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Primitive Equations with Horizontal Viscosity: The Initial Value and the Time-Periodic Problem for Physical Boundary ConditionsFeb 08 2019The $3D$-primitive equations with only horizontal viscosity are considered on a cylindrical domain $(-h,h)\times G$, $G\subset \mathbb{R}^2$ smooth, with the physical Dirichlet boundary conditions on the sides. Instead of considering a vanishing vertical ... More

Primitive Equations with half horizontal viscosityJul 13 2018Oct 22 2018We consider the $3D$ primitive equations and show, that one does need less than horizontal viscosity to obtain a well-posedness result in Sobolev spaces. Furthermore, we will also investigate the primitive equations with horizontal viscosity and show ... More

mSQG equations in distributional spaces and point vortex approximationDec 13 2018Existence of distributional solutions of a modified Surface Quasi-Geostrophic equation (mSQG) is proven for $\mu$-almost every initial condition, where $\mu$ is a suitable Gaussian measure. The result is the by-product of existence of a stationary solution ... More

Primitive Equations with Linearly Growing Initial DataOct 27 2017Oct 30 2017The primitive equations in a 3D infinite layer domain are considered with linearly growing initial data in the horizontal direction, which illustrates the global atmospheric rotating or straining flows. On the boundaries, Dirichlet, Neumann or mixed boundary ... More

Reality of non-Fock SpinorsJan 23 2003Feb 05 2003The infinite dimensional Clifford Algebra has a maze of irreducible unitary representations. Here we determine their type -real, complex or quaternionic. Some, related to the Fermi-Fock representations, have no real or quetrnionic structures. But there ... More

Optimal Sobolev regularity for the Stokes equations on a 2D wedge domainApr 18 2018May 24 2018In this note we prove that the solution of the stationary and the instationary Stokes equations subject to perfect slip boundary conditions on a 2D wedge domain admits optimal regularity in the $L^p$-setting, i.p. it is $W^{2,p}$ in space. This improves ... More

Horizontal submanifolds of groups of Heisenberg typeSep 26 2005Oct 20 2005We study maximal horizontal subgroups of Carnot groups of Heisenberg type. We classify those of dimension half of that of the canonical distribution ("lagrangians") and illustrate some notable ones of small dimension. An infinitesimal classification of ... More

A Cosmological Model of Holographic Brane GravitySep 18 2003A cosmological scenario with two branes (A and B) moving in a 5-dimensional bulk is considered. As in the case of ecpyrotic and born-again braneworld models it is possible that the branes collide. The energy-momentum tensor is taken to describe a perfect ... More

Multiplication in Vector-Valued Anisotropic Function Spaces and ApplicationsAug 29 2017We study multiplication as well as Nemytskij operators in anisotropic vector-valued Besov spaces $B^{s, \omega}_p$, Bessel potential spaces $H^{s, \omega}_p$, and Sobolev-Slobodeckij spaces $W^{s, \omega}_p$. Concerning multiplication we obtain optimal ... More

Explicit fundamental solutions of some second order differential operators on Heisenberg groupsMay 24 2012Let $p,q,n$ be natural numbers such that $p+q=n$. Let $\FF$ be either $\CC$, the complex numbers field, or $\HH$, the quaternionic division algebra. We consider the Heisenberg group $N(p,q,\FF)$ defined as $N(p,q,\FF)=\FF^{n}\times \mathfrak{Im}\FF$, ... More

Hamilton-Jacobi approach to pre-big bang cosmology and the problem of initial conditionsOct 26 1999Jul 10 2001The Hamilton-Jacobi equation for the string cosmology is solved using the gradient expansion method. The zeroth order solution is taken to be the standard pre-big bang model and the second order solution is found for the dilaton and the three-metric. ... More

Long-wavelength approximation for string cosmology with barotropic perfect fluidMay 21 2002The field equations derived from the low energy string effective action with a matter tensor describing a perfect fluid with a barotropic equation of state are solved iteratively using the long-wavelength approximation, i.e. the field equations are expanded ... More

Thermodynamic Stability of Mg-based Ternary Long-Period Stacking Ordered StructuresSep 12 2013Mg alloys containing long-period stacking ordered (LPSO) structures exhibit remarkably high tensile yield strength and ductility. They have been found in a variety of ternary Mg systems of the general form Mg-XL-XS, where XL and XS are elements larger ... More

