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First Class Constrained Systems and Twisting of Courant Algebroids by a Closed 4-formApr 04 2009We show that in analogy to the introduction of Poisson structures twisted by a closed 3-form by Park and Klimcik-Strobl, the study of three dimensional sigma models with Wess-Zumino term leads in a likewise way to twisting of Courant algebroid structures ... More

Quantization and the Issue of Time for Various Two-Dimensional Models of GravityAug 31 1993It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and $R^2$-Gravity are {\em embedded} in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above systems are ... More

General Yang-Mills type gauge theories for p-form gauge fields: From physics-based ideas to a mathematical framework OR From Bianchi identities to twisted Courant algebroidsJul 24 2014Jul 28 2014Starting with minimal requirements from the physical experience with higher gauge theories, i.e. gauge theories for a tower of differential forms of different form degrees, we discover that all the structural identities governing such theories can be ... More

Classical and Quantum Gravity in 1+1 Dimensions, Part II: The Universal CoveringsNov 30 1995Apr 26 1996A set of simple rules for constructing the maximal (e.g. analytic) extensions for any metric with a Killing field in an (effectively) two-dimensional spacetime is formulated. The application of these rules is extremely straightforward, as is demonstrated ... More

Time-of-Flight Three Dimensional Neutron Diffraction in Transmission Mode for Mapping Crystal Grain StructuresApr 20 2017The physical properties of polycrystalline materials depend on their microstructure, which is the nano-to-centimeter-scale arrangement of phases and defects in their interior. Such microstructure depends on the shape, crystallographic phase and orientation, ... More

Comment on Gravity and the Poincare GroupFeb 11 1993Following the approach of Grignani and Nardelli [1], we show how to cast the two-dimensional model $L \sim curv^2 + torsion^2 + cosm.const$ -- and in fact any theory of gravity -- into the form of a Poincare gauge theory. By means of the above example ... More

Gravity from Lie algebroid morphismsOct 17 2003Inspired by the Poisson Sigma Model and its relation to 2d gravity, we consider models governing morphisms from TSigma to any Lie algebroid E, where Sigma is regarded as d-dimensional spacetime manifold. We address the question of minimal conditions to ... More

Dirac Quantization Gravity-Yang-Mills Systems in 1+1 DimensionsMar 21 1994In two dimensions a large class of gravitational systems including, e.g., $R^2$-gravity can be quantized exactly also when coupled dynamically to a Yang-Mills theory. Some previous considerations on the quantization of pure gravity theories are improved ... More

On the Consistency of the Deterministic Local Volatility Function Model ('implied tree')Jan 10 2000We show that the frequent claim that the implied tree prices exotic options consistently with the market is untrue if the local volatilities are subject to change and the market is arbitrage-free. In the process, we analyse -- in the most general context ... More

Using EEG, SPECT, and Multivariate Resampling Methods to Differentiate Between Alzheimer's and other Cognitive ImpairmentsJun 29 2016The incidence of Alzheimer's disease (AD) and other forms of dementia is increasing in most western countries. For a precise and early diagnosis, several examination modalities exist, among them single-photon emission computed tomography (SPECT) and the ... More

Poisson Structure Induced Field Theories and Models of 1+1 Dimensional GravityNov 28 2000PhD thesis TU-Vienna, May 1994. Table of Contents: 1. Introduction, 2. Poisson Structure Induced Two Dimensional Field Theories, 3. Models of Gravity in 1+1 Dimensions

Target-Superspace in 2d Dilatonic SupergravityJun 29 1999The N=1 supersymmetric version of generalized 2d dilaton gravity can be cast into the form of a Poisson Sigma Model, where the target space and its Poisson bracket are graded. The target space consists of a 1+1 superspace and the dilaton, which is the ... More

2d quantum dilaton gravity as/versus finite dimensional quantum mechanical systemsFeb 18 1997I present the ``Chern--Simons'' formulation of generalized 2d dilaton gravity, summarize its Hamiltonian quantization (reduced phase space and Dirac quantization) and briefly discuss the statistical mechanical entropy of 2d black holes. Focus is put on ... More

