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Discovery of new stable and high-temperature Ti-Ta-X shape memory alloys from first principles calculationsMay 14 2019In conventional Ti-Ta shape memory alloys (SMAs), high (>100{\deg}C) transformation temperatures cannot be achieved without compromising the stability of the shape memory effect. A solution to this problem is the addition of other elements to form Ti-Ta-X ... More

Intrinsic room temperature ferromagnetism in Co-implanted ZnOMay 03 2008May 07 2008We report on the structural and magnetic properties of a cobalt-implanted ZnO film grown on a sapphire substrate. X-ray diffraction and transmission electron microscopy reveal the presence of a (10-10)-oriented hexagonal Co phase in the Al2O3 sapphire ... More

High temperature ferromagnetism in Co-implanted TiO2 rutileJul 09 2008We report on structural, magnetic and electronic properties of Co-implanted TiO2 rutile single crystals for different implantation doses. Strong ferromagnetism at room temperature and above is observed in TiO2 rutile plates after cobalt ion implantation, ... More

On sampling and interpolation by model setsSep 27 2018Nov 14 2018We refine a result of Matei and Meyer on stable sampling and stable interpolation for simple model sets. Our setting is model sets in locally compact second countable abelian groups and Fourier analysis of unbounded complex Radon measures as developed ... More

The diffeomorphism supergroup of a finite-dimensional supermanifoldApr 17 2009Sep 24 2009Using the categorical description of supergeometry we give an explicit construction of the diffeomorphism supergroup of a compact finite-dimensional supermanifold. The construction provides the diffeomorphism supergroup with the structure of a Frechet ... More

Equivalences of Smooth and Continuous Principal Bundles with Infinite-Dimensional Structure GroupApr 06 2006Jun 28 2012Let K be a a Lie group, modeled on a locally convex space, and M a finite-dimensional paracompact manifold with corners. We show that each continuous principal K-bundle over M is continuously equivalent to a smooth one and that two smooth principal K-bundles ... More

Deformation of cylinder knotsOct 24 2012Nov 20 2012Knots parametrized in cylinder coordinates by t -> (st, 3 + cos(nt), cos(mt + \phi)) share properties of Lissajous and billiard knots in a cylinder. We use these 'billiard knots in a flat solid torus' to study two topics: when is Z(s,n,m) equal to Z(s,m,n)? ... More

High dimensional finite elements for elliptic problems with multiple scales and stochastic dataMay 01 2003Multiple scale homogenization problems are reduced to single scale problems in higher dimension. It is shown that sparse tensor product Finite Element Methods (FEM) allow the numerical solution in complexity independent of the dimension and of the length ... More

Conscious observers clarify many worldsAug 03 2009In this brief note I argue that putting conscious observers at the center of the considerations clarifies and strengthens the many-worlds interpretation. The basic assumption, which seems extremely plausible based on our current understanding of the brain ... More

Towards global analysis of b --> s l^+ l^-Nov 15 2011Dec 15 2011Flavour changing neutral current decays mediated by b --> s l^+ l^- were under experimental investigation at B-factories and the Tevatron during the last decade and the final analysis are expected soon. Moreover, new data has been released this summer ... More

The Higgs Portal from LHC to ILCApr 20 2012Interpretations of searches for the Higgs boson are governed by model-dependent combinations of Higgs production cross sections and Higgs branching ratios. Mixing of the Higgs doublet with a hidden sector captures modifications from the Standard Model ... More

A Compositional Query Algebra for Second-Order Logic and Uncertain DatabasesJul 29 2008World-set algebra is a variable-free query language for uncertain databases. It constitutes the core of the query language implemented in MayBMS, an uncertain database system. This paper shows that world-set algebra captures exactly second-order logic ... More

On the Complexity of Nonrecursive XQuery and Functional Query Languages on Complex ValuesMar 23 2005Mar 24 2005This paper studies the complexity of evaluating functional query languages for complex values such as monad algebra and the recursion-free fragment of XQuery. We show that monad algebra with equality restricted to atomic values is complete for the class ... More

Wavelet-induced renormalization group for the Landau-Ginzburg modelSep 23 1999The scale hierarchy of wavelets provides a natural frame for renormalization. Expanding the order parameter of the Landau-Ginzburg/$\Phi^4$ model in a basis of compact orthonormal wavelets explicitly exhibits the coupling between scales that leads to ... More

