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Learning Selection Masks for Deep Neural NetworksJun 11 2019Data have often to be moved between servers and clients during the inference phase. For instance, modern virtual assistants collect data on mobile devices and the data are sent to remote servers for the analysis. A related scenario is that clients have ... More

The H-Covariant Strong Picard GroupoidSep 08 2004Apr 25 2005The notion of H-covariant strong Morita equivalence is introduced for *-algebras over C = R(i) with an ordered ring R which are equipped with a *-action of a Hopf *-algebra H. This defines a corresponding H-covariant strong Picard groupoid which encodes ... More

A shortcut to (sun)flowers: Kernels in logarithmic space or linear timeApr 30 2015We investigate whether kernelization results can be obtained if we restrict kernelization algorithms to run in logarithmic space. This restriction for kernelization is motivated by the question of what results are attainable for preprocessing via simple ... More

Reliability of regulatory networks and its evolutionMay 27 2008The problem of reliability of the dynamics in biological regulatory networks is studied in the framework of a generalized Boolean network model with continuous timing and noise. Using well-known artificial genetic networks such as the repressilator, we ... More

Reliability of genetic networks is evolvableJul 10 2007Control of the living cell functions with remarkable reliability despite the stochastic nature of the underlying molecular networks -- a property presumably optimized by biological evolution. We here ask to what extent the property of a stochastic dynamical ... More

On Semigroups of Two-Dimensional Upper-Triangular Integer MatricesMay 13 2019We analyze algorithmic problems in finitely generated semigroups of two-dimensional upper-triangular integer matrices. These semigroup problems are tightly connected with problems about compositions of affine functions over one variable. Building on a ... More

Weak Limit of the 3-State Quantum Walk on the LineApr 04 2014May 21 2014We revisit the one dimensional discrete time quantum walk with 3 states and the Grover coin. We derive analytic expressions for observed the localization, an long time approximation for the probability density function (PDF). We also connect the time ... More

Streaming KernelizationMay 06 2014Kernelization is a formalization of preprocessing for combinatorially hard problems. We modify the standard definition for kernelization, which allows any polynomial-time algorithm for the preprocessing, by requiring instead that the preprocessing runs ... More

On the commutability of homogenization and linearization in finite elasticityNov 16 2010May 16 2011We study non-convex elastic energy functionals associated to (spatially) periodic, frame indifferent energy densities with a single non-degenerate energy well at SO(n). Under the assumption that the energy density admits a quadratic Taylor expansion at ... More

Finite-Size Corrections for Ground States of Edwards-Anderson Spin GlassesOct 28 2011May 30 2012Extensive computations of ground state energies of the Edwards-Anderson spin glass on bond-diluted, hypercubic lattices are conducted in dimensions d=3,..,7. Results are presented for bond-densities exactly at the percolation threshold, p=p_c, and deep ... More

Superstability of the yeast cell cycle dynamics: Ensuring causality in the presence of biochemical stochasticityMay 05 2006Gene regulatory dynamics is governed by molecular processes and therefore exhibits an inherent stochasticity. However, for the survival of an organism it is a strict necessity that this intrinsic noise does not prevent robust functioning of the system. ... More

The midpoint between dipole and parton showersJun 16 2015Sep 19 2015We present a new parton-shower algorithm. Borrowing from the basic ideas of dipole cascades, the evolution variable is judiciously chosen as the transverse momentum in the soft limit. This leads to a very simple analytic structure of the evolution. A ... More

Interactive Natural Language Acquisition in a Multi-modal Recurrent Neural ArchitectureMar 24 2017Feb 07 2018For the complex human brain that enables us to communicate in natural language, we gathered good understandings of principles underlying language acquisition and processing, knowledge about socio-cultural conditions, and insights about activity patterns ... More

QCD Aspects of the NuTeV AnomalyMay 23 2004The weak mixing angle measured in neutrino scattering differs from the world average of other measurements by about 3 sigma. I discuss QCD corrections of perturbative and nonperturbative (parton structure) origin to the underlying neutrino observables. ... More

