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Glauber Gluons and Multiple Parton InteractionsMay 08 2014We show that for hadronic transverse energy $E_T$ in hadron-hadron collisions, the classic Collins-Soper-Sterman (CSS) argument for the cancellation of Glauber gluons breaks down at the level of two Glauber gluons exchanged between the spectators. Through ... More

Double Parton Splitting Diagrams and Interference and Correlation Effects in Double Parton ScatteringOct 07 2011We discuss two topics in double parton scattering (DPS) theory that have been the subject of recent research interest. First, the role of `double parton splitting' diagrams in DPS is discussed. We outline the `double PDF' description of DPS, which was ... More

Single Perturbative Splitting Diagrams in Double Parton ScatteringJul 02 2012Dec 06 2012We present a detailed study of a specific class of graph that can potentially contribute to the proton-proton double parton scattering (DPS) cross section. These are the `2v1' or `single perturbative splitting' graphs, in which two `nonperturbatively ... More

The GS09 double parton distribution functionsJun 06 2010It is anticipated that hard double parton scattering (DPS) will occur frequently in the collisions of the LHC, producing interesting signals and significant backgrounds to certain single scattering processes. In order to make theoretical predictions of ... More

Double parton scattering in the ultraviolet: addressing the double counting problemNov 04 2016An important question in the theory of double parton scattering is how to incorporate the possibility of the parton pairs being generated perturbatively via $1 \to 2$ splitting into the theory, whilst avoiding double counting with single parton scattering ... More

Transverse momentum dependence in double parton scatteringDec 21 2018In this review, we describe the status of transverse momentum dependence (TMD) in double parton scattering (DPS). The different regions of TMD DPS are discussed, and expressions given for the DPS cross section contributions that make use of as much perturbative ... More

Transverse momentum dependence in double parton scatteringDec 21 2018Feb 15 2019In this review, we describe the status of transverse momentum dependence (TMD) in double parton scattering (DPS). The different regions of TMD DPS are discussed, and expressions given for the DPS cross section contributions that make use of as much perturbative ... More

The Fully-Differential Quark Beam Function at NNLOSep 29 2014Jan 02 2015We present the first calculation of a fully-unintegrated parton distribution (beam function) at next-to-next-to-leading order (NNLO). We obtain the fully-differential beam function for quark-initiated processes by matching it onto standard parton distribution ... More

Double parton scattering in the ultraviolet: addressing the double counting problemMar 17 2016In proton-proton collisions there is a smooth transition between the regime of double parton scattering, initiated by two pairs of partons at a large relative distance, and the regime where a single parton splits into a parton pair in one or both protons. ... More

Double parton scattering theory overviewOct 12 2017The dynamics of double hard scattering in proton-proton collisions is quite involved compared with the familiar case of single hard scattering. In this contribution, we review our theoretical understanding of double hard scattering and of its interplay ... More

Double Parton Scattering Singularity in One-Loop IntegralsMar 09 2011May 05 2011We present a detailed study of the double parton scattering (DPS) singularity, which is a specific type of Landau singularity that can occur in certain one-loop graphs in theories with massless particles. A simple formula for the DPS singular part of ... More

Conventional versus single-ladder-splitting contributions to double parton scattering production of two quarkonia, two Higgs bosons and $c \bar c c \bar c$Jul 22 2014The double parton distributions (dPDF), both conventional and those corresponding to parton splitting, are calculated and compared for different two-parton combinations. The conventional and splitting dPDFs have very similar shape in $x_1$ and $x_2$. ... More

Single and Double Perturbative Splitting Diagrams in Double Parton ScatteringFeb 14 2012We discuss the role of two different types of diagram in the proton-proton double parton scattering (DPS) cross section - single and double perturbative splitting graphs. Using explicit calculations of simple graphs from these classes we show that the ... More

A Monte-Carlo Simulation of Double Parton ScatteringJun 11 2019In this work, a new Monte-Carlo simulation of double parton scattering (DPS) at parton level is presented. The simulation is based on the QCD framework developed recently by M. Diehl, J. R. Gaunt and K. Sch\"{o}nwald. With this framework, the dynamics ... More