On the Complexity of Finding Narrow ProofsApr 03 2012Sep 11 2012We study the complexity of the following "resolution width problem": Does a given 3-CNF have a resolution refutation of width k? We prove that the problem cannot be decided in time O(n^((k-3)/12)). This lower bound is unconditional and does not rely on ... More

Uniformly hyperbolic control theoryNov 25 2015May 30 2016This paper gives a summary of a body of work at the intersection of control theory and smooth nonlinear dynamics. The main idea is to transfer the concept of uniform hyperbolicity, central to the theory of smooth dynamical systems, to control-affine systems. ... More

Design and Implementation of a Master of Science in Information and Computer Sciences - An Inventory and retrospect for the last four yearsApr 16 2008This Master of Science in Computer and Information Sciences (MICS) is an international accredited master program that has been initiated in 2004 and started in September 2005. MICS is a research-oriented academic study of 4 semesters and a continuation ... More

A Simple Dynamic Mind-map Framework To Discover Associative Relationships in Transactional Data StreamsMay 09 2008In this paper, we informally introduce dynamic mind-maps that represent a new approach on the basis of a dynamic construction of connectionist structures during the processing of a data stream. This allows the representation and processing of recursively ... More

Superspace calculation of the three-loop dilatation operator of N=4 SYM theoryAug 19 2010Dec 07 2011We derive the three-loop dilatation operator of the flavor SU(2) subsector of N=4 supersymmetric Yang-Mills theory in the planar limit by a direct Feynman diagram calculation in N=1 superspace. The transcendentality three contributions which appear in ... More

On moduli spaces of flat connections with non-simply connected structure groupNov 12 1996We consider the moduli space of flat G-bundles over the twodimensional torus, where G is a real, compact, simple Lie group which is not simply connected. We show that the connected components that describe topologically non-trivial bundles are isomorphic ... More

Computational Complexity of Iterated Maps on the IntervalMar 31 2010Oct 11 2011The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The correctness ... More

Theta vacuum in different gaugesJun 25 1998In some recent papers it is claimed that the physical significance of the vacuum angle theta for QCD-like theories depends on the chosen gauge condition. We criticise the arguments that were given in support of this claim, and show by explicit construction ... More

A remark on higher order RUE-resolution with EXTRUEJan 23 2009We show that a prominent counterexample for the completeness of first order RUE-resolution does not apply to the higher order RUE-resolution approach EXTRUE.

From Super-Yang-Mills to QCDDec 16 2004This article contains lecture notes of M. Shifman from the Saalburg Summer School 2004. The topic is supersymmetric Yang-Mills theory, in particular the gluino condensate in pure SUSY gluodynamics.

The origin of physical variations in the star formation lawJul 04 2013Dec 10 2013Observations of external galaxies and of local star-forming clouds in the Milky Way have suggested a variety of star formation laws, i.e., simple direct relations between the column density of star formation (Sigma_SFR: the amount of gas forming stars ... More

Status of Measurements and Interpretation of Total Real and Virtual Photon-Proton Cross SectionsNov 04 1999The status of measurements and interpretation of the proton structure function F2 is summarized. The measurements are subjected to DGLAP fits, from which the gluon density is extracted and a comparison to measurements of F2c is performed. The longitudinal ... More

A Higher Order Isoparametric Fictitious Domain Method for Level Set DomainsDec 08 2016We consider a new fictitious domain approach of higher order accuracy. To implement Dirichlet conditions we apply the classical Nitsche method combined with a facet-based stabilization (ghost penalty). Both techniques are combined with a higher order ... More

What is Information?Jan 22 2016Information is a precise concept that can be defined mathematically, but its relationship to what we call "knowledge" is not always made clear. Furthermore, the concepts "entropy" and "information", while deeply related, are distinct and must be used ... More

Survival Prediction with Limited Features: a Top Performing Approach from the DREAM ALS Stratification Prize4Life ChallengeDec 02 2016Survival prediction with small sets of features is a highly relevant topic for decision-making in clinical practice. I describe a method for predicting survival of amyotrophic lateral sclerosis (ALS) patients that was developed as a submission to the ... More