Fragmentation of PartonsOct 15 2004The concept of parton fragmentation in QCD hard scattering phenomenology as well as NLO pQCD analysis of fragmentation functions are outlined. Hadroproduction of pions of a few GeV pT is discussed through the example of recent measurements at \sqrt{S_{RHIC}}=200 ... More

Data Unfolding Methods in High Energy PhysicsNov 07 2016Nov 30 2016A selection of unfolding methods commonly used in High Energy Physics is compared. The methods discussed here are: bin-by-bin correction factors, matrix inversion, template fit, Tikhonov regularisation and two examples of iterative methods. Two procedures ... More

Theory of optimal transport for Lorentzian cost functionsJan 18 2016The optimal transport problem is studied in the context of Lorentz-Finsler geometry. For globally hyperbolic Lorentz-Finsler spacetimes the first Kantorovich problem and the Monge problem are solved. Further the intermediate regularity of the transport ... More

On Game-Theoretic Risk Management (Part Two) - Algorithms to Compute Nash-Equilibria in Games with Distributions as PayoffsNov 27 2015The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to compute equilibria ... More

Tales of 1001 GluonsOct 17 2016These lectures are centred around tree-level scattering amplitudes in pure Yang-Mills theories, the most prominent example is given by the tree-level gluon amplitudes of QCD. I will discuss several ways of computing these amplitudes, illustrating in this ... More

A Short Note on Polynomial AutomorphismsOct 25 2016In this paper, we construct explicitely polynomial automorphisms of affine n-space for certain n. More precisely, we construct algebraic subgroups of the general polynomial group GA_n(k) where k is an arbitrary base ring of characteristic zero.

$C^0$-characterization and $C^0$-rigidity of symplectic and contact embeddingsJul 11 2016Jul 25 2016We present a novel C^0-characterization of symplectic embeddings and diffeomorphisms in terms of Lagrangian embeddings. Our approach is based on the shape invariant, which was discovered by J. C. Sikorav and Y. Eliashberg, intersection theory and the ... More

HS06 Benchmark for an ARM ServerNov 15 2013We benchmarked an ARM cortex-A9 based server system with a four-core CPU running at 1.1 GHz. The system used Ubuntu 12.04 as operating system and the HEPSPEC 2006 (HS06) benchmarking suite was compiled natively with gcc-4.4 on the system. The benchmark ... More

Power Corrections in Electron-Positron Annihilation: Experimental ReviewJun 20 2006Experimental studies of power corrections with e+e- data are reviewed. An overview of the available data for jet and event shape observables is given and recent analyses based on the Dokshitzer-Marchesini-Webber (DMW) model of power corrections are summarised. ... More

Deformation Quantization of Principal Fibre Bundles and Classical Gauge TheoriesMar 04 2010In this dissertation the notion of deformation quantization of principal fibre bundles is established and investigated in order to find a geometric formulation of classical gauge theories on noncommutative space-times. As a generalization, the notion ... More

D-branes in a marginally deformed WZW modelDec 17 2002In this talk we discuss symmetry preserving D-branes on a line of a marginally deformed SU(2) WZW model. A semiclassical and a quantum theoretical approach are presented.

D-branes on a Deformation of SU(2)Dec 20 2001Jan 04 2002We discuss D-branes on a line of conformal field theories connected by an exact marginal deformation. The line contains an SU(2) WZW model and two mutually T-dual SU(2)/U(1) cosets times a free boson. We find the D-branes preserving a U(1) isometry, an ... More

Membrany corrections to the string anti-string potential in M5-brane theoryFeb 10 1999Mar 06 2000We study the potential between a string and an anti-string source in M5-theory by using the adS/CFT duality conjecture. We find that the next to leading order corrections in a saddle point approximation renormalize the classical result.

