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Primordial fluctuations and non-Gaussianities in sidetracked inflationApr 30 2018Jul 27 2018Heavy scalar fields can undergo an instability during inflation as a result of their kinetic couplings with the inflaton. This is known as the geometrical destabilization of inflation, as it relies on the effect of the negative curvature of the field-space ... More

Hyper non-Gaussianities in inflation with strongly non-geodesic motionFeb 08 2019Several recent proposals to embed inflation into high-energy physics rely on inflationary dynamics characterized by a strongly non-geodesic motion in negatively curved field space. This naturally leads to a transient instability of perturbations on sub-Hubble ... More

Infinitely many knots admitting the same integer surgeryJul 06 2014The construction of knots via annular twisting has been used to create families of knots yielding the same manifold via Dehn surgery. Prior examples have all involved Dehn surgery where the surgery slope is an integral multiple of 2. In this note we prove ... More

Computing power series expansions of modular formsApr 30 2012Sep 30 2012We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra.

Optimal Bacon-Shor codesSep 04 2012We study the performance of Bacon-Shor codes, quantum subsystem codes which are well suited for applications to fault-tolerant quantum memory because the error syndrome can be extracted by performing two-qubit measurements. Assuming independent noise, ... More

Saddlepoint approximations for likelihood ratio like statistics with applications to permutation testsMar 14 2012We obtain two theorems extending the use of a saddlepoint approximation to multiparameter problems for likelihood ratio-like statistics which allow their use in permutation and rank tests and could be used in bootstrap approximations. In the first, we ... More

Bounding quantification in parametric expansions of Presburger arithmeticApr 21 2016We generalize Cooper's method of quantifier elimination for classical Presburger arithmetic to give a new proof that all parametric Presburger families (as defined by Kevin Woods) are definable by formulas with polynomially bounded quantifiers in an expanded ... More

Quantum theory from Hamilton's Principle with imperfect informationApr 16 2007Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the quantum mechanical ... More

Quantum Isomonodromic Deformations and the Knizhnik--Zamolodchikov EquationsJun 14 1994Jun 15 1994Viewing the Knizhnik--Zamolodchikov equations as multi--time, nonautonomous Shr\"odinger equations, the transformation to the Heisenberg representation is shown to yield the quantum Schlesinger equations. These are the quantum form of the isomonodromic ... More

The L-functions and modular forms database projectNov 13 2015Jan 28 2016The Langlands Programme, formulated by Robert Langlands in the 1960s and since much developed and refined, is a web of interrelated theory and conjectures concerning many objects in number theory, their interconnections, and connections to other fields. ... More

Bounding Lossy Compression using Lossless Codes at Reduced PrecisionDec 31 2012An alternative approach to two-part 'critical compression' is presented. Whereas previous results were based on summing a lossless code at reduced precision with a lossy-compressed error or noise term, the present approach uses a similar lossless code ... More

Stochastic Cooling OverviewAug 11 2003The status of stochastic cooling and developments over the years are reviewed with reference to much of the original work. Both theoretical and technological subjects are considered.

Crossed product duality for partial $C^*$-automorphismsApr 03 1996For partial automorphisms of $C^*$-algebras, Takai-Takesaki crossed product duality tends to fail, in proportion to the extent to which the partial automorphism is not an automorphism.

Galois extensions of structured ring spectraFeb 09 2005Dec 06 2005We introduce the notion of a Galois extension of commutative S-algebras (E_infty ring spectra), often localized with respect to a fixed homology theory. There are numerous examples, including some involving Eilenberg-Mac Lane spectra of commutative rings, ... More

Simpler semidefinite programs for completely bounded normsJul 24 2012Aug 02 2012The completely bounded trace and spectral norms, for finite-dimensional spaces, are known to be efficiently expressible by semidefinite programs (J. Watrous, Theory of Computing 5: 11, 2009). This paper presents two new, and arguably much simpler, semidefinite ... More

Quantum statistical zero-knowledgeFeb 20 2002In this paper we propose a definition for (honest verifier) quantum statistical zero-knowledge interactive proof systems and study the resulting complexity class, which we denote QSZK. We prove several facts regarding this class that establish close connections ... More