Mean-square stability and error analysis of implicit time-stepping schemes for linear parabolic SPDEs with multiplicative Wiener noise in the first derivativeAug 02 2012In this article, we extend a Milstein finite difference scheme introduced in [Giles & Reisinger(2011)] for a certain linear stochastic partial differential equation (SPDE), to semi- and fully implicit timestepping as introduced by [Szpruch(2010)] for ... More

Distinguishing mesoscopic quantum superpositions from statistical mixtures in periodically shaken double wellsOct 25 2011For Bose-Einstein condensates in double wells, N-particle Rabi-like oscillations often seem to be damped. Far from being a decoherence effect, the apparent damping can indicate the emergence of quantum superpositions in the many-particle quantum dynamics. ... More

Analytic Dirac approximation for real linear algebraic groupsFeb 24 2010For a real linear algebraic group G let A(G) be the algebra of analytic vectors for the left regular representation of G on the space of superexponentially decreasing functions. We present an explicit Dirac sequence in A(G). Since A(G) acts on E for every ... More

Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICAMay 17 2017Nov 29 2017The integration of differential equations of Feynman integrals can be greatly facilitated by using a canonical basis. This paper presents the Mathematica package CANONICA, which implements a recently developed algorithm to automatize the transformation ... More

The combinatorial essence of supercompactnessDec 09 2010We introduce combinatorial principles that characterize strong compactness and supercompactness for inaccessible cardinals but also make sense for successor cardinals. Their consistency is established from what is supposedly optimal. Utilizing the failure ... More

The impact of partially missing communities~on the reliability of centrality measuresSep 20 2017Network data is usually not error-free, and the absence of some nodes is a very common type of measurement error. Studies have shown that the reliability of centrality measures is severely affected by missing nodes. This paper investigates the reliability ... More

A Categorical Formulation of Superalgebra and SupergeometryFeb 27 2008We reformulate superalgebra and supergeometry in completely categorical terms by a consequent use of the functor of points. The increased abstraction of this approach is rewarded by a number of great advantages. First, we show that one can extend supergeometry ... More

Dense Dirac combs in Euclidean space with pure point diffractionFeb 21 2003May 19 2004Regular model sets, describing the point positions of ideal quasicrystallographic tilings, are mathematical models of quasicrystals. An important result in mathematical diffraction theory of regular model sets, which are defined on locally compact Abelian ... More

From asymptotic hypothesis testing to entropy inequalitiesDec 12 2018This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either fix quantum ... More

Technical Report: Inconsistency in Answer Set Programs and ExtensionsMay 31 2018Answer Set Programming (ASP) is a well-known problem solving approach based on nonmonotonic logic programs. HEX-programs extend ASP with external atoms for accessing arbitrary external information, which can introduce values that do not appear in the ... More

The turbulent formation of starsJun 14 2018Nov 30 2018How stars are born from clouds of gas is a rich physics problem whose solution will inform our understanding of not just stars but also planets, galaxies, and the universe itself. Star formation is stupendously inefficient. Take the Milky Way. Our galaxy ... More

Lepton Flavour Universality tests in $B$ decays as a probe for New PhysicsMay 11 2018In the Standard Model (SM), the coupling of the electroweak gauge bosons to the leptons is lepton flavour universal. Tests of this property constitute sensitive probes for new physics models that violate lepton flavour universality. Recent tests of lepton ... More

$h_{PI}$: The Citation Index for Principal InvestigatorsJul 17 2018A new citation index $h_{PI}$ for principal investigators (PIs) is defined in analogy to Hirsch's index $h$, but based on renormalized citations of a PI's papers. To this end, the authors of a paper are divided into two groups: PIs and non-PIs. A PI is ... More

Construction of Confidence IntervalsJul 10 2018Introductory texts on statistics typically only cover the classical "two sigma" confidence interval for the mean value and do not describe methods to obtain confidence intervals for other estimators. The present technical report fills this gap by first ... More

A Birman-Krein-Vishik-Grubb theory for sectorial operatorsOct 16 2017Jul 31 2018We consider densely defined sectorial operators $A_\pm$ that can be written in the form $A_\pm=\pm iS+V$ with $\mathcal{D}(A_\pm)=\mathcal{D}(S)=\mathcal{D}(V)$, where both $S$ and $V\geq \varepsilon>0$ are assumed to be symmetric. We develop an analog ... More

