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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

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

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

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

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

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

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 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

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

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

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

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

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

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

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

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

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

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 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.

Proximity in the curve complex: boundary reduction and bicompressible surfacesOct 11 2004Jan 12 2005Suppose N is a compressible boundary component of a compact orientable irreducible 3-manifold M and Q is an orientable properly embedded essential surface in M in which each component is incident to N and no component is a disk. Let VN and QN denote respectively ... More

On the least exponential growth admitting uncountably many closed permutation classesJul 31 2003We show that the least exponential growth of counting functions which admits uncountably many closed permutation classes lies between 2^n and (2.33529...)^n.

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

Stability of the global attractor under Markov-Wasserstein noiseMar 17 2011We develop a "weak Wa\.zewski principle" for discrete and continuous time dynamical systems on metric spaces having a weaker topology to show that attractors can be continued in a weak sense. After showing that the Wasserstein space of a proper metric ... More

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

Localization in Lattice Gauge Theory and a New Multigrid MethodMay 05 1994We show numerically that the lowest eigenmodes of the 2-dimensional Laplace-operator with SU(2) gauge couplings are strongly localized. A connection is drawn to the Anderson-Localization problem. A new Multigrid algorithm, capable to deal with these modes, ... More

The principle of indirect eliminationAug 14 1995The principle of indirect elimination states that an algorithm for solving discretized differential equations can be used to identify its own bad-converging modes. When the number of bad-converging modes of the algorithm is not too large, the modes thus ... 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

Matrix-valued Bessel processesDec 20 2012Jun 23 2015This paper introduces a matrix analog of the Bessel processes, taking values in the closed set $E$ of real square matrices with nonnegative determinant. They are related to the well-known Wishart processes in a simple way: the latter are obtained from ... More

Non-representability of finite projective planes by convex setsAug 27 2009We prove that there is no d such that all finite projective planes can be represented by convex sets in R^d, answering a question of Alon, Kalai, Matousek, and Meshulam. Here, if P is a projective plane with lines l_1,...,l_n, a representation of P by ... 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

Non-Equivalent Beliefs and Subjective Equilibrium BubblesJun 21 2013This paper develops a dynamic equilibrium model where agents exhibit a strong form of belief heterogeneity: they disagree about zero probability events. It is shown that, somewhat surprisingly, equilibrium exists in this setting, and that the disagreement ... 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

Interpolation in ortholatticesFeb 28 2000If L is a complete ortholattice, f any partial function from L^n to L, then there is a complete ortholattice L* containing L as a subortholattice, and an ortholattice polynomial with coefficients in L* which represents f on L^n. Iterating this construction ... 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

Study of some parameters interstellar transport using of magnetic umbrellaJan 28 2013Apr 30 2013Interstellar transport is an object of interest in many sci-fi stories. In history a lot of sci-fi predictions have turned into reality, such as communications satellites, deep-sea submarines and journies to the moon. In this work we study some physical ... More

On compatibility between isogenies and polarisations of abelian varietiesJun 12 2015Mar 18 2016We discuss the notion of polarised isogenies of abelian varieties, that is, isogenies which are compatible with given principal polarisations. This is motivated by problems of unlikely intersections in Shimura varieties. Our aim is to show that certain ... More

The central configurations of four masses x, -x, y, -ySep 20 2006The configuration of a homothetic motion in the N-body problem is called a central configuration. In this paper, we prove that there are exactly three planar non-collinear central configurations for masses x, -x, y, -y with x different from y (a parallelogram ... More

Families of abelian varieties with many isogenous fibresSep 17 2012Sep 13 2016Let Z be a subvariety of the moduli space of principally polarised abelian varieties of dimension g over the complex numbers. Suppose that Z contains a Zariski dense set of points which correspond to abelian varieties from a single isogeny class. A generalisation ... More

A Lie algebra for Frölicher groupsJun 24 2009Fr\"olicher spaces form a cartesian closed category which contains the category of smooth manifolds as a full subcategory. Therefore, mapping groups such as C^\infty(M,G) or \Diff(M), but also projective limits of Lie groups are in a natural way objects ... 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

Searching for an EBL attenuation signature in the Fermi/LAT 1st year catalog dataAug 25 2010Observations of distant sources of high-energy (HE) gamma-rays are affected by attenuation resulting from the interaction of the gamma-rays with low energy photons from the diffuse meta-galactic radiation fields at ultraviolet (UV) to infrared (IR) wavelengths ... More

Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear timeDec 15 2005We present an algorithm that computes a shortest non-contractible and a shortest non-separating cycle on an orientable combinatorial surface of bounded genus in O(n \log n) time, where n denotes the complexity of the surface. This solves a central open ... More

Field signature for apparently superluminal particle motionApr 06 2016In the context of Stueckelberg's covariant symplectic mechanics, Horwitz and Aharonovich have proposed a simple mechanism by which a particle traveling below light speed almost everywhere may exhibit a transit time that suggests superluminal motion. This ... More

Electrostatics in Stueckelberg-Horwitz-Piron ElectrodynamicsApr 06 2016In this paper, we study fundamental aspects of electrostatics as a special case in Stueckelberg-Horwitz electromagnetic theory. In this theory, spacetime events $x^\mu(\tau)$ evolve in an unconstrained 8-dimensional phase space, interacting through five ... More

Harmonic Oscillator States with Non-Integer Orbital Angular MomentumMar 10 2009Mar 27 2009We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as represents of their respective symmetry groups: O(2), O(3), and O(2,1). Solving the Schrodinger equation by separating variables ... More

Duality in Off-Shell ElectromagnetismMar 21 2006In this paper, we examine the Dirac monopole in the framework of Off-Shell Electromagnetism, the five dimensional U(1) gauge theory associated with Stueckelberg-Schrodinger relativistic quantum theory. After reviewing the Dirac model in four dimensions, ... More

Higher-Order Kinetic Term for Controlling Photon Mass in Off-Shell ElectrodynamicsMar 09 2006In a relativistic classical and quantum mechanics with Poincare-invariant parameter, particle worldlines are traced out by the evolution of spacetime events. In pre-Maxwell electrodynamics -- the local gauge theory associated with this framework -- events ... More

Compactified NCOS and dualitySep 12 2000Sep 20 2000We study four-dimensional U(1) on a non-commutative T^2 with rational Theta. This theory has dual descriptions as ordinary SYM or as NCOS. We identify a set of massive non-interacting KK states in the SYM theory and track them through the various dualities. ... More

Operads and PROPsJan 06 2006Feb 11 2006We review definitions and basic properties of operads, PROPs and algebras over these structures.

Ideal Perturbation LemmaFeb 16 2000May 26 2000We explain the essence of perturbation problems. The key to understanding is the structure of chain homotopy equivalence -- the standard one must be replaced by a finer notion which we call a strong chain homotopy equivalence. We prove an Ideal Perturbation ... More

Cyclic operads and homology of graph complexesJan 21 1998We will consider P-graph complexes, where P is a cyclic operad. P-graph complexes are natural generalizations of Kontsevich's graph complexes -- for P = the operad for associative algebras it is the complex of ribbon graphs, for P = the operad for commutative ... More