total 23710took 0.10s

Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficientsMar 26 2012May 09 2013Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method diverge for ... More

Existence of spatially differentiable solutions of stochastic differential equations with non-globally monotone coefficient functionsMar 22 2019Spatial differentiability of solutions of stochastic differential equations (SDEs) is required for the It\^o-Alekseev-Gr\"obner formula and other applications. In the literature, this differentiability is only derived if the coefficient functions of the ... More

Stochastic averaging for multiscale Markov processes with an application to a Wright-Fisher model with fluctuating selectionApr 07 2015Mar 05 2018Let $Z = (Z_t)_{t\in[0,\infty)}$ be an ergodic Markov process and, for every $n\in\mathbb{N}$, let $Z^n = (Z_{n^2 t})_{t\in[0,\infty)}$ drive a process $X^n$. Classical results show under suitable conditions that the sequence of non-Markovian processes ... More

Supercritical branching diffusions in random environmentSep 08 2011Sep 30 2013Supercritical branching processes in constant environment conditioned on eventual extinction are known to be subcritical branching processes. The case of random environment is more subtle. A supercritical branching diffusion in random environment (BDRE) ... More

Interacting diffusions and trees of excursions: convergence and comparisonApr 06 2011Sep 30 2013We consider systems of interacting diffusions with local population regulation. Our main result shows that the total mass process of such a system is bounded above by the total mass process of a tree of excursions with appropriate drift and diffusion ... More

A short proof and a generalization of the BKR-inequalityJul 25 2008Jul 26 2008There is a serious mistake in the proof.

The Virgin Island ModelFeb 21 2008Jun 02 2009A continuous mass population model with local competition is constructed where every emigrant colonizes an unpopulated island. The population founded by an emigrant is modeled as excursion from zero of an one-dimensional diffusion. With this excursion ... More

On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equationsAug 10 2017Parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) are key ingredients in a number of models in physics and financial engineering. In particular, parabolic PDEs and BSDEs are fundamental tools in the ... More

Graphical Representation of some Duality Relations in Stochastic Population ModelsJun 26 2007We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. http://www.ams.org/mathscinet-getitem?mr=MR2123250) and for the self-duality of Feller's branching diffusion with ... More

Multi-level Picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearitiesNov 03 2017Parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) have a wide range of applications. In particular, high-dimensional PDEs with gradient-dependent nonlinearities appear often in the state-of-the-art ... More

Propagation of chaos and the many-demes limit for weakly interacting diffusions in the sparse regimeApr 03 2018Propagation of chaos is a well-studied phenomenon and shows that weakly interacting diffusions may become independent as the system size converges to infinity. Most of the literature focuses on the case of exchangeable systems where all involved diffusions ... More

Differentiability of semigroups of stochastic differential equations with Hölder-continuous diffusion coefficientsMar 28 2018Differentiability of semigroups is useful for many applications. Here we focus on stochastic differential equations whose diffusion coefficient is the square root of a differentiable function but not differentiable itself. For every $m\in\{0,1,2\}$ we ... More

On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficientsJan 01 2014We develope a perturbation theory for stochastic differential equations (SDEs) by which we mean both stochastic ordinary differential equations (SODEs) and stochastic partial differential equations (SPDEs). In particular, we estimate the $ L^p $-distance ... More

Branching diffusions in random environmentJul 14 2011Sep 30 2013We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obtain the exact asymptotic behavior of the survival probability. ... More

Convergence of the stochastic Euler scheme for locally Lipschitz coefficientsDec 14 2009Nov 17 2011Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. The important case ... More

Stochastic averaging for multiscale Markov processes with an application to branching random walk in random environmentApr 07 2015Let $Z = (Z_t)_{t\in[0,\infty)}$ be an ergodic Markov process and, for $n\in\mathbb{N}$, let $Z^n = (Z_{n^2 t})_{t\in[0,\infty)}$ drive a process $X^n$. Classical results show under suitable conditions that the sequence of non-Markovian processes $(X^n)_{n\in\mathbb{N}}$ ... More

Time Reversal of Some Stationary Jump-Diffusion Processes from Population GeneticsNov 15 2010Jan 13 2011We describe the processes obtained by time reversal of a class of stationary jump-diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, ... More

Ergodic behavior of locally regulated branching populationsSep 26 2005Mar 30 2007For a class of processes modeling the evolution of a spatially structured population with migration and a logistic local regulation of the reproduction dynamics, we show convergence to an upper invariant measure from a suitable class of initial distributions. ... More