Measurement of the Pion Polarizability at COMPASSJan 20 2014Feb 12 2014The value of the pion polarizability is predicted with high precision by Chiral Perturbation Theory. However, the existing experimental values are at tension with this prediction as well as among themselves. The COMPASS experiment at the CERN SPS accesses ... More

Rho meson properties from combining QCD-based modelsMar 04 2003Aiming at the calculation of the properties of rho-mesons, non-perturbative QCD-based methods are discussed concerning their potentials as well as their short-comings. The latter are overcome by combining these techniques. The utilized methods are (i) ... More

Life time of resonances in transport simulationsAug 21 2000We calculate the life time of a resonance in our recently developed framework for a test-particle description of transport processes for states with continuous mass spectra. The result differs from the expression commonly used in transport simulations ... More

Information on the structure of the rho meson from the pion form-factorJul 01 2009The electromagnetic pion form-factor is calculated in a Bethe-Salpeter approach which accounts for pion rescattering. In the scattering kernel the pion-pion contact interaction from lowest-order chiral perturbation theory is considered together with an ... More

Spin Path Integrals, Berry phase, and the Quantum Phase Transition in the sub-Ohmic Spin-boson ModelJul 26 2010The quantum critical properties of the sub-Ohmic spin-1/2 spin-boson model and of the Bose-Fermi Kondo model have recently been discussed controversially. The role of the Berry phase in the breakdown of the quantum-to-classical mapping of quantum criticality ... More

A Rigidity Phenomenon for the Hardy-Littlewood Maximal FunctionOct 02 2014Nov 13 2015The Hardy-Littlewood maximal function $\mathcal{M}$ and the trigonometric function $\sin{x}$ are two central objects in harmonic analysis. We prove that $\mathcal{M}$ characterizes $\sin{x}$ in the following way: let $f \in C^{\alpha}(\mathbb{R}, \mathbb{R})$ ... More

A geometric uncertainty principle with an application to Pleijel's estimateJun 13 2013Nov 04 2013Consider partitions of an open, bounded domain in $\mathbb{R}^n$. Then an average element of the partition has either its Fraenkel asymmetry or its deviation from the smallest element in the partition bounded away from 0 by a universal constant. As an ... More

Period -- mass-loss rate relation of Miras with and without technetiumNov 05 2014We present the discovery that Mira variables separate in two distinct sequences in a near- to mid-IR color versus pulsation period diagram, if a distinction is made with respect to the presence of technetium (Tc) in the stars. Tc is an indicator of recent ... More

Period -- mass-loss rate relation of Miras with and without technetiumJun 23 2013Aims: We report the discovery that Mira variables with and without absorption lines of the element technetium (Tc) occupy two different regions in a diagram of near- to mid-infrared colour versus pulsation period. Tc is an indicator of a recent or ongoing ... More

Dynamical properties of a randomly diluted neural network with variable activityMar 08 1999The subject of study is a neural network with binary neurons, randomly diluted synapses and variable pattern activity. We look at the system with parallel updating using a probabilistic approach to solve the one step dynamics with one condensed pattern. ... More

The coherent states: old geometrical methods in new quantum clothesAug 02 1994A geometric characterization of transition amplitudes between coherent states, or equivalently, of the hermitian scalar product of holomorphic cross sections in the associated D - M tilda - module, in terms of the embedding of the cohe- rent state manifold ... More

Phase Diagram of Interacting Bosons on the Honeycomb LatticeJan 15 2007We study the ground state properties of repulsively interacting bosons on the honeycomb lattice using large-scale quantum Monte Carlo simulations. In the hard-core limit the half-filled system develops long ranged diagonal order for sufficiently strong ... More

Periods and Hodge structures in perturbative quantum field theoryFeb 04 2013Jul 06 2013There is a fruitful interplay between algebraic geometry on the one side and perturbative quantum field theory on the other side. I review the main relevant mathematical concepts of periods, Hodge structures and Picard-Fuchs equations and discuss the ... More

Feynman GraphsJan 29 2013In these lectures I discuss Feynman graphs and the associated Feynman integrals. Of particular interest are the classes functions, which appear in the evaluation of Feynman integrals. The most prominent class of functions is given by multiple polylogarithms. ... More

Introduction to Feynman IntegralsMay 11 2010In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced topics: Mathematical ... More

Status of NNLO 3-jet calculationsAug 25 2004The process e+ e- -> 3 jets offers the opportunity to measure the strong coupling constant. For an accurate determination, precise theoretical calculations are necessary. I will give an overview on the status of the next-to-next-to-leading order calculations. ... More

