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Maximizing Online Utilization with CommitmentApr 12 2019We investigate online scheduling with commitment for parallel identical machines. Our objective is to maximize the total processing time of accepted jobs. As soon as a job has been submitted, the commitment constraint forces us to decide immediately whether ... More

Efficient Similarity Search in Dynamic Data StreamsMay 12 2016The Jaccard index is an important similarity measure for item sets and Boolean data. On large datasets, an exact similarity computation is often infeasible for all item pairs both due to time and space constraints, giving rise to faster approximate methods. ... More

Sublinear Estimation of Weighted Matchings in Dynamic Data StreamsMay 08 2015Jul 09 2015This paper presents an algorithm for estimating the weight of a maximum weighted matching by augmenting any estimation routine for the size of an unweighted matching. The algorithm is implementable in any streaming model including dynamic graph streams. ... More

Random Projections for k-Means: Maintaining Coresets Beyond Merge & ReduceApr 07 2015Jul 09 2015We give a new construction for a small space summary satisfying the coreset guarantee of a data set with respect to the $k$-means objective function. The number of points required in an offline construction is in $\tilde{O}(k \epsilon^{-2}\min(d,k\epsilon^{-2}))$ ... More

Fair Coresets and Streaming Algorithms for Fair k-Means ClusteringDec 28 2018We study fair clustering problems as proposed by Chierichetti et al. Here, points have a sensitive attribute and all clusters in the solution are required to be balanced with respect to it (to counteract any form of data-inherent bias). Previous algorithms ... More

Generic transversality for unbranched covers of closed pseudoholomorphic curvesJul 02 2014Dec 12 2014We prove that in closed almost complex manifolds of any dimension, generic perturbations of the almost complex structure suffice to achieve transversality for all unbranched multiple covers of simple pseudoholomorphic curves with deformation index zero. ... More

Generic transversality for unbranched covers of closed pseudoholomorphic curvesJul 02 2014Nov 03 2016We prove that in closed almost complex manifolds of any dimension, generic perturbations of the almost complex structure suffice to achieve transversality for all unbranched multiple covers of simple pseudoholomorphic curves with deformation index zero. ... More

On the functor l^2Dec 21 2010Jul 29 2015We study the functor l^2 from the category of partial injections to the category of Hilbert spaces. The former category is finitely accessible, and in both categories homsets are algebraic domains. The functor preserves daggers, monoidal structures, enrichment, ... More

Complementarity in categorical quantum mechanicsSep 10 2010Mar 01 2016We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger ... More

Evidence for a hard equation of state in the cores of neutron starsDec 19 2008The equation of state for matter with energy density above 2 x10^14 g/cm^3 is parametrized by P = kN^Gamma, where N is the number density, Gamma is the adiabatic index, and k a constant. Using this scheme to generate thousands of models, together with ... More

Observational characteristics of accretion onto black holesAug 13 2010These notes resulted from a series of lectures at the IAC winter school. They are designed to help students, especially those just starting in subject, to get hold of the fundamental tools used to study accretion powered sources. As such, the references ... More

The origin of the soft excess in high L/L_Edd AGNMar 16 2007We discuss the origin of the soft X-ray excess seen in AGN. There are clear advantages to models where this arises from atomic processes in partially ionised material rather than where it is a true continuum component. However, current data cannot distinguish ... More

A short note on Simulation and AbstractionSep 20 2013This short note is written in celebration of David Schmidt's sixtieth birthday. He has now been active in the program analysis research community for over thirty years and we have enjoyed many interactions with him. His work on characterising simulations ... More

Implementation of classical communication in a quantum worldJun 19 2012Dec 18 2012Observations of quantum systems carried out by finite observers who subsequently communicate their results using classical data structures can be described as "local operations, classical communication" (LOCC) observations. The implementation of LOCC ... More

Consistent quantum mechanics admits no mereotopologyMay 13 2012Dec 09 2012It is standardly assumed in discussions of quantum theory that physical systems can be regarded as having well-defined Hilbert spaces. It is shown here that a Hilbert space can be consistently partitioned only if its components are assumed not to interact. ... More