Loss of regularity for Kolmogorov equationsSep 26 2012Mar 06 2015The celebrated H\"{o}rmander condition is a sufficient (and nearly necessary) condition for a second-order linear Kolmogorov partial differential equation (PDE) with smooth coefficients to be hypoelliptic. As a consequence, the solutions of Kolmogorov ... More

Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equationsSep 29 2013Jan 06 2014Exponential integrability properties of numerical approximations are a key tool for establishing positive rates of strong and numerically weak convergence for a large class of nonlinear stochastic differential equations. It turns out that well-known numerical ... More

Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficientsOct 18 2010Sep 12 2012On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient. On the other hand, the ... More

Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficientsMay 04 2009Jul 05 2011The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation with globally Lipschitz continuous drift and diffusion coefficient. Recent results extend this convergence to coefficients which grow at most ... More

Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equationsMay 02 2011Sep 10 2013The Euler-Maruyama scheme is known to diverge strongly and numerically weakly when applied to nonlinear stochastic differential equations (SDEs) with superlinearly growing and globally one-sided Lipschitz continuous drift coefficients. Classical Monte ... More

Altruistic defense traits in structured populationsMay 08 2015We propose a model for the frequency of an altruistic defense trait. More precisely, we consider Lotka-Volterra-type models involving a host/prey population consisting of two types and a parasite/predator population where one type of host individuals ... More

Strong convergence rates and temporal regularity for Cox-Ingersoll-Ross processes and Bessel processes with accessible boundariesMar 25 2014Cox-Ingersoll-Ross (CIR) processes are widely used in financial modeling such as in the Heston model for the approximative pricing of financial derivatives. Moreover, CIR processes are mathematically interesting due to the irregular square root function ... More

Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risksMar 14 2019Parabolic partial differential equations (PDEs) are widely used in the mathematical modeling of natural phenomena and man made complex systems. In particular, parabolic PDEs are a fundamental tool to determine fair prices of financial derivatives in the ... More

Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equationsSep 29 2013Nov 20 2016Exponential integrability properties of numerical approximations are a key tool for establishing positive rates of strong and numerically weak convergence for a large class of nonlinear stochastic differential equations. It turns out that well-known numerical ... More

Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equationsApr 07 2016May 17 2016This article introduces and analyzes a new explicit, easily implementable, and full discrete accelerated exponential Euler-type approximation scheme for additive space-time white noise driven stochastic partial differential equations (SPDEs) with possibly ... More

A stochastic Gronwall inequality and applications to moments, strong completeness, strong local Lipschitz continuity, perturbationsMar 20 2019There are numerous applications of the classical (deterministic) Gronwall inequality. Recently, Michael Scheutzow has discovered a stochastic Gronwall inequality which provides upper bounds for the $p$-th moments, $p\in(0,1)$, of the supremum of nonnegative ... More

Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equationsSep 22 2013Nov 24 2014Recently, Hairer et. al (2012) showed that there exist SDEs with infinitely often differentiable and globally bounded coefficient functions whose solutions fail to be locally Lipschitz continuous in the strong L^p-sense with respect to the initial value ... More

On full history recursive multilevel Picard approximations and numerical approximations of high-dimensional nonlinear parabolic partial differential equationsJul 12 2016Parabolic partial differential equations (PDEs) are a fundamental tool in the state-of-the-art pricing and hedging of financial derivatives. The PDEs appearing in such financial engineering applications are often high-dimensional and nonlinear. Since ... More

On the Itô-Alekseev-Gröbner formula for stochastic differential equationsDec 24 2018In this article we establish a new formula for the difference of a test function of the solution of a stochastic differential equation and of the test function of an It\^o process. The introduced formula essentially generalizes both the classical Alekseev-Gr\"obner ... More

Ecological and genetic effects of introduced species on their native competitorsAug 06 2012Jan 02 2013Species introductions to new habitats can cause a decline in the population size of competing native species and consequently also in their genetic diversity. We are interested in why these adverse effects are weak in some cases whereas in others the ... More

Multilevel Picard iterations for solving smooth semilinear parabolic heat equationsJul 12 2016Feb 22 2019We introduce a new family of numerical algorithms for approximating solutions of general high-dimensional semilinear parabolic partial differential equations at single space-time points. The algorithm is obtained through a delicate combination of the ... More

A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equationsJan 30 2019Deep neural networks and other deep learning methods have very successfully been applied to the numerical approximation of high-dimensional nonlinear parabolic partial differential equations (PDEs), which are widely used in finance, engineering, and natural ... More

Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equationsJul 03 2018For a long time it is well-known that high-dimensional linear parabolic partial differential equations (PDEs) can be approximated by Monte Carlo methods with a computational effort which grows polynomially both in the dimension and in the reciprocal of ... More

Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equationsJul 03 2018Mar 25 2019For a long time it is well-known that high-dimensional linear parabolic partial differential equations (PDEs) can be approximated by Monte Carlo methods with a computational effort which grows polynomially both in the dimension and in the reciprocal of ... More

Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensionsMay 03 2016Apr 09 2019We show that if a sequence of piecewise affine linear processes converges in the strong sense with a positive rate to a stochastic process which is strongly H\"older continuous in time, then this sequence converges in the strong sense even with respect ... More

Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensionsMay 03 2016We show that if a sequence of piecewise affine linear processes converges in the strong sense with a positive rate to a stochastic process which is strongly H\"older continuous in time, then this sequence converges in the strong sense even with respect ... More

Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensionsMay 03 2016Mar 16 2017We show that if a sequence of piecewise affine linear processes converges in the strong sense with a positive rate to a stochastic process which is strongly H\"older continuous in time, then this sequence converges in the strong sense even with respect ... More

Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearitiesMar 14 2019The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein scheme) are known to diverge strongly and numerically weakly in the case of one-dimensional stochastic ordinary differential equations with superlinearly growing ... More

Ground States and Singular Vectors of Convex Variational Regularization MethodsNov 09 2012Singular value decomposition is the key tool in the analysis and understanding of linear regularization methods. In the last decade nonlinear variational approaches such as $\ell^1$ or total variation regularizations became quite prominent regularization ... More

A tight bound on the speed-up through storage for quickest multi-commodity flowsJun 18 2014Multi-commodity flows over time exhibit the non-intuitive property that letting flow wait can allow us to send flow faster overall. Fleischer and Skutella (IPCO~2002) show that the speed-up through storage is at most a factor of~$2$, and that there are ... More

On the representation of polyhedra by polynomial inequalitiesMar 26 2002Oct 24 2002A beautiful result of Br\"ocker and Scheiderer on the stability index of basic closed semi-algebraic sets implies, as a very special case, that every $d$-dimensional polyhedron admits a representation as the set of solutions of at most $d(d+1)/2$ polynomial ... More

On a generalization of Matérn hard-core processes with applications to max-stable processesSep 18 2017The Mat\'ern hard-core processes are classical examples for point process models obtained from (marked) Poisson point processes. Points of the original Poisson process are deleted according to a dependent thinning rule, resulting in a process whose points ... More

A New Riemannian Setting for Surface RegistrationJun 03 2011Sep 19 2014We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the space of surfaces. In this article we compare our approach with the diffeomorphic ... More

Pebble Games and Linear EquationsApr 09 2012Mar 24 2015We give a new, simplified and detailed account of the correspondence between levels of the Sherali-Adams relaxation of graph isomorphism and levels of pebble-game equivalence with counting (higher-dimensional Weisfeiler-Lehman colour refinement). The ... More

I^K-convergenceSep 13 2011In this paper we introduce I^K-convergence which is a common generalization of the I^K-convergence of sequences, double sequences and nets. We show that many results that were shown before for these special cases are true for the I^K-convergence, too

Modern Regularization Methods for Inverse ProblemsJan 30 2018Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from linear towards ... More

Quantum integrable Toda like systemsOct 14 1998Using deformation quantization and suitable 2 by 2 quantum $R$-matrices we show that a list of Toda like classical integrable systems given by Y.B.Suris is quantum integrable in the sense that the classical conserved quantities (which are already in involution ... More

Algorithmic Optimisations for Iterative Deconvolution MethodsApr 26 2013We investigate possibilities to speed up iterative algorithms for non-blind image deconvolution. We focus on algorithms in which convolution with the point-spread function to be deconvolved is used in each iteration, and aim at accelerating these convolution ... More

Optimal Partitioning for Dual-Pivot QuicksortMar 21 2013Oct 13 2015Dual-pivot quicksort refers to variants of classical quicksort where in the partitioning step two pivots are used to split the input into three segments. This can be done in different ways, giving rise to different algorithms. Recently, a dual-pivot algorithm ... More

Open-closed modular operads, Cardy condition and string field theoryNov 26 2016We prove that the modular operad of diffeomorphism classes of Riemann surfaces with both `open' and `closed' boundary components, in the sense of string field theory, is the modular completion of its genus 0 part quotiented by the Cardy condition. We ... More

