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Unsupervised self-organised mapping: a versatile empirical tool for object selection, classification and redshift estimation in large surveysSep 30 2011We present an application of unsupervised machine learning - the self-organised map (SOM) - as a tool for visualising, exploring and mining the catalogues of large astronomical surveys. Self-organisation culminates in a low-resolution representation of ... More

Molecular and atomic line surveys of galaxies I: the dense, star-forming phase as a beaconJun 20 2012We predict the space density of molecular gas reservoirs in the Universe, and place a lower limit on the number counts of carbon monoxide (CO), hydrogen cyanide (HCN) molecular and [CII] atomic emission lines in blind redshift surveys in the submillimeter-centimeter ... More

Generative deep fields: arbitrarily sized, random synthetic astronomical images through deep learningApr 23 2019Generative Adversarial Networks (GANs) are a class of artificial neural network that can produce realistic, but artificial, images that resemble those in a training set. In typical GAN architectures these images are small, but a variant known as Spatial-GANs ... More

Molecular and atomic line surveys of galaxies II: unbiased estimates of their star formation modeJun 20 2012Aug 07 2012We make use of our 'minimal' cold interstellar medium (ISM) emission line model that predicts the molecular and atomic line emission per unit dense, star-forming gas mass (Geach & Papadopoulos 2012; Paper I) to examine the utility of key line ratios in ... More

Star formation in galaxies hosting AGN: A flat trend of star-formation rate with X-ray luminosity of galaxies hosting AGN in the SCUBA-2 Cosmology Legacy SurveyApr 16 2019Feedback processes from active galactic nuclei (AGN) are thought to play a crucial role in regulating star formation in massive galaxies. Previous studies using \textit{Herschel} have resulted in conflicting conclusions as to whether star formation is ... More

The Atacama Large Aperture Submillimeter Telescope (AtLAST)Jul 10 2019The sub-mm sky is a unique window for probing the architecture of the Universe and structures within it. From the discovery of dusty sub-mm galaxies, to the ringed nature of protostellar disks, our understanding of the formation, destruction, and evolution ... More

4098 galaxy clusters to z~0.6 in the Sloan Digital Sky Survey equatorial Stripe 82Jan 24 2011We present a catalogue of 4098 photometrically selected galaxy clusters with a median redshift <z> = 0.32 in the 270 square degree 'Stripe 82' region of the Sloan Digital Sky Survey (SDSS), covering the celestial equator in the Southern Galactic Cap (-50 ... More

A unifying evolutionary framework for infrared-selected obscured and unobscured quasar host haloesOct 11 2016Recent measurements of the dark matter halo masses of infrared-selected obscured quasars are in tension --- some indicate that obscured quasars have higher halo mass compared to their unobscured counterparts, while others find no difference. The former ... More

Teaching a machine to see: unsupervised image segmentation and categorisation using growing neural gas and hierarchical clusteringJul 06 2015We present a novel unsupervised learning approach to automatically segment and label images in astronomical surveys. Automation of this procedure will be essential as next-generation surveys enter the petabyte scale: data volumes will exceed the capability ... More

An automatic taxonomy of galaxy morphology using unsupervised machine learningSep 18 2017We present an unsupervised machine learning technique that automatically segments and labels galaxies in astronomical imaging surveys using only pixel data. Distinct from previous unsupervised machine learning approaches used in astronomy we use no pre-selection ... More

The IRX-Beta Dust Attenuation Relation in Cosmological Galaxy Formation SimulationsMay 16 2017We utilise a series of high-resolution cosmological zoom simulations of galaxy formation to investigate the relationship between the ultraviolet (UV) slope, beta, and the ratio of the infrared luminosity to UV luminosity (IRX) in the spectral energy distributions ... More

Star formation at z=1.47 from HiZELS: An Hα+[OII] double-blind studySep 08 2011Oct 10 2011This paper presents the results from the first wide and deep dual narrow-band survey to select H-alpha (Ha) and [OII] line emitters at z=1.47+-0.02 (using matched narrow-band filters in the H and z' bands), exploiting synergies between the UKIRT and Subaru ... More