If physics is an information science, what is an observer?Aug 24 2011Feb 11 2012Interpretations of quantum theory have traditionally assumed a "Galilean" observer, a bare "point of view" implemented physically by a quantum system. This paper investigates the consequences of replacing such an informationally-impoverished observer ... More

Autonomy all the way down: Systems and dynamics in quantum BayesianismAug 09 2011Apr 07 2012Quantum Bayesianism ("QBism") has been put forward as an approach to quantum theory that avoids foundational problems by altogether disavowing the objective existence of quantum states. It is shown that QBism suffers its own versions of the familiar foundational ... More

On the Ollivier-Poulin-Zurek definition of objectivityFeb 14 2011Jun 25 2013The Ollivier-Poulin-Zurek definition of objectivity provides a philosophical basis for the environment as witness formulation of decoherence theory and hence for quantum Darwinism. It is shown that no account of the reference of the key terms in this ... More

Information contents and architectural requirements of observer "ready" statesAug 09 2009Mar 05 2011A functional analysis of the task of observing multiple macroscopic quantum systems over an extended period of time and then reporting the accumulated results is used to investigate the information that must be encoded in the "ready" state |O^r> of any ... More

A sharp bilinear estimate for the Klein-Gordon equation in arbitrary space-time dimensionsFeb 21 2013We prove a sharp bilinear inequality for the Klein-Gordon equation on $\sr^{d+1}$, for any $d \geq 2$. This extends work of Ozawa-Rogers and Quilodr\'an for the Klein-Gordon equation and generalises work of Bez-Rogers for the wave equation. As a consequence ... More

Particle Physics: Themes and ChallengesNov 28 1995Opening Lecture at the Second Rencontres du Vietnam, October 21-28, 1995.

Ramification of Compatible Systems on Curves and Independence of $\ell$Jun 12 2014Oct 02 2014We show that certain ramification invariants associated to a compatible system of $\ell$-adic sheaves on a curve are independent of $\ell$.

Coupled one-dimensional dynamical systemsJan 19 2012This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of self-mappings of the ... More

Some Notes on Standard Borel and Related SpacesSep 18 2008These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

Quantum convolution and quantum correlation algorithms are physically impossibleSep 08 2003Dec 03 2003The key step in classical convolution and correlation algorithms, the componentwise multiplication of vectors after initial Fourier Transforms, is shown to be physically impossible to do on quantum states. Then this is used to show that computing the ... More

A new form of the Kerr solutionOct 27 1999Jan 31 2000A new form of the Kerr solution is presented. The solution involves a time coordinate which represents the local proper time for free-falling observers on a set of simple trajectories. Many physical phenomena are particularly clear when related to this ... More

Periodic GraphsJun 12 2008Oct 15 2010Let $X$ be a graph on $n$ vertices with with adjacency matrix $A$ and let $H(t)$ denote the matrix-valued function $\exp(iAt)$. If $u$ and $v$ are distinct vertices in $X$, we say perfect state transfer}from $u$ to $v$ occurs if there is a time $\tau$ ... More

Locally Cartesian Closed Quasicategories from Type TheoryJul 09 2015We prove that the quasicategories arising from models of Martin-L\"of type theory via simplicial localization are locally cartesian closed.

Business Models for e-Health: Evidence from Ten Case StudiesJul 02 2015An increasingly aging population and spiraling healthcare costs have made the search for financially viable healthcare models an imperative of this century. The careful and creative application of information technology can play a significant role in ... More

Probing Light Dark Matter via Evaporation from the SunJun 13 2015Dark matter particles can be captured by the sun with rates that depend on the dark matter mass and the DM-nucleon cross section. However, for masses below $\sim 3.3$ GeV, the captured dark matter particles evaporate, leading to an equilibrium where the ... More