Thermodynamic Stability of Co-Al-W L12 γ'Oct 04 2012Co-based superalloys in the Co-Al-W system exhibit coherent L12 Co3(Al,W) \gamma' precipitates in an fcc Co \gamma matrix, analogous to Ni3Al in Ni-based systems. Unlike Ni3Al however, experimental observations of Co3(Al,W) suggest that it is not a stable ... More

Scalar-tensor cosmologies with a potential in the general relativity limit: time evolutionJun 07 2010We consider Friedmann-Lema\^{\i}tre-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological energy density of ... More

The dynamics of scalar-tensor cosmology from RS two-brane modelJan 08 2007We consider Randall-Sundrum two-brane cosmological model in the low energy gradient expansion approximation by Kanno and Soda. It is a scalar-tensor theory with a specific coupling function. We find a first integral of equations for the A-brane metric ... More

Potential dominated scalar-tensor cosmologies in the general relativity limit: phase space viewMar 08 2010We consider the potential dominated era of Friedmann-Lemaitre-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling functions, and focus upon the phase space of the ... More

Scalar-tensor cosmologies: general relativity as a fixed point of the Jordan frame scalar fieldOct 28 2008We study the evolution of homogeneous and isotropic, flat cosmological models within the general scalar-tensor theory of gravity with arbitrary coupling function and potential and scrutinize its limit to general relativity. Using the methods of dynamical ... More

Remarks on (super-)accelerating cosmological models in general scalar-tensor gravityMar 25 2009We consider Friedmann-Lemaitre-Robertson-Walker cosmological models in the framework of general scalar-tensor theories of gravity (STG) with arbitrary coupling functions, set in the Jordan frame. First we describe the general properties of the phase space ... More

Scalar-tensor cosmologies with dust matter in the general relativity limitDec 22 2011We consider flat Friedmann-Lema\^{\i}tre-Robertson-Walker cosmological models in the framework of general scalar-tensor theories of gravity with arbitrary coupling functions, set in the Jordan frame, in the cosmological epoch when the energy density of ... More

The dynamics of scalar-tensor cosmology from RS two-brane modelAug 24 2006We consider a Randall-Sundrum two-brane cosmological model in the low energy gradient expansion approximation by Kanno and Soda. It is a scalar-tensor theory with a specific coupling function and a specific potential. Upon introducing the FLRW metric ... More

Analysis of a Living Fluid Continuum ModelApr 07 2016Generalized Navier-Stokes equations which were proposed recently to describe active turbulence in living fluids are analyzed rigorously. Results on wellposedness and stability in the $L^2(\mathbb{R}^n)$-setting are derived. Due to the presence of a Swift-Hohenberg ... More

Scalar-tensor cosmologies: fixed points of the Jordan frame scalar fieldJul 14 2008Oct 28 2008We study the evolution of homogeneous and isotropic, flat cosmological models within the general scalar-tensor theory of gravity with arbitrary coupling function and potential. After introducing the limit of general relativity we describe the details ... More

Split Clifford modules over a Hilbert spaceApr 10 2002May 31 2002A description of the real, complete modules over the Clifford algebra of a Hilbert space, with the elements of the latter acting by skew-symmetric operators.

Global well-posedness and stability of electro-kinetic flowsJun 07 2012Jun 09 2012We consider a coupled system of Navier-Stokes and Nernst-Planck equations, describing the evolution of the velocity and the concentration fields of dissolved constituents in an electrolyte solution. Motivated by recent applications in the field of micro- ... More

Bounded H_\infty-calculus for pseudodifferential Douglis-Nirenberg systems of mild regularityJan 24 2008Parameter-ellipticity with respect to a closed subsector of the complex plane for pseudodifferential Douglis-Nirenberg systems is discussed and shown to imply the existence of a bounded H_\infty-calculus in suitable scales of Sobolev, Besov, and Hoelder ... More

Singular limits for the two-phase Stefan problemDec 28 2012We prove strong convergence to singular limits for a linearized fully inhomogeneous Stefan problem subject to surface tension and kinetic undercooling effects. Different combinations of $\sigma \to \sigma_0$ and $\delta \to\delta_0$, where $\sigma,\sigma_0 ... More