PSPACE has 2-round quantum interactive proof systemsJan 27 1999In this paper we consider quantum interactive proof systems, i.e., interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages. It is proved that every language in PSPACE has a quantum interactive ... More

Quantum simulations of classical random walks and undirected graph connectivityDec 11 1998It is not currently known if quantum Turing machines can efficiently simulate probabilistic computations in the space-bounded case. In this paper we show that space-bounded quantum Turing machines can efficiently simulate a limited class of random processes: ... More

Reliable Quantum ComputersMay 16 1997Aug 26 1997The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors ... More

Sufficient condition on noise correlations for scalable quantum computingJul 25 2012Nov 10 2012I study the effectiveness of fault-tolerant quantum computation against correlated Hamiltonian noise, and derive a sufficient condition for scalability. Arbitrarily long quantum computations can be executed reliably provided that noise terms acting collectively ... More

Quantum Computing: Pro and ConMay 16 1997Aug 26 1997I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantum computers ... More

On a Conjecture of Harvey and LawsonJul 23 2008We consider complex projective space P^{n} and a smooth closed curve gamma in P^{n}. Harvey and Lawson have defined the notion of the projective hull \hat{K} of a compact subset K in P^n. This concept is an analogue of the polynomial hull of compact subsets ... More

ggRandomForests: Visually Exploring a Random Forest for RegressionJan 28 2015Feb 13 2015Random Forests [Breiman:2001] (RF) are a fully non-parametric statistical method requiring no distributional assumptions on covariate relation to the response. RF are a robust, nonlinear technique that optimizes predictive accuracy by fitting an ensemble ... More

Fault-Tolerant Modular Reconstruction of Rational NumbersMar 12 2013Jul 21 2015In this paper we present two efficient methods for reconstructing a rational number from several residue-modulus pairs, some of which may be incorrect. One method is a natural generalization of that presented by Wang, Guy and Davenport in \cite{WGD1982} ... More

Quantum Revivals in Conformal Field Theories in Higher DimensionsMar 27 2016Apr 27 2016We investigate the behavior of the return amplitude ${\cal F}(t)= |\langle\Psi(0)|\Psi(t)\rangle|$ following a quantum quench in a conformal field theory (CFT) on a compact spatial manifold of dimension $d-1$ and linear size $O(L)$, from a state $|\Psi(0)\rangle$ ... More

Discrete Holomorphicity at Two-Dimensional Critical PointsJul 23 2009After a brief review of the historical role of analyticity in the study of critical phenomena, an account is given of recent discoveries of discretely holomorphic observables in critical two-dimensional lattice models. These are objects whose correlation ... More

Some Results on Mutual Information of Disjoint Regions in Higher DimensionsApr 30 2013Jun 13 2013We consider the mutual Renyi information I^n(A,B)=S^n_A+S^n_B-S^n_{AUB} of disjoint compact spatial regions A and B in the ground state of a d+1-dimensional conformal field theory (CFT), in the limit when the separation r between A and B is much greater ... More

Measuring entanglement using quantum quenchesDec 22 2010Mar 22 2011We show that block entanglement entropies in one-dimensional systems close to a quantum critical point can in principle be measured in terms of the population of low-lying energy levels following a certain type of local quantum quench.

The Ubiquitous 'c': from the Stefan-Boltzmann Law to Quantum InformationAug 13 2010Sep 13 2010I discuss various aspects of the role of the conformal anomaly number c in 2- and 1+1-dimensional critical behaviour: its appearance as the analogue of Stefan's constant, its fundamental role in conformal field theory, in the classification of 2d universality ... More

Conformal Field Theory and Statistical MechanicsJul 22 2008The lectures provide a pedagogical introduction to the methods of CFT as applied to two-dimensional critical behaviour.

Lecture on Branched Polymers and Dimensional ReductionFeb 24 2003Mar 25 2003This is a pedagogical account of the recent results of Brydges and Imbrie, described from the point of view of Grassmann integration. Some simple extensions are pointed out.

