to the identity. We prove that any (discrete) group homomorphism between $\text{Diff}_c(M)$ and $\text{Diff}_c(N)$ ... More

Theoretical overview of b->s hadronic decaysFeb 10 2010A wealth of data on hadronic b -> s transitions is available from the B-factories and will be improved at the LHCb experiment and possible future super-B-factories. I review the theory of these decays as it pertains to the search for physics beyond the ... More

SUSY beyond minimal flavour violationOct 29 2007Dec 06 2007We review aspects of the phenomenology of the MSSM with non-minimal flavour violation, including a discussion of important constraints and the sensitivity to fundamental scales.

Saturation in central-forward jet production in p-Pb collisions at LHCDec 20 2012We show that saturation can manifest itself in central-forward dijet production in p-A collisions. In spite of large transverse momenta of the jets, the almost back-to-back dijet configurations are able to probe gluon density at low x and low kt. We perform ... More

Particle Filters in Robotics (Invited Talk)Dec 12 2012This presentation will introduce the audience to a new, emerging body of research on sequential Monte Carlo techniques in robotics. In recent years, particle filters have solved several hard perceptual robotic problems. Early successes were limited to ... More

Introduction to Measurement Space and Application to Operationally Useful Entanglement and Mode EntanglementApr 27 2010Aug 28 2010We introduce the idea that the knowable quantum reality depends not only on the state but also on measurements. Mathematically, we map the states from the ordinary Hilbert space into new states in what we call the measurement space. The state vectors ... More

Retardation magnification and the appearance of relativistic jetsJun 24 2008Jul 03 2008Thanks to the availability of high-resolution high-sensitivity telescopes such as the Very Large Array, the Hubble Space Telescope, and the Chandra X-ray Observatory, there is now a wealth of observational data on relativistic jets from active galactic ... More

Cluster Transformations from Bipartite Field TheoriesJan 02 2013Oct 17 2013Bipartite field theories (BFTs) are a new class of 4d N=1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. In this paper we derive, purely in terms of the gauge theory, the cluster transformations of face weights under ... More

Experimental Challenges of the European Strategy for Particle PhysicsSep 30 2013Oct 07 2013In planning for the Phase II upgrades of CMS and ATLAS major considerations are: 1)being able to deal with degradation of tracking and calorimetry up to the radiation doses to be expected with an integrated luminosity of 3000 $fb^{-1}$ and 2)maintaining ... More

Neutron Production and Zero Degree Calorimeter Acceptance at LHCDec 22 2009May 10 2010We calculate cross sections for the far forward LHC detectors to be used for luminosity measurement. A simple model, based on a parametrization of available inclusive neutron data and the assumption that 2 arm rates in non-diffractive events are uncorrelated, ... More

Diffractive J/$ψ$ production in Ultraperipheral AuAu Collisions at RHICOct 31 2005We report on the first measurement of diffractive J/psi production in Ultraperipheral Au+Au collisions at \sqrt{s_{NN}}=200 GeV.

MusicMood: Predicting the mood of music from song lyrics using machine learningNov 01 2016Sentiment prediction of contemporary music can have a wide-range of applications in modern society, for instance, selecting music for public institutions such as hospitals or restaurants to potentially improve the emotional well-being of personnel, patients, ... More

Brackets, Sigma Models and Integrability of Generalized Complex StructuresSep 04 2006Nov 27 2008It is shown how derived brackets naturally arise in sigma-models via Poisson- or antibracket, generalizing a recent observation by Alekseev and Strobl. On the way to a precise formulation of this relation, an explicit coordinate expression for the derived ... More

Derived Brackets from Super-Poisson BracketsMar 08 2007The relation between Poisson brackets in supersymmetric one or two-dimensional sigma-models and derived brackets is summarized.

Relative tensor triangular Chow groups, singular varieties and localizationOct 01 2015We extend the scope of Balmer's tensor triangular Chow groups to compactly generated triangulated categories $\mathcal{K}$ that only admit an action by a compactly-rigidly generated tensor triangulated category $\mathcal{T}$ as opposed to having a compatible ... More

Coupled intertwiner dynamics: A toy model for coupling matter to spin foam modelsJun 15 2015Sep 17 2015The universal coupling of matter and gravity is one of the most important features of general relativity. In quantum gravity, in particular spin foams, matter couplings have been defined in the past, yet the mutual dynamics, in particular if matter and ... More