Subtraction terms for one-loop amplitudes with one unresolved partonJun 25 2003Fully differential next-to-next-to-leading order calculations require a method to cancel infrared singularities. In a previous publication, I discussed the general setup for the subtraction method at NNLO. In this paper I give all subtraction terms for ... More

gTybalt - a free computer algebra systemApr 29 2003This article documents the free computer algebra system "gTybalt". The program is build on top of other packages, among others GiNaC, TeXmacs and Root. It offers the possibility of interactive symbolic calculations within the C++ programming language. ... More

Computer Algebra in Particle PhysicsSep 20 2002These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in particle physics. ... More

Theoretical overview on top pair production and single top productionJan 19 2012In this talk I will give an overview on theoretical aspects of top quark physics. The focus lies on top pair production and single top production.

Symmetry breaking of gauge theories down to Abelian sub-groupsFeb 14 2008I re-derive the lowest order effective Lagrangian for electro-weak symmetry breaking without the use of Goldstone's theorem for spontaneously broken global symmetries and without the assumption of a custodial symmetry. I consider the breaking of a local ... More

Automated computation of spin- and colour-correlated Born matrix elementsOct 12 2005I report on an implementation of an algorithm for the automated numerical calculation of spin- and colour-correlated Born matrix elements in QCD. These spin- and colour-correlated matrix elements are needed for NLO calculations in combination with the ... More

Algebraic Algorithms in Perturbative CalculationsMay 30 2003I discuss algorithms for the evaluation of Feynman integrals. These algorithms are based on Hopf algebras and evaluate the Feynman integral to (multiple) polylogarithms.

Status of Identification of VHE gamma-ray sourcesSep 20 2006With the recent advances made by Cherenkov telescopes such as H.E.S.S., the field of very high-energy (VHE) gamma-ray astronomy has recently entered a new era in which for the first time populations of Galactic sources such as e.g. Pulsar wind nebulae ... More

Uncertainties of Sudakov form factorsDec 22 2004We study the uncertainties of Sudakov form factors as the basis for parton shower evolution in Monte Carlo event generators. We discuss the particular cases of systematic uncertainties of parton distribution functions and scale uncertainties.

Event Generators - New DevelopmentsOct 22 2002After an introduction to event generators we give an overview of developments in the field of joining matrix elements with parton showers. Starting with matrix element corrections, we also discuss implementations that match LO and NLO matrix elements ... More

NLO corrections to the photon impact factorAug 15 2002We review the program of the calculation of next-to-leading order corrections to the virtual photon impact factor. Following a brief introduction we present some technical aspects for the various contributions. Recently obtained results for transversely ... More

γ-rays from starburst galaxiesOct 25 2012In this paper the current status of \gamma-ray observations of starburst galaxies from hundreds of MeV up to TeV energies with space-based instruments and ground-based Imaging Atmospheric Cherenkov Telescopes (IACTs) is summarised. The properties of the ... More

Transport through a Constriction in a FQH AnnulusSep 30 1997The composite fermion perspective is used, to study the flux dependence of thermodynamic properties of an annulus in the fractional quantum hall state at odd inverse filling factor. It is shown that $\phi_0$- periodicity is restored, if there is tunneling ... More

Flavour-Dependent Type II LeptogenesisApr 12 2007Sep 11 2008We reanalyse leptogenesis via the out-of-equilibrium decay of the lightest right-handed neutrino in type II seesaw scenarios, taking into account flavour-dependent effects. In the type II seesaw mechanism, in addition to the type I seesaw contribution, ... More

Renormalization Group Analysis of Neutrino Mass ParametersAug 20 2002Tools for calculating the Renormalization Group Equations for renormalizable and non-renormalizable operators in various theories are reviewed, which are essential for comparing experimental results with predictions from models beyond the Standard Model. ... More

Plateau's problem for integral currents in locally non-compact metric spacesMar 23 2012The purpose of this article is to prove existence of mass minimizing integral currents with prescribed possibly non-compact boundary in all dual Banach spaces and furthermore in certain spaces without linear structure, such as injective metric spaces ... More