Neutralino Dark Matter and the CurvatonNov 30 2006Mar 09 2007We build a realistic model of curvaton cosmology, in which the energy content is described by radiation, WIMP dark matter and a curvaton component. We calculate the curvature and isocurvature perturbations, allowing for arbitrary initial density perturbations ... More

Confluence of singularities of non-linear differential equations via Borel--Laplace transformationsJul 31 2013Nov 03 2015Borel summable divergent series usually appear when studying solutions of analytic ODE near a multiple singular point. Their sum, uniquely defined in certain sectors of the complex plane, is obtained via the Borel--Laplace transformation. This article ... More

Well-posedness and blow-up for a two-component Degasperis-Procesi equation with infinitely fast propagating solutionsMar 30 2011Apr 11 2012In this paper, a two-component variant of the Degasperis-Procesi equation on the real line is discussed. Applying Kato's theory, we first prove the local well-posedness for the equation under consideration in $H^s\times H^{s-1}$, for $s\geq 2$. Second ... More

Twistors and supertwistors for exceptional field theoryOct 08 2015Dec 03 2015As a means of examining the section condition and its possible solutions and relaxations, we perform twistor transforms related to versions of exceptional field theory with Minkowski signature. The spinor parametrisation of the momenta naturally solves ... More

The geometry behind double geometryFeb 11 2014Aug 27 2014Generalised diffeomorphisms in double field theory rely on an O(d,d) structure defined on tangent space. We show that any (pseudo-)Riemannian metric on the doubled space defines such a structure, in the sense that the generalised diffeomorphisms defined ... More

Non-gravitational exceptional supermultipletsFeb 27 2013Feb 28 2013We examine non-gravitational minimal supermultiplets which are based on the tensor gauge fields appearing as matter fields in exceptional generalised geometry. When possible, off-shell multiplets are given. The fields in the multiplets describe non-gravitational ... More

The geometry of pure spinor spaceNov 08 2011Jan 03 2012We investigate the complex geometry of D=10 pure spinor space. The K\"ahler structure and the corresponding metric giving rise to the desired Calabi-Yau property are determined, and an explicit covariant expression for the Laplacian is given. The metric ... More

Superfield actions for N=8 and N=6 conformal theories in three dimensionsSep 02 2008Sep 07 2008The manifestly supersymmetric pure spinor formulations of the Bagger-Lambert-Gustavsson models with N=8 supersymmetry and the Aharony-Bergman-Jafferis-Maldacena models with N=6 supersymmetry are given. The structures of the pure spinors are investigated ... More

Problems with Duality in N=2 Super-Yang-Mills TheoryJun 17 1996Actual calculations of monopole and dyon spectra have previously been performed in N=4 SYM and in N=2 SYM with gauge group SU(2), and are in total agreement with duality conjectures for the finite theories. These calculations are extended to N=2 SYM with ... More

From supergeometry to pure spinorsDec 15 2010In this talk, we review how the superspace formulation of maximally supersymmetric field theories (including supergravity) naturally leads to introduction of pure spinors and pure spinor superfields, and why the formalism provides off-shell formulations. ... More

Geometric Construction of AdS TwistorsFeb 25 2000Time-like geodesics in AdS_4, AdS_5 and AdS_7 are constructed geometrically and independently of choice of AdS coordinates from division algebra spinors of the corresponding AdS groups, explaining and generalising the construction by Claus et al. of AdS_5 ... More

On the Direction of Casimir ForcesAug 28 2008The Casimir force due to a massless scalar field satisfying Dirichlet boundary conditions may attract or repel a piston in the neck of a flask-like container. Using the world-line formalism this behavior is related to the competing contribution to the ... More

A Quantum Approach to Stock Price FluctuationsMay 20 2002May 09 2003A simple quantum model explains the Levy-unstable distributions for individual stock returns observed by ref.[1]. The probability density function of the returns is written as the squared modulus of an amplitude. For short time intervals this amplitude ... More

Semiclassical Electromagnetic Casimir Self-EnergiesApr 17 2006Jul 17 2006The electromagnetic Casimir energies of a spherical and a cylindrical cavity are analyzed semiclassically. The field theoretical self-stress of a spherical cavity with ideal metallic boundary conditions is reproduced to better than 1%. The subtractions ... More

Ordering phenomena in quasi one-dimensional organic conductorsMay 14 2007Low-dimensional organic conductors could establish themselves as model systems for the investigation of the physics in reduced dimensions. In the metallic state of a one-dimensional solid, Fermi-liquid theory breaks down and spin and charge degrees of ... More

