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Collisions and close encounters involving massive main-sequence starsFeb 02 2006We study close encounters involving massive main sequence stars and the evolution of the exotic products of these encounters as common--envelope systems or possible hypernova progenitors. We show that parabolic encounters between low-- and high--mass ... More

A Survey for Low-Surface-Brightness Galaxies Around M31. I. The Newly Discovered Dwarf Andromeda VJul 22 1998We present images and a color-magnitude diagram for And V, a new dwarf spheroidal companion to M31 that was found using a digital filtering technique applied to 1550 square degrees of the second Palomar Sky Survey. And V resolves into stars easily in ... More

A Survey for Low Surface Brightness Dwarf Galaxies Around M31Oct 20 1998By applying a digital filtering technique to 1550 square degrees of the POSS-II in the vicinity of M31, we found two previously unidentified very low surface brightness dwarf galaxies which we designate And V and VI. Follow-up imaging with the KPNO 4-m ... More

A Survey for Low Surface Brightness Galaxies Around M31. II. The Newly Discovered Dwarf Andromeda VIMay 18 1999We present B-, V-, and I-band images, as well as an H alpha image, of And VI. This is the second newly identified dwarf spheroidal (dSph) companion to M31 found using a digital filtering technique applied to the second Palomar Sky Survey for which 1550 ... More

The "Green Bean" Galaxy SDSS J224024.1--092748: Unravelling the emission signature of a quasar ionization echoFeb 26 2015Mar 02 2015"Green Bean" Galaxies (GBs) are the most [O III]-luminous type-2 active galactic nuclei (AGN) at z~0.3. However, their infrared luminosities reveal AGN in very low activity states, indicating that their gas reservoirs must be ionized by photons from a ... More

Circle graphs are quadratically $χ$-boundedMay 28 2019We prove that the chromatic number of a circle graph with clique number $\omega$ is at most $7\omega^2$.

Red giant stellar collisions in the Galactic CentreNov 19 2008We show that collisions with stellar--mass black holes can partially explain the absence of bright giant stars in the Galactic Centre, first noted by Genzel et al, 1996. We show that the missing objects are low--mass giants and AGB stars in the range ... More

Dynamics of galactic nuclei: Mass segregation and collisionsOct 02 2007Massive black holes (MBHs) with a mass below ~ 1e7 Msun are likely to reside at the centre of dense stellar nuclei shaped by 2-body relaxation, close interactions with the MBH and direct collisions. In this contribution, we stress the role of mass segregation ... More

NuSTAR hard X-ray data and Gemini 3D spectra reveal powerful AGN and outflow histories in two low-redshift Lyman-$α$ blobsSep 20 2017We have shown that Lyman-$\alpha$ blobs (LABs) may still exist even at $z\sim0.3$, about 7 billion years later than most other LABs known (Schirmer et al. 2016). Their luminous Ly$\alpha$ and [OIII] emitters at $z\sim0.3$ offer new insights into the ionization ... More

Semigroup Growth BoundsFeb 12 2003We prove lower bounds on $||T_t||$, where $T_t$ is a one-parameter semigroup, starting from information on the resolvent norms, i.e. the pseudospectra. We provide a physically important example in which the growth of the semigroup norm cannot be derived ... More

Algebraic aspects of spectral theoryJun 23 2010We describe some aspects of spectral theory that involve algebraic considerations but need no analysis. Some of the important applications of the results are to the algebra of $n\times n$ matrices with entries that are polynomials or more general analytic ... More

A Hierarchical Method for obtaining Eigenvalue EnclusuresMar 17 1998Mar 27 1998We propose a method for obtaining rigorous and accurate upper and lower bounds on the eigenvalues of ordinary and partial differential operators in bounded regions of Euclidean space. It uses a boundary condition homotopy method starting from a decomposition ... More

Eigenvalues of an elliptic systemAug 08 2001We describe the spectrum of a non-self-adjoint elliptic system on a finite interval. Under certain conditions we find that the eigenvalues form a discrete set and converge asymptotically at infinity to one of several straight lines. The eigenfunctions ... More