Exact Scaling Functions for Self-Avoiding Loops and Branched PolymersJul 11 2001Sep 24 2001It is shown that a recently conjectured form for the critical scaling function for planar self-avoiding polygons weighted by their perimeter and area also follows from an exact renormalization group flow into the branched polymer problem, combined with ... More

Linking numbers for self-avoiding walks and percolation: application to the spin quantum Hall transitionNov 29 1999Feb 21 2000Non-local twist operators are introduced for the O(n) and Q-state Potts models in two dimensions which, in the limits n -> 0 (resp. Q -> 1) count the numbers of self-avoiding loops (resp. percolation clusters) surrounding a given point. This yields many ... More

The Number of Incipient Spanning Clusters in Two-Dimensional PercolationMay 14 1997May 15 1997Using methods of conformal field theory, we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k, in the limit when k is large.

Geometrical Properties of Loops and Cluster BoundariesSep 19 1994We discuss how the statistical properties of the area and radius of gyration of single self-avoiding loops, and of Ising and percolation cluster boundaries, may be calculated using ideas of two-dimensional field theory. For cluster boundaries, we show ... More

Holographic duality with a view toward many-body physicsSep 03 2009May 08 2010These are notes based on a series of lectures given at the KITP workshop "Quantum Criticality and the AdS/CFT Correspondence" in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT correspondence. Discussion ... More

Duke's Theorem and Continued FractionsFeb 20 2008For uniformly chosen random $\alpha \in [0,1]$, it is known the probability the $n^{\rm th}$ digit of the continued-fraction expansion, $[\alpha]_n$ converges to the Gauss-Kuzmin distribution $\mathbb{P}([\alpha]_n = k) \approx \log_2 (1 + 1/ k(k+2))$ ... More

When does elementary bi-embeddability imply isomorphism?May 13 2007A first-order theory has the Schroder-Bernstein property if any two of its models that are elementarily bi-embeddable are isomorphic. We prove that if a countable theory T has the Schroder-Bernstein property then it is classifiable (it is superstable ... More

Pulsar-driven Jets in Supernovae, Gamma-Ray Bursts, and the UniverseMay 23 2012Jul 02 2013The bipolarity of Supernova 1987A can be understood through its very early light curve observed from the CTIO 0.4-m telescope and IUE FES, and following speckle observations of the `Mystery Spot' by two groups. These indicate a highly directional beam/jet ... More

Pulsed Gamma-Ray-Burst AfterglowsSep 14 2009The bipolarity of Supernova 1987A can be understood in terms of its very early light curve as observed from the CTIO 0.4-m telescope, as well as the IUE FES, and the slightly later speckle observations of the "Mystery Spot" by two groups. These observations ... More

Core-collapse, GRBs, Type Ia Supernovae, and CosmologyAug 17 2006Aug 01 2007Type Ia Supernovae (SNe) have been used by many to argue for an accelerated expansion of the universe. However, high velocity and polarized features in many nearby SNe Ia, and their inverse relation to luminosity, particularly for polarization, are consistent ... More

A White Dwarf Merger Paradigm for Supernovae and Gamma-Ray BurstsNov 20 2003Dec 17 2003Gamma-ray bursts can appear to be a hundred times as luminous as supernovae, but their underlying energy source(s) have remained a mystery. However, there has been evidence for some time now of an association of gamma-ray bursts with supernovae of Type ... More

On a Mean Value of Gadiyar and PadmaJun 24 2015Nov 18 2015Building on the earlier works of Gadiyar and Padma, the main result of this paper is to prove: \begin{equation} \lim_{n \to \infty} \frac{1}{N} \sum_{n=1}^{N} \frac{\phi(n) \Lambda\left(n \right)}{n} \frac{\phi(n+h) \Lambda\left(n +h\right)}{n+h} = \sum\limits_{q=1}^{\infty} ... More

Solar Neutrinos: Where We AreFeb 06 1997Feb 06 1997This talk compares standard model predictions for solar neutrino experiments with the results of actual observations. Here `standard model' means the combined standard model of minimal electroweak theory plus a standard solar model. I emphasize the importance ... More

Can Evidence Be Combined in the Dempster-Shafer TheoryMar 27 2013Dempster's rule of combination has been the most controversial part of the Dempster-Shafer (D-S) theory. In particular, Zadeh has reached a conjecture on the noncombinability of evidence from a relational model of the D-S theory. In this paper, we will ... More