The Impact of the Dusty Torus on Obscured Quasar Halo Mass MeasurementsApr 22 2016Recent studies have found that obscured quasars cluster more strongly and are thus hosted by dark matter haloes of larger mass than their unobscured counterparts. These results pose a challenge for the simplest unification models, in which obscured objects ... More

Observational constraints on the physical nature of submillimetre source multiplicity: chance projections are commonFeb 01 2018Interferometric observations have demonstrated that a significant fraction of single-dish submillimetre (submm) sources are blends of multiple submm galaxies (SMGs), but the nature of this multiplicity, i.e. whether the galaxies are physically associated ... More

The dependence of star formation activity on environment and stellar mass at z~1 from the HiZELS H-alpha surveyJul 15 2010Sep 14 2010(Abridged) This paper presents an environment and stellar mass study of a large sample of star-forming (SF) galaxies at z=0.84 from the HiZELS survey, over 1.3 deg^2 in the COSMOS and UKIDSS UDS fields. By taking advantage of a truly panoramic coverage, ... More

The merger rates and sizes of galaxies across the peak epoch of star formation from the HiZELS surveyDec 19 2012Jan 09 2013We use the HiZELS narrow-band H-alpha survey in combination with CANDELS, UKIDSS and WIRDS near-infrared imaging, to investigate the morphologies, merger rates and sizes of a sample of H-alpha emitting galaxies in the redshift range z=0.40 - 2.23, an ... More

CO interferometry of gas-rich spiral galaxies in the outskirts of an intermediate redshift clusterFeb 16 2009We present IRAM Plateau de Bure Interferometer 3mm observations of CO(1-0) emission in two 24um-selected starburst galaxies in the outskirts (2-3xR_virial) of the rich cluster Cl0024+16 (z=0.395). The galaxies' inferred far-infrared luminosities place ... More

Herschel-PACS observations of [OI]63um towards submillimetre galaxies at z~1Aug 23 2012We present Herschel-PACS spectroscopy of the [OI]63um far-infrared cooling line from a sample of six unlensed and spectroscopically-confirmed 870um-selected submillimetre (submm) galaxies (SMGs) at 1.1<z<1.6 from the LABOCA Extended Chandra Deep Field ... More

Taking Census of Massive, Star-Forming Galaxies formed <1 Gyr After the Big BangMar 13 2019Two decades of effort have been poured into both single-dish and interferometric millimeter-wave surveys of the sky to infer the volume density of dusty star-forming galaxies (DSFGs, with SFR>100M$_\odot$ yr$^{-1}$) over cosmic time. Though obscured galaxies ... More

The K-band Hubble diagram of sub-mm galaxies and hyperluminous galaxiesOct 22 2003We present the K-band Hubble diagrams (K-z relations) of sub-mm-selected galaxies and hyperluminous galaxies (HLIRGs). We report the discovery of a remarkably tight K-z relation of HLIRGs, indistinguishable from that of the most luminous radiogalaxies. ... More

A submillimetre galaxy at z=4.76 in the LABOCA survey of the Extended Chandra Deep Field SouthFeb 25 2009We report on the identification of the highest redshift submm-selected source currently known: LESSJ033229.4-275619. This source was detected in the Large Apex BOlometer CAmera (LABOCA) Extended Chandra Deep Field South (ECDFS) Submillimetre Survey (LESS), ... More

Evolution of Dust-Obscured Star Formation and Gas to z=2.2 from HiZELSFeb 20 2017We investigate the far-infrared properties of galaxies selected via deep, narrow-band imaging of the H$\alpha$ emission line in four redshift slices from $z=0.40$--$2.23$ over $\sim 1$deg$^2$ as part of the High-redshift Emission Line Survey (HiZELS). ... More

SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES): Faint-End Counts at 450 umJul 04 2017Oct 18 2017The SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES) is a three-year JCMT Large Program aiming at reaching the 450 $\mu$m confusion limit in the COSMOS-CANDELS region, to study a representative sample of the high-redshift far-infrared galaxy population ... More

