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Quantum optimality of photon counting for temperature measurement of thermal astronomical sourcesApr 08 2015Jul 28 2015Using the quantum Cram\'{e}r-Rao bound from quantum estimation theory, we derive a fundamental quantum limit on the sensitivity of a temperature measurement of a thermal astronomical source. This limit is expressed in terms of the source temperature $T_s$, ... More

Fundamental quantum limits to waveform detectionApr 17 2012Oct 16 2012Ever since the inception of gravitational-wave detectors, limits imposed by quantum mechanics to the detection of time-varying signals have been a subject of intense research and debate. Drawing insights from quantum information theory, quantum detection ... More

Semiclassical Theory of Superresolution for Two Incoherent Optical Point SourcesFeb 15 2016Using a semiclassical model of photodetection with Poissonian noise and insights from quantum metrology, we prove that linear optics and photon counting can optimally estimate the separation between two incoherent point sources without regard to Rayleigh's ... More

Subdiffraction incoherent optical imaging via spatial-mode demultiplexing: semiclassical treatmentMar 26 2017Feb 21 2018I present a semiclassical analysis of a spatial-mode demultiplexing (SPADE) measurement scheme for far-field incoherent optical imaging under the effects of diffraction and photon shot noise. Building on previous results that assume two point sources ... More

Volterra filters for quantum estimation and detectionSep 07 2015Dec 14 2015The implementation of optimal statistical inference protocols for high-dimensional quantum systems is often computationally expensive. To avoid the difficulties associated with optimal techniques, here I propose an alternative approach to quantum estimation ... More

Quantum transition-edge detectorsMay 08 2013Aug 14 2013Small perturbations to systems near critical points of quantum phase transitions can induce drastic changes in the system properties. Here I show that this sensitivity can be exploited for weak-signal detection applications. This is done by relating a ... More

Ultimate Energy Densities for Electromagnetic PulsesMar 06 2008The ultimate electric and magnetic energy densities that can be attained by bandlimited electromagnetic pulses in free space are calculated using an ab initio quantized treatment, and the quantum states of electromagnetic fields that achieve the ultimate ... More

On the Relationship between Resolution Enhancement and Multiphoton Absorption Rate in Quantum LithographyJul 17 2006Feb 28 2007The proposal of quantum lithography [Boto et al., Phys. Rev. Lett. 85, 2733 (2000)] is studied via a rigorous formalism. It is shown that, contrary to Boto et al.'s heuristic claim, the multiphoton absorption rate of a ``NOON'' quantum state is actually ... More

Subdiffraction incoherent optical imaging via spatial-mode demultiplexingAug 09 2016I propose a spatial-mode demultiplexing (SPADE) scheme for the far-field imaging of arbitrary incoherent optical sources. For an object too small to be resolved by direct imaging under the diffraction limit, I show that SPADE can estimate the moments ... More

Quantum Semiparametric EstimationJun 24 2019Jul 08 2019In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here I propose a theory of quantum semiparametric estimation ... More

Quantum limits on the time-bandwidth product of an optical resonatorSep 28 2017Dec 22 2017A thought-provoking proposal by Tsakmakidis et al. [Science 356, 1260 (2017)] suggests that nonreciprocal optics can break a time-bandwidth limit to passive resonators. Here I quantize their resonator model and show that quantum mechanics does impose ... More

Quantum Imaging beyond the Diffraction Limit by Optical Centroid MeasurementsJan 30 2009Jun 22 2009I propose a quantum imaging method that can beat the Rayleigh-Abbe diffraction limit and achieve de Broglie resolution without requiring a multiphoton absorber as the detector. Using the same non-classical states of light as those for quantum lithography, ... More

Multiparameter Heisenberg limitMar 17 2014Feb 01 2016Using a quantum version of the Bell-Ziv-Zakai bound, I derive a Heisenberg limit to multiparameter estimation for any Gaussian prior probability density. The mean-square error lower bound is shown to have a universal quadratic scaling with respect to ... More

Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing. II. Applications to atomic magnetometry and Hardy's paradoxSep 13 2009The quantum smoothing theory [Tsang, Phys. Rev. Lett. 102, 250403 (2009); Phys. Rev. A, in press (e-print arXiv:0906.4133)] is extended to account for discrete jumps in the classical random process to be estimated, discrete variables in the quantum system, ... More