Scalar-tensor cosmology at the general relativity limit: Jordan vs Einstein frameMay 31 2007Jul 14 2008We consider the correspondence between the Jordan frame and the Einstein frame descriptions of scalar-tensor theory of gravitation. We argue that since the redefinition of the scalar field is not differentiable at the limit of general relativity the correspondence ... More

The formalism of invariants in scalar-tensor and multiscalar-tensor theories of gravitationDec 30 2015We give a brief summary of the formalism of invariants in general scalar-tensor and multiscalar-tensor gravities without derivative couplings. By rescaling of the metric and reparametrization of the scalar fields, the theory can be presented in different ... More

Invariant slow-roll parameters in scalar-tensor theoriesMay 23 2016Oct 11 2016A general scalar-tensor theory can be formulated in different parametrizations that are related by a conformal rescaling of the metric and a scalar field redefinition. We compare formulations of slow-roll regimes in the Einstein and Jordan frames using ... More

Invariant quantities in the scalar-tensor theories of gravitationNov 07 2014Jan 30 2015We consider the general scalar-tensor gravity without derivative couplings. By rescaling of the metric and reparametrization of the scalar field, the theory can be presented in different conformal frames and parametrizations. In this work we argue, that ... More

Nonmetricity formulation of general relativity and its scalar-tensor extensionFeb 01 2018May 10 2018Einstein's celebrated theory of gravitation can be presented in three forms: general relativity, teleparallel gravity, and the rarely considered before symmetric teleparallel gravity. Extending the latter, we introduce a new class of theories where a ... More

Parametrizations in scalar-tensor theories of gravity and the limit of general relativityJan 30 2015We consider a general scalar-tensor theory of gravity and review briefly different forms it can be presented (different conformal frames and scalar field parametrizations). We investigate the conditions under which its field equations and the parametrized ... More

Transformation properties and general relativity regime in scalar-tensor theoriesApr 10 2015Nov 13 2015We consider first generation scalar-tensor theories of gravitation in a completely generic form, keeping the transformation functions of the local rescaling of the metric and the scalar field redefinition explicitly distinct from the coupling functions ... More

Global Strong Solutions for a Class of Heterogeneous Catalysis ModelsOct 21 2015Jul 28 2016We consider a mathematical model for heterogeneous catalysis in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. The system under consideration consists of a diffusion-advection system inside ... 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

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

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

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

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

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

A frame independent classification of single field inflationary modelsDec 20 2016Mar 16 2017Seemingly unrelated models of inflation that originate from different physical setups yield, in some cases, identical predictions for the currently constrained inflationary observables. In order to classify the available models, we propose to express ... 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

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

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

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

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

Quirky Quantifiers: Optimal Models and Complexity of Computation Tree LogicOct 29 2015The satisfiability problem of the branching time logic CTL is studied in terms of computational complexity. Tight upper and lower bounds are provided for each temporal operator fragment. In parallel the minimal model size is studied with a suitable notion ... More

Infinity - A simple, but not too simple introductionJun 21 2015This text tries to give an elementary introduction to the mathematical properties of infinite sets. The aim is to keep the approach as simple as possible. Advanced knowledge of mathematics is not necessary for a proper understanding, and there is (almost) ... More

Analysis of a mathematical model for the growth of cancer cellsApr 13 2011Apr 11 2012In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or cell dead. The ... More

Global existence and blow-up for a weakly dissipative $μ$DP equationOct 12 2010Jun 07 2011In this paper, we study a weakly dissipative variant of the periodic Degasperis-Procesi equation. We show the local well-posedness of the associated Cauchy problem in $H^s(\S)$, $s>3/2$, and discuss the precise blow-up scenario for $s=3$. We also present ... More

Evaluating the Magnetic Field Strength in Molecular CloudsOct 12 2004We discuss an extension to the Chandrasekhar-Fermi method for the evaluation of the mean magnetic field strength in molecular clouds to cases where the spatial orientation of the field is known. We apply the results to M17, using previously published ... More

N=8 superfield formulation of the Bagger-Lambert-Gustavsson modelAug 24 2008Sep 02 2008We reformulate the Bagger-Lambert-Gustavsson model using an N=8 superspace, thus making the full supersymmetry manifest. The formulation is based on appropriate "pure spinor wave functions" for the Chern-Simons and matter multiplets. The Lagrangian has ... More