Intersection products for tensor triangular Chow groupsMay 28 2015We show that under favorable circumstances, one can construct an intersection product on the Chow groups of a tensor triangulated category $\mathcal{T}$ (as defined by Balmer) which generalizes the usual intersection product on a non-singular algebraic ... More

Why Is Dual-Pivot Quicksort Fast?Nov 03 2015Sep 28 2016I discuss the new dual-pivot Quicksort that is nowadays used to sort arrays of primitive types in Java. I sketch theoretical analyses of this algorithm that offer a possible, and in my opinion plausible, explanation why (a) dual-pivot Quicksort is faster ... More

Two-Qubit Pulse Gate for the Three-Electron Double Quantum Dot QubitSep 04 2014Jan 22 2015The three-electron configuration of gate-defined double quantum dots encodes a promising qubit for quantum information processing. I propose a two-qubit entangling gate using a pulse-gated manipulation procedure. The requirements for high-fidelity entangling ... More

Post-Newtonian dynamics at order 1.5 in the Vlasov-Maxwell systemFeb 13 2006We study the dynamics of many charges interacting with the Maxwell field. The particles are modeled by means of non-negative distribution functions $f^+$ and $f^-$ representing two species of charged matter with positive and negative charge, respectively. ... More

From ADM to Brane-World chargesOct 12 2000We first recall a covariant formalism used to compute conserved charges in gauge invariant theories. We then study the case of gravity for two different boundary conditions, namely spatial infinity and a Brane-World boundary. The new conclusion of this ... More

Universality of ac-conduction in anisotropic disordered systems: An effective medium approximation studyFeb 03 2004Apr 12 2005Anisotropic disordered system are studied in this work within the random barrier model. In such systems the transition probabilities in different directions have different probability density functions. The frequency-dependent conductivity at low temperatures ... More

Toric Poisson Ideals in Cluster AlgebrasSep 15 2010Feb 29 2012This paper investigates the Poisson geometry associated to a cluster algebra over the complex numbers, and its relationship to compatible torus actions. We show, under some assumptions, that each Noetherian cluster algebra has only finitely many torus ... More

Recurrence and Transience for Branching Random Walks in an iid Random EnvironmentJun 02 2006We give three different criteria for transience of a Branching Markov Chain. These conditions enable us to give a classification of Branching Random Walks in Random Environment (BRWRE) on Cayley Graphs in recurrence and transience. This classification ... More

Totally geodesic submanifolds of the exceptional Riemannian symmetric spaces of rank 2Sep 08 2008The present article is the final part of a series on the classification of the totally geodesic submanifolds of the irreducible Riemannian symmetric spaces of rank 2. After this problem has been solved for the 2-Grassmannians in my previous papers cited ... More

Hölder-Zygmund Estimates for Degenerate Parabolic SystemsJul 19 2013We consider energy solutions of the inhomogeneous parabolic $p$-Laplacien system $\partial_t u-\text{div}(|D u|^{p-2}D u)=-\text{div} g$. We show in the case $p\geq 2$ that if the right hand side $g$ is locally in $L^\infty(\text{BMO})$, then $u$ is locally ... More

A spectral curve approach to Lawson symmetric CMC surfaces of genus 2Sep 14 2012Apr 11 2013Minimal and CMC surfaces in $S^3$ can be treated via their associated family of flat $\SL(2,\C)$-connections. In this the paper we parametrize the moduli space of flat $\SL(2,\C)$-connections on the Lawson minimal surface of genus 2 which are equivariant ... More

Conformally Flat Circle Bundles over SurfacesFeb 26 2009We classify conformally flat Riemannian $3-$manifolds which possesses a free isometric $S^1-$action.

Scalar Curvature Estimates by Parallel Alternating TorsionSep 28 2007We generalize Llarull's scalar curvature comparison to Riemannian manifolds admitting metric connections with parallel and alternating torsion and having a nonnegative curvature operator on 2-vectors. As a byproduct, we show that Euler number and signature ... More

On Kesten's Multivariate Choquet-Deny LemmaFeb 21 2013Mar 14 2014Let $d >1$ and $(A_n)_{n \ge 1}$ be a sequence of independent identically distributed random matrices with nonnegative entries and no zero column. This induces a Markov chain $M_n = A_n M_{n-1}$ on the cone of d-vectors with nonnegative entries. We study ... More