Gromov hyperbolic spaces and the sharp isoperimetric constantSep 11 2006Mar 20 2007In this article we exhibit the largest constant in a quadratic isoperimetric inequality which ensures that a geodesic metric space is Gromov hyperbolic. As a particular consequence we obtain that Euclidean space is a borderline case for Gromov hyperbolicity ... More

Equivariant properties of symmetric productsMar 06 2014The filtration on the infinite symmetric product of spheres by the number of factors provides a sequence of spectra between the sphere spectrum and the integral Eilenberg-Mac Lane spectrum. This filtration has received a lot of attention and the subquotients ... More

Effective descent maps for schemesJun 11 2001Feb 01 2003The paper is withdrawn due to mistakes in the proofs for Proposition 1.2 and Theorem 2.2.

Simulation of Z plus Graviton/Unparticle Production at the LHCSep 27 2008Feb 09 2009Theories with extra dimensions have gained much interest in recent years as candidates for a possible extension of the SM. The observation of large extra dimensions through real graviton emission is one of the most popular related new phenomena. The main ... More

Status of the Forward Physics Projects in ATLASJun 05 2007The ATLAS experiment at the LHC is building several detector systems for forward physics studies and to determine the luminosity. The main forward systems consist of a Cerenkov detector called LUCID, a Zero Degree Calorimeter (ZDC) and Roman Pots which ... More

Recent developments in deformation quantizationJan 31 2015In this review an overview on some recent developments in deformation quantization is given. After a general historical overview we motivate the basic definitions of star products and their equivalences both from a mathematical and a physical point of ... More

Deformation Quantization: Observable Algebras, States and Representation TheoryMar 10 2003In these lecture notes I give an introduction to deformation quantization. The quantization problem is discussed in some detail thereby motivating the notion of star products. Starting from a deformed observable algebra, i.e. the star product algebra, ... More

A Nuclear Weyl AlgebraSep 25 2012Jun 13 2013A bilinear form on a possibly graded vector space $V$ defines a graded Poisson structure on its graded symmetric algebra together with a star product quantizing it. This gives a model for the Weyl algebra in an algebraic framework, only requiring a field ... More

Positivity in Rieffel's strict deformation quantizationSep 15 2009We review a recent result on Rieffel's deformation quantization by actions of R^d: it is shown that for every state omega_0 of the undeformed C*-algebra A_0 there is a continuous section of states omega(hbar) through omega_0. We outline the physical interpretation ... More

Introduction to parton-shower event generatorsNov 14 2014Jun 18 2015This lecture discusses the physics implemented by Monte Carlo event generators for hadron colliders. It details the construction of parton showers and the matching of parton showers to fixed-order calculations at higher orders in perturbative QCD. It ... More

Genetic algorithm dynamics on a rugged landscapeMar 04 1999The genetic algorithm is an optimization procedure motivated by biological evolution and is successfully applied to optimization problems in different areas. A statistical mechanics model for its dynamics is proposed based on the parent-child fitness ... More

Stochastic Methods for Quantum ScatteringFeb 25 1994Quantum scattering at zero energy is studied with stochastic methods. A path integral representation for the scattering cross section is developed. It is demonstrated that Monte Carlo simulation can be used to compare effective potentials which are frequently ... More

Off-shell effects in Higgs decays to heavy gauge bosons and signal-background interference in Higgs decays to photons at a linear colliderMar 26 2015We discuss off-shell contributions in Higgs decays to heavy gauge bosons $H\rightarrow VV^{(*)}$ with $V\in\lbrace Z,W\rbrace$ for a standard model (SM) Higgs boson for both dominant production processes $e^+e^-\rightarrow ZH\rightarrow ZVV^{(*)}$ and ... More

Neutral Higgs production at proton colliders in the CP-conserving NMSSMFeb 27 2015May 21 2015We discuss neutral Higgs boson production through gluon fusion and bottom-quark annihilation in the CP-conserving $\mathbb{Z}_3$-invariant Next-to-Minimal Supersymmetric Standard Model (NMSSM) at proton colliders. For gluon fusion we adapt known asymptotic ... More