Spectral Theory of Pseudo-Ergodic OperatorsAug 17 2000We define a class of pseudo-ergodic non-self-adjoint Schr\"odinger operators acting in spaces $l^2(X)$ and prove some general theorems about their spectral properties. We then apply these to study the spectrum of a non-self-adjoint Anderson model acting ... More

Archimedes' calculations of square rootsJan 03 2011We reconsider Archimedes' evaluations of several square roots in 'Measurement of a Circle'. We show that several methods proposed over the last century or so for his evaluations fail one or more criteria of plausibility. We also provide internal evidence ... More

Decomposing the Essential SpectrumSep 30 2008We use C*-algebra theory to provide a new method of decomposing the eseential spectra of self-adjoint and non-self-adjoint Schrodinger operators in one or more space dimensions.

Embeddable Markov MatricesJan 11 2010We give an account of some results, both old and new, about any $n\times n$ Markov matrix that is embeddable in a one-parameter Markov semigroup. These include the fact that its eigenvalues must lie in a certain region in the unit ball. We prove that ... More

A review of Hardy inequalitiesSep 28 1998We review the literature concerning the Hardy inequality for regions in Euclidean space and in manifolds, concentrating on the best constants. We also give applications of these inequalities to boundary decay and spectral approximation.

Semi-classical Analysis and PseudospectraFeb 11 2004We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second order differential operators in the semi-classical limit. This leads to the construction of a twisted FBI transform. We also investigate ... More

Approximating semigroups by using pseudospectraMar 19 2003We study evolution equations with non-self-adjoint generators, for example the convection-diffusion equation. Spectral expansions are not a reliable method of solving such equations, because they are so ill-conditioned. We introduce a new method using ... More

An Inverse Spectral TheoremOct 01 2010We prove a substantial extension of an inverse spectral theorem of Ambarzumyan, and show that it can be applied to arbitrary compact Riemannian manifolds, compact quantum graphs and finite combinatorial graphs, subject to the imposition of Neumann (or ... More

Semi-classical States for Non-self-adjoint Schrodinger OperatorsMar 26 1998We prove that the spectrum of certain non-self-adjoint Schrodinger operators is unstable in the semi-classical limit. Similar results hold for a fixed operator in the high energy limit. The method involves the construction of approximate semi-classical ... More

The Role of Astronomy in the History of ScienceJul 10 2002We discuss the extent to which the visibility of the heavens was a necessary condition for the development of science, with particular reference to the measurement of time. Our conclusion is that while astronomy had significant importance, the growth ... More

An Indefinite Convection-Diffusion OperatorFeb 05 2007We give a mathematically rigorous analysis which confirms the surprising results in a recent paper of Benilov, O'Brien and Sazonov about the spectrum of a highly singular non-self-adjoint operator that arises in a problem in fluid mechanics.

Triviality of the Peripheral Point SpectrumFeb 03 2005If $T_t=\rme^{Zt}$ is a positive one-parameter contraction semigroup acting on $l^p(X)$ where $X$ is a countable set and $1\leq p <\infty$, then the peripheral point spectrum $P$ of $Z$ cannot contain any non-zero elements. The same holds for Feller semigroups ... More

Singular Schrodinger operators in one dimensionDec 17 2011We consider a class of singular Schr\"odinger operators $H$ that act in $L^2(0,\infty)$, each of which is constructed from a positive function $\phi$ on $(0,\infty)$. Our analysis is direct and elementary. In particular it does not mention the potential ... More

Asymptotic behaviour of quasi-orthogonal polynomialsJul 04 2003We obtain explicit upper and lower bounds on the norms of the spectral projections of the non-self-adjoint harmonic oscillator. Some of our results apply to a variety of other families of orthogonal polynomials.

