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A Framework for Adaptive MCMC Targeting Multimodal DistributionsDec 06 2018Jan 11 2019We propose a new Monte Carlo method for sampling from multimodal distributions. The idea of this technique is based on splitting the task into two: finding the modes of a target distribution $\pi$ and sampling, given the knowledge of the locations of ... More

Generalized Bayesian Updating and the Loss-Likelihood BootstrapSep 22 2017In this paper, we revisit the weighted likelihood bootstrap and show that it is well-motivated for Bayesian inference under misspecified models. We extend the underlying idea to a wider family of inferential problems. This allows us to calibrate an analogue ... More

Population-Based Reversible Jump Markov Chain Monte CarloNov 01 2007In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target measures. In such ... More

A Bayesian nonparametric approach to testing for dependence between random variablesJun 02 2015May 12 2016Nonparametric and nonlinear measures of statistical dependence between pairs of random variables are important tools in modern data analysis. In particular the emergence of large data sets can now support the relaxation of linearity assumptions implicit ... More

Approximate Models and Robust DecisionsFeb 25 2014Mar 06 2015Decisions based partly or solely on predictions from probabilistic models may be sensitive to model misspecification. Statisticians are taught from an early stage that "all models are wrong", but little formal guidance exists on how to assess the impact ... More

A Néron model of the universal jacobianDec 06 2014Sep 07 2015The jacobian of the universal curve over $\mathcal{M}_{g,n}$ is an abelian scheme over $\mathcal{M}_{g,n}$. Our main result is the construction of an algebraic space $\beta\colon \tilde{\mathcal{M}}_{g,n} \rightarrow \bar{\mathcal{M}}_{g,n}$ over which ... More

Computing Néron-Tate heights of points on hyperelliptic JacobiansApr 26 2010Jun 03 2011It was shown by Faltings and Hriljac that the N\'eron-Tate height of a point on the Jacobian of a curve can be expressed as the self-intersection of a corresponding divisor on a regular model of the curve. We make this explicit and use it to give an algorithm ... More

An Arakelov-Theoretic Approach to Naïve Heights on Hyperelliptic JacobiansJul 25 2012Oct 28 2014We use Arakelov theory to define a height on divisors of degree zero on a hyperelliptic curve over a global field, and show that this height has computably bounded difference from the N\'eron-Tate height of the corresponding point on the Jacobian. We ... More

On the diameter of dual graphs of Stanley-Reisner rings with Serre $(S_2)$ property and Hirsch type bounds on abstractions of polytopesNov 22 2016Dec 07 2017Let $R$ be a Noetherian commutative ring of positive dimension. The Hochster-Huneke graph of $R$ (sometimes called the dual graph of Spec $R$ and denoted by $\mathcal{G} (R)$) is defined as follows: the vertices are the minimal prime ideals of $R$, and ... More

Characterising variation of nonparametric random probability measures using the Kullback-Leibler divergenceNov 24 2014This work studies the variation in Kullback-Leibler divergence between random draws from some popular nonparametric processes and their baseline measure. In particular we focus on the Dirichlet process, the P\'olya tree and the frequentist and Bayesian ... More

On Markov chain Monte Carlo methods for tall dataMay 11 2015Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also known as tall ... More

A General Framework for Updating Belief DistributionsJun 27 2013Jan 28 2016We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood ... More

Scalable Nonparametric Sampling from Multimodal Posteriors with the Posterior BootstrapFeb 08 2019Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior modes. Further, ... More

Scalable Bayesian nonparametric regression via a Plackett-Luce model for conditional ranksJun 24 2015We present a novel Bayesian nonparametric regression model for covariates X and continuous, real response variable Y. The model is parametrized in terms of marginal distributions for Y and X and a regression function which tunes the stochastic ordering ... More