Non-abelian Gerbes and Enhanced Leibniz AlgebrasJun 30 2016We present the most general gauge-invariant action functional for coupled 1- and 2-form gauge fields with kinetic terms in generic dimensions, i.e. dropping eventual contributions that can be added in particular space-time dimensions only such as higher ... More

Monopole star products are non-alternativeOct 26 2016Non-associative algebras appear in some quantum-mechanical systems, for instance if a charged particle in a distribution of magnetic monopoles is considered. Using methods of deformation quantization it is shown here, that algebras for such systems cannot ... More

Algebroid Yang-Mills TheoriesJun 23 2004Nov 11 2004A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions, we show that ... More

Gravity in Two Spacetime DimensionsNov 27 2000In this habilitation thesis we provide an introduction to gravitational models in two spacetime dimensions. Focus is put on exactly solvable models. We begin by introducing and motivating different possible gravitational actions, including those of generalized ... More

All Symmetries of Non-Einsteinian Gravity in $d =2$Jul 01 1992Nov 24 1992The covariant form of the field equations for two--dimensional $R^2$--gravity with torsion as well as its Hamiltonian formulation are shown to suggest the choice of the light--cone gauge. Further a one--to--one correspondence between the Hamiltonian gauge ... More

Improvements for Vachaspati-Vilenkin-type Algorithms for Cosmic String and Disclination FormationAug 15 1996Aug 16 1996We derive various consistency requirements for Vachaspati-Vilenkin type Monte-Carlo simulations of cosmic string formation or disclination formation in liquid crystals. We argue for the use of a tetrakaidekahedral lattice in such simulations. We also ... More

Laue three dimensional neutron diffractionFeb 08 2019This article presents a measurement technique and data analysis tool to perform 3D grain distribution mapping and indexing of oligocrystalline samples using neutrons: Laue three-dimensional neutron diffraction (Laue3DND). The approach builds on forward ... More

Poisson Geometry in Constrained SystemsDec 10 2001Feb 20 2002Constrained Hamiltonian systems fall into the realm of presymplectic geometry. We show, however, that also Poisson geometry is of use in this context. For the case that the constraints form a closed algebra, there are two natural Poisson manifolds associated ... More

Euclidian 2D Gravity with TorsionJul 03 1993Closing a gap in the literature on the subject, the local solutions of 2D-gravity with torsion are given for Euclidian signature. For the topology of a cylinder the system is quantized.

Gauging without Initial SymmetryMar 31 2014Apr 10 2014The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Sigma, the original functional is extended appropriately by additional Lie(G)-valued ... More

Improved Causal Discovery from Longitudinal Data Using a Mixture of DAGsJan 28 2019Many causal processes in biomedicine contain cycles and evolve. However, most causal discovery algorithms assume that the underlying causal process follows a single directed acyclic graph (DAG) that does not change over time. The algorithms can therefore ... More

Diffeomorphisms Versus Non Abelian Gauge Transformations: An Example of 1+1 Dimensional GravityJan 21 1994We investigate the phase space of a typical model of 1+1 dimensional gravity (Jackiw-Teitelboim model with cylindrical topology) using its reformulation as a non abelian gauge theory based on the sl(2,R) algebra. Modifying the conventional approach we ... More

Poisson-Sigma-Models: A Generalization of 2-D Gravity Yang-Mills-SystemsNov 22 1994A new class of two dimensional integrable field theories, based on the mathematical notion of Poisson manifolds, and containing gravity-Yang-Mills systems as well as the G/G gauged Wess-Zumino Witten-model, are presented. The local solutions of the classical ... More

Quantization of Field Theories Generalizing Gravity-Yang-Mills Systems on the CylinderJun 16 1994Pure gravity and gauge theories in two dimensions are shown to be special cases of a much more general class of field theories each of which is characterized by a Poisson structure on a finite dimensional target space. A general scheme for the quantization ... More

Curving Yang-Mills-Higgs Gauge TheoriesOct 26 2015Established fundamental physics can be described by fields, which are maps. The source of such a map is space-time, which can be curved due to gravity. The map itself needs to be curved in its gauge field part so as to describe interaction forces like ... More