On the Crepant Resolution Conjecture for Donaldson-Thomas InvariantsJun 27 2012Dec 14 2014We prove a comparison formula for curve-counting invariants in the setting of the McKay correspondence, related to the crepant resolution conjecture for Donaldson-Thomas invariants. The conjecture is concerned with comparing the invariants of a (hard ... More

Symplectic Noise & The Classical Analog of the Lindblad GeneratorDec 23 2014Aug 26 2015We introduce the concepts of Poisson brackets for classical noise, and of canonically conjugate Wiener processes (symplectic noise). Phase space diffusions driven by these processes are considered and the general form of a stochastic process preserving ... More

Optimal Quantum Feedback Control for Canonical ObservablesApr 13 2005Apr 16 2005We show that the stochastic Schrodinger equation for the filtered state of a system, with linear free dynamics, undergoing continual non-demolition measurement or either position or momentum, or both together, can be solved explicitly within a class of ... More

The Stochastic Sector of Interacting-Free Quantum Field TheorySep 11 2003Nov 09 2004The Quantum Stochastic Limit of a quantum mechanical particle coupled to a quantum field without the neglect of the response details of the interaction (i.e. not making the dipole approximation) is made following the treatment of Accardi and Lu [6] and ... More

Quantum Shannon TheoryApr 25 2016Apr 30 2016This is the 10th and final chapter of my book on Quantum Information, based on the course I have been teaching at Caltech since 1997. An earlier version of this chapter (originally Chapter 5) has been available on the course website since 1998, but this ... More

Subtraction method for NLO corrections in Monte-Carlo event generators for leptoproductionJan 05 2000Aug 07 2000In the case of the gluon-fusion process in deep-inelastic leptoproduction, I explicitly show how to incorporate NLO corrections in a Monte-Carlo event generator by a subtraction method. I calculate the parton densities to be used by the event generator ... More

2-soft-gluon exchange and factorization breakingAug 31 2007A previous counterexample to disprove k_T-factorization for H_1+H_2 --> H_3+H_4+X is extended calculationally to one higher order in gluon exchange. The result is that, by explicit calculation, standard k_T-factorization fails for the unpolarized cross-section ... More

Fragmentation of Transversely Polarized Quarks Probed in Transverse Momentum DistributionsAug 06 1992May 10 2002It is shown that the azimuthal dependence of the distribution of hadrons in a quark jet is a probe of the transverse spin of the quark initiating the jet. This results in a new spin-dependent fragmentation function that acts at the twist-2 level. One ... More

Monsters at the Heart of Galaxy FormationJul 26 2000Surveys with the Hubble Space Telescope find supermassive black holes (BHs) of 10**6 to 10**9.5 solar masses in every galaxy that has an elliptical-galaxy-like "bulge" component. BHs appear to be standard equipment in galaxy bulges. At the 2000 June meeting ... More

Strings on Plane Waves and AdS x SDec 01 2003Jan 12 2004We consider the RNS superstrings in $AdS_3 \times S^3 \times {\cal M}$, where $\cal M$ may be $K3$ or $T^4$, based on $SL(2,R)$ and SU(2) WZW models. We construct the physical states and calculate the spectrum. A subsector of this theory describes strings ... More

Dishing up the Data: A Decade of Space MissionsOct 03 2012The past decade has seen Parkes once again involved in a wide range of space tracking activities that have added to its illustrious legacy. This contribution is a personal recollection of those tracking efforts - both real and celluloid. We begin in a ... More

The Origin of the Brightest Cluster GalaxiesSep 11 1997Feb 18 1998Most clusters and groups of galaxies contain a giant elliptical galaxy in their centres which far outshines and outweighs normal ellipticals. The origin of these brightest cluster galaxies is intimately related to the collapse and formation of the cluster. ... More

The Picard-Lefschetz theory of complexified Morse functionsJun 08 2009Given a closed manifold N and a self-indexing Morse function f: N --> R with up to four distinct Morse indices, we construct a symplectic Lefschetz fibration pi: E --> C which models the complexification of f on the disk cotangent bundle, f_C : D(T*N) ... More