Double Parton Distributions Incorporating Perturbative QCD Evolution and Momentum and Quark Number Sum RulesOct 22 2009Mar 19 2010It is anticipated that hard double parton scatterings will occur frequently in the collisions of the LHC, producing interesting signals and significant backgrounds to certain single scattering processes. For double scattering processes in which the same ... More

N-jettiness Subtractions for NNLO QCD CalculationsMay 18 2015Sep 27 2015We present a subtraction method utilizing the N-jettiness observable, Tau_N, to perform QCD calculations for arbitrary processes at next-to-next-to-leading order (NNLO). Our method employs soft-collinear effective theory (SCET) to determine the IR singular ... More

The Quark Beam Function at Two LoopsJan 21 2014May 16 2014In differential measurements at a hadron collider, collinear initial-state radiation is described by process-independent beam functions. They are the field-theoretic analog of initial-state parton showers. Depending on the measured observable they are ... More

Two-Loop Beam and Soft Functions for Rapidity-Dependent Jet VetoesAug 05 2016Jet vetoes play an important role in many analyses at the LHC. Traditionally, jet vetoes have been imposed using a restriction on the transverse momentum $p_{Tj}$ of jets. Alternatively, one can also consider jet observables for which $p_{Tj}$ is weighted ... More

Two-loop splitting in double parton distributionsFeb 21 2019Double parton distributions (DPDs) receive a short-distance contribution from a single parton splitting to yield the two observed partons. We investigate this mechanism at next-to-leading order (NLO) in perturbation theory. Technically, we compute the ... More

Study of scalar mesons in chiral Lagrangian frameworksJan 16 2008We review two approaches to studying pseudoscalar meson-meson scattering amplitudes to beyond 1 GeV using non-linear and linear chiral Lagrangians. These approaches use two different unitarisation techniques - a generalised Breit Wigner prescription and ... More

Cancellation of Glauber gluon exchange in the double Drell-Yan processOct 29 2015An essential part of any factorisation proof is the demonstration that the exchange of Glauber gluons cancels for the considered observable. We show this cancellation at all orders for double Drell-Yan production (the double parton scattering process ... More

Same-sign W pair production as a probe of double parton scattering at the LHCMar 20 2010Jun 04 2010We study the production of same-sign W boson pairs at the LHC in double parton interactions. Compared with simple factorised double parton distributions (dPDFs), we show that the recently developed dPDFs, GS09, lead to non-trivial kinematic correlations ... More

Probing double parton scattering with leptonic final states at the LHCOct 06 2011We discuss the prospects of observing double parton scattering (DPS) processes with purely leptonic final states at the LHC. We first study same-sign W pair production, which is particularly suited for studying momentum and valence number conservation ... More

Colour unwound - disentangling colours for azimuthal asymmetries in Drell-Yan scatteringSep 14 2017Dec 18 2017It has been suggested that a colour-entanglement effect exists in the Drell-Yan cross section for the 'double T-odd' contributions at low transverse momentum $Q_T$, rendering the colour structure different from that predicted by the usual factorisation ... More

The Gluon Beam Function at Two LoopsMay 05 2014Aug 28 2014The virtuality-dependent beam function is a universal ingredient in the resummation for observables probing the virtuality of incoming partons, including N-jettiness and beam thrust. We compute the gluon beam function at two-loop order. Together with ... More

Two-current correlations in the pion on the latticeJul 09 2018Nov 28 2018We perform a systematic study of the correlation functions of two quark currents in a pion using lattice QCD. We obtain good signals for all but one of the relevant Wick contractions of quark fields. We investigate the quark mass dependence of our results ... More

Phenomenology of Production and Decay of Spinning Extra-Dimensional Black Holes at Hadron CollidersApr 06 2009Oct 16 2009We present results of CHARYBDIS2, a new Monte Carlo simulation of black hole production and decay at hadron colliders in theories with large extra dimensions and TeV-scale gravity. The main new feature of CHARYBDIS2 is a full treatment of the spin-down ... More

Derivative formulas for Bessel, Struve and Anger-Weber functionsNov 06 2012We derive formulas for the derivatives of general order for the functions $z^{-\nu}h_{\nu}(z)$ and $z^{\nu}h_{\nu}(z)$, where $h_{\nu}(z)$ is a Bessel, Struve or Anger-Weber function. These formulas are motivated by the occurrence of the expressions $\frac{d^n}{dz^n}(z^{-\nu}I_{\nu}(z))$ ... More