Flavour Physics in the Littlest Higgs Model with T-Parity: Effects in the K, B_d/s and D systemsAug 21 2009The Littlest Higgs Model with T parity (LHT) is an interesting alternative model for New Physics at the TeV scale. Although Flavour Physics was not the reason for creating the LHT model, significant effects (such as large CP violation where not predicted ... More

Electron-ion merged-beam experiments at heavy-ion storage ringsJul 24 2014In the past two decades, the electron-ion merged-beams technique has extensively been exploited at heavy-ion storage rings equipped with electron coolers for spectroscopic studies of highly charged ions as well as for measuring absolute cross sections ... More

Not So Easy Problems for Tree Decomposable GraphsJul 06 2011We consider combinatorial problems that can be solved in polynomial time for graphs of bounded treewidth but where the order of the polynomial that bounds the running time is expected to depend on the treewidth bound. First we review some recent results ... More

Permanents in linear optical networksJun 18 2004We develop an abstract look at linear optical networks from the viewpoint of combinatorics and permanents. In particular we show that calculation of matrix elements of unitarily transformed photonic multi-mode states is intimately linked to the computation ... More

Electronic Structure Methods Exhibiting Linear Scaling of the Computational Effort with Respect to the Size of the SystemJun 05 1998Oct 29 1998Methods exhibiting linear scaling with respect to the size of the system, so called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms which take advantage ... More

Satisfiability Algorithms for Restricted Circuit ClassesJun 17 2013In recent years, finding new satisfiability algorithms for various circuit classes has been a very active line of research. Despite considerable progress, we are still far away from a definite answer on which circuit classes allow fast satisfiability ... More

Renormalized Quantum Yang-Mills Fields in Curved SpacetimeMay 23 2007Feb 28 2008We present a proof that quantum Yang-Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime. To this end, we construct the non-commutative algebra ... More

Black hole uniqueness theorems and new thermodynamic identities in eleven dimensional supergravityApr 16 2012Aug 30 2012We consider stationary, non-extremal black holes in 11-dimensional supergravity having isometry group $\mathbb{R} \times U(1)^8$. We prove that such a black hole is uniquely specified by its angular momenta, its electric charges associated with the various ... More

MADMAX: A new way of probing QCD Axion Dark Matter with a Dielectric Haloscope -- FoundationsDec 04 2017In contrast to WIMPs, light Dark Matter candidates have increasingly come under the focus of scientific interest. In particular the QCD axion is also able to solve other fundamental problems such as CP-conservation in strong interactions. Galactic axions, ... More

Valuation theoretic methods in the birational geometry of algebraic varietiesOct 31 2016In this paper, we give a valuation formula for rational top differential forms of function fields in characteristic zero for arbitrary Abhyankar places generalizing the classical valuation at prime divisors. This enables us to define log discrepancies ... More

$Λ_c \to Λ\ell^+ ν_\ell$ form factors and decay rates from lattice QCD with physical quark massesNov 29 2016The decays $\Lambda_c \to \Lambda \ell^+ \nu_\ell$, where $\ell=e,\mu$, are the most important baryonic $c \to s \ell^+ \nu_\ell$ transitions. These processes can be used to determine the Cabibbo-Kobayashi-Maskawa quark mixing matrix element $|V_{cs}|$, ... More

Stably irrational hypersurfaces of small slopesJan 16 2018We show that a very general complex projective hypersurface of dimension N and degree at least $ \lceil \log_2N \rceil+2$ is not stably rational. The same statement holds over any uncountable field of characteristic p>>N. This significantly improves earlier ... More

QCD sum rules as applied to heavy baryonsJun 08 2000We give an overview over recent calculations of baryonic correlator functions with finite mass quarks in view on their applicability for QCD sum rules. The QCD sum rule method is then demonstrated within the Heavy Quark Effective Theory.