Optimal waveform estimation for classical and quantum systems via time-symmetric smoothingJun 22 2009Aug 11 2009Classical and quantum theories of time-symmetric smoothing, which can be used to optimally estimate waveforms in classical and quantum systems, are derived using a discrete-time approach, and the similarities between the two theories are emphasized. Application ... More

Decoherence of Quantum-Enhanced Timing AccuracyApr 05 2007Quantum enhancement of optical pulse timing accuracy is investigated in the Heisenberg picture. Effects of optical loss, group-velocity dispersion, and Kerr nonlinearity on the position and momentum of an optical pulse are studied via Heisenberg equations ... More

Semiparametric estimation for incoherent optical imagingJun 11 2019Jun 17 2019The theory of semiparametric estimation offers an elegant way of computing the Cram\'er-Rao bound for a parameter of interest in the midst of infinitely many nuisance parameters. Here I apply the theory to the problem of moment estimation for incoherent ... More

Conservative error measures for classical and quantum metrologyMay 12 2016The classical and quantum Cram\'er-Rao bounds have become standard measures of parameter-estimation uncertainty for a variety of sensing and imaging applications in recent years, but their assumption of unbiased estimators potentially undermines their ... More

Quantum limits to optical point-source localizationNov 11 2014Jul 27 2015Motivated by the importance of optical microscopes to science and engineering, scientists have pondered for centuries how to improve their resolution and the existence of fundamental resolution limits. In recent years, a new class of microscopes that ... More

Mismatched Quantum Filtering and Entropic InformationOct 01 2013Jan 27 2014Quantum filtering is a signal processing technique that estimates the posterior state of a quantum system under continuous measurements and has become a standard tool in quantum information processing, with applications in quantum state preparation, quantum ... More

Beating the spatial standard quantum limits via adiabatic soliton expansionApr 18 2006May 09 2006Spatial quantum enhancement effects are studied under a unified framework. It is shown that the multiphoton absorption rate of photons with a quantum-enhanced lithographic resolution is reduced, not enhanced, contrary to popular belief. The use of adiabatic ... More

Quantum Semiparametric EstimationJun 24 2019Jul 31 2019In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here I propose a theory of quantum semiparametric estimation ... More

Subdiffraction incoherent optical imaging via spatial-mode demultiplexingAug 09 2016Nov 15 2016I propose a spatial-mode demultiplexing (SPADE) measurement scheme for the far-field imaging of arbitrary incoherent optical sources. For any object too small to be resolved by direct imaging under the diffraction limit, I show that SPADE can estimate ... More

Semiparametric estimation for incoherent optical imagingJun 11 2019The theory of semiparametric estimation offers an elegant way to compute the Cram\'er-Rao bound for a parameter of interest in the midst of infinitely many nuisance parameters. Here I apply the theory to the problem of moment estimation for incoherent ... More

Quantum limit to subdiffraction incoherent optical imagingJun 07 2018Jan 03 2019The application of quantum estimation theory to the problem of imaging two incoherent point sources has recently led to new insights and better measurements for incoherent imaging and spectroscopy. To establish a more general limit beyond the case of ... More

Subdiffraction incoherent optical imaging via spatial-mode demultiplexingAug 09 2016Feb 28 2017I propose a spatial-mode demultiplexing (SPADE) measurement scheme for the far-field imaging of spatially incoherent optical sources. For any object too small to be resolved by direct imaging under the diffraction limit, I show that SPADE can estimate ... More

Quantum metrology with open dynamical systemsJan 24 2013Jun 12 2013This paper studies quantum limits to dynamical sensors in the presence of decoherence. A modified purification approach is used to obtain tighter quantum detection and estimation error bounds for optical phase sensing and optomechanical force sensing. ... More

Spectral phase conjugation via extended phase matchingJun 15 2005Nov 21 2005It is shown that the copropagating three-wave-mixing parametric process, with appropriate type-II extended phase matching and pumped with a short second-harmonic pulse, can perform spectral phase conjugation and parametric amplification, which shows a ... More

Ziv-Zakai Error Bounds for Quantum Parameter EstimationNov 15 2011May 10 2012I propose quantum versions of the Ziv-Zakai bounds as alternatives to the widely used quantum Cram\'er-Rao bounds for quantum parameter estimation. From a simple form of the proposed bounds, I derive both a "Heisenberg" error limit that scales with the ... More