Persistence Lenses: Segmentation, Simplification, Vectorization, Scale Space and Fractal Analysis of ImagesApr 25 2016Jun 21 2016A persistence lens is a hierarchy of disjoint upper and lower level sets of a continuous luminance image's Reeb graph. The boundary components of a persistence lens's interior components are Jordan curves that serve as a hierarchical segmentation of the ... More

National Information Infrastructure Development in Canada and the U.S.: Redefining Universal Service and Universal Access in the Age of Techno-Economic ConvergenceSep 24 2001This exploratory and descriptive research compares the policy-making processes and policy recommendations regarding universal service and universal access developed by the U.S. National Information Infrastructure Advisory Council (NIIAC) and the Canadian ... More

Order of precedence and age of Y-DNA haplotypesMar 04 2011A simple method, inspired by procedures used in physics of nuclear multifragmentation, allows to establish order of precedence and age of pairs of haplotypes separated by one mutation. For both haplotypes of the pair, searches for existing haplotypes, ... More

Isotopic trends in nuclear multifragmentationJul 02 2004An overview of the recent progress in the studies of nuclear multifragmentation is presented. Special emphasis is put on the exploration of isotopic trends in nuclear multifragmentation and the possibilities to extract physical information related to ... More

Abraham-Lorentz-Dirac Equation in 5D Stuekelberg ElectrodynamicsApr 06 2016We derive the Abraham-Lorentz-Dirac (ALD) equation in the framework of the electrodynamic theory associated with Stueckelberg manifestly covariant canonical mechanics. In this framework, a particle worldline is traced out through the evolution of an event ... More

Fluctuation energies in quantum cosmologyApr 21 2014Quantum fluctuations or other moments of a state contribute to energy expectation values and can imply interesting physical effects. In quantum cosmology, they turn out to be important for a discussion of density bounds and instabilities of initial-value ... More

A loop quantum multiverse?Dec 20 2012Inhomogeneous space-times in loop quantum cosmology have come under better control with recent advances in effective methods. Even highly inhomogeneous situations, for which multiverse scenarios provide extreme examples, can now be considered at least ... More

Harmonic cosmology: How much can we know about a universe before the big bang?Oct 25 2007Quantum gravity may remove classical space-time singularities and thus reveal what a universe at and before the big bang could be like. In loop quantum cosmology, an exactly solvable model is available which allows one to address precise dynamical coherent ... More

Quantum gravity in the very early universeSep 01 2011General relativity describes the gravitational field geometrically and in a self-interacting way because it couples to all forms of energy, including its own. Both features make finding a quantum theory difficult, yet it is important in the high-energy ... More

Spherically Symmetric Quantum Geometry: States and Basic OperatorsJul 05 2004Jul 08 2004The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory aspects arise. ... More

Loop Quantum Cosmology: Recent ProgressFeb 12 2004Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is sensitive to the quantum ... More

Homogeneous Loop Quantum CosmologyMar 19 2003Loop quantum cosmological methods are extended to homogeneous models in diagonalized form. It is shown that the diagonalization leads to a simplification of the volume operator such that its spectrum can be determined explicitly. This allows the calculation ... More

Abelian BF-Theory and Spherically Symmetric ElectromagnetismAug 26 1999Jun 15 2000Three different methods to quantize the spherically symmetric sector of electromagnetism are presented: First, it is shown that this sector is equivalent to Abelian BF-theory in four spacetime dimensions with suitable boundary conditions. This theory, ... More

Initial Conditions for a UniverseMay 19 2003In physical theories, boundary or initial conditions play the role of selecting special situations which can be described by a theory with its general laws. Cosmology has long been suspected to be different in that its fundamental theory should explain ... More

Quantization Ambiguities in Isotropic Quantum GeometryJun 18 2002Some typical quantization ambiguities of quantum geometry are studied within isotropic models. Since this allows explicit computations of operators and their spectra, one can investigate the effects of ambiguities in a quantitative manner. It is shown ... More

Angular Momentum in Loop Quantum GravityAug 22 2000An angular momentum operator in loop quantum gravity is defined using spherically symmetric states as a non-rotating reference system. It can be diagonalized simultaneously with the area operator and has the familiar spectrum. The operator indicates how ... More