Recent Results from (Full) Lattice QCDMay 04 2000An overview of the Lattice technique for studies of the strong interaction is given. Recent results from the UKQCD lattice collaboration are presented. These concentrate on spectral quantities calculated using full (i.e. unquenched) QCD. A comparison ... More

Quantum Darwinism requires an extra-theoretical assumption of encoding redundancyMar 26 2010May 30 2010Observers restricted to the observation of pointer states of apparatus cannot conclusively demonstrate that the pointer of an apparatus A registers the state of a system of interest S without perturbing S. Observers cannot, therefore, conclusively demonstrate ... More

Decompositional equivalenceApr 12 2010Apr 21 2010Both classical and quantum mechanics assume that physical laws are invariant under changes in the way that the world is labeled. This Principle of Decompositional Equivalence is formalized, and shown to forbid finite experimental demonstrations that given ... More

Three consequences of decompositional consistencyJun 12 2009Decompositions of the world into systems have typically been regarded as arbitrary extra-theoretical assumptions in discussions of quantum measurement. One can instead regard decompositions as part of the theory, and ask what conditions they must satisfy ... More

A Brief Summary of the Group-Variation EquationsApr 29 2001A brief summary is given of the Group-Variation Equations and the island diagram confinement mechanism, with an explanation of the prediction that the cylinder-topology minimal-area spanning surface term in the correlation function of two Wilson loops ... More

Eigenvalues of the static, spherically-symmetric Einstein-Proca equationsSep 20 2016The Proca potential has been used in many contexts in flat spacetime, but not so often in curved spacetime. Here, the static Proca potentials are derived on a Schwarzschild background, and are found to have very different forms from those in flat space. ... More

Roulettes: A weak lensing formalism for strong lensing - I. OverviewMar 15 2016Jul 26 2016We present a new perspective on gravitational lensing. We describe a new extension of the weak lensing formalism capable of describing strongly lensed images. By integrating the non-linear geodesic deviation equation, the amplification matrix of weak ... More

Cosmological Perturbation Theory as a Tool for Estimating Box-Scale Effects in N-body SimulationsDec 17 2013Jun 16 2014In performing cosmological N-body simulations, it is widely appreciated that the growth of structure on the largest scales within a simulation box will be inhibited by the finite size of the simulation volume. Following ideas set forth in Seto (1999), ... More

Localised Solutions of the Maxwell-Dirac EquationsOct 11 1995The full ``classical" Dirac-Maxwell equations are considered under various simplifying assumptions. A reduction of the equations is performed in the case when the Dirac field is {\em static} and a further reduction is performed in the case of {\em spherical ... More

Power spectrum modelling of galaxy and radio intensity maps including observational effectsFeb 20 2019Fluctuations in the large-scale structure of the Universe contain significant information about cosmological physics, but are modulated in survey datasets by various observational effects. Building on existing literature, we provide a general treatment ... More

Glueballs, hybrid and exotic mesons and string breakingSep 11 2000We review lattice QCD results for glueballs (including a discussion of mixing with scalar mesons), hybrid mesons and exotic mesons (such as $B_s B_s$ molecules). We also discuss string breaking as a mixing between colour flux states and $B \bar{B}$ states. ... More

Hadronic decays from the latticeSep 06 2006I review the lattice QCD approach to determining hadronic decay transitions. Examples considered include rho to pi pi; b_1 to pi omega; hybrid meson decays and scalar meson decays. I discuss what lattices can provide to help understand the composition ... More

Smooth Volume Rigidity for Manifolds with Negatively Curved TargetsOct 04 2007We establish conditions for a continuous map of nonzero degree between a smooth closed manifold and a negatively curved manifold of dimension greater than four to be homotopic to a smooth cover, and in particular a diffeomorphism when the degree is one. ... More

Decoherence as a sequence of entanglement swapsFeb 02 2019Standard semi-classical models of decoherence do not take explicit account of the classical information required to specify the system - environment boundary. I show that this information can be represented as a finite set of reference eigenvalues that ... More