Quantum Nonlocality in Weak-Thermal-Light InterferometryAug 08 2011Nov 17 2011In astronomy, interferometry of light collected by separate telescopes is often performed by physically bringing the optical paths together in the form of Young's double-slit experiment. Optical loss severely limits the efficiency of this so-called direct ... More

Quantum Semiparametric EstimationJun 24 2019In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here I propose a theory of quantum semiparametric estimation ... More

Quantum Semiparametric EstimationJun 24 2019Jun 27 2019In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here I propose a theory of quantum semiparametric estimation ... More

Resolving starlight: a quantum perspectiveJun 05 2019The wave-particle duality of light introduces two fundamental problems to imaging, namely, the diffraction limit and the photon shot noise. Quantum information theory can tackle them both in one holistic formalism: model the light as a quantum object, ... More

Conservative classical and quantum resolution limits for incoherent imagingMay 12 2016Mar 26 2017I propose classical and quantum limits to the statistical resolution of two incoherent optical point sources from the perspective of minimax parameter estimation. Unlike earlier results based on the Cram\'er-Rao bound, the limits proposed here, based ... More

A Bayesian quasi-probability approach to inferring the past of quantum observablesMar 13 2014Apr 01 2014I describe a method of inferring the past of quantum observables given the initial state and the subsequent measurement results using Wigner quasi-probability representations. The method is proved to be compatible with logic for large subclasses of quantum ... More

Testing quantum mechanics: a statistical approachJun 12 2013Jan 27 2014As experiments continue to push the quantum-classical boundary using increasingly complex dynamical systems, the interpretation of experimental data becomes more and more challenging: when the observations are noisy, indirect, and limited, how can we ... More

Continuous Quantum Hypothesis TestingOct 23 2011Apr 27 2012I propose a general quantum hypothesis testing theory that enables one to test hypotheses about any aspect of a physical system, including its dynamics, based on a series of observations. For example, the hypotheses can be about the presence of a weak ... More

Time-Symmetric Quantum Theory of SmoothingApr 13 2009Jul 14 2009Smoothing is an estimation technique that takes into account both past and future observations, and can be more accurate than filtering alone. In this Letter, a quantum theory of smoothing is constructed using a time-symmetric formalism, thereby generalizing ... More

Fundamental Quantum Limit to Multiphoton Absorption Rate for Monochromatic LightFeb 04 2008Jul 22 2008The local multiphoton absorption rate for an arbitrary quantum state of monochromatic light, taking into account the photon number, momentum, and polarization degrees of freedom, is shown to have an upper bound that can be reached by coherent fields. ... More

Quantum temporal correlations and entanglement via adiabatic control of vector solitonsMar 10 2006May 29 2007It is shown that optical pulses with a mean position accuracy beyond the standard quantum limit can be produced by adiabatically expanding an optical vector soliton followed by classical dispersion management. The proposed scheme is also capable of entangling ... More

Cavity quantum electro-optics. II. Input-output relations between traveling optical and microwave fieldsMay 11 2011Aug 12 2011In the previous paper [M. Tsang, Phys. Rev. A 81, 063837 (2010), e-print arXiv:1003.0116], I proposed a quantum model of a cavity electro-optic modulator, which can coherently couple an optical cavity mode to a microwave resonator mode and enable novel ... More

Cavity quantum electro-opticsFeb 27 2010Jun 30 2010The quantum dynamics of the coupling between a cavity optical field and a resonator microwave field via the electro-optic effect is studied. This coupling has the same form as the opto-mechanical coupling via radiation pressure, so all previously considered ... More

Metaphoric optical computing of fluid dynamicsApr 18 2006We present theoretical and numerical evidence to show that self-defocusing nonlinear optical propagation can be used to compute Euler fluid dynamics and possibly Navier-Stokes fluid dynamics. In particular, the formation of twin vortices and the K\'arm\'an ... More

Electromagnetically induced transparency and optical memories in an optomechanical system with $N$ membranesMar 06 2014We study the propagation of a weak probe field through an optomechanical system in which $N$ nearly degenerate mechanical membranes are inside a Febry-Perot cavity, and couple dispersively to an intracavity field. We derive a general analytical expression ... More

Coupled-Resonator Optical Near-Field LithographyApr 21 2008The problem of pattern formation in resonantly-enhanced near-field lithography by the use of dielectric or plasmonic planar resonators is investigated. