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Neural Likelihoods for Multi-Output Gaussian ProcessesMay 31 2019We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of models. An ... More

Pathwise Derivatives Beyond the Reparameterization TrickJun 05 2018Jul 05 2018We observe that gradients computed via the reparameterization trick are in direct correspondence with solutions of the transport equation in the formalism of optimal transport. We use this perspective to compute (approximate) pathwise gradients for probability ... More

Angular Scaling in JetsJan 12 2012Apr 06 2012We introduce a jet shape observable defined for an ensemble of jets in terms of two-particle angular correlations and a resolution parameter R. This quantity is infrared and collinear safe and can be interpreted as a scaling exponent for the angular distribution ... More

Uncovering the Spatiotemporal Patterns of Collective Social ActivityJan 10 2017Social media users and microbloggers post about a wide variety of (off-line) collective social activities as they participate in them, ranging from concerts and sporting events to political rallies and civil protests. In this context, people who take ... More

Jet Substructure Without TreesApr 08 2011Jun 30 2011We present an alternative approach to identifying and characterizing jet substructure. An angular correlation function is introduced that can be used to extract angular and mass scales within a jet without reference to a clustering algorithm. This procedure ... More

Non-Conforming Multiscale Finite Element Method for Stokes Flows in Heterogeneous Media. Part II: error estimates for periodic microstructureFeb 12 2018This paper is dedicated to the rigorous numerical analysis of a Multiscale Finite Element Method (MsFEM) for the Stokes system, when dealing with highly heterogeneous media, as proposed in [B.P.~Muljadi et al., arXiv:1404.2837]. The method is in the vein ... More

Jet Dipolarity: Top Tagging with Color FlowFeb 04 2011Apr 18 2012A new jet observable, dipolarity, is introduced that can distinguish whether a pair of subjets arises from a color singlet source. This observable is incorporated into the HEPTopTagger and is shown to improve discrimination between top jets and QCD jets ... More

LHC probes the hidden sectorDec 14 2012Jul 18 2013In this note we establish LHC limits on a variety of benchmark models for hidden sector physics using 2011 and 2012 data. First, we consider a "hidden" U(1) gauge boson under which all Standard Model particles are uncharged at tree-level and which interacts ... More

Nearly Supersymmetric Dark AtomsSep 17 2010Theories of dark matter that support bound states are an intriguing possibility for the identity of the missing mass of the Universe. This article proposes a class of models of supersymmetric composite dark matter where the interactions with the Standard ... More

Constraining CP-violating Higgs Sectors at the LHC using gluon fusionJun 12 2014We investigate the constraints that the LHC can set on a 126 GeV Higgs boson that is an admixture of CP eigenstates. Traditional analyses rely on Higgs couplings to massive vector bosons, which are suppressed for CP-odd couplings, so that these analyses ... More

Learning How to Count: A High Multiplicity Search for the LHCFeb 07 2013Sep 02 2013We introduce a search technique that is sensitive to a broad class of signals with large final state multiplicities. Events are clustered into large radius jets and jet substructure techniques are used to count the number of subjets within each jet. The ... More

Experimental constraints on the free fall acceleration of antimatterJul 23 2009In light of recent experimental proposals to measure the free fall acceleration of antihydrogen in the earth's gravitational field, we investigate the bounds that existing experiments place on any asymmetry between the free fall of matter and antimatter. ... More

Modelling adhesion-independent cell migrationMar 22 2019A two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modelled as an elastic curve, subject to an internal pressure force. Net polymerization or ... More

Jet Substructure Templates: Data-driven QCD Backgrounds for Fat Jet SearchesFeb 03 2014Oct 20 2014QCD is often the dominant background to new physics searches for which jet substructure provides a useful handle. Due to the challenges associated with modeling this background, data-driven approaches are necessary. This paper presents a novel method ... More

Tensor Variable Elimination for Plated Factor GraphsFeb 08 2019May 17 2019A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to ... More

Variational Estimators for Bayesian Optimal Experimental DesignMar 13 2019Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected information ... More

Variational Bayesian Optimal Experimental DesignMar 13 2019Jun 03 2019Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected information ... More

Tensor Variable Elimination for Plated Factor GraphsFeb 08 2019A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to ... More

Sobolev and Hardy-Littlewood-Sobolev inequalitiesDec 09 2013May 01 2014This paper is devoted to improvements of Sobolev and Onofri inequalities. The additional terms involve the dual counterparts, i.e. Hardy-Littlewood-Sobolev type inequalities. The Onofri inequality is achieved as a limit case of Sobolev type inequalities. ... More