Progress in Double Parton Scattering StudiesOct 24 2014An overview of theoretical and experimental progress in double parton scattering (DPS) is presented. The theoretical topics cover factorization in DPS, models for double parton distributions and DPS in charm production and nuclear collisions. On the experimental ... More

Summary - TerpreT: A Probabilistic Programming Language for Program InductionDec 02 2016We study machine learning formulations of inductive program synthesis; that is, given input-output examples, synthesize source code that maps inputs to corresponding outputs. Our key contribution is TerpreT, a domain-specific language for expressing program ... More

TerpreT: A Probabilistic Programming Language for Program InductionAug 15 2016We study machine learning formulations of inductive program synthesis; given input-output examples, we try to synthesize source code that maps inputs to corresponding outputs. Our aims are to develop new machine learning approaches based on neural networks ... More

Rates of convergence in normal approximation under moment conditions via new bounds on solutions of the Stein equationNov 27 2013Jun 24 2014New bounds for the $k$-th order derivatives of the solutions of the normal and multivariate normal Stein equations are obtained. Our general order bounds involve fewer derivatives of the test function than those in the existing literature. We apply these ... More

On Stein's method for products of normal random variables and zero bias couplingsSep 17 2013Mar 29 2016In this paper we extend Stein's method to the distribution of the product of $n$ independent mean zero normal random variables. A Stein equation is obtained for this class of distributions, which reduces to the classical normal Stein equation in the case ... More

Bounds for modified Lommel functions of the first kind and their ratiosJan 04 2019The modified Lommel function $t_{\mu,\nu}(x)$ is an important special function, but to date there has been little progress on the problem of obtaining functional inequalities for $t_{\mu,\nu}(x)$. In this paper, we advance the literature substantially ... More

A basis theorem for the degenerate affine oriented Brauer-Clifford supercategoryJun 30 2017Mar 21 2018We introduce the oriented Brauer-Clifford and degenerate affine oriented Brauer-Clifford supercategories. These are diagrammatically defined monoidal supercategories which provide combinatorial models for certain natural monoidal supercategories of supermodules ... More

Modified Traces on Deligne's Category Rep(S_{t})Mar 10 2011Deligne has defined a category which interpolates among the representations of the various symmetric groups. In this paper we show Deligne's category admits a unique nontrivial family of modified trace functions. Such modified trace functions have already ... More

Products of normal, beta and gamma random variables: Stein operators and distributional theoryJul 28 2015Mar 29 2016In this paper, we extend Stein's method to products of independent beta, gamma, generalised gamma and mean zero normal random variables. In particular, we obtain Stein characterisations for mixed products of these distributions, which include the classical ... More

Inequalities for integrals of the modified Struve function of the first kind IIOct 09 2018Simple inequalities are established for integrals of the type $\int_0^x \mathrm{e}^{-\gamma t} t^{-\nu} \mathbf{L}_\nu(t)\,\mathrm{d}t$, where $x>0$, $0\leq\gamma<1$, $\nu>-\frac{3}{2}$ and $\mathbf{L}_{\nu}(x)$ is the modified Struve function of the ... More

A Probabilistic proof of some integral formulas involving the Meijer $G$-functionFeb 25 2016Sep 28 2016New integral formulas involving the Meijer $G$-function are derived using recent results concerning distributional characterisations and distributional transformations in probability theory.

A note on the distribution of the product of zero mean correlated normal random variablesJul 11 2018The problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables dates back to 1936. Perhaps surprisingly, this problem was not resolved until 2016. This is all the more surprising given ... More

A Stein characterisation of the generalized hyperbolic distributionMar 17 2016Mar 24 2016The generalized hyperbolic (GH) distributions form a five parameter family of probability distributions that includes many standard distributions as special or limiting cases, such as the generalized inverse Gaussian distribution, Student's $t$-distribution ... More

Bounds for modified Struve functions of the first kind and their ratiosMar 20 2018May 29 2018We obtain a simple two-sided inequality for the ratio $\mathbf{L}_\nu(x)/\mathbf{L}_{\nu-1}(x)$ in terms of the ratio $I_\nu(x)/I_{\nu-1}(x)$, where $\mathbf{L}_\nu(x)$ is the modified Struve function of the first kind and $I_\nu(x)$ is the modified Bessel ... More

Products of normal, beta and gamma random variables: Stein operators and distributional theoryJul 28 2015Dec 13 2016In this paper, we extend Stein's method to products of independent beta, gamma, generalised gamma and mean zero normal random variables. In particular, we obtain Stein operators for mixed products of these distributions, which include the classical beta, ... More

Wasserstein and Kolmogorov error bounds for variance-gamma approximation via Stein's method INov 20 2017Oct 18 2018The variance-gamma (VG) distributions form a four parameter family that includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and approximation on Wiener space. ... More

Inequalities for some integrals involving modified Bessel functionsJun 01 2018Oct 09 2018Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double inequality, involving ... More

Inequalities for integrals of modified Bessel functions and expressions involving themAug 21 2017Feb 01 2018Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits. We apply these ... More

Inequalities for the modified Bessel function of the second kind and the kernel of the Krätzel integral transformationJan 11 2017We obtain new inequalities for the modified Bessel function of the second kind $K_\nu$ in terms of the gamma function. These bounds follow as special cases of inequalities that we derive for the kernel of the Kr\"{a}tzel integral transformation.

Stein's method for functions of multivariate normal random variablesJul 30 2015It is a well-known fact that if the random vector $\mathbf{W}$ converges in distribution to a multivariate normal random variable $\Sigma^{1/2}\mathbf{Z}$, then $g(\mathbf{W})$ converges in distribution to $g(\Sigma^{1/2}\mathbf{Z})$ if $g$ is continuous. ... More

A Stein characterisation of the generalized hyperbolic distributionMar 17 2016Mar 15 2017The generalized hyperbolic (GH) distributions form a five parameter family of probability distributions that includes many standard distributions as special or limiting cases, such as the generalized inverse Gaussian distribution, Student's $t$-distribution ... More

Stein's method for functions of multivariate normal random variablesJul 30 2015Jun 12 2019By the continuous mapping theorem, if a sequence of $d$-dimensional random vectors $(\mathbf{W}_n)_{n\geq1}$ converges in distribution to a multivariate normal random variable $\Sigma^{1/2}\mathbf{Z}$, then the sequence of random variables $(g(\mathbf{W}_n))_{n\geq1}$ ... More

Stein's method and the distribution of the product of zero mean correlated normal random variablesJun 11 2019Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables. Motivated by this historical interest, we use a recent technique ... More

Inequalities for integrals of the modified Struve function of the first kindFeb 06 2018Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality, involving the ... More

Uniform bounds for expressions involving modified Bessel functionsSep 17 2013Feb 15 2016In this paper, we obtain uniform bounds for a number of expressions that involve derivatives and integrals of modified Bessel functions. These uniform bounds are motivated by the need to bound such expressions in the study of variance-gamma and product ... More

Inequalities for integrals of the modified Struve function of the first kindFeb 06 2018Apr 23 2018Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality, involving the ... More

Inequalities for modified Bessel functions and their integralsNov 30 2012Jun 24 2014Simple inequalities for some integrals involving the modified Bessel functions $I_{\nu}(x)$ and $K_{\nu}(x)$ are established. We also obtain a monotonicity result for $K_{\nu}(x)$ and a new lower bound, that involves gamma functions, for $K_0(x)$.

Derivative formulas for Bessel, Struve and Anger-Weber functionsNov 06 2012May 29 2017We derive formulas for the derivatives of general order for the functions $z^{-\nu}h_{\nu}(z)$ and $z^{\nu}h_{\nu}(z)$, where $h_{\nu}(z)$ is a Bessel, Struve or Anger--Weber function.