Boundaries of 11-Dimensional MembranesApr 23 1997The action for an 11-dimensional supermembrane contains a chiral Wess-Zumino-Witten model coupling to the E8 super-Yang-Mills theory on the end-of-the-world 9-brane. It is demonstrated that this boundary string theory is dictated both by gauge invariance ... More

Introduction to Division Algebras, Sphere Algebras and TwistorsOct 19 1993A very basic introduction is given to the r\^oles of division algebras and the related sphere algebras concerning the structure of space-time in the dimensionalities $D\is 3,4,6$ and $10$, with special emphasis on twistors transformations for light-likeness ... More

Pure spinor superfields, with application to D=3 conformal modelsJun 30 2009I review and discuss the construction of supersymmetry multiplets and manifestly supersymmetric Batalin-Vilkovisky actions using pure spinors, with emphasis on models with maximal supersymmetry. The special cases of D=3, N=8 (Bagger-Lambert-Gustavsson) ... More

Open and Winding Membranes, Affine Matrix Theory and Matrix String TheoryOct 16 2002Nov 12 2002We examine the structure of winding toroidal and open cylindrical membranes, especially in cases where they are stretched between boundaries. Non-zero winding or stretching means that there are linear terms in the mode expansion of the coordinates obeying ... More

Quantization and Renormalization and the Casimir Energy of a Scalar Field Interacting with a Rotating RingNov 12 2012Effects due to vacuum fluctuations in a semi-classical model of a massless scalar field interacting with a rotating ring are investigated by introducing a collective coordinate for the motion of the background potential. The model is solved for a repulsive ... More

Irreducible Many-Body Casimir Energies of Intersecting ObjectsNov 10 2010Feb 13 2011The vacuum energy of a bosonic field interacting locally with objects is decomposed into irreducible $N$-body parts. The irreducible $N$-body contribution to the vacuum energy is finite if the common intersection $O_1\cap O_2...\cap O_N$ of all $N$ objects ... More

SU(2) Gauge Theory in Covariant (Maximal) Abelian GaugesMar 03 2000The local covariant continuum action of an SU(2) gauge theory in covariant Abelian gauges is investigated. It describes the critical limit of an Abelian Lattice Gauge Theory (LGT) with an equivariant BRST-symmetry. This Abelian LGT has previously been ... More

The Vacuum Energy Density of QCD with n_f=3 Quark FlavorsFeb 22 1998Feb 28 1998An equivariant BRST-construction is used to define the continuum SU(3) gauge theory on a finite torus. I corroborate previous results using renormalization group techniques by explicitly computing the measure on the moduli-space of the model with 3 quark ... More

Quantum FinanceMar 04 2002Aug 06 2002Quantum theory is used to model secondary financial markets. Contrary to stochastic descriptions, the formalism emphasizes the importance of trading in determining the value of a security. All possible realizations of investors holding securities and ... More

Mass Generation, Ghost Condensation and Broken Symmetry: SU(2) in Covariant Abelian GaugesAug 07 2001The local action of an SU(2) gauge theory in general covariant Abelian gauges and the associated equivariant BRST symmetry that guarantees the perturbative renormalizability of the model are given. A global SL(2,R) symmetry of the model is spontaneously ... More

Reparametrizations with given stop dataFeb 13 2009In the recent paper "Reparametrizations of continuous paths", J. Homotopy Relat. Struct. 2 (2007), 93-117 (with U. Fahrenberg), we performed a systematic investigation of reparametrizations of continuous paths in a Hausdorff space that relies crucially ... More

Real numbers as infinite decimals and irrationality of $\sqrt{2}$Oct 30 2009In order to prove irrationality of \sqrt{2} by using only decimal expansions (and not fractions), we develop in detail a model of real numbers based on infinite decimals and arithmetic operations with them.

On the Deformation Quantization of super-Poisson BracketsMay 24 1996We show that for every vector bundle E over any given symplectic manifold M there exists an explicitly given super-Poisson bracket on the space of sections of the dual Grassmann bundle associated to E built out of symplectic structure of M, a fibre metric ... More

A (short) survey on Dominated SplittingMar 24 2014We present here the concept of Dominated Splitting and give an account of some important results on its dynamics.