Sectorial perturbations of self-adjoint matrices and operatorsJun 08 2012This paper considers $N\times N$ matrices of the form $A_\gamma =A+ \gamma B$, where $A$ is self-adjoint, $\gamma \in C$ and $B$ is a non-self-adjoint perturbation of $A$. We obtain some monodromy-type results relating the spectral behaviour of such matrices ... More

Sharp boundary estimates for elliptic operatorsSep 29 1998We prove sharp L^2 boundary decay estimates for the eigenfunctions of certain second order elliptic operators acting in a bounded region, and of their first order space derivatives, using only the Hardy inequality. We then deduce bounds on the change ... More

Spectral Properties of Random Non-self-adjoint Matrices and OperatorsFeb 19 2000We describe some numerical experiments which determine the degree of spectral instability of medium size randomly generated matrices which are far from self-adjoint. The conclusion is that the eigenvalues are likely to be intrinsically uncomputable for ... More

Dark-Ages Reionisation & Galaxy Formation Simulation XVI: The Thermal Memory of ReionisationApr 12 2019Intergalactic medium temperature is a powerful probe of the epoch of reionisation, as information is retained long after reionisation itself. However, mean temperatures are highly degenerate with the timing of reionisation, with the amount heat injected ... More

Masses of the Planetary-Nebula Central Stars in the Galactic Globular-Cluster System from HST Imaging and SpectroscopyJan 12 2017The globular cluster (GC) system of our Galaxy contains four planetary nebulae (PNe): K 648 (or Ps 1) in M15, IRAS 18333-2357 in M22, JaFu 1 in Pal 6, and JaFu 2 in NGC 6441. Because single-star evolution at the low stellar mass of present-epoch GCs was ... More

Iterative Hard Thresholding for Compressed SensingMay 05 2008Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding algorithm when ... More

Higher conservation laws for the quantum non-linear Schroedinger equationSep 29 2011Quantum non-linear SCHROEDINGER equation is equivalent to Lieb-Liniger model. It has non-trivial conservation laws. Recently these conservation laws were used for evaluation of the three-body recombination rate for interacting gas of quantum bosons. These ... More

C*-algebras associated with some second order differential operatorsMar 20 2011Jan 11 2012We compare two C*-algebras that have been used to study the essential spectrum. This is done by considering a simple second order elliptic differential operator acting in L^2(R^N), which is affiliated with one or both of the algebras depending on the ... More

Near optimal compressed sensing without priors: Parametric SURE Approximate Message PassingAug 12 2014Both theoretical analysis and empirical evidence confirm that the approximate message passing (AMP) algorithm can be interpreted as recursively solving a signal denoising problem: at each AMP iteration, one observes a Gaussian noise perturbed original ... More

Spectral Instability for Some Schroedinger OperatorsOct 09 1998We define the concept of instability index of an isolated eigenvalue of a non-self-adjoint operator, and prove some of its general properties. We also describe a stable procedure for computing this index for Schroedinger operators in one dimension, and ... More

Non-Weyl Resonance Asymptotics for Quantum GraphsMar 01 2010We consider the resonances of a quantum graph $\mathcal G$ that consists of a compact part with one or more infinite leads attached to it. We discuss the leading term of the asymptotics of the number of resonances of $\mathcal G$ in a disc of a large ... More

Spectral PollutionFeb 12 2003We discuss the problems arising when computing eigenvalues of self-adjoint operators which lie in a gap between two parts of the essential spectrum. Spectral pollution, i.e. the apparent existence of eigenvalues in numerical computations, when no such ... More

Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circleMar 03 2006We prove that for any $n\times n$ matrix, $A$, and $z$ with $|z|\geq \|A\|$, we have that $\|(z-A)^{-1}\|\leq\cot (\frac{\pi}{4n}) \dist (z, \spec(A))^{-1}$. We apply this result to the study of random orthogonal polynomials on the unit circle.

Perturbations of Jordan MatricesDec 06 2006We consider perturbations of a large Jordan matrix, either random and small in norm or of small rank. In both cases we show that most of the eigenvalues of the perturbed matrix are very close to a circle with centre at the origin. In the case of random ... More

Level sets of the resolvent norm of a linear operator revisitedAug 11 2014Apr 10 2015It is proved that the resolvent norm of an operator with a compact resolvent on a Banach space $X$ cannot be constant on an open set if the underlying space or its dual is complex strictly convex. It is also shown that this is not the case for an arbitrary ... More

Sample Distortion for Compressed ImagingMar 22 2013Jul 29 2013We propose the notion of a sample distortion (SD) function for independent and identically distributed (i.i.d) compressive distributions to fundamentally quantify the achievable reconstruction performance of compressed sensing for certain encoder-decoder ... More

Convergence of eigenvalues for a highly non-self-adjoint differential operatorSep 04 2008In this paper we study a family of operators dependent on a small parameter $\epsilon > 0$, which arise in a problem in fluid mechanics. We show that the spectra of these operators converge to N as $\epsilon \to 0$, even though, for fixed $\epsilon > ... More

Separation of variables in perturbed cylindersDec 14 2000We study the Laplace operator subject to Dirichlet boundary conditions in a two-dimensional domain that is one-to-one mapped onto a cylinder (rectangle or infinite strip). As a result of this transformation the original eigenvalue problem is reduced to ... More

Spectra of a class of non-self-adjoint matricesNov 26 2013We consider a new class of non-self-adjoint matrices that arise from an indefinite self-adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum ... More

On eigenfunction approximations for typical non-self-adjoint Schroedinger operatorsApr 19 1999We construct efficient approximations for the eigenfunctions of non-self-adjoint Schroedinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schroedinger operators which have dilation analytic potentials. ... More

About AGN ionization echoes, thermal echoes, and ionization deficits in low redshift Lyman-alpha blobsJul 21 2016We report the discovery of 14 Lyman-alpha blobs (LABs) at z~0.3, existing at least 4-7 billion years later in the Universe than all other LABs known. Their optical diameters are 20-70 kpc, and GALEX data imply Ly-alpha luminosities of (0.4-6.3)x10^43 ... More

A Survey for Planetary Nebulae in M31 Globular ClustersMar 15 2013We report the results of an [O III] 5007 spectroscopic survey for planetary nebulae (PNe) located within the star clusters of M31. By examining R ~ 5000 spectra taken with the WIYN+Hydra spectrograph, we identify 3 PN candidates in a sample of 274 likely ... More

Hot Jupiters and Super-EarthsMar 31 2016We explore the role of dynamics in shaping planetary system multiplicities, focussing on two particular problems. (1) We propose that the lack of close-in super-Earths in hot Jupiter systems is a signature of the migration history of the hot Jupiters ... More

Multidimensional method-of-lines transport for atmospheric flows over steep terrain using arbitrary meshesFeb 01 2017Apr 21 2017Including terrain in atmospheric models gives rise to mesh distortions near the lower boundary that can degrade accuracy and challenge the stability of transport schemes. Multidimensional transport schemes avoid splitting errors on distorted, arbitrary ... More

On the Lack of a Soft X-Ray Excess from Clusters of GalaxiesFeb 24 2006A soft X-ray excess has been claimed to exist in and around a number of galaxy clusters and this emission has been attributed to the warm-hot intergalactic medium that may constitute most of the baryons in the local universe. We have re-examined a study ... More

Heat Flow and Boundary Heterogeneity in Rotating ConvectionAug 31 2017Convection in the metallic cores of terrestrial planets is likely to be subjected to lateral variations in heat flux through the outer boundary imposed by creeping flow in the overlying silicate mantles. Boundary anomalies can significantly influence ... More

Learning Discriminative Representation with Signed Laplacian Restricted Boltzmann MachineAug 28 2018We investigate the potential of a restricted Boltzmann Machine (RBM) for discriminative representation learning. By imposing the class information preservation constraints on the hidden layer of the RBM, we propose a Signed Laplacian Restricted Boltzmann ... More

Spectrum of a Feinberg-Zee Random Hopping MatrixOct 04 2011Dec 23 2011This paper provides a new proof of a theorem of Chandler-Wilde, Chonchaiya and Lindner that the spectra of a certain class of infinite, random, tridiagonal matrices contain the unit disc almost surely. It also obtains an analogous result for a more general ... More

Dictionary Subselection Using an Overcomplete Joint Sparsity ModelDec 12 2012Jun 10 2013Many natural signals exhibit a sparse representation, whenever a suitable describing model is given. Here, a linear generative model is considered, where many sparsity-based signal processing techniques rely on such a simplified model. As this model is ... More

Rank Awareness in Joint Sparse RecoveryApr 26 2010In this paper we revisit the sparse multiple measurement vector (MMV) problem where the aim is to recover a set of jointly sparse multichannel vectors from incomplete measurements. This problem has received increasing interest as an extension of the single ... More