Fractional Sobolev and Hardy-Littlewood-Sobolev inequalitiesApr 03 2014Jul 15 2014This work focuses on an improved fractional Sobolev inequality with a remainder term involving the Hardy-Littlewood-Sobolev inequality which has been proved recently. By extending a recent result on the standard Laplacian to the fractional case, we offer ... More

Pyro: Deep Universal Probabilistic ProgrammingOct 18 2018Pyro is a probabilistic programming language built on Python as a platform for developing advanced probabilistic models in AI research. To scale to large datasets and high-dimensional models, Pyro uses stochastic variational inference algorithms and probability ... More

Stationary solutions of Keller-Segel type crowd motion and herding models: multiplicity and dynamical stabilityMay 08 2013Jul 29 2013In this paper we study two models for crowd motion and herding. Each of the models is of Keller-Segel type and involves two parabolic equations, one for the evolution of the density and one for the evolution of a mean field potential. We classify all ... More

The Moser-Trudinger-Onofri inequalityMar 20 2014May 21 2015This paper is devoted to results on the Moser-Trudinger-Onofri inequality, or Onofri inequality for brevity. In dimension two this inequality plays a role similar to the Sobolev inequality in higher dimensions. After justifying this statement by recovering ... More

Onofri inequalities and rigidity resultsApr 29 2014Jun 10 2016This paper is devoted to the Moser-Trudinger-Onofri inequality on smooth compact connected Riemannian manifolds. We establish a rigidity result for the Euler-Lagrange equation and deduce an estimate of the optimal constant in the inequality on two-dimensional ... More

A surprising method for polarising antiprotonsJun 26 2007Nov 14 2007We propose a method for polarising antiprotons in a storage ring by means of a polarised positron beam moving parallel to the antiprotons. If the relative velocity is adjusted to $v/c \approx 0.002$ the cross section for spin-flip is as large as about ... More

An effective method for polarising antiprotonsMay 15 2006Sep 05 2006There exists an inconsistency in the value of the kinetic energies of the antiproton in the electron laboratory reference frame and of the electron in the antiproton laboratory reference frame taken wrongly both as 0.65 keV (see figure 1 and table 2) ... More

Cosmologically inspired Kastor-Traschen solutionJul 29 2013Jan 25 2014Kastor-Traschen (KT) type solution in a cosmological set up is studied in this article. We examine a hybrid of a KT metric and a Friedmann-Robertson-Walker-Lemaitre (FRWL) solution. The problem is treated in a general number of dimensions D>=4 and we ... More

Thin static charged dust Majumdar-Papapetrou shells with high symmetry in D >= 4Feb 28 2012Apr 27 2012We present a systematical study of static D >= 4 space-times of high symmetry with the matter source being a thin charged dust hypersurface shell. The shell manifold is assumed to have the following structure S_(beta) X R^(D-2-beta), beta (in the interval ... More

Learning first-order definable concepts over structures of small degreeJan 19 2017We consider a declarative framework for machine learning where concepts and hypotheses are defined by formulas of a logic over some background structure. We show that within this framework, concepts defined by first-order formulas over a background structure ... 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

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

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

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

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

Short-axis-mode rotation of a free rigid body by perturbation seriesAug 03 2013A simple rearrangement of the torque free motion Hamiltonian shapes it as a perturbation problem for bodies rotating close to the principal axis of maximum inertia, independently of their triaxiality. The complete reduction of the main part of this Hamiltonian ... More

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

The Local HI Mass FunctionJun 18 1998The local HI mass function (HIMF), like the optical luminosity function, is an important observational input into models of cosmology and galaxy evolution. It is a helpful framework for assessing the number density of gas rich dwarf galaxies, which are ... More

The two-leg t-J ladder: a spin liquid generated by Gutzwiller projection of magnetic bandsApr 01 1998Apr 17 1998The ground state of the two-leg Heisenberg ladder is identified as an RVB type spin liquid, which is generated by Gutzwiller projection of tight-binding bands with flux pi per plaquet. Explicit trial wave functions for the magnon and hole excitations ... More

Landau Level Quantization on the SphereJan 20 2011Mar 06 2011It is well established that the Hilbert space for charged particles in a plane subject to a uniform magnetic field can be described by two mutually commuting ladder algebras. We propose a similar formalism for Landau level quantization involving two mutually ... More

On the linear dispersion--linear potential quantum oscillatorJan 28 2010We solve the bi-linear quantum oscillator H=v|p|+F|x| both quasi-classically and numerically.