Optimizing large applicationsMar 27 2014Both uppermost open source compilers, GCC and LLVM, are mature enough to link-time optimize large applications. In case of large applications, we must take into account, except standard speed efficiency and memory consumption, different aspects. We focus ... More

Speeds of light and mass stability in Stueckelberg-Horwitz-Piron electrodynamicsApr 06 2016It is well-known that the 5D gauge structure of Stueckelberg-Horwitz-Piron (SHP) electrodynamics permits the exchange of mass between particles and the fields induced by their motion, even at the classical level. This phenomenon presents two closely related ... More

Dirac Monopole from Lorentz Symmetry in N-Dimensions: I. The Generator ExtensionMar 07 2006Mar 15 2006It is by now well-known that a Lorentz force law and the homogeneous Maxwell equations can be derived from commutation relations among Euclidean coordinates and velocities, without explicit reference to momentum, action or variational principle. This ... More

Discrete Symmetries of Off-Shell ElectromagnetismMar 28 2006We discuss the discrete symmetries of the Stueckelberg-Schrodinger relativistic quantum theory and its associated 5D local gauge theory, a dynamical description of particle/antiparticle interactions, with monotonically increasing Poincare-invariant parameter. ... More

A Note on Isometric Embeddings of Surfaces of RevolutionJan 18 2002In the special case of S^1 invariant metrics on S^2, we find necessary and sufficient conditions for the existence of isometric embeddings into the canonical R^3, in other words: a Weyl type theorem with converse.

The covered components polynomial: A new representation of the edge elimination polynomialMar 11 2011Sep 07 2011Motivated by the definition of the edge elimination polynomial of a graph we define the covered components polynomial counting spanning subgraphs with respect to their number of components, edges and covered components. We prove a recurrence relation, ... More

Generalized-ensemble simulations and cluster algorithmsJun 19 2010The importance-sampling Monte Carlo algorithm appears to be the universally optimal solution to the problem of sampling the state space of statistical mechanical systems according to the relative importance of configurations for the partition function ... More

Genetic embedded matching approach to ground states in continuous-spin systemsJun 29 2007Dec 21 2007Due to an extremely rugged structure of the free energy landscape, the determination of spin-glass ground states is among the hardest known optimization problems, found to be NP-hard in the most general case. Owing to the specific structure of local (free) ... More

Globular cluster abundances in the light of 3D hydrodynamical model atmospheresOct 16 2003The new generation of 3D hydrodynamical model atmospheres have been employed to study the impact of a realistic treatment of stellar convection on element abundance determinations of globular cluster stars for a range of atomic and molecular lines. Due ... More

A spectral study of gamma-ray emitting AGNDec 10 1996In this paper I investigate the $\gamma$-ray spectra of AGN by summing up the intensity and the power-law fit statistic of Quasars and OVV's and BL Lac's separately. The spectrum of the average AGN is softer than that of the extragalactic $\gamma$-ray ... More

Diffuse gamma-ray emission: Galactic and extragalacticJul 27 1998Here is reviewed our current understanding of Galactic and extragalactic diffuse gamma-ray emission. The spectrum of the extragalactic gamma-ray background above 30 MeV can be well described by a power law with photon index s=2.1. In the 2-10 MeV range ... More

The galactic center arc as source of high-energy gamma-raysMay 23 1996We discuss the radio {\it arc} at the galactic center to be the counterpart of the high-energy \gr source 2EG J1746-2852. The observed \gr flux is constant within the statistical limits and the spectrum is very hard. The lack of variability makes it highly ... More

Galactic Wind Shells and High Redshift Radio Galaxies On the Nature of Associated AbsorbersMar 15 2005A jet is simulated on the background of a galactic wind headed by a radiative bow shock. The wind shell, which is due to the radiative bow shock, is effectively destroyed by the impact of the jet cocoon, thanks to Rayleigh-Taylor instabilities. Associated ... More

Very Light Jets I. Axisymmetric Parameter Study and Analytic ApproximationNov 20 2002The propagation of extragalactic jets is studied by a series of twelve axisymmetric hydrodynamic simulations. Motivated by observational constraints, but unlike most previous simulations, the regime of jet to external medium density (eta) from 10^-5 to ... More

Some covariance models based on normal scale mixturesFeb 25 2011Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new class is described ... More