Smooth Extensions and Spaces of Smooth and Holomorphic MappingsNov 02 2005In this paper we present another notion of a smooth manifold with corners and relate it to the commonly used concept in the literature. Afterwards we introduce complex manifolds with corners and show that if $M$ is a compact (respectively complex) manifold ... More

Curve neighborhoods and minimal degrees in quantum productsDec 13 2016Let $G$ be a connected, simply connected, simple, complex, linear algebraic group. Let $P$ be an arbitrary parabolic subgroup of $G$. Let $X=G/P$ be the $G$-homogeneous projective space attached to this situation. We consider the (small) quantum cohomology ... More

What is a proof? What should it be?Apr 08 2019Mathematical proofs should be paired with formal proofs, whenever feasible.

On Low-Dimensional SolvmanifoldsMar 17 2009Aug 31 2009A nilmanifold resp. solvmanifold is a compact homogeneous space of a connected and simply-connected nilpotent resp. solvable Lie group by a lattice, i.e. a discrete co-compact subgroup. There is an easy criterion for nilpotent Lie groups which enables ... More

On the transfer reducibility of certain Farrell-Hsiang groupsSep 30 2014We show how the existing proof of the Farrell-Jones Conjecture for virtually poly-$\mathbb{Z}$-groups can be improved to rely only on the usual inheritance properties in combination with transfer reducibility as a sufficient criterion for the validity ... More

The Face Structure and Geometry of Marked Order PolyhedraOct 05 2016Nov 29 2017We study a class of polyhedra associated to marked posets. Examples of these polyhedra are Gelfand-Tsetlin polytopes and cones, as well as Berenstein-Zelevinsky polytopes, all of which have appeared in the representation theory of semi-simple Lie algebras. ... More

Skew divided difference operators in the Nichols algebra associated to a finite Coxeter groupApr 17 2018Let $(W,S)$ be a finite Coxeter system with root system $R$ and with set of positive roots $R^+$. For $\alpha\in R$, $v,w\in W$, we denote by $\partial_\alpha$, $\partial_w$ and $\partial_{w/v}$ the divided difference operators and skew divided difference ... More

A Schrödinger Operator Approach to Higher Spin XXZ Systems on General GraphsNov 24 2018Feb 11 2019We consider the spin-$J$ XXZ-Hamiltonian on general graphs $\mathcal{G}$ and show its equivalence to a direct sum of discrete many-particle Schr\"odinger type operators on what we call "$N$-particle graphs with maximal local occupation number $M$", where ... More

Quantitative uniform distribution results for geometric progressionsOct 15 2012Aug 15 2013By a classical theorem of Koksma the sequence of fractional parts $(\{x^n\})_{n \geq 1}$ is uniformly distributed for almost all values of $x$. In the present paper we obtain an exact quantitative version of Koksma's theorem, by calculating the precise ... More

Analysis of Linear Difference Schemes in the Sparse Grid Combination TechniqueOct 02 2007Jun 08 2011Sparse grids are tailored to the approximation of smooth high-dimensional functions. On a $d$-dimensional tensor product space, the number of grid points is $N = \mathcal O(h^{-1} |\log h|^{d-1})$, where $h$ is a mesh parameter. The so-called combination ... More

Bifurcation of Positive Equilibria in Nonlinear Structured Population Models with Varying Mortality RatesFeb 09 2010A parameter-dependent model involving nonlinear diffusion for an age-structured population is studied. The parameter measures the intensity of the mortality. A bifurcation approach is used to establish existence of positive equilibrium solutions.