The clustering and evolution of H-alpha emitters at z~1 from HiZELSDec 21 2009Jan 15 2010(Abridged) The clustering properties of a well-defined sample of 734 H-alpha emitters at z=0.84 obtained as part of the Hi-z Emission Line Survey (HiZELS) are investigated. The spatial correlation function is very well-described by (r/r_0)^-1.8, with ... More

Predictions for the CO emission of galaxies from a coupled simulation of galaxy formation and photon dominated regionsApr 03 2012Aug 09 2012We combine the galaxy formation model GALFORM with the Photon Dominated Region code UCL_PDR to study the emission from the rotational transitions of 12CO (CO) in galaxies from z=0 to z=6 in the Lambda CDM framework. GALFORM is used to predict the molecular ... More

A large Hα survey at z=2.23, 1.47, 0.84 & 0.40: the 11 Gyr evolution of star-forming galaxies from HiZELSFeb 15 2012Sep 28 2012This paper presents new deep and wide narrow-band surveys undertaken with UKIRT, Subaru and the VLT; a combined effort to select large, robust samples of H-alpha (Ha) emitters at z=0.40, 0.84, 1.47 and 2.23 (corresponding to look-back times of 4.2, 7.0, ... More

On the evolution of the molecular gas fraction of star forming galaxiesFeb 17 2011We present IRAM Plateau de Bure interferometric detections of CO(1-0) emission from a 24um-selected sample of star-forming galaxies at z=0.4. The galaxies have PAH 7.7um-derived star formation rates of SFR~30-60 M_Sun/yr and stellar masses M*~10^{11} ... More

Obscured star formation at z = 0.84 with HiZELS: the relationship between star formation rate and H-alpha or ultra-violet dust extinctionNov 13 2009[Abridged] We compare H-alpha, ultraviolet (UV) and infrared (IR) indicators of star formation rate (SFR) for a sample of z = 0.84 galaxies from the High-z Emission Line Survey (HiZELS). Using multi-wavelength diagnostics, we estimate that 5 - 11 per ... More

A fundamental metallicity relation for galaxies at z = 0.84 - 1.47 from HiZELSSep 02 2013Sep 26 2013We obtained Subaru FMOS observations of Halpha emitting galaxies selected from the HiZELS narrow-band survey, to investigate the relationship between stellar mass, metallicity and star-formation rate at z = 0.84 - 1.47, for comparison with the Fundamental ... More

Two sub-millimetre bright protoclusters bounding the epoch of peak star-formation activitySep 18 2018Jun 20 2019We present James Clerk Maxwell Telescope Submillimetre Common-User Bolometer Array 2 (SCUBA-2) 850 & 450 $\mu$m observations ($\sigma_{850}\sim0.5$ mJy, $\sigma_{450}\sim5$ mJy) of the HS1549+19 and HS1700+64 survey fields containing two of the largest ... More

A relationship between specific star formation rate and metallicity gradient within z=1 galaxies from KMOS-HiZELSJul 03 2014Jul 23 2014We have observed a sample of typical z=1 star forming galaxies, selected from the HiZELS survey, with the new KMOS near-infrared, multi-IFU instrument on the VLT, in order to obtain their dynamics and metallicity gradients. The majority of our galaxies ... More

Two sub-millimetre bright protoclusters bounding the epoch of peak star formation activitySep 18 2018Sep 26 2018We present James Clerk Maxwell Telescope (JCMT) Submillimetre Common-User Bolometer Array 2 (SCUBA-2) 850 \& 450 $\mu$m observations ($\sigma_{850}\sim0.5$ mJy, $\sigma_{450}\sim5$ mJy) of the HS1549+19 and HS1700+64 survey fields containing two of the ... More

The dynamics of z=0.8 H-alpha-selected star-forming galaxies from KMOS/CF-HiZELSOct 14 2013Dec 09 2013We present the spatially resolved H-alpha (Ha) dynamics of sixteen star-forming galaxies at z~0.81 using the new KMOS multi-object integral field spectrograph on the ESO VLT. These galaxies were selected using 1.18 um narrow-band imaging from the 10 deg^2 ... More