Spectral Stability of the Neumann LaplacianJun 19 2001We prove the equivalence of Hardy- and Sobolev-type inequalities, certain uniform bounds on the heat kernel and some spectral regularity properties of the Neumann Laplacian associated with an arbitrary region of finite measure in Euclidean space. We also ... More

Spectral Properties of Matrices Associated with Some Directed GraphsFeb 11 2008We study the spectral properties of certain non-self-adjoint matrices associated with large directed graphs. Asymptotically the eigenvalues converge to certain curves, apart from a finite number that have limits not on these curves.

Compressible Distributions for High-dimensional StatisticsFeb 07 2011Apr 25 2012We develop a principled way of identifying probability distributions whose independent and identically distributed (iid) realizations are compressible, i.e., can be well-approximated as sparse. We focus on Gaussian random underdetermined linear regression ... More

Red giant depletion in globular cluster coresJan 23 2003We investigate the observed depletion of red giants in the cores of post-core-collapse globular clusters. In particular, the evolutionary scenario we consider is a binary consisting of two low-mass stars which undergoes two common envelope phases. The ... More

Non-Weyl asymptotics for quantum graphs with general coupling conditionsApr 06 2010Jun 15 2010Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced ... More

Fast online 3D reconstruction of dynamic scenes from individual single-photon detection eventsMay 08 2019In this paper, we present an algorithm for online 3D reconstruction of dynamic scenes using individual times of arrival (ToA) of photons recorded by single-photon detector arrays. One of the main challenges in 3D imaging using single-photon Lidar is the ... More

Galaxy And Mass Assembly (GAMA): Timescales for galaxies crossing the green valleyMar 18 2019We explore the constraints that can be placed on the evolutionary timescales for typical low redshift galaxies evolving from the blue cloud through the green valley and onto the red sequence. We utilise galaxies from the GAMA survey with 0.1 < z < 0.2 ... More

The WiFeS S7 AGN survey: Current status and recent results on NGC 6300Jul 07 2015The Siding Spring Southern Seyfert Spectroscopic Snapshot Survey (S7) is a targeted survey probing the narrow-line regions (NLRs) of a representative sample of ~140 nearby (z<0.02) Seyfert galaxies by means of optical integral field spectroscopy. The ... More

A Detailed Look at Chemical Abundances in Magellanic Cloud Planetary Nebulae. I. The Small Magellanic CloudMay 12 2010We present an analysis of elemental abundances of He, N, O, Ne, S, and Ar in Magellanic Cloud planetary nebulae (PNe), and focus initially on 14 PNe in the Small Magellanic Cloud (SMC). We derived the abundances from a combination of deep, high dispersion ... More

Improving the generalizability of convolutional neural network-based segmentation on CMR imagesJul 02 2019Convolutional neural network (CNN) based segmentation methods provide an efficient and automated way for clinicians to assess the structure and function of the heart in cardiac MR images. While CNNs can generally perform the segmentation tasks with high ... More

Improving the generalizability of convolutional neural network-based segmentation on CMR imagesJul 02 2019Jul 03 2019Convolutional neural network (CNN) based segmentation methods provide an efficient and automated way for clinicians to assess the structure and function of the heart in cardiac MR images. While CNNs can generally perform the segmentation tasks with high ... More

Metallicity and Age of the Stellar Stream Around the Disk Galaxy NGC 5907Jul 13 2016Stellar streams have become central to studies of the interaction histories of nearby galaxies. To characterize the most prominent parts of the stellar stream around the well-known nearby (d = 17 Mpc) edge-on disk galaxy NGC 5907, we have obtained and ... More

Air Entrainment in Dynamic Wetting: Knudsen Effects and the Influence of Ambient Air PressureFeb 16 2015Mar 02 2015Recent experiments on coating flows and liquid drop impact both demonstrate that wetting failures caused by air entrainment can be suppressed by reducing the ambient gas pressure. Here, it is shown that non-equilibrium effects in the gas can account for ... More