Variance-Gamma approximation via Stein's methodSep 17 2013Mar 30 2014Variance-Gamma distributions are widely used in financial modelling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein's method to this class of distributions. In particular, we obtain a Stein equation ... More

Inequalities for some integrals involving modified Lommel functions of the first kindJan 24 2019In this paper, we obtain inequalities for some integrals involving the modified Lommel function of the first kind $t_{\mu,\nu}(x)$. In most cases, these inequalities are tight in certain limits. We also deduce a tight double inequality, involving the ... More

Stein operators for variables form the third and fourth Wiener chaosesMay 22 2018Sep 02 2018Let $Z$ be a standard normal random variable and let $H_n$ denote the $n$-th Hermite polynomial. In this note, we obtain Stein equations for the random variables $H_3(Z)$ and $H_4(Z)$, which represents a first step towards developing Stein's method for ... More

The Conway-Maxwell-Poisson distribution: distributional theory and approximationMar 24 2015Jul 08 2016The Conway-Maxwell-Poisson (CMP) distribution is a natural two-parameter generalisation of the Poisson distribution which has received some attention in the statistics literature in recent years by offering flexible generalisations of some well-known ... More

Approximate waveform templates for detection of extreme mass ratio inspirals with LISAMar 06 2007The inspirals of compact objects into massive black holes are some of the most exciting of the potential sources of gravitational waves for the planned Laser Interferometer Space Antenna (LISA). Observations of such extreme mass ratio inspirals (EMRIs) ... More

Host Galaxy Morphology and the AGN Unified ModelDec 16 2011We use a sample of active galaxies from the Cosmic Evolution Survey to show that host galaxy morphology is tied to the accretion rate and X-ray obscuration of its active galactic nucleus (AGN). Unobscured and rapidly accreting broad-line AGNs are more ... More

Probing black holes at low redshift using LISA EMRI observationsNov 02 2008Mar 08 2009One of the most exciting potential sources of gravitational waves for the Laser Interferometer Space Antenna (LISA) are the inspirals of approximately solar mass compact objects into massive black holes in the centres of galaxies - extreme mass ratio ... More

The scientific potential of space-based gravitational wave detectorsJul 08 2014Aug 28 2014The millihertz gravitational wave band can only be accessed with a space-based interferometer, but it is one of the richest in potential sources. Observations in this band have amazing scientific potential. The mergers between massive black holes with ... More

Robust Digital Holography For Ultracold Atom TrappingNov 25 2011Oct 15 2012We have formulated and experimentally demonstrated an improved algorithm for design of arbitrary two-dimensional holographic traps for ultracold atoms. Our method builds on the best previously available algorithm, MRAF, and improves on it in two ways. ... More

Multivariate normal approximation of the maximum likelihood estimator via the delta methodSep 13 2016We use the delta method and Stein's method to derive, under regularity conditions, explicit upper bounds for the distributional distance between the distribution of the maximum likelihood estimator (MLE) of a $d$-dimensional parameter and its asymptotic ... More

The rate of convergence of some asymptotically chi-square distributed statistics by Stein's methodMar 06 2016Mar 24 2016We build on recent works on Stein's method for functions of multivariate normal random variables to derive bounds for the rate of convergence of some asymptotically chi-square distributed statistics. We obtain some general bounds and establish some simple ... More

Stein's Method for the Single Server Queue in Heavy TrafficMay 21 2018Following recent developments in the application of Stein's method in queueing theory, this paper is intended to be a short treatment showing how Stein's method can be developed and applied to the single server queue in heavy traffic. Here we provide ... More

Multivariate normal approximation of the maximum likelihood estimator via the delta methodSep 13 2016Aug 09 2018We use the delta method and Stein's method to derive, under regularity conditions, explicit upper bounds for the distributional distance between the distribution of the maximum likelihood estimator (MLE) of a $d$-dimensional parameter and its asymptotic ... More

An algebra of Stein operatorsApr 22 2016Sep 11 2018We build upon recent advances on the distributional aspect of Stein's method to propose a novel and flexible technique for computing Stein operators for random variables that can be written as products of independent random variables. We show that our ... More

Detecting extreme mass ratio inspirals with LISA using time-frequency methodsFeb 24 2005The inspirals of stellar-mass compact objects into supermassive black holes are some of the most important sources for LISA. Detection techniques based on fully coherent matched filtering have been shown to be computationally intractable. We describe ... More

Cosmic Microwave Background Fluctuations from Gravitational Waves: An Analytic ApproachDec 21 2004We develop an analytic approach to calculation of the temperature and polarisation power spectra of the cosmic microwave background due to inflationary gravitational waves. This approach complements the more precise numerical results by providing insight ... More