On the evolution and environmental dependence of the star formation rate versus stellar mass relation since z~2Feb 21 2013Jun 15 2013This paper discusses the evolution of the correlation between galaxy star formation rates (SFRs) and stellar mass (M*) over the last ~10 Gyrs, particularly focusing on its environmental dependence. We first present the mid-infrared (MIR) properties of ... More

The Star-Formation History of BCGs to z = 1.8 from the SpARCS/SWIRE Survey: Evidence for significant in-situ star formation at high-redshiftAug 28 2015We present the results of a MIPS-24um study of the Brightest Cluster Galaxies (BCGs) of 535 high-redshift galaxy clusters. The clusters are drawn from the Spitzer Adaptation of the Red-Sequence Cluster Survey (SpARCS), which effectively provides a sample ... More

A SCUBA-2 survey of FeLoBAL QSOs: Are FeLoBALs in a `transition phase' between ULIRGs and QSOs?Dec 17 2015It is thought that a class of broad absorption line (BAL) QSOs, characterised by Fe absorption features in their UV spectra (called `FeLoBALs'), could mark a transition stage between the end of an obscured starburst event and a youthful QSO beginning ... More

Effects of cosmological model assumptions on galaxy redshift survey measurementsJun 03 2010Dec 14 2012The clustering of galaxies observed in future redshift surveys will provide a wealth of cosmological information. Matching the signal at different redshifts constrains the dark energy driving the acceleration of the expansion of the Universe. In tandem ... More

PdBI Cold Dust Imaging of Two Extremely Red H-[4.5]>4 Galaxies Discovered with SEDS and CANDELSMar 06 2014May 23 2014We report Plateau de Bure Interferometer (PdBI) 1.1 mm continuum imaging towards two extremely red H-[4.5]>4 (AB) galaxies at z>3, which we have previously discovered making use of Spitzer SEDS and Hubble Space Telescope CANDELS ultra-deep images of the ... More

Existence and Blowup Results for Asymptotically Euclidean Initial Data Sets Generated by the Conformal MethodSep 02 2016For each set of (freely chosen) seed data, the conformal method reduces the Einstein constraint equations to a system of elliptic equations, the conformal constraint equations. We prove an admissibility criterion, based on a (conformal) prescribed scalar ... More

Star formation in quasar hosts and the origin of radio emission in radio-quiet quasarsOct 30 2015Nov 24 2015Radio emission from radio-quiet quasars may be due to star formation in the quasar host galaxy, to a jet launched by the supermassive black hole, or to relativistic particles accelerated in a wide-angle radiatively-driven outflow. In this paper we examine ... More

Designing a space-based galaxy redshift survey to probe dark energyJun 17 2010Jul 08 2010A space-based galaxy redshift survey would have enormous power in constraining dark energy and testing general relativity, provided that its parameters are suitably optimized. We study viable space-based galaxy redshift surveys, exploring the dependence ... More

The Herschel Filament: a signature of the environmental drivers of galaxy evolution during the assembly of massive clusters at z=0.9Feb 29 2012We have discovered a 2.5 Mpc (projected) long filament of infrared-bright galaxies connecting two of the three ~5x10^14 Msun clusters making up the RCS 2319+00 supercluster at z=0.9. The filament is revealed in a deep Herschel Spectral and Photometric ... More

The Evolution of Dusty Star formation in Galaxy Clusters to z = 1: Spitzer IR Observations of the First Red-Sequence Cluster SurveyApr 11 2013We present an IR study of high-redshift galaxy clusters with the MIPS camera on the Spitzer Space Telescope. Employing a sample of 42 clusters from the RCS-1 over the redshift range 0.3 < z < 1.0 and spanning an approximate range in mass of 10^{14-15} ... More

The hidden circumgalactic mediumMar 11 2019The cycling of baryons in and out of galaxies is what ultimately drives galaxy formation and evolution. The circumgalactic medium (CGM) represents the interface between the interstellar medium and the cosmic web, hence its properties are directly shaped ... More