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

Cosmic Ray Rejection by Linear Filtering of Single ImagesFeb 02 2000We present a convolution-based algorithm for finding cosmic rays in single well-sampled astronomical images. The spatial filter used is the point spread function (approximated by a Gaussian) minus a scaled delta function, and cosmic rays are identified ... More

Afterglows as Diagnostics of Gamma Ray Burst BeamingDec 03 1997If gamma ray bursts are highly collimated, radiating into only a small fraction of the sky, the energy requirements of each event may be reduced by several (up to 4 - 6) orders of magnitude, and the event rate increased correspondingly. The large Lorentz ... More

Massive stars as important contributors to two micron lightMar 20 1995Near infrared light at 2 micrometers is relatively insensitive to the presence of hot young stars and dust in galaxies, and there has been recent interest in using it as a mass tracer in spiral galaxies. I present evidence that young, cool supergiant ... More

Mirror Images of String CosmologiesMay 11 1999A discrete symmetry of the four-dimensional string effective action is employed to derive spatially homogeneous and inhomogeneous string cosmologies from vacuum solutions of general relativity that admit two commuting spacelike Killing vectors. In particular, ... More

Thermodynamics of Anomaly-Driven CosmologyDec 15 2008The Friedmann equations of general relativity can be derived from the first law of thermodynamics when the entropy of the apparent horizon of a spatially isotropic universe is given by the Bekenstein-Hawking entropy. We point out that if the entropy of ... More

Cosmic No Hair for Collapsing UniversesNov 17 2005Apr 11 2006It is shown that all contracting, spatially homogeneous, orthogonal Bianchi cosmologies that are sourced by an ultra-stiff fluid with an arbitrary and, in general, varying equation of state asymptote to the spatially flat and isotropic universe in the ... More

Inflationary and Deflationary Branches in Extended Pre--Big Bang CosmologyMay 08 1996The pre--big bang cosmological scenario is studied within the context of the Brans--Dicke theory of gravity. An epoch of superinflationary expansion may occur in the pre--big bang phase of the Universe's history in a certain region of parameter space. ... More

How to Build a SuperbeamJun 28 2012A discussion of design issues for future conventional neutrino beam-lines with proton beam power above a megawatt.

Canonical Quantization of Two Dimensional Gauge FieldsMay 26 1993$SU(N)$ gauge fields on a cylindrical spacetime are canonically quantized via two routes revealing almost equivalent but different quantizations. After removing all continuous gauge degrees of freedom, the canonical coordinate $A_\mu$ (in the Cartan subalgebra ... More

Some Non-Perturbative Aspects of Gauge Fixing in Two Dimensional Yang-Mills TheoryDec 02 1993Gauge fixing in general is incomplete, such that one solves some of the gauge constraints, quantizes, then imposes any residual gauge symmetries (Gribov copies) on the wavefunctions. While the Fadeev-Popov determinant keeps track of the local metric on ... More

Geometric realization of algebraic conformal field theoriesNov 03 2016We explore new connections between the fields and local observables in two dimensional chiral conformal field theory. We show that in a broad class of examples, the von Neumann algebras of local observables (a conformal net) can be obtained from the fields ... More

Ultrafilters on omegaNov 15 1993A variety of classes of naturally arising ultrafilters on omega is discussed, and the question is raised whether it is consistent that the classes are empty. Since all the classes contain the P-point ultrafilters, a negative answer would greatly extend ... More

Information-adaptive clinical trials with selective recruitment and binary outcomesSep 03 2015May 30 2017Selective recruitment designs preferentially recruit individuals that are estimated to be statistically informative onto a clinical trial. Individuals that are expected to contribute less information have a lower probability of recruitment. Furthermore, ... More

Paraconformal Structures and Integrable SystemsJun 15 1999We consider some natural connections which arise between right-flat (p, q) paraconformal structures and integrable systems. We find that such systems may be formulated in Lax form, with a "Lax p-tuple" of linear differential operators, depending a spectral ... More

A Spinorial Hamiltonian Approach to GravityDec 15 1998Jul 05 2000We give a spinorial set of Hamiltonian variables for General Relativity in any dimension greater than 2. This approach involves a study of the algebraic properties of spinors in higher dimension, and of the elimination of second-class constraints from ... More