Is electromagnetic gauge invariance spontaneously violated in superconductors?Mar 16 2005We aim to give a pedagogical introduction to those elementary aspects of superconductivity which are not treated in the classic textbooks. In particular, we emphasize that global U(1) phase rotation symmetry, and not gauge symmetry, is spontaneously violated, ... More

Morse theory in the 1990'sApr 15 2001This is a survey article on Morse theory based on lectures to graduate students and advanced undergraduates. After a brief review of standard material, mostly without proofs, the Morse theory of complex Grassmannian manifolds is worked out in detail. ... More

Algebraic gamesMay 13 2012Jan 02 2013Two players alternate moves in the following game: Given a finitely generated abelian group A, a move consists of picking some non-zero element a of A. The game then continues with A/<a>. Under the normal play rule, the player with the last possible move ... More

Dynamics of heuristic optimization algorithms on random graphsMar 13 2002Jun 24 2002In this paper, the dynamics of heuristic algorithms for constructing small vertex covers (or independent sets) of finite-connectivity random graphs is analysed. In every algorithmic step, a vertex is chosen with respect to its vertex degree. This vertex, ... More

Status of CMB observations in 2015Jun 10 2016Jun 15 2016The 2.725 K cosmic microwave background has played a key role in the development of modern cosmology by providing a solid observational foundation for constraining possible theories of what happened at very large redshifts and theoretical speculation ... More

A statistical inference course based on p-valuesJun 07 2016Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sample approximations. Here I present an alternative approach to teaching ... More

On similarity of jet quenching and charmonia suppressionJun 02 2016We quantify the magnitude of the parton energy loss in jets in lead-lead collisions at the LHC. We extract the effective color factor characterizing the difference between the in-medium radiation of quark-initiated jets and gluon-initiated jets from the ... More

BW - Eye Ophthalmologic decision support system based on clinical workflow and data mining techniques-image registration algorithmDec 17 2013Blueworks - Medical Expert Diagnosis is developing an application, BWEye, to be used as an ophthalmology consultation decision support system. The implementation of this application involves several different tasks and one of them is the implementation ... More

AGB stars in the Local Group, and beyondJul 14 2004I summarize the current status of surveys for late-type M, and Carbon stars in the Local Group based on three different approaches that make use of the characteristics of these stars: spectral characteristics using narrow-band filters, infrared characteristics, ... More

A minimal surface with unbounded curvatureJun 17 2010We construct a complete, embedded minimal surface in euclidean 3-space which has unbounded Gaussian curvature. It has infinite genus, infinitely many catenoidal type ends and one limit end.

Automorphisms of the 3-sphere that preserve a genus two Heegaard splittingJul 16 2003An updated proof of a 1933 theorem of Goeritz, exhibiting a finite set of generators for the group of automorphisms of the 3-sphere that preserve a genus two Heegaard splitting. The group is analyzed via its action on a certain connected 2-complex. (The ... More

Heegaard splittings of compact 3-manifoldsJul 24 2000An expository survey article on Heegaard splittings

Large photon number extraction from individual atoms trapped in an optical latticeNov 24 2010Mar 22 2011The atom-by-atom characterization of quantum gases requires the development of novel measurement techniques. One particularly promising new technique demonstrated in recent experiments uses strong fluorescent laser scattering from neutral atoms confined ... More

Fast (Multi-)Evaluation of Linearly Recurrent Sequences: Improvements and ApplicationsNov 08 2005For a linearly recurrent vector sequence P[n+1] = A(n) * P[n], consider the problem of calculating either the n-th term P[n] or L<=n arbitrary terms P[n_1],...,P[n_L], both for the case of constant coefficients A(n)=A and for a matrix A(n) with entries ... More

Real Hypercomputation and ContinuityAug 15 2005Feb 22 2006By the sometimes so-called 'Main Theorem' of Recursive Analysis, every computable real function is necessarily continuous. We wonder whether and which kinds of HYPERcomputation allow for the effective evaluation of also discontinuous f:R->R. More precisely ... More

Time's Arrow from the Multiverse Point of ViewAug 31 2006Jul 22 2014In this paper I suggest a possible explanation for the asymmetry of time. In the case that I study, the dynamical laws and the boundary conditions are symmetric, but the behavior of time is not. The underlying mechanism is statistical and closely related ... More

A Semi-Classical Approach to Gravitation, Mass and SpinAug 16 2000Jul 22 2014In this paper, we use methods from differential geometry and statistical mechanics to investigate a model for the concept of mass. The theory is not quantum mechanical in the usual sense, although certain features like multiple histories and uncertainty ... More

On the E-polynomials of a family of Character VarietiesJun 07 2010We compute the E-polynomials of a family of twisted character varieties by proving they have polynomial count, and applying a result of N. Katz on the counting functions. To compute the number of GF(q)-points of these varieties as a function of q, we ... More

Newton's Constant isn't constantDec 08 2000This article contains a brief pedagogical introduction to various renormalization group related aspects of quantum gravity with an emphasis on the scale dependence of Newton's constant and on black hole physics.