Considerations for Cloud Security OperationsJan 23 2016Information Security in Cloud Computing environments is explored. Cloud Computing is presented, security needs are discussed, and mitigation approaches are listed. Topics covered include Information Security, Cloud Computing, Private Cloud, Public Cloud, ... More

On embeddings of finite subsets of $\ell_2$Sep 28 2016We study finite subsets of $\ell_2$, and more generally any metric space, and consider whether these isometrically embed into a Banach space. Our results partially answer a question of Ostrovskii, on whether every infinite-dimensional Banach space contains ... More

Discrete analogue computing with rotor-routersJul 14 2010Aug 19 2010Rotor-routing is a procedure for routing tokens through a network that can implement certain kinds of computation. These computations are inherently asynchronous (the order in which tokens are routed makes no difference) and distributed (information is ... More

R-symmetric High Scale SupersymmetryOct 17 2012Dec 07 2012Introducing an R-symmetry to models of high scale supersymmetry (SUSY) can have interesting consequences, and we focus on two aspects. If Majorana masses are forbidden by an R-symmetry and the main source of electroweak gaugino masses are Dirac terms, ... More

Contact structures on open 3-manifoldsAug 03 2004Sep 09 2004In this paper, we study contact structures on any open 3-manifold V which is the interior of a compact 3-manifold. To do this, we introduce proper contact isotopy invariants called the slope at infinity and the division number at infinity. We first prove ... More

Regular Expression Subtyping for XML Query and Update LanguagesJan 04 2008XML database query languages such as XQuery employ regular expression types with structural subtyping. Subtyping systems typically have two presentations, which should be equivalent: a declarative version in which the subsumption rule may be used anywhere, ... More

Homotopy approximations to the space of knots, Feynman diagrams, and a conjecture of Scannell and SinhaJan 26 2006Aug 26 2010Scannell and Sinha considered a spectral sequence to calculate the rational homotopy groups of spaces of long knots in n-dimensional Euclidean space, for n greater than or equal to 4. At the end of their paper they conjecture that when n is odd, the terms ... More

Gropes and the rational lift of the Kontsevich integralApr 14 2004Oct 11 2004In this note, we calculate the leading term of the rational lift of the Kontsevich integral, introduced by Garoufalidis and Kricker, on the boundary of an embedded grope of class 2n. We observe that it lies in the subspace spanned by connected diagrams ... More

Presentations for rook partition monoids and algebras and their singular idealsJun 02 2016We obtain several presentations by generators and relations for the rook partition monoids and algebras, as well as their singular ideals. Among other results, we also calculate the minimal sizes of generating sets (some of our presentations use such ... More

Managing resonant trapped orbits in our GalaxyAug 04 2016Galaxy modelling is greatly simplified by assuming the existence of a global system of angle-action coordinates. Unfortunately, global angle-action coordinates do not exist because some orbits become trapped by resonances, especially where the radial ... More

Distribution functions for the Milky WayOct 08 2009Analytic distribution functions (DFs) for the Galactic disc are discussed. The DFs depend on action variables and their predictions for observable quantities are explored under the assumption that the motion perpendicular to the Galactic plane is adiabatically ... More

Actions for axisymmetric potentialsJul 20 2012We give an algorithm for the economical calculation of angles and actions for stars in axisymmetric potentials. We test the algorithm by integrating orbits in a realistic model of the Galactic potential, and find that, even for orbits characteristic of ... More

The Cosmological Context of Extraplanar GasSep 27 2004I review evidence that galaxies form from gas that falls into potential wells cold, rather than from virialized gas, and that formation stops once an atmosphere of trapped virialized gas has accumulated. Disk galaxies do not have such atmospheres, so ... More

Black holes, cuspy atmospheres, and galaxy formationJul 12 2004In cuspy atmospheres, jets driven by supermassive black holes (BHs) offset radiative cooling. The jets fire episodically, but often enough that the cuspy atmosphere does not move very far towards a cooling catastrophe in the intervals of jet inactivity. ... More