Lifestyle Tradeoffs and the Decline of Societal Well-being: An Agent-based ModelJul 20 2015Jan 01 2016This paper presents a semi-quantitative mathematical model of the changes over time in the statistical distribution of well-being of individuals in a society. The model predicts that when individuals overvalue the more socially conspicuous aspects of ... More

Colloquium: A Century of Noether's TheoremFeb 06 2019In the summer of 1918, Emmy Noether published the theorem that now bears her name, establishing a profound two-way connection between symmetries and conservation laws. The influence of this insight is pervasive in physics; it underlies all of our theories ... More

On the functor l^2Dec 21 2010Sep 18 2018We study the functor l^2 from the category of partial injections to the category of Hilbert spaces. The former category is finitely accessible, and its homsets are algebraic domains; the latter category has conditionally algebraic domains for homsets. ... More

Lectures on Symplectic Field TheoryDec 03 2016Dec 08 2016This is the preliminary manuscript of a book on symplectic field theory based on a lecture course for PhD students given in 2015-16. It covers the essentials of the analytical theory of punctured pseudoholomorphic curves, taking the opportunity to fill ... More

Multi-scale Renormalisation Group Improvement of the Effective PotentialApr 14 1994Oct 12 1994Using the renormalisation group and a conjecture concerning the perturbation series for the effective potential, the leading logarithms in the effective potential are exactly summed for $O(N)$ scalar and Yukawa theories.

A description of the Parry-Sullivan number of a graph using circuitsMar 11 2009In this short note, we give a description of the Parry-Sullivan number of a graph in terms of the cycles in the graph. This tool is occasionally useful in reasoning about the Parry-Sullivan numbers of graphs.

Rigidity of Spreadings and Fields of DefinitionApr 11 2017Varieties without deformations are defined over a number field. Several old and new examples of this phenomenon are discussed such as Bely\u \i\ curves and Shimura varieties. Rigidity is related to maximal Higgs fields which come from variations of Hodge ... More

On finite congruence-simple semiringsMay 08 2002Aug 19 2003In this paper, we describe finite, additively commutative, congruence simple semirings. The main result is that the only such semirings are those of order 2, zero-multiplication rings of prime order, matrix rings over finite fields, those that are additively ... More

Transversality and super-rigidity for multiply covered holomorphic curvesSep 30 2016Aug 14 2018We develop new techniques to study regularity questions for moduli spaces of pseudoholomorphic curves that are multiply covered. Among the main results, we show that unbranched multiple covers of closed holomorphic curves are generically regular, and ... More

Distinguishing Primitive Permutation GroupsJun 12 2008Nov 04 2009Let $G$ be a permutation group acting on a set $V$. A partition $\pi$ of $V$ is distinguishing if the only element of $G$ that fixes each cell of $\pi$ is the identity. The distinguishing number of $G$ is the minimum number of cells in a distinguishing ... More

Random planar graphs with bounds on the maximum and minimum degreesJan 27 2011Let P_{n,d,D} denote the graph taken uniformly at random from the set of all labelled planar graphs on {1,2,...,n} with minimum degree at least d(n) and maximum degree at most D(n). We use counting arguments to investigate the probability that P_{n,d,D} ... More

Lifting non-ordinary cohomology classes for SL(3)Feb 19 2016Jul 27 2017In this paper, we present a generalisation of a theorem of David and Rob Pollack. In 'A construction of rigid analytic cohomology classes for congruence subgroups of SL(3,Z)', they give a very general argument for lifting ordinary eigenclasses (with respect ... More

C*-algebras from actions of congruence monoids on rings of algebraic integersJan 13 2019Let $K$ be a number field with ring of integers $R$. Given a modulus $\mathfrak{m}$ for $K$ and a group $\Gamma$ of residues modulo $\mathfrak{m}$, we consider the semi-direct product $R\rtimes R_{\mathfrak{m},\Gamma}$ obtained by restricting the multiplicative ... More

Reversible Markov chains: variational representations and orderingSep 06 2018This pedagogical document explains three variational representations that are useful when comparing the efficiencies of reversible Markov chains: (i) the Dirichlet form and the associated variational representations of the spectral gaps; (ii) a variational ... More