Quantum dynamics in transverse-field Ising models from classical networksJul 20 2017Jan 23 2018The efficient representation of quantum many-body states with classical resources is a key challenge in quantum many-body theory. In this work we analytically construct classical networks for the description of the quantum dynamics in transverse-field ... More

Three Dimensional Polarimetric Neutron Tomography of Magnetic FieldsApr 17 2017Feb 02 2018Through the use of Time-of-Flight Three Dimensional Polarimetric Neutron Tomography (ToF 3DPNT) we have for the first time successfully demonstrated a technique capable of measuring and reconstructing three dimensional magnetic field strengths and directions ... More

Poisson Structure Induced (Topological) Field TheoriesMay 17 1994A class of two dimensional field theories, based on (generically degenerate) Poisson structures and generalizing gravity-Yang-Mills systems, is presented. Locally, the solutions of the classical equations of motion are given. A general scheme for the ... More

Dirac Sigma Models from GaugingNov 27 2013The G/G WZW model results from the WZW-model by a standard procedure of gauging. G/G WZW models are members of Dirac sigma models, which also contain twisted Poisson sigma models as other examples. We show how the general class of Dirac sigma models can ... More

Classical and Quantum Gravity in 1+1 Dimensions, Part III: Solutions of Arbitrary TopologyJul 30 1996Aug 13 1997All global solutions of arbitrary topology of the most general 1+1 dimensional dilaton gravity models are obtained. We show that for a generic model there are globally smooth solutions on any non-compact 2-surface. The solution space is parametrized explicitly ... More

Generalizing Geometry - Algebroids and Sigma ModelsApr 05 2010In this contribution we review some of the interplay between sigma models in theoretical physics and novel geometrical structures such as Lie (n-)algebroids. The first part of the article contains the mathematical background, the definition of various ... More

WZW-Poisson manifoldsApr 19 2001Oct 02 2001We observe that a term of the WZW-type can be added to the Lagrangian of the Poisson Sigma model in such a way that the algebra of the first class constraints remains closed. This leads to a natural generalization of the concept of Poisson geometry. The ... More

Universality and Critical Phenomena in String Defect StatisticsAug 15 1996The idea of biased symmetries to avoid or alleviate cosmological problems caused by the appearance of some topological defects is familiar in the context of domain walls, where the defect statistics lend themselves naturally to a percolation theory description, ... More

Statistical Properties of StringsOct 13 1994We investigate numerically the configurational statistics of strings. The algorithm models an ensemble of global $U(1)$ cosmic strings, or equivalently vortices in superfluid $^4$He. We use a new method which avoids the specification of boundary conditions ... More

Explicit Global Coordinates for Schwarzschild and Reissner-NordstroemJul 05 1995Mar 16 1996We construct coordinate systems that cover all of the Reissner-Nordstroem solution with m>|q| and m=|q|, respectively. This is possible by means of elementary analytical functions. The limit of vanishing charge q provides an alternative to Kruskal which, ... More

Classical and Quantum Gravity in 1+1 Dimensions, Part I: A Unifying ApproachAug 08 1995Aug 11 1997We provide a concise approach to generalized dilaton theories with and without torsion and coupling to Yang-Mills fields. Transformations on the space of fields are used to trivialize the field equations locally. In this way their solution becomes accessible ... More

Classical Solutions for Poisson Sigma Models on a Riemann surfaceApr 29 2003We determine the moduli space of classical solutions to the field equations of Poisson Sigma Models on arbitrary Riemann surfaces for Poisson structures with vanishing Poisson form class. This condition ensures the existence of a presymplectic form on ... More

Symplectic Cuts and Projection QuantizationDec 10 1999Jun 07 2000The recently proposed projection quantization, which is a method to quantize particular subspaces of systems with known quantum theory, is shown to yield a genuine quantization in several cases. This may be inferred from exact results established within ... More

Deep Multiple Kernel LearningOct 11 2013Deep learning methods have predominantly been applied to large artificial neural networks. Despite their state-of-the-art performance, these large networks typically do not generalize well to datasets with limited sample sizes. In this paper, we take ... More