Secular Evolution of the Galactic DiskSep 20 2000In the solar-neighbourhood, older stars have larger random velocities than younger ones. It is argued that the increase in velocity dispersion with time is predominantly a gradual process rather than one induced by discrete events such as minor mergers. ... More

Microlensing and Galactic StructureApr 26 2000Because we know little about the Galactic force-field away from the plane, the Galactic mass distribution is very ill-determined. I show that a microlensing survey of galaxies closer than 50 Mpc would enable us to map in three dimensions the Galactic ... More

Time-Integrated Gamma-Ray Burst Synchrotron Spectra from Blast Wave/Cloud InteractionsOct 15 1998We show that the spectral shape of the low energy tails found for the time-integrated spectra of gamma-ray bursts, even in the absence of strong synchrotron cooling, can be significantly softer than the $\nu F_\nu \propto \nu^{4/3}$ asymptote predicted ... More

An X-ray Reprocessing Model of Disk Thermal Emission in Type 1 Seyfert GalaxiesFeb 12 2002Using a geometry consisting of a hot central Comptonizing plasma surrounded by a thin accretion disk, we model the optical through hard X-ray spectral energy distributions of the type 1 Seyfert galaxies NGC 3516 and NGC 7469. As in the model proposed ... More

On tadpole relations via Verdier specializationNov 12 2015Feb 26 2016Using the construct of "Verdier specialization", we provide a purely mathematical derivation of Chern class identities which upon integration yield the D3-brane tadpole relations coming from the equivalence between F-theory and associated weakly coupled ... More

On embeddings of finite subsets of $\ell_2$Sep 28 2016Sep 29 2016We study finite subsets of $\ell_2$, and more generally any metric space, and consider whether these isometrically embed into a Banach space. Our results partially answer a question of Ostrovskii, on whether every infinite-dimensional Banach space contains ... More

A perturbative quantized twist embedded in Minkowski spacetimeApr 28 2016Oct 31 2016In this article, spatially-structured gravitational waves are investigated. Drawing upon analogies between electrodynamics and general relativity, a new gauge is found. We investigate the polarization and degrees of freedom of the resulting radiation. ... More

A lagrangian description of elastic motion in riemannian manifolds and an angular invariant of axially-symmetric elasticity tensorsDec 24 2013This article is a description of elasticity theory for readers with mathematical background. The first sections are an abridgment of parts of the book by Marsden and Hughes, including a compact identification of the equations of motion as the Euler-Lagrange ... More

Self-consistent solutions of canonical proper self-gravitating quantum systemsAug 24 2011Generic self-gravitating quantum solutions that are not critically dependent on the specifics of microscopic interactions are presented. The solutions incorporate curvature effects, are consistent with the universality of gravity, and have appropriate ... More

Quantum Behaviors on an Excreting Black HoleOct 24 2008Often, geometries with horizons offer insights into the intricate relationships between general relativity and quantum physics. However, some subtle aspects of gravitating quantum systems might be difficult to ascertain using static backgrounds, since ... More

A Model of Unified Gauge InteractionsMar 23 2016Linear spinor fields are a generalization of the Dirac field that have direct correspondence with the known physics of fermions, inherent causality properties in their most fundamental constructions, and positive mass eigenvalues for all particle types. ... More

Group Structure of an Extended Lorentz GroupSep 30 2003In a previous paper we extended the Lorentz group to include a set of Dirac boosts that give a direct correspondence with a set of generators which for spin 1/2 systems are proportional to the Dirac matrices. The group is particularly useful for developing ... More

XMM-Newton Observations of AGN Iron Line ProfilesNov 18 2002XMM-Newton observations of type I AGN are presented. The properties of the iron K emission line are reviewed, the majority of AGN observed by XMM-Newton show narrow, unresolved (by XMM) iron lines at 6.4 keV from cold matter that must originate far from ... More

Exactly Solvable Supercritical String Theories?Nov 25 2005By analytically continuing the string equations of the subcritical Type 0A (2, 4|m|) minimal string theories, we reveal a whole new family of differential and integro-differential equations associated with the naively supercritical (2, -4|m|) theories. ... More