Lsdiff M and the Einstein EquationsNov 22 1994May 10 1996We give a formulation of the vacuum Einstein equations in terms of a set of volume-preserving vector fields on a four-manifold ${\cal M}$. These vectors satisfy a set of equations which are a generalisation of the Yang-Mills equations for a constant connection ... More

Dark Matter Halos from the Inside OutAug 24 2010Oct 24 2010The balance of evidence indicates that individual galaxies and groups or clusters of galaxies are embedded in enormous distributions of cold, weakly interacting dark matter. These dark matter 'halos' provide the scaffolding for all luminous structure ... More

Snapshot Identification of Gamma Ray Burst Optical AfterglowsAug 29 2000Apr 18 2001Gamma ray burst afterglows can be identified in single epoch observations using three or more optical filters. This method relies on color measurements to distinguish the power law spectrum of an afterglow from the curved spectra of stars. Observations ... More

The Dynamics and Light Curves of Beamed Gamma Ray Burst AfterglowsMar 25 1999The energy requirements of gamma ray bursts have in past been poorly constrained because of three major uncertainties: The distances to bursts, the degree of burst beaming, and the efficiency of gamma ray production. The first of these has been resolved, ... More

How to Tell a Jet from a Balloon: A Proposed Test for Beaming in Gamma Ray BurstsMay 21 1997Sep 15 1997If gamma ray bursts are highly collimated, the energy requirements of each event may be reduced by several (~ 4-6) orders of magnitude, and the event rate increased correspondingly. Extreme conditions in gamma ray bursters lead to highly relativistic ... More

Supergravity Brane CosmologiesJul 03 2000Solitonic brane cosmologies are found where the world-volume is curved due to the evolution of the dilaton field on the brane. In many cases, these may be related to the solitonic Dp- and M5-branes of string and M-theory. An eleven-dimensional interpretation ... More

Separable Brane Cosmologies in Heterotic M-TheoryNov 18 1999It is shown that any anisotropic and inhomogeneous cosmological solution to the lowest-order, four-dimensional, dilaton-graviton string equations of motion may be employed as a seed to derive a curved, three-brane cosmological solution to five-dimensional ... More

The Embedding of Superstring Backgrounds in Einstein GravityJul 13 1999A theorem of differential geometry is employed to locally embed a wide class of superstring backgrounds that admit a covariantly constant null Killing vector field in eleven-dimensional, Ricci-flat spaces. Included in this class are exact type IIB superstring ... More

Symmetric vacuum scalar--tensor cosmologyMar 27 1996The existence of point symmetries in the cosmological field equations of generalized vacuum scalar--tensor theories is considered within the context of the spatially homogeneous cosmologies. It is found that such symmetries only occur in the Brans--Dicke ... More

Cosmology and the Korteweg-de Vries EquationMay 25 2012Jul 11 2012The Korteweg-de Vries (KdV) equation is a non-linear wave equation that has played a fundamental role in diverse branches of mathematical and theoretical physics. In the present paper, we consider its significance to cosmology. It is found that the KdV ... More

On the Cosmology and Symmetry of Dilaton-Axion GravitySep 27 1996A global O$(2,2)$ symmetry is found in the Brans-Dicke theory of gravity when the dilaton is coupled to axion and moduli fields. The symmetry is broken if a cosmological constant is introduced. Within the class of spatially homogeneous Bianchi cosmologies, ... More

Smooth interpolation of lattice gauge fields by signal processing methodsSep 29 1995We digitally filter the Fourier modes of the link angles of an abelian lattice gauge field which produces the Fourier modes of a continuum $A_\mu(x)$ that exactly reproduces the lattice links through their definition as phases of finite parallel transport. ... More

Atmospheric Escape and the Evolution of Close-in ExoplanetsJul 19 2018Aug 15 2018Exoplanets with substantial Hydrogen/Helium atmospheres have been discovered in abundance, many residing extremely close to their parent stars. The extreme irradiation levels these atmospheres experience causes them to undergo hydrodynamic atmospheric ... More

A Spinorial Hamiltonian Approach to Ricci-Flat GeometryOct 09 1998Jul 10 2000The author has removed this paper, following the publication of a more complete version.