Forecasted 21 cm constraints on compensated isocurvature perturbationsJul 30 2009Sep 23 2009A "compensated" isocurvature perturbation consists of an overdensity (or underdensity) in the cold dark matter which is completely cancelled out by a corresponding underdensity (or overdensity) in the baryons. Such a configuration may be generated by ... More

Studying the morphology of reionisation with the triangle correlation function of phasesMar 27 2019We present a new statistical tool, called the triangle correlation function, inspired by the earlier work of Obreschkow et al. (2013). It is derived from the 3-point correlation function (3-PCF) and aims to probe the characteristic scale of ionised regions ... More

Norms of truncated Toeplitz operators and numerical radii of restricted shiftsNov 16 2017May 02 2018This paper gives a new approach to the calculation of the numerical radius of a restricted shift operator by linking it to the norm of a truncated Toeplitz operator (TTO), which can be be calculated by various methods. Further results on the norm of a ... More

Bending a Beam to Significantly Reduce Wakefields of Short BunchesAug 23 2011A method of significantly reducing wakefields generated at collimators is proposed, in which the path of a beam is slightly bent before collimation. This is applicable for short bunches and can reduce the wakefields by a factor of around 7 for present ... More

The reproducing kernel thesis for lower bounds of weighted composition operatorsDec 19 2018Feb 25 2019It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including reproducing kernels. The methods used in ... More

Detecting extreme mass ratio inspiral events in LISA data using the Hierarchical Algorithm for Clusters and Ridges (HACR)Oct 10 2006Jan 04 2007One of the most exciting prospects for the Laser Interferometer Space Antenna (LISA) is the detection of gravitational waves from the inspirals of stellar-mass compact objects into supermassive black holes. Detection of these sources is an extremely challenging ... More

Projective Splitting with Forward Steps only Requires ContinuitySep 17 2018A recent innovation in projective splitting algorithms for monotone operator inclusions has been the development of a procedure using two forward steps instead of the customary proximal steps for operators that are Lipschitz continuous. This paper shows ... More

Multivariable approximate Carleman-type theorems for complex measuresMar 27 2007We prove a multivariable approximate Carleman theorem on the determination of complex measures on ${\mathbb{R}}^n$ and ${\mathbb{R}}^n_+$ by their moments. This is achieved by means of a multivariable Denjoy--Carleman maximum principle for quasi-analytic ... More

The origin of the Schott term in the electromagnetic self force of a classical point chargeAug 23 2011The Schott term is the third order term in the electromagnetic self force of a charged point particle. The self force may be obtained by integrating the electromagnetic stress-energy-momentum tensor over the side of a narrow hypertube enclosing a section ... More

Improved approximate inspirals of test-bodies into Kerr black holesOct 31 2005Apr 10 2006We present an improved version of the approximate scheme for generating inspirals of test-bodies into a Kerr black hole recently developed by Glampedakis, Hughes and Kennefick. Their original "hybrid" scheme was based on combining exact relativistic expressions ... More

Jet Veto Clustering Logarithms Beyond Leading OrderNov 20 2013Nov 23 2014Many experimental analyses separate events into exclusive jet bins, using a jet algorithm to cluster the final state and then veto on jets. Jet clustering induces logarithmic dependence on the jet radius R in the cross section for exclusive jet bins, ... More

Admissibility of diagonal state-delayed systems with a one-dimensional input spaceMay 12 2018Dec 08 2018In this paper we investigate admissibility of the control operator $B$ in a Hilbert space state-delayed dynamical system setting of the form $\dot{z}(t)=Az(t-\tau)+Bu(t)$, where $A$ generates a diagonal semigroup and $u$ is a scalar input function. Our ... More

On the admissibility of retarded delay systemsSep 24 2017Apr 23 2018We investigate a Hilbert space dynamical system of the form $\dot{z}(t)=Az(t)+A_1z(t-\tau)+Bu(t)$, where $A$ generates a semigroup of contractions and $A_1$ is a bounded operator, in order to determine whether the operator $B$ is admissible. Our approach ... More

Phragmén--Lindelöf principles for generalized analytic functions on unbounded domainsFeb 16 2015Mar 18 2015We prove versions of the Phragm\'en--Lindel\"of strong maximum principle for generalized analytic functions defined on unbounded domains. A version of Hadamard's three-lines theorem is also derived.