Representations of Temperley--Lieb AlgebrasOct 17 2007We define a commuting family of operators $T_0,T_1,...,T_n$ in the Temperley--Lieb algebra $\mathcal{A}_n(x)$ of type $A_{n-1}$. Using an appropriate analogue to Murphy basis of the Iwahori--Hecke algebra of the symmetric group, we describe the eigenvalues ... More

Constraining black hole masses from stellar kinematics by summing over all possible distribution functionsSep 08 2006When faced with the task of constraining a galaxy's potential given limited stellar kinematical information, what is the best way of treating the galaxy's unknown distribution function (DF)? Using the example of estimating black hole (BH) masses, I argue ... More

Convex RP^2 Structures and Cubic Differentials under Neck SeparationJun 12 2015Let S be a closed oriented surface of genus at least two. Labourie and the author have independently used the theory of hyperbolic affine spheres to find a natural correspondence between convex RP^2 structures on S and pairs (\Sigma,U) consisting of a ... More

Diagram spaces, diagram spectra, and spectra of unitsAug 07 2009Nov 22 2012This article compares the infinite loop spaces associated to symmetric spectra, orthogonal spectra, and EKMM S-modules. Each of these categories of structured spectra has a corresponding category of structured spaces that receives the infinite loop space ... More

Future Accelerators (?)Aug 09 2003I describe the future accelerator facilities that are currently foreseen for electroweak scale physics, neutrino physics, and nuclear structure. I will explore the physics justification for these machines, and suggest how the case for future accelerators ... More

Summary and Highlights of the 14th Topical Conference on Hadron Collider Physics (HCP2002)Nov 04 2002Nov 11 2002Conference summary presentation given at HCP2002, Karlsruhe, Germany, Sep 29-Oct 4, 2002.

Tests of Perturbative QCD and Jet PhysicsDec 04 1999Dec 11 1999I describe the current status of tests of perturbative QCD, using measurements of jet, photon, weak boson and heavy flavor production from the Tevatron, LEP and HERA. Measurements of the strong coupling constant are described, and I conclude with a "wish ... More

Discovering Technicolor at Hadron CollidersDec 06 1996Strategies are presented for discovering light, color-singlet technipions (pi_T) produced in association with a vector boson through s-channel technirho production, at the Tevatron and LHC. Signal and W+jets background were simulated including detector ... More

Chiral Technicolor and Precision Electroweak MeasurementsOct 06 1994I consider the possibility that electroweak symmetry is broken by a strongly interacting chiral gauge theory. I argue that some of the discrepancies between precision electroweak measurements and the predictions of QCD-like technicolor models can be resolved ... More

Anyons as Dirac Strings the $A_x=0$ GaugeJan 20 1993We show how to quantize the anyon particle theory in the gauge $A_x=0$, where the statistical potential $\vec A(\vec x)$ is a Dirac string. In this gauge, anyons obey normal statistics.

Explaining the Dark Energy, Baryon and Dark Matter Coincidence via Domain-Dependent Random DensitiesJan 17 2013May 15 2013The dark energy, dark matter and baryon densities in the Universe are observed to be similar, with a factor of no more than 20 between the largest and smallest densities. We show that this coincidence can be understood via superhorizon domains of randomly ... More

Conditions for a Successful Right-Handed Majorana Sneutrino CurvatonApr 19 2004Sep 10 2004We consider the conditions which must be satisfied for a Majorana RH sneutrino, a massive right-handed (RH) sneutrino associated with the see-saw mechanism of Majorana neutrino masses, to play the role of the curvaton. Planck-scale suppressed non-renormalizable ... More

Supersymmetric Curvatons and Phase-Induced Curvaton FluctuationsOct 10 2003Oct 11 2003We consider the curvaton scenario in the context of supersymmetry (SUSY) with gravity-mediated SUSY breaking. In the case of a large initial curvaton amplitude during inflation and a negative order H^2 correction to the mass squared term after inflation, ... More

Reheating Temperature and Inflaton Mass Bounds from Thermalization After InflationSep 22 1999Oct 20 1999We consider the conditions for the decay products of perturbative inflaton decay to thermalize. The importance of considering the full spectrum of inflaton decay products in the thermalization process is emphasized. It is shown that the delay between ... More