Crystal rules for $(\ell,0)$-JM partitionsJul 19 2011Vazirani and the author \cite{BV} gave a new interpretation of what we called $\ell$-partitions, also known as $(\ell,0)$-Carter partitions. The primary interpretation of such a partition $\lambda$ is that it corresponds to a Specht module $S^{\lambda}$ ... More

Identities for hyperelliptic P-functions of genus one, two and three in covariant formAug 22 2008We give a covariant treatment of the quadratic differential identities satisfied by the P-functions on the Jacobian of smooth hyperelliptic curves of genera 1, 2 and 3.

Locally Cartesian Closed Quasicategories from Type TheoryJul 09 2015Sep 17 2017We prove that the quasicategories arising from models of Martin-L\"of type theory via simplicial localization are locally cartesian closed.

Statistical testing of shared genetic control for potentially related traitsJan 23 2013Apr 30 2013Integration of data from genome-wide single nucleotide polymorphism (SNP) association studies of different traits should allow researchers to disentangle the genetics of potentially related traits within individually associated regions. Formal statistical ... More

The Density Variance Mach Number Relation in the Taurus Molecular CloudFeb 05 2010Supersonic turbulence in molecular clouds is a key agent in generating density enhancements that may subsequently go on to form stars. The stronger the turbulence - the higher the Mach number - the more extreme the density fluctuations are expected to ... More

Learning and Complexity in Genetic Auto-Adaptive SystemsJan 27 1994We describe and investigate the learning capablities displayed by a population of self-replicating segments of computer-code subject to random mutation: the tierra environment. We find that learning is achieved through phase transitions that adapt the ... More

Semisymmetric cubic graphs of twice odd orderAug 09 2004The groups which can act semisymmetrically on a cubic graph of twice odd order are determined modulo a normal subgroup which acts semiregularly on the vertices of the graph.

Leptophobic U(1)'s and R_b, R_c at LEPJun 20 1996In the context of explaining the experimental deviations in R_b and R_c from their Standard Model predictions, a new type of U(1) interaction is proposed which couples only to quarks. Special attention will be paid to the supersymmetric \eta-model coming ... More

Stable counteralignment of a circumbinary discApr 18 2012In general, when gas accretes on to a supermassive black hole binary it is likely to have no prior knowledge of the binary angular momentum. Therefore a circumbinary disc forms with a random inclination angle, theta, to the binary. It is known that for ... More

Decompositional equivalence: A fundamental symmetry underlying quantum theoryFeb 26 2014Apr 28 2016Decompositional equivalence is the principle that there is no preferred decomposition of the universe into subsystems. It is shown here, by using simple thought experiments, that quantum theory follows from decompositional equivalence together with Landauer's ... More

Finite Sets and CountingAug 31 2008Jun 19 2010We start by presenting a theory of finite sets using the approach which is essentially that taken by Whitehead and Russell in Principia Mathematica}, and which does not involve the natural numbers (or any other infinite set). This theory is then applied ... More

Robust String Matching in O(\sqrt{N}+M) Quantum QueriesNov 07 2003Aug 10 2004This paper was withdrawn by the author due to a fatal error.

Quantum Circuit IdentitiesJul 16 2003There are quantum circuit identities that simplify quantum circuits, reducing the effort needed physically to implement them. This paper constructs all identities made from 3 or fewer operations taken from a common set of one qubit operations, and explains ... More

The Hidden Subgroup Problem - Review and Open ProblemsNov 04 2004An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it easier to absorb ... More

Yet More Projective Curves Over F2May 31 2001All binary plane curves of degree less than 7 are examined for curves with a large number of Fq rational points on their smooth model, for q = 2^m ; m = 3, 4,...,11. Previous results are improved, and many new curves are found meeting or close to Serre's, ... More