Semiclassical Estimates of Electromagnetic Casimir Self-Energies of Spherical and Cylindrical Metallic ShellsJun 16 2010The leading semiclassical estimates of the electromagnetic Casimir stresses on a spherical and a cylindrical metallic shell are within 1% of the field theoretical values. The electromagnetic Casimir energy for both geometries is given by two decoupled ... More

Comments on the Sign and Other Aspects of Semiclassical Casimir EnergiesSep 16 2005Oct 27 2005The Casimir energy of a massless scalar field is semiclassically given by contributions due to classical periodic rays. The required subtractions in the spectral density are determined explicitly. The so defined semiclassical Casimir energy coincides ... More

Causal Space-Times on a Null LatticeSep 10 2015Mar 10 2016I investigate a discrete model of quantum gravity on a causal null-lattice with \SLC structure group. The description is geometric and foliates in a causal and physically transparent manner. The general observables of this model are constructed from local ... More

Irreducible Scalar Many-Body Casimir Energies: Theorems and Numerical StudiesDec 14 2011We define irreducible N-body spectral functions and Casimir energies and consider a massless scalar quantum field interacting locally by positive potentials with classical objects. Irreducible N-body spectral functions in this case are shown to be conditional ... More

Numerical Analysis of some Generalized Casimir PistonsOct 06 2008The Casimir force due to a scalar field on a piston in a cylinder of radius $r$ with a spherical cap of radius $R>r$ is computed numerically in the world-line approach. A geometrical subtraction scheme gives the finite interaction energy that determines ... More

Equivariant Gauge Fixing of SU(2) Lattice Gauge TheoryMay 21 1998Oct 21 1998I construct a Lattice Gauge Theory (LGT) with discrete Z_2 structure group and an equivariant BRST symmetry that is physically equivalent to the standard SU(2)-LGT. The measure of this Z_2-LGT is invariant under all the discrete symmetries of the lattice ... More

The periodic $μ$-$b$-equation and Euler equations on the circleOct 09 2010May 04 2011In this paper, we study the $\mu$-variant of the periodic $b$-equation and show that this equation can be realized as a metric Euler equation on the Lie group $\Diff^{\infty}(\S)$ if and only if $b=2$ (for which it becomes the $\mu$-Camassa-Holm equation). ... More

The curvature of semidirect product groups associated with two-component Hunter-Saxton systemsOct 12 2010May 04 2011In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its $\mu$-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group $\Diff(\S)$ with a space of scalar ... More

Theory of electric dipole moments and lepton flavour violationAug 12 2016Electric dipole moments and charged-lepton flavour-violating processes are extremely sensitive probes for new physics, complementary to direct searches as well as flavour-changing processes in the quark sector. Beyond the "smoking-gun" feature of a potential ... More

Tensor categorical foundations of algebraic geometryOct 07 2014Tannaka duality and its extensions by Lurie, Sch\"appi et al. reveal that many schemes as well as algebraic stacks may be identified with their tensor categories of quasi-coherent sheaves. In this thesis we study constructions of cocomplete tensor categories ... More

On the volume of tubular neighborhoods of real algebraic varietiesOct 13 2012Sep 28 2013The problem of determining the volume of a tubular neighbourhood has a long and rich history. Bounds on the volume of neighbourhoods of algebraic sets have turned out to play an important role in the probabilistic analysis of condition numbers in numerical ... More

Pure spinor superfields -- an overviewJul 06 2013Maximally supersymmetric theories do not allow off-shell superspace formulations with traditional superfields containing a finite set of auxiliary fields. It has become clear that off-shell supersymmetric action formulations of such models can be achieved ... More

Towards a manifestly supersymmetric action for 11-dimensional supergravityDec 09 2009Dec 11 2009We investigate the possibility of writing a manifestly supersymmetric action for 11-dimensional supergravity. The construction involves an explicit relation between the fields in the super-vielbein and the super-3-form, and uses non-minimal pure spinors. ... More

Why Don't We Have a Covariant Superstring Field Theory?Oct 04 1994This talk deals with the old problem of formulatingn a covariant quantum theory of superstrings, ``covariant'' here meaning having manifest Lorentz symmetry and supersymmetry. The advantages and disadvantages of several quantization methods are reviewed. ... More

Double supergeometryMar 15 2016Mar 17 2016A geometry of superspace corresponding to double field theory is developed, with type II supergravity in D=10 as the main example. The formalism is based on an orthosymplectic extension OSp(d,d|2s) of the continuous T-duality group. Covariance under generalised ... More

D=11 supergravity with manifest supersymmetryDec 31 2009The complete supersymmetric action for eleven-dimensional supergravity is presented. The action is polynomial in the scalar fermionic pure spinor superfield, and contains only a minor modification to the recently proposed three-point coupling.