Geometry on Lie algebroids I: compatible geometric structures on the baseMar 14 2016The object of our study is a Lie algebroid $A$ or a Cartan-Lie algebroid $(A,\nabla)$ (a Lie algebroid with a compatible connection) over a base manifold $M$ equipped with appropriately compatible geometrical structures. The main focus is on a Riemannian ... More

Discretisation of stochastic control problems for continuous time dynamics with delayFeb 17 2006As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space. A new feature in this context is to allow for delay in ... More

A Global View of Kinks in 1+1 GravityJul 25 1997Following Finkelstein and Misner, kinks are non-trivial field configurations of a field theory, and different kink-numbers correspond to different disconnected components of the space of allowed field configurations for a given topology of the base manifold. ... More

Complete Classification of 1+1 Gravity SolutionsNov 25 1997A classification of the maximally extended solutions for 1+1 gravity models (comprising e.g. generalized dilaton gravity as well as models with non-trivial torsion) is presented. No restrictions are placed on the topology of the arising solutions, and ... More

Group Theoretical Quantization and the Example of a Phase Space S^1 x R^+Aug 27 1999Dec 13 1999The group theoretical quantization scheme is reconsidered by means of elementary systems. Already the quantization of a particle on a circle shows that the standard procedure has to be supplemented by an additional condition on the admissibility of group ... More

Generalized 2d dilaton gravity with matter fieldsMay 15 1998Jun 04 1998We extend the classical integrability of the CGHS model of 2d dilaton gravity [1] to a larger class of models, allowing the gravitational part of the action to depend more generally on the dilaton field and, simultaneously, adding fermion- and U(1)-gauge-fields ... More

A Brief Introduction to Poisson Sigma-ModelsJul 04 1995The theory of Poisson-$\sigma$-models employs the mathematical notion of Poisson manifolds to formulate and analyze a large class of topological and almost topological two dimensional field theories. As special examples this class of field theories includes ... More

Canonical Quantization of Non-Einsteinian Gravity and the Problem of TimeNov 12 1992For a 1+1 dimensional theory of gravity with torsion different approaches to the formulation of a quantum theory are presented. They are shown to lead to the same finite dimensional quantum system. Conceptual questions of quantum gravity like e.g.\ the ... More

Lie Algebroid Yang Mills with Matter FieldsAug 21 2009Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge theories, replacing the structural Lie algebra by a Lie algebroid E. In this note we relax the conditions on the fiber metric of E for gauge invariance of the action functional. ... More

Current Algebras and Differential GeometryOct 18 2004Mar 20 2005We show that symmetries and gauge symmetries of a large class of 2-dimensional sigma models are described by a new type of a current algebra. The currents are labeled by pairs of a vector field and a 1-form on the target space of the sigma model. We compute ... More

Second Law of Black Hole Mechanics for all 2d Dilaton TheoriesSep 19 2000Sep 26 2000It is shown that all generalized two--dimensional dilaton theories with arbitrary matter content (with a curvature independent coupling to gravity) do not only obey a first law of black hole mechanics (which follows from Wald's general considerations, ... More

Characteristic classes associated to Q-bundlesNov 26 2007A Q-manifold is a graded manifold endowed with a vector field of degree one squaring to zero. We consider the notion of a Q-bundle, that is, a fiber bundle in the category of Q-manifolds. To each homotopy class of ``gauge fields'' (sections in the category ... More

OT SIMPLE - a construction-kit approach to Optimality Theory implementationNov 12 1996This paper details a simple approach to the implementation of Optimality Theory (OT, Prince and Smolensky 1993) on a computer, in part reusing standard system software. In a nutshell, OT's GENerating source is implemented as a BinProlog program interpreting ... More

Pointwise estimates for B-spline Gram matrix inversesDec 12 2012Nov 26 2013We present a new method for proving a certain geometric-decay inequality for entries of inverses of B-spline Gram matrices, which is given in [Passenbrunner,Shadrin 2013, arXiv:1308.4824].

Brauer spaces for commutative rings and structured ring spectraOct 13 2011Jul 30 2013Using an analogy between the Brauer groups in algebra and the Whitehead groups in topology, we first use methods of algebraic K-theory to give a natural definition of Brauer spectra for commutative rings, such that their homotopy groups are given by the ... More

A non-trivial ghost kernel for the equivariant stable cohomotopy of projective spacesOct 11 2011It is shown that the ghost kernel for certain equivariant stable cohomotopy groups of projective spaces is non-trivial. The proof is based on the Borel cohomology Adams spectral sequence and the calculations with the Steenrod algebra afforded by it.