Properties of the Dirac spectrum on three dimensional lens spacesApr 13 2015Aug 14 2015We present a spectral rigidity result for the Dirac operator on lens spaces. More specifically, we show that each homogeneous lens space and each three dimensional lens space $L(q;p)$ with $q$ prime is completely characterized by its Dirac spectrum in ... More

For which positive $p$ is the integral Menger curvature $\mathcal{M}_{p}$ finite for all simple polygons?Feb 02 2012In this brief note we show that the integral Menger curvature $\mathcal{M}_{p}$ is finite for all simple polygons if and only if $p\in (0,3)$. For the intermediate energies $\mathcal{I}_{p}$ and $\mathcal{U}_{p}$ we obtain the analogous result for $p\in ... More

Machine learning-assisted discovery of GPCR bioactive ligandsDec 16 2018While G-protein coupled receptors (GPCRs) constitute the largest class of membrane proteins, structures and endogenous ligands of a large portion of GPCRs remain unknown. Due to the involvement of GPCRs in various signaling pathways and physiological ... More

Model Evaluation, Model Selection, and Algorithm Selection in Machine LearningNov 13 2018Dec 03 2018The correct use of model evaluation, model selection, and algorithm selection techniques is vital in academic machine learning research as well as in many industrial settings. This article reviews different techniques that can be used for each of these ... More

Feature Learning for Meta-Paths in Knowledge GraphsSep 07 2018In this thesis, we study the problem of feature learning on heterogeneous knowledge graphs. These features can be used to perform tasks such as link prediction, classification and clustering on graphs. Knowledge graphs provide rich semantics encoded in ... More

An Automatic Speedup Theorem for Distributed ProblemsFeb 26 2019Recently, Brandt et al. [STOC'16] proved a lower bound for the distributed Lov\'asz Local Lemma, which has been conjectured to be tight for sufficiently relaxed LLL criteria by Chang and Pettie [FOCS'17]. At the heart of their result lies a speedup technique ... More

Black Hole Evaporation: Sparsity in Analogue and General Relativistic Space-TimesJan 17 2019Our understanding of black holes changed drastically, when Stephen Hawking discovered their evaporation due to quantum mechanical processes. One core feature of this effect is both its similarity and simultaneous dissimilarity to classical black body ... More

Equivalences between localisations of categories provided by replacementsOct 09 2018We give a characterisation of functors whose induced functor on the level of localisations is an equivalence and where the isomorphism inverse is induced by some kind of replacements such as projective resolutions or cofibrant replacements.

Recovery of the absorption coefficient in radiative transport from a single measurementAug 21 2013Feb 14 2015In this paper, we investigate the recovery of the absorption coefficient from boundary data assuming that the region of interest is illuminated at an initial time. We consider a sufficiently strong and isotropic, but otherwise unknown initial state of ... More

Discrete knot energiesMar 08 2016The present chapter gives an overview on results for discrete knot energies. These discrete energies are designed to make swift numerical computations and thus open the field to computational methods. Additionally, they provide an independent, geometrically ... More

A spectral theory for simply periodic solutions of the sinh-Gordon equationJul 29 2016In this work a spectral theory for 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation is developed. Spectral data for such solutions are defined (following Hitchin and Bobenko) and the space of spectral data is described ... More

A characterisation of inner product spaces by the maximal circumradius of spheresFeb 02 2012We give a new characterisation of inner product spaces amongst normed vector spaces in terms of the maximal cirumradius of spheres. It turns out that a normed vector space $(X,\norm{\cdot})$ with $\dim X\geq 2$ is an inner product space if and only if ... More

The third cohomology group classifies crossed module extensionsNov 15 2009Sep 29 2010We give an elementary proof of the well-known fact that the third cohomology group H^3(G, M) of a group G with coefficients in an abelian G-module M is in bijection to the set Ext^2(G, M) of equivalence classes of crossed module extensions of G with M. ... More

High order surface radiation conditions for time-harmonic waves in exterior domainsFeb 23 2017We formulate a new family of high order on-surface radiation conditions to approximate the outgoing solution to the Helmholtz equation in exterior domains. Motivated by the pseudo-differential expansion of the Dirichlet-to-Neumann operator developed by ... More

Bernoulli Percolation on random TessellationsSep 15 2016We generalize the standard site percolation model on the $d$-dimensional lattice to a model on random tessellations of $\mathbb R^d$. We prove the uniqueness of the infinite cluster by adapting the Burton-Keane argument \cite{burton1989density}, develop ... 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

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

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

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

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

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

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

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.

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

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.

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

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

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.

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

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

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

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

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