Global Bifurcation of Positive Equilibria in Nonlinear Population ModelsJul 07 2009Existence of nontrivial nonnegative equilibrium solutions for age structured population models with nonlinear diffusion is investigated. Introducing a parameter measuring the intensity of the fertility, global bifurcation is shown of a branch of positive ... More

Tractability results for the weighted star-discrepancyJul 22 2013Dec 05 2013The weighted star-discrepancy has been introduced by Sloan and Wo{\'z}niakowski to reflect the fact that in multidimensional integration problems some coordinates of a function may be more important than others. It provides upper bounds for the error ... More

Lattice Green's Functions of the Higher-Dimensional Face-Centered Cubic LatticesAug 10 2011Mar 11 2013We study the face-centered cubic lattice (fcc) in up to six dimensions. In particular, we are concerned with lattice Green's functions (LGF) and return probabilities. Computer algebra techniques, such as the method of creative telescoping, are used for ... More

A Fast Approach to Creative TelescopingApr 19 2010Jun 27 2011In this note we reinvestigate the task of computing creative telescoping relations in differential-difference operator algebras. Our approach is based on an ansatz that explicitly includes the denominators of the delta parts. We contribute several ideas ... More

Characteristic Polynomials of Symmetric Matrices over the Univariate Polynomial RingOct 21 2016Viewing a bivariate polynomial f in R[x,t] as a family of univariate polynomials in t parametrized by real numbers x, we call f real rooted if this family consists of monic polynomials with only real roots. If f is the characteristic polynomial of a symmetric ... More

Quasi-homogeneity of the moduli space of stable maps to homogeneous spaces (II)Dec 28 2018Let $G$ be a connected, simply connected, simple, complex, linear algebraic group. Let $P$ be an arbitrary parabolic subgroup of $G$. Let $X=G/P$ be the $G$-homogeneous projective space attached to this situation. Let $d\in H_2(X)$ be a degree. Let $\overline{M}_{0,3}(X,d)$ ... More

Poisson transforms adapted to BGG-complexesJun 22 2018We present a new construction for Poisson transforms between vector bundle valued differential forms on homogeneous parabolic geometries and the corresponding Riemannian symmetric space, which can be described in terms of finite dimensional representations ... More

On rational homotopy and minimal modelsFeb 25 2019Mar 13 2019We prove a result that enables us to calculate the rational homotopy of a wide class of spaces by the theory of minimal models.

Lower Bounds for Existential Pebble Games and k-Consistency TestsMay 03 2012Oct 07 2013The existential k-pebble game characterizes the expressive power of the existential-positive k-variable fragment of first-order logic on finite structures. The winner of the existential k-pebble game on two given finite structures can be determined in ... More

Symmetric union presentations for 2-bridge ribbon knotsFeb 17 2006Symmetric unions have been defined as generalizations of Kinoshita-Terasaka's construction in 1957. They are given by diagrams which look like the connected sum of a knot and its mirror image with additional twist tangles inserted near the symmetry axis. ... More

Supersymmetric leptogenesis and light hidden sectorsSep 29 2010Thermal leptogenesis and supergravity are attractive scenarios for physics beyond the standard model. However, it is well known that the super-weak interaction of the gravitino often leads to problems with primordial nucleosynthesis in the standard scenario ... More

Computational Complexity of Iterated Maps on the Interval (Extended Abstract)Jun 02 2010The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of the algorithm ... More

Magnetic field amplification in turbulent astrophysical plasmasOct 26 2016Magnetic fields play an important role in astrophysical accretion discs, and in the interstellar and intergalactic medium. They drive jets, suppress fragmentation in star-forming clouds and can have a significant impact on the accretion rate of stars. ... More

D-branes in group manifolds and flux stabilizationDec 06 2000We consider D-branes in group manifolds, from the point of view of open strings and using the Born-Infeld action on the brane worldvolume. D-branes correspond to certain integral (twined) conjugacy classes. We explain the integrality condition on the ... More

Information theory in molecular biologyMay 05 2004This article introduces the physics of information in the context of molecular biology and genomics. Entropy and information, the two central concepts of Shannon's theory of information and communication, are often confused with each other but play transparent ... More

The use of information theory in evolutionary biologyDec 16 2011Information is a key concept in evolutionary biology. Information is stored in biological organism's genomes, and used to generate the organism as well as to maintain and control it. Information is also "that which evolves". When a population adapts to ... More

Luminosity of young Jupiters revisited. Massive cores make hot planetsJun 24 2013The intrinsic luminosity of young Jupiters is of high interest for planet formation theory. It is an observable quantity that is determined by important physical mechanisms during formation, namely the accretion shock structure, and even more fundamentally, ... More

Simple Type Theory as Framework for Combining LogicsApr 30 2010Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be elegantly embedded ... More