Anomalous Anisotropies of Cosmic Rays from Turbulent Magnetic FieldsOct 21 2013Jan 15 2014The propagation of cosmic rays (CRs) in turbulent interstellar magnetic fields is typically described as a spatial diffusion process. This formalism predicts only a small deviation from an isotropic CR distribution in the form of a dipole in the direction ... More

Supersymmetry on the RocksOct 26 2006In R-parity conserving supersymmetric (SUSY) models the lightest SUSY particle (LSP) is stable and a candidate for dark matter. Depending on the coupling and mass of this particle the life time of the next-to-lightest SUSY particle (NLSP) may be large ... More

Higgs Physics at a Future e+e- Linear ColliderJul 26 2001This letter reviews the potential of a high luminosity e+e- linear collider (LC) in the precision study of the Higgs boson profile. The complementarity with the Large Hadron Collider (LHC) Higgs physics program is briefly discussed.

Flexible Time and the Evolution of One-Dimensional Cellular AutomataDec 22 2008Jul 17 2010Here I describe a view of the evolution of cellular automata that allows to operate on larger structures. Instead of calculating the next state of all cells in one step, the method here developed uses a time slice that can proceed at different places ... More

The use of geometric and quantum group techniques for wild quiversApr 15 2003This overview paper reviews several results relating the representation theory of quivers to algebraic geometry and quantum group theory. (Potential) applications to the study of the representation theory of wild quivers are discussed. To appear in the ... More

Quivers, desingularizations and canonical basesApr 30 2001A class of desingularizations for orbit closures of representations of Dynkin quivers is constructed, which can be viewed as a graded analogue of the Springer resolution. A stratification of the singular fibres is introduced; its geometry and combinatorics ... More

Coincidence of Lyapunov exponents for random walks in weak random potentialsAug 14 2006Aug 27 2008We investigate the free energy of nearest-neighbor random walks on $\mathbb{Z}^d$, endowed with a drift along the first axis and evolving in a nonnegative random potential given by i.i.d. random variables. Our main result concerns the ballistic regime ... More

The group reduction for bounded cosine functions on UMD spacesSep 18 2007Sep 19 2007It is shown that if A generates a bounded cosine operator function on a UMD space X, then i(-A)^{1/2} generates a bounded C_0-group. The proof uses a transference principle for cosine functions.

A Construction of Metabelian GroupsJul 29 2004Oct 25 2004In 1934, Garrett Birkhoff has shown that the number of isomorphism classes of finite metabelian groups of order $p^{22}$ tends to infinity with $p$. More precisely, for each prime number $p$ there is a family $(M_\lambda)_{\lambda=0,...,p-1}$ of indecomposable ... More

Local unitary symmetries and entanglement invariantsJan 09 2014Oct 31 2014We investigate the relation between local unitary symmetries and entanglement invariants of multi-qubit systems. The Hilbert space of such systems can be stratified in terms of states with different types of symmetry. We review the connection between ... More

On embedded trees and lattice pathsJun 02 2009Jun 29 2009Bouttier, Di Francesco and Guitter introduced a method for solving certain classes of algebraic recurrence relations arising the context of embedded trees and map enumeration. The aim of this note is to apply this method to three problems. First, we discuss ... More

Active laser frequency stabilization and resolution enhancement of interferometers for the measurement of gravitational waves in spaceJun 27 2005Aug 23 2005Laser frequency stabilization is notably one of the major challenges on the way to a space-borne gravitational wave observatory. The proposed Laser Interferometer Space Antenna (LISA) is presently under development in an ESA, NASA collaboration. We present ... More

Multiple interactions and generalized parton distributionsJul 30 2010Multiple parton interactions in a single proton-proton collision are expected to play an important role for many observables at LHC. To a large part their phenomenological description relies on rather simple and physically intuitive assumptions. We report ... More

Some news about generalised parton distributionsAug 07 2008I briefly discuss some recent developments (and recall some old news) in the theory and phenomenology of generalised parton distributions.