Warm Dark Matter via Ultra-Violet Freeze-In: Reheating Temperature and Non-Thermal Distribution for Fermionic Higgs Portal Dark MatterDec 20 2015Aug 16 2016Warm dark matter (WDM) of order keV mass may be able to resolve the disagreement between structure formation in cold dark matter simulations and observations. The detailed properties of WDM will depend upon its energy distribution, in particular how it ... More

Non-Minimally Coupled Inflation with Initial Conditions from a Pre-Inflation Anamorphic Contracting EraNov 24 2015Aug 08 2016Inflation due to a non-minimally coupled scalar field with a large non-minimal coupling, as first proposed by Salopek, Bardeen and Bond (SBB), is in good agreement with the observed value of the spectral index and constraints on the tensor-to-scalar ratio. ... More

RH Sneutrino Condensate CDM and the Baryon-to-Dark Matter RatioOct 12 2007The similarity of the observed mass densities of baryons and cold dark matter may be a sign they have a related origin. The baryon-to-dark matter ratio can be understood in the MSSM with right-handed (RH) neutrinos if CDM is due to a d = 4 flat direction ... More

Right-Handed Sneutrino Condensate Cold Dark Matter and the Baryon-to-Dark Matter RatioSep 13 2006Dec 10 2006The similarity of the observed densities of baryons and cold dark matter suggests that they have a common or related origin. This can be understood in the context of the MSSM with right-handed (RH) sneutrinos if cold dark matter is due to a d = 4 flat ... More

F-Term Inflation Q-BallsSep 19 2005Jan 27 2006A general analysis of Q-ball solutions of the supersymmetric F-term hybrid inflation field equations is given. The solutions consist of a complex inflaton field and a real symmetry breaking field, with a conserved global charge associated with the inflaton. ... More

Curvaton Potential Terms, Scale-Dependent Perturbation Spectra and Chaotic Initial ConditionsAug 28 2003Dec 08 2003The curvaton scenario predicts an almost scale-invariant spectrum of perturbations in most inflation models. We consider the possibility that renormalisable phi^4 or Planck scale-suppressed non-renormalisable curvaton potential terms may result in an ... More

Flat Direction Dynamics in a Non-Topological Soliton-Dominated UniverseMay 28 2003Jun 01 2004In hybrid inflation and running mass inflation models it is possible that the inflaton field will fragment into non-topological solitons, resulting in a highly inhomogeneous post-inflation era prior to reheating. In supersymmetric models with a conventional ... More

Contact homology and virtual fundamental cyclesAug 16 2015Oct 28 2015We give a construction of contact homology in the sense of Eliashberg--Givental--Hofer. Specifically, we construct coherent virtual fundamental cycles on the relevant compactified moduli spaces of pseudo-holomorphic curves.

Fractional Branes, Confinement, and Dynamically Generated SuperpotentialsMar 17 1998Jul 26 1998We examine the effects of instantons in four dimensional N=1 supersymmetric gauge theory by including D0-branes in type IIA brane constructions. We examine instanton generated superpotentials in supersymmetric QCD and find that they are due to a repulsive ... More

H-closed Spaces and H-sets in the Convergence SettingOct 27 2015We use convergence theory as the framework for studying H-closed spaces and H-sets in topological spaces. From this viewpoint, it becomes clear that the property of being H-closed and the property of being an H-set in a topological space are pretopological ... More

The Majorana representation of spins and the relation between $SU(\infty)$ and $SDiff(S^2)$Apr 30 2004The Majorana representation of spin-$\frac{n}{2}$ quantum states by sets of points on a sphere allows a realization of SU(n) acting on such states, and thus a natural action on the two-dimensional sphere $S^2$. This action is discussed in the context ... More

Anisotropies in Ultrahigh Energy Cosmic RaysJan 30 2004The present status of anisotropy studies for the highest energy cosmic rays is presented including the first full sky survey. Directions and prospects for the future are also discussed in light of new statistical methods and the last quantities of data ... More

The Pierre Auger ObservatorySep 18 2003One of the most fascinating puzzles in particle astrophysics today is that of the origin and nature of the highest energy cosmic rays. The Pierre Auger Observatory (PAO), currently under construction in Province of Mendoza, Argentina, and with another ... More