Average mixing of continuous quantum walksMar 14 2011Oct 01 2011If $X$ is a graph with adjacency matrix $A$, then we define $H(t)$ to be the operator $\exp(itA)$. The Schur (or entrywise) product $H(t)\circ H(-t)$ is a doubly stochastic matrix and, because of work related to quantum computing, we are concerned the ... More

Particle Physics after the Higgs-Boson Discovery: Opportunities for the Large Hadron ColliderJul 10 2015Aug 26 2015The first run of the Large Hadron Collider at CERN brought the discovery of the Higgs boson, an apparently elementary scalar particle with a mass of 125 GeV, the avatar of the mechanism that hides the electroweak symmetry. A new round of experimentation ... More

Building the Observer into the System: Toward a Realistic Description of Human Interaction with the WorldNov 13 2014Nov 10 2016Human beings do not observe the world from the outside, but rather are fully embedded in it. The sciences, however, often give the observer both a "god's eye" perspective and substantial a~priori knowledge. Motivated by W. Ross Ashby's statement, "the ... More

The general theory of secondary weak gravitational lensingMar 30 2015Weak gravitational lensing is normally assumed to have only two principle effects: a magnification of a source and a distortion of the sources shape in the form of a shear. However, further distortions are actually present owing to changes in the gravitational ... More

The many classical faces of quantum structuresDec 05 2014Mar 25 2015Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey this programme ... More

d = 11 Supergravity on almost flat R^4 times a compact hyperbolic 7-manifold, and the dip and bump seen in ATLAS-CONF-2010-088Mar 14 2011Jul 11 2011Rough estimates are presented to show that the bump at 1.7 to 1.9 TeV seen in ATLAS-CONF-2010-088 could arise from about 10^{30} approximately degenerate Kaluza-Klein states of the d = 11 supergravity multiplet in the s channel, that could arise from ... More

Natural TeV-Scale Gravity and coupling constant unification, in Heterotic M-Theory, with the usual hidden and visible sectors swappedJan 15 2002I consider a class of Grand Unified models, in which E8 is broken to SU(3)xSU(2)xSU(2)xSU(2)xU(1)_Y, then to SU(3)xSU(2)_{diag}xU(1)_Y. The breaking of (SU(2))^3 to SU(2)_{diag} reduces the SU(2) coupling constant, at unification, by a factor of 1/\sqrt{3}, ... More

Lattice QCD with Dynamical Quarks from the UKQCD CollaborationMar 05 2002A brief overview of the lattice technique of studying QCD is presented. Recent results from the UKQCD Collaboration's simulations with dynamical quarks are then presented. In this work, the calculations are all at a fixed lattice spacing and volume, but ... More

Searching for dynamical fermion effects in UKQCD simulationsNov 08 2001We present recent results from the UKQCD collaboration's dynamical QCD simulations. This data has fixed lattice spacing but varying dynamical quark mass. We concentrate on searching for an unquenching signal in the mesonic mass spectrum where we do not ... More

What can the outskirts of galaxies tell us about dark matter?Aug 17 2016Deep observations of galaxy outskirts reveal faint extended stellar components (ESCs) of streams, shells, and halos, which are ghostly remnants of the tidal disruption of satellite galaxies. We use cosmological galaxy formation simulations in Cold Dark ... More

Roulettes: A weak lensing formalism for strong lensing - II. Derivation and analysisMar 15 2016Nov 14 2016We present a new extension of the weak lensing formalism capable of describing strongly lensed images. This paper accompanies Paper I, arXiv:1603.04698 where we provided a condensed overview of the approach and illustrated how it works. Here we give all ... More

Electromagnetic Energy Momentum Tensor in a Spatially Dispersive MediumFeb 24 2016We derive a generalized Minkowski Energy Momentum Tensor for a monochromatic wave in a lossless medium exhibiting temporal and spatial dispersion. The Energy Momentum Tensor is then related to familiar expressions for energy density and energy flux, as ... More

$P$-adic $L$-functions of Bianchi modular formsApr 08 2014Jan 22 2015The theory of overconvergent modular symbols, developed by Rob Pollack and Glenn Stevens, gives a beautiful and effective construction of the $p$-adic $L$-function of a modular form. In this paper, we give an analogue of their results for Bianchi modular ... More