Supervised variable selection in randomised controlled trials prior to exploration of treatment effect heterogeneity: an example from severe malariaJan 11 2019Exploration of treatment effect heterogeneity (TEH) is an increasingly important aspect of modern statistical analysis for stratified medicine in randomised controlled trials (RCTs) as we start to gather more information on trial participants and wish ... More

Multiscale Blind Source SeparationAug 25 2016We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an $\epsilon$-neighborhood of ... More

A review of homomorphic encryption and software tools for encrypted statistical machine learningAug 26 2015Recent advances in cryptography promise to enable secure statistical computation on encrypted data, whereby a limited set of operations can be carried out without the need to first decrypt. We review these homomorphic encryption schemes in a manner accessible ... More

Encrypted statistical machine learning: new privacy preserving methodsAug 27 2015We present two new statistical machine learning methods designed to learn on fully homomorphic encrypted (FHE) data. The introduction of FHE schemes following Gentry (2009) opens up the prospect of privacy preserving statistical machine learning analysis ... More

Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process MixturesApr 27 2016In this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying distributions. A key ... More

Bayesian Sparsity-Path-Analysis of Genetic Association Signal using Generalized t PriorsJun 01 2011We explore the use of generalized t priors on regression coefficients to help understand the nature of association signal within "hit regions" of genome-wide association studies. The particular generalized t distribution we adopt is a Student distribution ... More

Biased random walk on the trace of biased random walk on the trace of...Jan 15 2019We study the behaviour of a sequence of biased random walks X(i), i>=0 on a sequence of random graphs, where the initial graph is Zd and otherwise the graph for the i-th walk is the trace of the (i - 1)-st walk. The sequence of bias vectors is chosen ... More

Relating land use and human intra-city mobilityMay 27 2015Sep 20 2015Understanding human mobility patterns -- how people move in their everyday lives -- is an interdisciplinary research field. It is a question with roots back to the 19th century that has been dramatically revitalized with the recent increase in data availability. ... More

A Hierarchical Bayesian Framework for Constructing Sparsity-inducing PriorsSep 09 2010Sep 16 2010Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant. In this context, ... More

A System of Dependent Types, with an Implementation and a PhilosophyJul 06 2016This is my working paper on a proposed logical framework for the practice of mathematics, which is paralleled by philosophical considerations and a computer implementation (a variant of Automath).

Spin and Valence-Fluctuation Mediated Superconductivity in Pressurized Fe and CeCu2(Si/Ge)2Oct 06 2004We review the evidence supporting valence-fluctuation mediated superconductivity in CeCu2Si2 and CeCu2Ge2, where Tc reaches 2.4 K at high pressure. In these systems the valence and magnetic critical points, at p_V and p_c respectively, are well separated. ... More

Free energy of singular sticky-sphere clustersMay 27 2016Aug 16 2016Networks of particles connected by springs model many condensed-matter systems, from colloids interacting with a short-range potential, to complex fluids near jamming, to self-assembled lattices, to origami-inspired materials. Under small thermal fluctuations ... 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

Two-sample Bayesian Nonparametric Hypothesis TestingOct 27 2009May 11 2015In this article we describe Bayesian nonparametric procedures for two-sample hypothesis testing. Namely, given two sets of samples $\mathbf{y}^{\scriptscriptstyle(1)}\;$\stackrel{\scriptscriptstyle{iid}}{\s im}$\;F^{\scriptscriptstyle(1)}$ and $\mathbf{y}^{\scriptscriptstyle(2 ... More

Interval graph limitsFeb 14 2011We work out the graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function $W(x,y)$ on the unit square, with $x$ and $y$ uniform on the interval $(0,1)$. Instead, we fix ... More

Gait transitions in a phase oscillator model of an insect central pattern generatorApr 19 2017Aug 21 2017Legged locomotion involves various gaits. It has been observed that fast running insects (cockroaches) employ a tripod gait with three legs lifted off the ground simultaneously in swing, while slow walking insects (stick insects) use a tetrapod gait with ... More