Simplicial Gravity and StringsOct 23 2011String theory, as a theory containing quantum gravity, is usually thought to require more dimensions of spacetime than the usual 3+1. Here I argue on physical grounds that needing extra dimensions for strings may well be an artefact of forcing a fixed ... More

Gravitatomagnetic Analogs of Electric TransformersJun 30 2010Linearized general relativity admits a formulation in terms of gravitoelectric and gravitomagnetic fields that closely parallels the description of the electromagnetic field by Maxwell's equations. For steady mass currents, this formalism has been used ... More

Black Holes and the Strong CP ProblemMay 06 2010Jun 30 2010The strong CP problem is that SU(3) gauge field instantons naturally induce a CP violating term in the QCD Lagrangian which is constrained by experiment to be very small for no obvious reason. We show that this problem disappears if one assumes the existence ... More

Composite Operators, Supersymmetry Anomalies and Supersymmetry Breaking in the Wess-Zumino ModelMar 17 2003The field equations of the auxiliary fields are nonlinear and free of derivatives. Hence, it is argued, a Legendre transform to generate the 1PI Generating Functionals is not correct for the auxiliary fields. A corrected formulation of the BRS symmetry ... More

BRS Cohomology, Composite Operators and the Supersymmetric Standard ModelJan 20 2006Jan 21 2006Supersymmetry might be broken, in the real world, by anomalies that affect composite operators, while leaving the action supersymmetric. New constraint equations that govern the composite operators and their anomalies are examined. It is shown that the ... More

Relating Complexity to Practical Performance in Parsing with Wide-Coverage Unification GrammarsMay 31 1994The paper demonstrates that exponential complexities with respect to grammar size and input length have little impact on the performance of three unification-based parsing algorithms, using a wide-coverage grammar. The results imply that the study and ... More

Translation of Reidemeister's "Einführung in die kombinatorische Topologie"Feb 17 2014This is an English translation of Reidemeister's book "Einf\"uhrung in die kombinatorische Topologie" from 1932, the first monograph on combinatorial group theory and topology, with some added comments by the translator and Warren Dicks.

Shimura curves of genus at most twoFeb 07 2008Nov 07 2010In this article, we enumerate all Shimura curves X^D_0(N) of genus at most two.

Computing fundamental domains for Fuchsian groupsFeb 01 2008Jan 16 2009We exhibit an algorithm to compute a Dirichlet domain for a cofinite Fuchsian group Gamma. As a consequence, we compute the invariants of Gamma, including an explicit finite presentation for Gamma.

Orbifold finiteness under geometric and spectral constraintsJan 03 2014May 12 2015The class of Riemannian orbifolds of dimension n defined by a lower bound on the sectional curvature and the volume and an upper bound on the diameter has only finitely many members up to orbifold homeomorphism. Furthermore, any class of isospectral Riemannian ... More

Equivariant Alexandrov geometry and orbifold finitenessJan 02 2014May 12 2015Let a compact Lie group act isometrically on a non-collapsing sequence of compact Alexandrov spaces with fixed dimension and uniform lower curvature and upper diameter bounds. If the sequence of actions is equicontinuous and converges in the equivariant ... More

Fields of rationality of automorphic representations: the case of unitary groupsMay 31 2016This paper examines fields of rationality in families of cuspidal automorphic representations of unitary groups. Specifically, for a fixed $A$ and a sufficiently large family $\mathcal{F}$, a small proportion of representations $\pi\in \mathcal{F}$ will ... More

A Parameter Space Exploration of Galaxy Cluster Mergers I: Gas Mixing and the Generation of Cluster EntropyApr 21 2010Jan 28 2011We present a high-resolution set of adiabatic binary galaxy cluster merger simulations using FLASH. These are the highest-resolution simulations to date of such mergers using an AMR grid-based code with Eulerian hydrodynamics. In this first paper in a ... More

Symmetrization procedures for the isoperimetric problem in symmetric spaces of noncompact typeApr 20 2005We establish a new symmetrization procedure for the isoperimetric problem in symmetric spaces of noncompact type. This symmetrization generalizes the well known Steiner symmetrization in euclidean space. In contrast to the classical construction the symmetrized ... More