Casimir forces between spheresNov 13 2009We discuss the calculation of Casimir forces between a collection of $N$-dielectric spheres. This is done by evaluating directly the force on a sphere constructed from a stress tensor, rather than an interaction energy. Two and three body forces between ... More

Graphene membranes and the Dirac-Born-Infeld actionMay 03 2010Jul 08 2011We propose the use of the Dirac-Born-Infeld action in the phenomenological description of graphene sheet dynamics and interactions. Both the electronic properties of the Dirac fermions and the overall dynamics can be incorporated into this model. Classical ... More

Colourful antenna subtraction for gluon scatteringNov 24 2013In this talk I discuss the application and generalization of the antenna subtraction method to processes involving incoherent interferences of partial amplitudes, which are generically present for the sub-leading colour contributions to processes involving ... More

Feasibly Reducing KAT Equations to KA EquationsJan 15 2008Kleene algebra (KA) is the algebra of regular events. Familiar examples of Kleene algebras include regular sets, relational algebras, and trace algebras. A Kleene algebra with tests (KAT) is a Kleene algebra with an embedded Boolean subalgebra. The addition ... More

Completely Regular Semigroups and the Discrete Log ProblemJan 31 2018We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear to offer protection ... More

On Parallel Transport in Quantum Bundles over Robertson-Walker SpacetimesMay 30 1996Dec 03 1996A recently-developed theory of quantum general relativity provides a propagator for free-falling particles in curved spacetimes. These propagators are constructed by parallel-transporting quantum states within a quantum bundle associated to the Poincare ... More

Solitonic supersymmetry restorationNov 22 2010Jan 12 2011Q-balls are a possible feature of any model with a conserved, global U(1) symmetry and no massless, charged scalars. It is shown that for a broad class of models of metastable supersymmetry breaking they are extremely influential on the vacuum lifetime ... More

Simulations of superhumps and superoutburstsOct 22 1997We numerically study the tidal instability of accretion discs in close binary systems using a two-dimensional SPH code. We find that the precession rate of tidally unstable, eccentric discs does not only depend upon the binary mass ratio q. Although the ... More

Development of a MATLAB/STK TLE Accuracy Assessment Tool, in support of the NASA Ames Space Traffic Management ProjectApr 03 2013In order to improve the effectiveness of conjunction analysis using publically available Two Line Elements (TLEs) a number of strategies are being investigated as part of the Space Traffic Management project at NASA Ames Research Center. To assist in ... More

Lambda-determinants and domino-tilingsJun 15 2004Consider the $2n$-by-$2n$ matrix $M=(m_{i,j})_{i,j=1}^{2n}$ with $m_{i,j} = 1$ for $i,j$ satisfying $|2i-2n-1|+|2j-2n-1| \leq 2n$ and $m_{i,j} = 0$ for all other $i,j$, consisting of a central diamond of 1's surrounded by 0's. When $n \geq 4$, the $\lambda$-determinant ... More

An asymptotic for the average number of amicable pairs for elliptic curvesOct 22 2014Jan 25 2016Amicable pairs for a fixed elliptic curve defined over $\mathbb{Q}$ were first considered by Silverman and Stange where they conjectured an order of magnitude for the function that counts such amicable pairs. This was later refined by Jones to give a ... More

Cosmological constraints from the correlation function of galaxy clustersApr 03 2000I compare various semi-analytic models for the bias of dark matter halos with halo clustering properties observed in recent numerical simulations. The best fitting model is one based on the collapse of ellipsoidal perturbations proposed by Sheth, Mo & ... More

Indecomposability for differential algebraic groupsJun 03 2011Oct 22 2014We study a notion of indecomposability in differential algebraic groups which is inspired by both model theory and differential algebra. After establishing some basic definitions and results, we prove an indecomposability theorem for differential algebraic ... More

A remark on double cosetsOct 07 2008If a soluble group $G$ contains two finitely generated abelian subgroups $A,B$ such that the number of double cosets $AgB$ is finite, then $G$ is shown to be virtually polycyclic.