Single-Forward-Step Projective Splitting: Exploiting CocoercivityFeb 24 2019This work describes a new variant of projective splitting in which cocoercive operators can be processed with a single forward step per iteration. This result establishes a symmetry between projective splitting algorithms, the classical forward-backward ... More

On the relationship between classical and deformed Hopf fibrationsNov 27 2018The $\theta$-deformed Hopf fibration $\mathbb{S}^3_\theta\to \mathbb{S}^2$ over the commutative $2$-sphere is compared with its classical counterpart. It is shown that there exists a natural isomorphism between the corresponding associated module functors ... More

Stability of multi-field cosmological solutions in the presence of a fluidApr 22 2010Jul 27 2010We explore the stability properties of multi-field solutions in the presence of a perfect fluid, as appropriate to assisted quintessence scenarios. We show that the stability condition for multiple fields $\phi_i$ in identical potentials $V_i$ is simply ... More

Constraining the unexplored period between reionization and the dark ages with observations of the global 21 cm signalMay 21 2010Observations of the frequency dependence of the global brightness temperature of the redshifted 21 cm line of neutral hydrogen may be possible with single dipole experiments. In this paper, we develop a Fisher matrix formalism for calculating the sensitivity ... More

Evolution of the 21 cm signal throughout cosmic historyFeb 15 2008The potential use of the redshifted 21 cm line from neutral hydrogen for probing the epoch of reionization is motivating the construction of several low-frequency interferometers. There is also much interest in the possibility of constraining the initial ... More

Projective Splitting with Forward Steps: Asynchronous and Block-Iterative Operator SplittingMar 19 2018Aug 08 2018This work is concerned with the classical problem of finding a zero of a sum of maximal monotone operators. For the projective splitting framework recently proposed by Combettes and Eckstein, we show how to replace the fundamental subproblem calculation ... More

Phase transitions for random geometric preferential attachment graphsNov 15 2013We study an evolving spatial network in which sequentially arriving vertices are joined to existing vertices at random according to a rule that combines preference according to degree with preference according to spatial proximity. We investigate phase ... More

Approximate Waveforms for Extreme-Mass-Ratio Inspirals in Modified Gravity SpacetimesJun 30 2011Aug 03 2011Extreme-mass-ratio inspirals, in which a stellar-mass compact object spirals into a supermassive black hole, are prime candidates for detection with space-borne milliHertz gravitational wave detectors, similar to the Laser Interferometer Space Antenna. ... More

The reproducing kernel thesis for lower bounds of weighted composition operatorsDec 19 2018It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including reproducing kernels. The methods used in ... More

21-cm cosmologySep 27 2011Jan 05 2012Imaging the Universe during the first hundreds of millions of years remains one of the exciting challenges facing modern cosmology. Observations of the redshifted 21 cm line of atomic hydrogen offer the potential of opening a new window into this epoch. ... More

Norms of truncated Toeplitz operators and numerical radii of restricted shiftsNov 16 2017May 16 2019This paper gives a new approach to the calculation of the numerical radius of a restricted shift operator by linking it to the norm of a truncated Toeplitz operator (TTO), which can be be calculated by various methods. Further results on the norm of a ... More

Poisson approximation of subgraph counts in stochastic block models and a graphon modelSep 25 2015Mar 03 2016Small subgraph counts can be used as summary statistics for large random graphs. We use the Stein-Chen method to derive Poisson approximations for the distribution of the number of subgraphs in the stochastic block model which are isomorphic to some fixed ... More

Can we Detect Intermediate Mass Ratio Inspirals?Nov 02 2008Apr 20 2009Gravitational waves emitted during intermediate-mass-ratio inspirals (IMRIs) of intermediate-mass black holes (IMBHs) into supermassive black holes could represent a very interesting source for LISA. Similarly, IMRIs of stellar-mass compact objects into ... More

Exploring a string-like landscapeJan 08 2011Feb 15 2011We explore inflationary trajectories within randomly-generated two-dimensional potentials, considered as a toy model of the string landscape. Both the background and perturbation equations are solved numerically, the latter using the two-field formalism ... More