Shaping tail dependencies by nesting box copulasJun 26 2009Aug 11 2009We introduce a family of copulas which are locally piecewise uniform in the interior of the unit cube of any given dimension. Within that family, the simultaneous control of tail dependencies of all projections to faces of the cube is possible and we ... More

Seven-Dimensional Super-Yang-Mills Theory in N=1 SuperfieldsFeb 01 2011We give a gauge-covariant formulation of seven-dimensional super-Yang-Mills theory in terms of N=1 superfields. Furthermore, we show that five and seven dimensions are the only cases where such a formulation exists by analysing the interplay of Lorentz ... More

Algebraic Multigrid for Disordered Systems and Lattice Gauge TheoriesNov 30 2000The construction of multigrid operators for disordered linear lattice operators, in particular the fermion matrix in lattice gauge theories, by means of algebraic multigrid and block LU decomposition is discussed. In this formalism, the effective coarse-grid ... More

Geometrical aspects of qudits concerning Bell inequalitiesJul 07 2009The aim of this thesis is to investigate quantum entanglement and quantum nonlocality of bipartite finite-dimensional systems (bipartite qudits). Entanglement is one of the most fascinating non-classical features of quantum theory, and besides its impact ... More

INTEGRAL: status of the mission - after 10 yearsDec 18 2012The ESA gamma-ray observatory INTEGRAL, launched on 17 October 2002, continues to produce a wealth of discoveries and new results on compact high energy Galactic objects,nuclear gamma-ray line emission, diffuse line and continuum emission, cosmic background ... More

INTEGRAL - status of the missionOct 27 2011The ESA gamma-ray observatory INTEGRAL, launched on 17 October 2002, continues to produce a wealth of discoveries and new results on compact high energy Galactic objects, nuclear gamma-ray line emission, diffuse line and continuum emission, cosmic background ... More

Survival probabilities of some iterated processesJun 15 2011Jul 19 2011We study the asymptotic behaviour of the probability that a stochastic process $(Z_t)_{t \geq 0}$ does not exceed a constant barrier up to time $T$ (the so called survival probability) when Z is the composition of two independent processes $(X_t)_{t \in ... More

Simulating cosmic rays in clusters of galaxies - III. Non-thermal scaling relations and comparison to observationsJul 11 2007Feb 06 2008Complementary views of galaxy clusters in the radio synchrotron, hard X-ray inverse Compton, and high-energy gamma-ray regimes are critical in calibrating them as high-precision cosmological probes. We present predictions for scaling relations between ... More

Hörmander Functional Calculus for Poisson EstimatesFeb 25 2013Apr 09 2014The aim of the article is to show a H\"ormander spectral multiplier theorem for an operator $A$ whose kernel of the semigroup $\exp(-zA)$ satisfies certain Poisson estimates for complex times $z.$ Here $\exp(-zA)$ acts on $L^p(\Omega),\,1 < p < \infty,$ ... More

Natural Entanglement in Bose-Einstein CondensatesOct 18 2001Every Bose-Einstein condensate is in a highly entangled state, as a consequence of the fact that the particles in a condensate are distributed over space in a coherent way. It is proved that any two regions within a condensate of finite particle number ... More

Schmüdgen's theorem and results of positivityNov 17 2014This is a translation of a final paper. It contains proofs of some well-known Positivstellens\"atze. The approach in this paper differs in two respects from presentations in literature. We use the Stone-Weierstrass Theorem directly to prove an inductive ... More

Analysis of discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methodsNov 30 2016In this paper, we present the analysis of the discontinuous Galerkin dual-primal isogeometric tearing and interconnecting method (dG-IETI-DP) for the two-dimensional case where we only consider vertex primal variables. The dG-IETI-DP method is a combination ... More

The maximal excess charge for a family of density-matrix-functional theories including Hartree-Fock and Müller theoriesSep 20 2016We will give a proof that the maximal excess charge for an atom described by a family of density-matrix-functionals, which includes Hartree-Fock and M\"uller theories, is bounded by an universal constant. We will use the new technique introduced by Frank ... More