Moments of Products of Elliptic IntegralsJan 06 2011We consider the moments of products of complete elliptic integrals of the first and second kinds. In particular, we derive new results using elementary means, aided by computer experimentation and a theorem of W. Zudilin. Diverse related evaluations, ... More

A note on the geometry of linear Hamiltonian systems of signature 0 in R^4Oct 17 2005It is shown that a linear Hamiltonian system of signature zero in 4 dimensions is elliptic or hyperbolic according to the number of Lagrangian planes in the null-cone $H^{-1}(0)$, or equivalently the number of invariant Lagrangian planes. An extension ... More

Counterexamples to Rational Dilation on Symmetric Multiply Connected DomainsNov 26 2007Sep 02 2008We show that if R is a compact domain in the complex plane with two or more holes and an anticonformal involution onto itself (or equivalently a hyperelliptic Schottky double), then there is an operator T which has R as a spectral set, but does not dilate ... More

RDCSim: a GPU-Accelerated, Interactive Simulator for Reaction--Diffusion ChemistryJan 19 2019This paper presents RDCSim, an interactive simulator for reaction--diffusion chemistry (RDC) research, being developed as part of an ongoing project studying how humans interact with unconventional computing systems. While much research into the computational ... More

Henon's Isochrone ModelNov 17 2014Henon sought the most general spherical potential in which the radial periods of orbits depended only on energy. He named this potential the isochrone, and discovered that it provided a good representation of data for globular clusters. He sought an explanation ... More

Operadic comodules and (co)homology theoriesMar 19 2014An operad describes a category of algebras and a (co)homology theory for these algebras may be formulated using the homological algebra of operads. A morphism of operads $f:\mathcal{O}\rightarrow\mathcal{P}$ describes a functor allowing a $\mathcal{P}$-algebra ... More

Phantom Maps and Finiteness ConditionsDec 01 2015Mar 31 2016A phantom map is a potentially nontrivial map which induces the zero map on every homology theory and on homotopy groups. Zabrodsky has shown that in the presence of particular finiteness conditions on spaces $X$ and $Y$ every map $X\to Y$ is a phantom ... More

On Spaces of Infinitesimal Motions and Henneberg ExtensionsMay 01 2013We investigate certain spaces of infinitesimal motions arising naturally in the rigidity theory of bar and joint frameworks. We prove some structure theorems for these spaces and as a consequence are able to deduce some special cases of a long standing ... More

Extending Group ActionsSep 09 2012Sep 28 2014We show sufficient criteria for a group of homeomorphisms acting on a metric space X to extend to one acting on a given compactification of X. We give examples for when this can fail when one of the criteria is not met.

Functional inequalities for Feynman-Kac semigroupsNov 08 2018Apr 15 2019Using the tools of stochastic analysis, we prove various gradient estimates and Harnack inequalities for Feynman-Kac semigroups with possibly unbounded potentials. One of the main results is a derivative formula which can be used to characterize a lower ... More

Complex Iterations and Bounded Analytic Hyper-operatorsMar 25 2015Feb 05 2016We give a method of solution to the problem of iterating holomorphic functions to fractional or complex heights. We construct an auxiliary function from natural iterates of a holomorphic function; the auxiliary function will be differintegrable and the ... More

On The Indefinite Sum In Fractional CalculusMar 22 2015We present a theorem on taking the repeated indefinite summation of a holomorphic function $\phi(z)$ in a vertical strip of $\mathbb{C}$ satisfying exponential bounds as the imaginary part grows. We arrive at this result using transforms from fractional ... More

Unbased rational homotopy theory: a Lie algebra approachNov 24 2015Jan 15 2018In this paper an algebraic model for unbased rational homotopy theory from the perspective of curved Lie algebras is constructed. As part of this construction a model structure for the category of pseudo-compact curved Lie algebras with curved morphisms ... More

Generalised triangle groups of type (3,3,2)Dec 13 2010If G is a group with a presentation of the form < x,y|x^3=y^3=W(x,y)^2=1 >, then either G is virtually soluble or G contains a free subgroup of rank 2. This provides additional evidence in favour of a conjecture of Rosenberger.