A Note on the Relation between Different Forms of Superparticle Dynamics'Oct 27 1993A formulation of $D\is 10$ superparticle dynamics is given that contain space-time and twistor variables. The set of constraints is entirely first class, and gauge conditions may be imposed that reduces the system to a Casalbuoni-Brink-Schwarz superparticle, ... More

$E_7$ as $D=10$ space-time symmetry --- Origin of the twistor transformDec 18 1992Massless particle dynamics in $D=10$ Minkowski space is given an $E_7$-covariant formulation, including both space-time and twistor variables. $E_7$ contains the conformal algebra as a subalgebra. Analogous constructions apply to $D=3,4$ and 6.

A Deep Infrared Search for AXP 1E 1841-045Jun 13 2005Multi-colour (JHKs) imaging and photometry of the field of the Anomalous X-ray Pulsar AXP 1E 1841-045 is analysed in the light of new, accurate coordinates from Chandra (Wachter et al, 2004). From excellentquality images, we find multiple sources in and ... More

An Algorithm to Compute the Topological Euler Characteristic, the Chern-Schwartz-MacPherson Class and the Segre class of Subschemes of Some Smooth Complete Toric VarietiesAug 16 2015Aug 20 2015Let $X_{\Sigma}$ be a complete smooth toric variety of dimension $n$ defined by a fan $\Sigma$ where all Cartier divisors in $\mathrm{Pic}(X_{\Sigma})$ are nef and let $V$ be a subscheme of $X_{\Sigma}$. We show a new expression for the Segre class $s(V,X_{\Sigma})$ ... More

Tangles and Connectivity in GraphsFeb 15 2016This paper is a short introduction to the theory of tangles, both in graphs and general connectivity systems. An emphasis is put on the correspondence between tangles of order k and k-connected components. In particular, we prove that there is a one-to-one ... More

Multi-Clique-WidthNov 13 2015Multi-clique-width is obtained by a simple modification in the definition of clique-width. It has the advantage of providing a natural extension of tree-width. Unlike clique-width, it does not explode exponentially compared to tree-width. Efficient algorithms ... More

Varilets: Additive Decomposition, Topological Total Variation, and Filtering of Scalar FieldsMar 16 2015Apr 26 2016Continuous interpolation of real-valued data is characterized by piecewise monotone functions on a compact metric space. Topological total variation of piecewise monotone function f:X->R is a homeomorphism-invariant generalization of 1D total variation. ... More

Quantum cosmology: a reviewJan 20 2015In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical questions. This review ... More

Information loss, made worse by quantum gravity?Sep 10 2014May 17 2015Quantum gravity is often expected to solve both the singularity problem and the information-loss problem of black holes. This article presents an example from loop quantum gravity in which the singularity problem is solved in such a way that the information-loss ... More

Consistent Loop Quantum CosmologyNov 25 2008A consistent combination of quantum geometry effects rules out a large class of models of loop quantum cosmology and their critical densities as they have been used in the recent literature. In particular, the critical density at which an isotropic universe ... More

Canonical Relativity and the Dimensionality of the WorldJul 30 2008Different aspects of relativity, mainly in a canonical formulation, relevant for the question "Is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a mathematical ... More

Loop quantum cosmology and inhomogeneitiesSep 08 2006Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of background independent ... More

Loop quantum gravity as an effective theoryAug 07 2012As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable ambiguities at the ... More

Quantum gravity effects on space-timeFeb 12 2010General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like generic states ... More

Elements of Loop Quantum CosmologyMay 12 2005The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity combined with matter theories is not able to describe them ... More

The Inverse Scale Factor in Isotropic Quantum GeometryMay 18 2001The inverse scale factor, which in classical cosmological models diverges at the singularity, is quantized in isotropic models of loop quantum cosmology by using techniques which have been developed in quantum geometry for a quantization of general relativity. ... More

Absence of Singularity in Loop Quantum CosmologyFeb 14 2001It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded operator even ... More