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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

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

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

Principles of Bayesian Inference using General Divergence CriteriaFeb 26 2018May 17 2018When it is acknowledged that all candidate parameterised statistical models are misspecified relative to the data generating process, the decision maker (DM) must currently concern themselves with inference for the parameter value minimising the KL-divergence ... More

Assigning a value to a power likelihood in a general Bayesian modelJan 30 2017Bayesian approaches to data analysis and machine learning are widespread and popular as they provide intuitive yet rigorous axioms for learning from data; see Bernardo and Smith (2004) and Bishop (2006). However, this rigour comes with a caveat that the ... 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

On the marginal likelihood and cross-validationMay 21 2019In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using cross-validation ... More

The norm of the saturation of a binomial ideal, and applications to Markov basesJul 24 2019Given a pure binomial ideal I in variables x_i, we define a new measure of the complexity of the saturation of I with respect to the product of the variables x_i, which we call the norm. We give a bound on the norm in terms of easily-computed invariants ... 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

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

Multiscale Blind Source SeparationAug 25 2016Aug 30 2017We 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 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

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

Remembering the Tevatron: The Machine(s)Sep 13 2011For 25 years the Tevatron proton-antiproton collider was the highest energy collider in the world. This presentation will trace the origins of the Tevatron, the challenges that were overcome in creating high luminosity collisions of protons and antiprotons, ... More

An Inversion Formula for the Gaussian Radon Transform for Banach SpacesAug 06 2013We provide a disintegration theorem for the Gaussian Radon transform Gf on Banach spaces and use the Segal-Bargmann transform on abstract Wiener spaces to find a procedure to obtain f from its Gaussian Radon transform Gf.

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

Néron models of jacobians over base schemes of dimension greater than 1Feb 04 2014Feb 26 2016We investigate to what extent the theory of N\'eron models of jacobians and of abel-jacobi maps extends to relative curves over base schemes of dimension greater than 1. We give a necessary and sufficient criterion for the existence of a N\'eron model. ... More

TensOrMachine: Probabilistic Boolean Tensor DecompositionMay 11 2018Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate scalable sampling-based ... 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

General Bayesian Updating and the Loss-Likelihood BootstrapSep 22 2017May 22 2018In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian nonparametric ... 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

An Exposition of Götze's Estimation of the Rate of Convergence in the Multivariate Central Limit TheoremMar 22 2010We provide an explanation of the main ideas underlying G\"otze's main result in using Stein's method. We also provide detailed derivations of various intermediate estimates. Curiously, we are led to a different dimensional dependence of the constant than ... More

The Brauer-Manin obstruction on Kummer varieties and ranks of twists of abelian varietiesApr 14 2014Aug 18 2015Let r > 0 be an integer. We present a sufficient condition for an abelian variety A over a number field k to have infinitely many quadratic twists of rank at least r, in terms of density properties of rational points on the Kummer variety Km(A^r) of the ... More

Rank Selection and Depth Conditions for Balanced Simplicial ComplexesFeb 09 2018Feb 22 2019We prove some new rank selection theorems for balanced simplicial complexes. Specifically, we prove that rank selected subcomplexes of balanced simplicial complexes satisfying Serre's condition $(S_{\ell})$ retain $(S_{\ell})$. We also provide a formula ... More

Encrypted accelerated least squares regressionMar 02 2017Information that is stored in an encrypted format is, by definition, usually not amenable to statistical analysis or machine learning methods. In this paper we present detailed analysis of coordinate and accelerated gradient descent algorithms which are ... 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

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

Partial trace of a full symmetrizerMay 24 2018A formula for the partial trace of a full symmetrizer is obtained. The formula is used to provide an inductive proof of the well-known formula for the dimension of a full symmetry class of tensors.

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

Semi-unsupervised Learning of Human Activity using Deep Generative ModelsOct 29 2018Dec 11 2018We introduce 'semi-unsupervised learning', a problem regime related to transfer learning and zero-shot learning where, in the training data, some classes are sparsely labelled and others entirely unlabelled. Models able to learn from training data of ... More

Comment on "Regularizing capacity of metabolic networks"May 28 2007Feb 06 2008In a recent paper, Marr, Muller-Linow and Hutt [Phys. Rev. E 75, 041917 (2007)] investigate an artificial dynamic system on metabolic networks. They find a less complex time evolution of this dynamic system in real networks, compared to networks of reference ... More

Discovery and analysis of biochemical subnetwork hierarchiesSep 23 2003Sep 30 2003The representation of a biochemical network as a graph is the coarsest level of description in cellular biochemistry. By studying the network structure one can draw conclusions on the large scale organisation of the biochemical processes. We describe ... More

Bayesian Boolean Matrix FactorisationFeb 20 2017Feb 25 2017Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a combination ... 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

Disentangling Improves VAEs' Robustness to Adversarial AttacksJun 01 2019This paper is concerned with the robustness of VAEs to adversarial attacks. We highlight that conventional VAEs are brittle under attack but that methods recently introduced for disentanglement such as $\beta$-TCVAE (Chen et al., 2018) improve robustness, ... 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

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

The Gaussian Radon Transform and Machine LearningOct 17 2013Mar 13 2014There has been growing recent interest in probabilistic interpretations of kernel-based methods as well as learning in Banach spaces. The absence of a useful Lebesgue measure on an infinite-dimensional reproducing kernel Hilbert space is a serious obstacle ... 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

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

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).

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

Two Weight Inequalities for Iterated Commutators with Calderón-Zygmund OperatorsSep 12 2015Given a Calder\'on-Zygmund operator $T$, a classic result of Coifman-Rochberg-Weiss relates the norm of the commutator $[b, T]$ with the BMO norm of $b$. We focus on a weighted version of this result, obtained by Bloom and later generalized by Lacey and ... More

A Gaussian Radon Transform for Banach SpacesAug 28 2012Sep 29 2012We develop a Radon transform on Banach spaces using Gaussian measure and prove that if a bounded continuous function on a separable Banach space has zero Gaussian integral over all hyperplanes outside a closed bounded convex set in the Hilbert space corresponding ... More

Asymptotics of the Néron height pairingApr 17 2013Jan 06 2014The aim of this paper is twofold. First, we study the asymptotics of the N\'eron height pairing between degree-zero divisors on a family of degenerating compact Riemann surfaces parametrized by an algebraic curve. We show that if the monodromy is unipotent ... 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

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

Better together? Statistical learning in models made of modulesAug 29 2017In modern applications, statisticians are faced with integrating heterogeneous data modalities relevant for an inference, prediction, or decision problem. In such circumstances, it is convenient to use a graphical model to represent the statistical dependencies, ... More

Machine learning and AI research for Patient Benefit: 20 Critical Questions on Transparency, Replicability, Ethics and EffectivenessDec 21 2018Machine learning (ML), artificial intelligence (AI) and other modern statistical methods are providing new opportunities to operationalize previously untapped and rapidly growing sources of data for patient benefit. Whilst there is a lot of promising ... 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

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

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

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

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

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

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.

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

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

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

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