Heterotic supersymmetry, anomaly cancellation and equations of motionAug 20 2009Jan 15 2010We show that the heterotic supersymmetry (Killing spinor equations) and the anomaly cancellation imply the heterotic equations of motion in dimensions five, six, seven, eight if and only if the connection on the tangent bundle is an instanton. For heterotic ... More

Baryon chiral perturbation theoryOct 02 2009We provide an introduction to the power-counting issue in baryon chiral perturbation theory and discuss some recent developments in the manifestly Lorentz-invariant formulation of the one-nucleon sector. As explicit applications we consider the chiral ... More

Chiral perturbation theory - Success and challengeDec 22 2005Chiral perturbation theory is the effective field theory of the strong interactions at low energies. We will give a short introduction to chiral perturbation theory for mesons and will discuss, as an example, the electromagnetic polarizabilities of the ... More

A Remark on Disk Packings and Numerical Integration of Harmonic FunctionsMar 31 2014Dec 07 2014We are interested in the following problem: given an open, bounded domain $\Omega \subset \mathbb{R}^2$, what is the largest constant $\alpha = \alpha(\Omega) > 0$ such that there exist an infinite sequence of disks $B_1, B_2, \dots, B_N, \dots \subset ... More

Quantitative Homogenization and Convergence of Moving AveragesOct 31 2018We study homogenization it its most basic form $$-\left(a\left(\frac{x}{\varepsilon}\right) u_{\varepsilon}'(x)\right)' = f(x) \quad \mbox{for} ~x \in (0,1),$$ where $a(\cdot)$ is a positive $1-$periodic continuous function, $f$ is smooth and $u_{\varepsilon}$ ... More

Relative entropy close to the edgeMay 25 2018We show that the relative entropy between the reduced density matrix of the vacuum state in some region $A$ and that of an excited state created by a unitary operator localized at a small distance $\ell$ of a boundary point $p$ is insensitive to the global ... More

An Endpoint Alexandrov Bakelman Pucci Estimate in the PlaneApr 25 2018Jul 31 2018The classical Alexandrov-Bakelman-Pucci estimate for the Laplacian states $$ \max_{x \in \Omega}{ |u(x)|} \leq \max_{x \in \partial \Omega}{|u(x)|} + c_{s,n} \mbox{diam}(\Omega)^{2-\frac{n}{s}} \left\| \Delta u\right\|_{L^s(\Omega)}$$ where $\Omega \subset ... More

Fast multigrid solvers for conforming and non-conforming multi-patch Isogeometric AnalysisFeb 05 2019Isogeometric Analysis allows high-order discretizations of boundary value problems using a number of degrees of freedom which is as small as for a low-order method. To be able to choose high spline degrees in practice, suitable numerical solvers are required. ... More

Differential forms on singular spaces, the minimal model program, and hyperbolicity of moduli stacksJul 21 2011Dec 20 2011This survey discusses hyperbolicity properties of moduli stacks and generalisations of the Shafarevich Hyperbolicity Conjecture to higher dimensions. It concentrates on methods and results that relate moduli theory with recent progress in higher dimensional ... More

The Process of price formation and the skewness of asset returnsMar 02 2006Distributions of assets returns exhibit a slight skewness. In this note we show that our model of endogenous price formation \cite{Reimann2006} creates an asymmetric return distribution if the price dynamics are a process in which consecutive trading ... More

Coherent states and geometryJul 14 1998The coherent states are viewed as a powerful tool in differential geometry. It is shown that some objects in differential geometry can be expressed using quantities which appear in the construction of the coherent states. The following subjects are discussed ... More

The high energy semiclassical asymptotics of loci of roots of fundamental solutions for polynomial potentialsMar 03 2008May 24 2008In the case of polynomial potentials all solutions to 1-D Schroedinger equation are entire functions totally determined by loci of their roots and their behaviour at infinity. In this paper a description of the first of the two properties is given for ... More

Superscar states in rational polygon billiards - a reality or an illusion?Nov 12 2017Nov 15 2017The superscars phenomena (Heller, E.J., Phys. Rev. Lett. 53, (1984) 1515) in the rational polygon billiards (RPB) are analysed using the high energy semiclassical wave functions (SWF) built on classical trajectories forming skeletons. Considering examples ... More

Level-Structures of Drinfeld-Modules -- Closing a small gapMay 22 2009The aim of this article is to compare two different definitions of level-structers of Drinfeld modules and to prove that they are equivalent.