On the existence of regular vectorsOct 29 2015Nov 06 2015Let $G$ be a locally convex Lie group and $\pi:G \to \mathrm{U}(\mathcal{H})$ be a continuous unitary representation. $\pi$ is called smooth if the space of $\pi$-smooth vectors $\mathcal{H}^\infty\subset \mathcal{H}$ is dense. In this article we show ... More

Fast Multiplication of Large Integers: Implementation and Analysis of the DKSS AlgorithmMar 17 2015The Sch\"onhage-Strassen algorithm (SSA) is the de-facto standard for multiplication of large integers. For $N$-bit numbers it has a time bound of $O(N \cdot \log N \cdot \log \log N)$. De, Kurur, Saha and Saptharishi (DKSS) presented an asymptotically ... More

Polar codes in quantum information theoryJan 15 2015Polar codes are the first capacity achieving and efficiently implementable codes for classical communication. Recently they have also been generalized to communication over classical-quantum and quantum channels. In this work we present our recent results ... More

Inefficient star formation through turbulence, magnetic fields and feedbackApr 14 2015May 15 2015Star formation is inefficient. Only a few percent of the available gas in molecular clouds forms stars, leading to the observed low star formation rate (SFR). The same holds when averaged over many molecular clouds, such that the SFR of whole galaxies ... More

Positrons in Surface PhysicsNov 14 2016Within the last decade powerful methods have been developed to study surfaces using bright low-energy positron beams. These novel analysis tools exploit the unique properties of positron interaction with surfaces, which comprise the absence of exchange ... More

The Face Structure and Geometry of Marked Order PolyhedraOct 05 2016We study a class of polyhedra associated to marked posets. Examples of these polyhedra are Gelfand--Tsetlin polytopes and related polytopes that have appeared in the representation theory of semi-simple Lie algebras in the last decades. The faces of these ... More

Implementation of $hp$-adaptive discontinuous finite element methods in Dune-FemApr 25 2016In this paper we describe generic algorithms and data structures for the implementation of $hp$-adaptive discontinuous finite element methods in the Dune-Fem library. Special attention is given to the often tedious and error-prone task of transferring ... More

Determining Metallicities of Globular Clusters using Simulated Integrated Spectra and Bayesian StatisticsJun 08 2015Using Monte Carlo simulations of globular clusters we developed a method separating metallicity effects from age effects on observed integrated ugriz colors. We demonstrate that these colors do not evolve with time significantly after an age of 4 Gyr ... More

Effective time-reversal via periodic shakingJun 15 2012For a periodically shaken optical lattice, effective time-reversal is investigated numerically. For interacting ultra-cold atoms, the scheme of [J. Phys. B 45, 021002 (2012)] involves a quasi-instantaneous change of both the shaking-amplitude and the ... More

SWiM -- A Semantic Wiki for Mathematical Knowledge ManagementMar 26 2010SWiM is a semantic wiki for collaboratively building, editing and browsing mathematical knowledge represented in the domain-specific structural semantic markup language OMDoc. It motivates users to contribute to collections of mathematical knowledge by ... More

wiki.openmath.org - how it works, how you can participateMar 26 2010At http://wiki.openmath.org, the OpenMath 2 and 3 Content Dictionaries are accessible via a semantic wiki interface, powered by the SWiM system. We shortly introduce the inner workings of the system, then describe how to use it, and conclude with first ... More

Categorified central extensions, étale Lie 2-groups and Lie's Third Theorem for locally exponential Lie algebrasDec 09 2008Jul 01 2011Lie's Third Theorem, asserting that each finite-dimensional Lie algebra is the Lie algebra of a Lie group, fails in infinite dimensions. The modern account on this phenomenon is the integration problem for central extensions of infinite-dimensional Lie ... More

Configuration spaces of $\mathbb{C} \setminus k$Jan 12 2018In this note, we collect mostly known formulas and methods to compute the standard and virtual Poincar\'e polynomials of the configuration spaces of the plane $\mathbb{C} \setminus k$ with $k$ deleted points and compare the answers.

Heinrich Behmann's Contributions to Second-Order Quantifier Elimination from the View of Computational LogicDec 19 2017For relational monadic formulas (the L\"owenheim class) second-order quantifier elimination, which is closely related to computation of uniform interpolants, projection and forgetting - operations that currently receive much attention in knowledge processing ... More