Loop Quantum Cosmology IV: Discrete Time EvolutionAug 22 2000Using general features of recent quantizations of the Hamiltonian constraint in loop quantum gravity and loop quantum cosmology, a dynamical interpretation of the constraint equation as evolution equation is presented. This involves a transformation from ... More

Loop Quantum Cosmology II: Volume OperatorsOct 28 1999Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs constraint imposed on the reduced connection variables is ... More

Four-dimensional gravity on a thick domain wallDec 08 1999Dec 11 1999We consider an especially simple version of a thick domain wall in $AdS$ space and investigate how four-dimensional gravity arises in this context. The model we consider has the advantage, that the equivalent quantum mechanics problem can be stated in ... More

Transversality theory, cobordisms, and invariants of symplectic quotientsJan 01 2000This paper gives methods for understanding invariants of symplectic quotients. The symplectic quotients considered here are compact symplectic manifolds (or more generally orbifolds), which arise as the symplectic quotients of a symplectic manifold by ... More

On Interpolation and Curvature via Wasserstein GeodesicsNov 21 2013Jan 06 2014In this article, a proof of the interpolation inequality along geodesics in $p$-Wasserstein spaces is given. This interpolation inequality was the main ingredient to prove the Borel-Brascamp-Lieb inequality for general Riemannian and Finsler manifolds ... More

Polarizabilities of the nucleon and spin dependent photo-absorptionMay 27 2009The polarizabilities $\alpha$ (electric), $\beta$ (magnetic) and $\gamma_\pi$ (backward spin) of the nucleon are investigated in terms of degrees of freedom of the nucleon using recent results for the CGLN amplitudes and resonance couplings $A_{1/2}$ ... More

The Mean Interference-to-Signal Ratio and its Key Role in Cellular and Amorphous NetworksJun 11 2014We introduce a simple yet powerful and versatile analytical framework to approximate the SIR distribution in the downlink of cellular systems. It is based on the mean interference-to-signal ratio and yields the horizontal gap (SIR gain) between the SIR ... More

The Secrecy Graph and Some of its PropertiesApr 14 2008A new random geometric graph model, the so-called secrecy graph, is introduced and studied. The graph represents a wireless network and includes only edges over which secure communication in the presence of eavesdroppers is possible. The underlying point ... More

Wavefunctions, Green's functions and expectation values in terms of spectral determinantsJun 27 2007We derive semiclassical approximations for wavefunctions, Green's functions and expectation values for classically chaotic quantum systems. Our method consists of applying singular and regular perturbations to quantum Hamiltonians. The wavefunctions, ... More

Spectral statistics in chaotic systems with a point interactionMar 08 2000Aug 14 2000We consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K(tau) for these systems is evaluated semiclassically in terms of periodic and diffractive orbits. It is shown for order ... More

A polarized version of the CCFM equation for gluonsNov 03 2001Mar 30 2002A derivation for a polarized CCFM evolution equation which is suitable to describe the scaling behavior of the the unintegrated polarized gluon density is given. We discuss the properties of this polarized CCFM equation and compare it to the standard ... More

Some Concepts of Modern Algebraic Geometry: Point, Ideal and HomomorphismJun 16 1994Starting from classical algebraic geometry over the complex numbers (as it can be found for example in Griffiths and Harris it was the goal of these lectures to introduce some concepts of the modern point of view in algebraic geometry. Of course, it was ... More

Vetoed jet clustering: The mass-jump algorithmOct 17 2014Apr 23 2015A new class of jet clustering algorithms is introduced. A criterion inspired by successful mass-drop taggers is applied that prevents the recombination of two hard prongs if their combined jet mass is substantially larger than the masses of the separate ... More

High-Dimensional Estimation of Structured Signals from Non-Linear Observations with General Convex Loss FunctionsFeb 10 2016Aug 29 2016In this paper, we study the issue of estimating a structured signal $x_0 \in \mathbb{R}^n$ from non-linear and noisy Gaussian observations. Supposing that $x_0$ is contained in a certain convex subset $K \subset \mathbb{R}^n$, we prove that accurate recovery ... More

Implicit infinite lattice summations for real space ab initio correlation methodsMay 04 2005We suggest a local wave function based ab initio correlation method for infinite periodic systems, which can describe both the near range as well as the long range correlation effects coherently in the same scheme. Specifically, this work introduces a ... More

Towards a frequency independent incremental ab initio scheme for the self energyAug 13 2004Aug 18 2004The frequency dependence of the self energy of a general many--body problem is identified as a main obstacle in correlation calculations based on local approaches. A frequency independent formulation is proposed instead and proven to yield exactly the ... More