Loop Quantum Gravity and Cosmology: A dynamical introductionJan 28 2011Loop quantum gravity and cosmology are reviewed with an emphasis on evaluating the dynamics, rather than constructing it. The three crucial parts of such an analysis are (i) deriving effective equations, (ii) controlling the theory's microscopic degrees ... More

The Dark Side of a Patchwork UniverseMay 30 2007While observational cosmology has recently progressed fast, it revealed a serious dilemma called dark energy: an unknown source of exotic energy with negative pressure driving a current accelerating phase of the universe. All attempts so far to find a ... More

Quantum Riemannian Geometry and Black HolesFeb 24 2006Black Holes have always played a central role in investigations of quantum gravity. This includes both conceptual issues such as the role of classical singularities and information loss, and technical ones to probe the consistency of candidate theories. ... More

Degenerate Configurations, Singularities and the Non-Abelian Nature of Loop Quantum GravityAug 29 2005Jan 24 2006Degenerate geometrical configurations in quantum gravity are important to understand if the fate of classical singularities is to be revealed. However, not all degenerate configurations arise on an equal footing, and one must take into account dynamical ... More

Nonsingular Black Holes and Degrees of Freedom in Quantum GravityJun 28 2005Spherically symmetric space-times provide many examples for interesting black hole solutions, which classically are all singular. Following a general program, space-like singularities in spherically symmetric quantum geometry, as well as other inhomogeneous ... More

The Early Universe in Loop Quantum CosmologyMar 07 2005Loop quantum cosmology applies techniques derived for a background independent quantization of general relativity to cosmological situations and draws conclusions for the very early universe. Direct implications for the singularity problem as well as ... More

Quantum Gravity and the Big BangSep 17 2003Quantum gravity has matured over the last decade to a theory which can tell in a precise and explicit way how cosmological singularities of general relativity are removed. A branch of the universe "before" the classical big bang is obtained which is connected ... More

Dynamical Initial Conditions in Quantum CosmologyApr 23 2001Loop quantum cosmology is shown to provide both the dynamical law and initial conditions for the wave function of a universe by one discrete evolution equation. Accompanied by the condition that semiclassical behavior is obtained at large volume, a unique ... More

On the origin of higher braces and higher-order derivationsSep 30 2013In Part I we show that the classical Koszul braces, as well as their non-commutative counterparts constructed recently by Borjeson, are the twistings of the trivial L-infinity- (resp. A-infinity-) algebra by a specific automorphism. This gives an astonishingly ... More

Invariant tensors and graphsJan 02 2008Feb 28 2008We describe a correspondence between GL_n-invariant tensors and graphs, and show how this correspondence accomodates various types of symmetries and orientations.

Natural differential operators and graph complexesDec 07 2006Feb 28 2008We show how the machine of PROP profiles invented by S. Merkulov can be used to study and classify natural operators in differential geometry. We also give an interpretation of graph complexes arising in this context in terms of representation theory. ... More

An E-infty-extension of the associahedra and the Tamarkin cell mysteryApr 13 2003Sep 24 2010We study a cofibrant E-infty operad generated by the Fox-Neuwirth cells of the configuration space of points in the Euclidean space. We show that, below the `critical dimensions' in which `bad cells' exist, this operad is modeled by the geometry of the ... More

Cohomology operations and the Deligne conjectureJun 09 2005The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples.

Homotopy Algebras via Resolutions of OperadsAug 23 1998Mar 10 1999The aim of this brief note is mainly to advocate our approach to homotopy algebras based on the minimal model of an operad. Our exposition is motivated by two examples which we discuss very explicitly - the example of strongly homotopy associative algebras ... More

Simplex, associahedron, and cyclohedronJul 09 1997The aim of the paper is to give an `elementary' introduction to the theory of modules over operads and discuss three prominent examples of these objects - simplex, associahedron (= the Stasheff polyhedron) and cyclohedron (= the compactification of the ... More

Pre-Galaxy Formation: A Non-Linear Analysis of the Evolution of Cosmological PerturbationsOct 31 1994A higher-order analysis of the evolution of cosmological perturbations in a Friedman universe is given by using the PMF method. The essence of the PMF approach is to choose a gauge where all fluctuations of the density, the pressure, and the four-velocity ... More