Gauged Floer theory of toric moment fibersApr 16 2010Mar 26 2015We investigate the small area limit of the gauged Lagrangian Floer cohomology of Frauenfelder. The resulting cohomology theory, which we call quasimap Floer cohomology, is an obstruction to displaceability of Lagrangians in the symplectic quotient. We ... More

Multiplicity-free Hamiltonian actions need not be KählerJun 22 1995We show that Tolman's example (of a six dimensional Hamiltonian $T^2$-space with isolated fixed points and no compatible K\"{a}hler structure) can be constructed from the flag variety $U(3)/U(1)^3$ by $U(2)$-equivariant symplectic surgery. This implies ... More

Transversality and super-rigidity for multiply covered holomorphic curvesSep 30 2016We develop new techniques to study regularity questions for moduli spaces of pseudoholomorphic curves that are multiply covered. Among the main results, we show that unbranched multiple covers of closed holomorphic curves are generically regular, and ... More

Positivity of Intersection Multiplicity Over a Two-Dimensional BaseOct 17 2015We show that Serre's Intersection Multiplicity Conjecture holds for a formal power series ring A over a complete, two-dimensional regular local ring R. From this, we deduce the corresponding result for the local rings of any scheme X which is a smooth ... More

Inequalities for semi-stable surface fibrations, and strictly maximal Higgs fieldsMay 18 2014I give a simplified proof of one of the main results in the recent preprint arXiv:1311.5858 by X. Luo and K. Zuo

Hadron Spectroscopy from the LatticeOct 28 1997Lattice QCD determinations appropriate to hadron spectroscopy are reviewed with emphasis on the glueball and hybrid meson states in the quenched approximation. Hybrids are discussed for heavy and for light quarks. The effects of sea quarks (unquenching) ... More

The QCD SpectrumDec 05 1994Recent results in light hadron spectroscopy are reviewed. Attention is given to the requirements of precision determinations in lattice gauge theory. Different methods for extracting the running coupling constant $\alpha_S$ are compared. Some recent results ... More

The Running Coupling from Lattice Gauge TheoryMay 14 1992From an accurate determination of the inter-quark potential, one can study the running coupling constant for a range of $R$-values and hence estimate the scale $\Lambda_{\msbar} $. Detailed results are presented for $SU(2)$ pure gauge theory to illustrate ... More

Abelian Duality for Generalised Maxwell TheoriesFeb 04 2014We describe a construction of generalised Maxwell theories -- higher analogues of abelian gauge theories -- in the factorisation algebra formalism of Costello and Gwilliam, allowing for analysis of the structure of local observables. We describe the phenomenon ... More

Bell's Theorem from Moore's TheoremJan 18 2012Dec 06 2012It is shown that the restrictions of what can be inferred from classically-recorded observational outcomes that are imposed by the no-cloning theorem, the Kochen-Specker theorem and Bell's theorem also follow from restrictions on inferences from observations ... More

A model-theoretic interpretation of environmentally-induced superselectionFeb 05 2012May 13 2012Environmentally-induced superselection or "einselection" has been proposed as an observer-independent mechanism by which apparently classical systems "emerge" from physical interactions between degrees of freedom described completely quantum-mechanically. ... More

Tracking eigenvalues to the frontier of moduli space I: Convergence and spectral accumulationFeb 28 2001May 23 2001We study the limiting behavior of eigenfunctions/eigenvalues of the Laplacian of a family of Riemannian metrics that degenerates on a hypersurface. Our results generalize earlier work concerning the degeneration of hyperbolic surfaces.

Strongly Fillable Contact Manifolds and J-holomorphic FoliationsJun 19 2008Jul 17 2009We prove that every strong symplectic filling of a planar contact manifold admits a symplectic Lefschetz fibration over the disk, and every strong filling of the 3-torus similarly admits a Lefschetz fibration over the annulus. It follows that strongly ... More