Exploring skewed parton distribution with polarized targetOct 18 2000I briefly review the physics of skewed parton distributions. Special emphasis is put on the relevance of target polarization, and on the different roles of small and of intermediate x_B.

Transversity measurements at HERMESJul 02 2005Azimuthal single-spin asymmetries (SSA) in semi-inclusive electroproduction of charged pions in deep-inelastic scattering (DIS) of positrons on a transversely polarised hydrogen target are presented. Azimuthal moments for both the Collins and the Sivers ... More

Optimal Synchronization in SpaceJan 27 2010In this Rapid Communication we investigate spatially constrained networks that realize optimal synchronization properties. After arguing that spatial constraints can be imposed by limiting the amount of `wire' available to connect nodes distributed in ... More

Determination of the Dark Matter profile from the EGRET excess of diffuse Galactic gamma radiationOct 26 2007The excess above 1 GeV in the energy spectrum of the diffuse Galactic gamma radiation, measured with the EGRET experiment, can be interpreted as the annihilation of Dark Matter (DM) particles. The DM is distributed in a halo around the Milky Way. Considering ... More

Relations between slices and quotients of the algebraic cobordism spectrumDec 03 2008May 27 2009We prove a relative statement about the slices of the algebraic cobordism spectrum. If the map from MGL to a certain quotient of MGL introduced by Hopkins and Morel is the map to the zero-slice then a relative version of Voevodsky's conjecture on the ... More

On moduli spaces of sheaves on K3 or abelian surfacesApr 29 2011We investigate the moduli spaces of one- and two-dimensional sheaves on projective K3 and abelian surfaces that are semistable with respect to a nongeneral ample divisor with regard to the symplectic resolvability. We can exclude the existence of new ... More

k-Disjunctive cuts and a finite cutting plane algorithm for general mixed integer linear programsJul 26 2007In this paper we give a generalization of the well known split cuts of Cook, Kannan and Schrijver to cuts which are based on multi-term disjunctions. They will be called k-disjunctive cuts. The starting point is the question what kind of cuts is needed ... More

Moduli of representations of quiversFeb 15 2008An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is motivated, and ... More

Properties of Extensive Air ShowersFeb 12 2004Some general properties of extensive air showers are discussed. The main focus is put on the longitudinal development, in particular the energy flow, and on the lateral distribution of different air shower components. The intention of the paper is to ... More

A Pettis-Type Integral and Applications to Transition SemigroupsJan 13 2009Apr 08 2014Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study a class ... More

Fredholm theory for band-dominated and related operators: a surveyJul 05 2013This paper presents the Fredholm theory on l^p-spaces for band-dominated operators and important subclasses, such as operators in the Wiener algebra. It particularly closes several gaps in the previously known results for the case p=\infty and addresses ... More

On the non-uniform motion of dislocations: The retarded elastic fields, the retarded dislocation tensor potentials and the Liénard-Wiechert tensor potentialsOct 11 2012The purpose of this paper is the fundamental theory of the non-uniform motion of dislocations in two and three space-dimensions. We investigate the non-uniform motion of an arbitrary distribution of dislocations, a dislocation loop and straight dislocations ... More

The elastodynamic Liénard-Wiechert potentials and elastic fields of non-uniformly moving point and line forcesMay 23 2012The purpose of this paper is to investigate the fundamental problem of the non-uniform subsonic motion of a point force and line forces in an unbounded, homogeneous, isotropic medium in analogy to the electromagnetic Li\'enard-Wiechert potentials. The ... More

An elastoplastic theory of dislocations as a physical field theory with torsionMay 14 2001Feb 25 2002We consider a static theory of dislocations with moment stress in an anisotropic or isotropic elastoplastical material as a T(3)-gauge theory. We obtain Yang-Mills type field equations which express the force and the moment equilibrium. Additionally, ... More

Derived Fundamental Groups for Tate MotivesMay 15 2010Nov 01 2010We construct derived fundamental group schemes for Tate motives over connected smooth schemes over fields. We show that there exists a pro affine derived group scheme over the rationals such that its category of perfect representations models the triangulated ... More