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

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

Compactness for Embedded Pseudoholomorphic Curves in 3-manifoldsMar 17 2007Mar 07 2008We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection theory to show ... 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

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

An open image theorem for a general class of abelian varietiesMar 11 2008Let K be a number field and A/K be a polarized abelian variety with absolutely trivial endomorphism ring. We show that if the Neron model of A/K has at least one fiber with potential toric dimension one, then for almost all rational primes ell, the Galois ... 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

Error Correcting Codes on Algebraic SurfacesSep 07 2003Error correcting codes are defined and important parameters for a code are explained. Parameters of new codes constructed on algebraic surfaces are studied. In particular, codes resulting from blowing up points in $\proj^2$ are briefly studied, then codes ... 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

A GKM Description of the Equivariant Coinvariant Ring of a Pseudo Reflection GroupSep 03 2016We identify the equivariant coinvariant ring of a pseudo-reflection group with its image under the localization map. We then show that this image can be realized as the equivariant cohomology of a sort linear hypergraph, analogous to a GKM 1-skeleton. ... 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

Contact Hypersurfaces in Uniruled Symplectic Manifolds Always SeparateFeb 21 2012Dec 21 2013We observe that nonzero Gromov-Witten invariants with marked point constraints in a closed symplectic manifold imply restrictions on the homology classes that can be represented by contact hypersurfaces. As a special case, contact hypersurfaces must always ... 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

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

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 $\ell$.

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.

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

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

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

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

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

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

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

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

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

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

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

Model Building with Multiple Dependent Variables and ConstraintsSep 04 2011The most widely used method for finding relationships between several quantities is multiple regression. This however is restricted to a single dependent variable. We present a more general method which allows models to be constructed with multiple variables ... More

Talbot Workshop 2010 Talk 2: K-Theory and Index TheoryOct 24 2010These are notes from a talk at the 2010 Talbot Workshop on Twisted K-theory and Loop Groups. This particular talk is an overview of index theory from the point of view of topological K-theory. Assuming little background in analysis, but some familiarity ... More

Hilbert-space factorization is a limited and expensive information-processing resourceJan 20 2014Feb 05 2014By taking the need for quantum reference frames into account, it is shown that Hilbert-space factorization is a dissipative process requiring on the order of kT to reduce by one bit an observer's uncertainty in the provenance of a classically-recorded ... More

Quantum mechanics from five physical assumptionsFeb 03 2011Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions concern fundamental ... More

Classical system boundaries cannot be determined within quantum DarwinismAug 02 2010May 19 2011Multiple observers who interact with environmental encodings of the states of a macroscopic quantum system S as required by quantum Darwinism cannot demonstrate that they are jointly observing S without a joint a priori assumption of a classical boundary ... More

Morse Theory on 1-SkeletaJun 05 2014Guillemin and Zara gave necessary and sufficient conditions under which Morse theoretic techniques could be used to construct an additive basis for the equivariant cohomology of a 1-skeleton that is either 3-independent or GKM. We show that their conditions ... More

The Kaon B-parameter from Two-Flavour Dynamical Domain Wall FermionsOct 26 2004We report on the calculation of the kaon B-parameter using two dynamical flavours of domain wall fermions. Our analysis is based on three ensembles of configurations, each consisting of about 5,000 HMC trajectories, with a lattice spacing of approximately ... More

Beaming models and the correlations between the core dominance parameter and the core and extended powers of quasarsAug 20 1998We investigate the recent claim by Qin et al. that the observed correlations (or lack thereof) between the core dominance parameter and the core and extended powers of samples of lobe- and core-dominated quasars is in contradiction with beaming models. ... More

On the equivariant algebraic Jacobian for curves of genus twoNov 11 2011We present a treatment of the algebraic description of the Jacobian of a generic genus two plane curve which exploits an SL2(k) equivariance and clarifes the structure of E.V.Flynn's 72 defining quadratic relations. The treatment is also applied to the ... More