Notes on the sum and maximum of independent exponentially distributed random variables with different scale parametersJul 15 2013We consider the distribution of the sum and the maximum of a collection of independent exponentially distributed random variables. The focus is laid on the explicit form of the density functions (pdf) of non-i.i.d. sequences. Those are recovered in a ... More

Comment on 'Reasonable fermionic quantum information theories require relativity'Oct 03 2016In [N. Friis, New J. Phys. 18, 033014 (2016)] the non-relativistic description of fermions is considered and in particular the role of the parity superselection rule in relation to the characterization of entanglement. An argument based on the spin-statistics ... More

Orthogonal projectors onto spaces of periodic splinesAug 24 2016Oct 13 2016The main result of this paper is a proof that for any integrable function $f$ on the torus, any sequence of its orthogonal projections $(\widetilde{P}_n f)$ onto periodic spline spaces with arbitrary knots $\widetilde{\Delta}_n$ and arbitrary polynomial ... More

A direct Proof for Quadratic Convergence of the Geometric Newton MethodJul 07 2016We consider the problem of numerically computing a critical point of a functional $J\colon M\rightarrow R$ where $M$ is a Riemannian manifold. Due to local quadratic convergence a popular choice to solve this problem is the geometric Newton method. The ... More

Periodic solutions of the sinh-Gordon equation and integrable systemsJun 06 2016We study the space of periodic solutions of the elliptic $\sinh$-Gordon equation by means of spectral data consisting of a Riemann surface $Y$ and a divisor $D$. We show that the space $M_g^{\mathbf{p}}$ of real periodic finite type solutions with fixed ... More

Spin Excitations and Correlations in Scanning Tunneling SpectroscopyMay 17 2015In recent years inelastic spin-flip spectroscopy using a lowtemperature scanning tunneling microscope has been a very successful tool for studying not only individual spins but also complex coupled systems. When these systems interact with the electrons ... More

Deciphering the Dipole Anisotropy of Galactic Cosmic RaysMay 20 2016Oct 12 2016Recent measurements of the dipole anisotropy in the arrival directions of Galactic cosmic rays (CRs) indicate a strong energy dependence of the dipole amplitude and phase in the TeV-PeV range. We argue here that these observations can be well understood ... More

Computational aspects of rational residuosityApr 26 2016Nov 21 2016In this paper, we consider an extension of Jacobi's symbol, the so called rational $2^k$-th power residue symbol. In Section 3, we prove a novel generalization of Zolotarev's lemma. In Sections 4, 5 and 6, we establish polynomial-time reductions from ... More

Deterministic factorization of sums and differences of powersDec 20 2015Let $a,b\in \mathbb{N}$ be fixed and coprime such that $a>b$, and let $N$ be any number of the form $a^n\pm b^n$, $n\in\mathbb{N}$. We will generalize a result of Bostan, Gaudry and Schost and prove that we may compute the prime factorization of $N$ in ... More

On a conjecture of John Hoffman regarding sums of palindromic numbersOct 26 2015We disprove the conjecture that every sufficiently large natural number $n$ is the sum of three palindromic natural numbers where one of them can be chosen to be the largest or second largest palindromic natural number smaller than or equal to $n$.

The Relative CapacityJun 09 2008Jul 10 2008The purpose of this article is to introduce the relative $p$-capacity $\Cap_{p,\Omega}$ with respect to an open set $\Omega$ in $\IR^N$. It is a Choquet capacity on the closure of $\Omega$ and extends the classical $p$-capacity $\Cap_p$ in the sense that ... More

Navigation in the Ancient Mediterranean and BeyondAug 25 2017Aug 31 2017This lesson unit has been developed within the framework the EU Space Awareness project. It provides an insight into the history and navigational methods of the Bronze Age Mediterranean peoples. The students explore the link between exciting history and ... More

Uncertainty and auto-correlation in MeasurementJul 07 2017Dec 30 2017Although a system is described by a well-known set of equations leading to a deterministic behavior, in the real world the value of a measurand obtained by an experiment will mostly scatter. Accordingly, an uncertainty is associated with that value of ... More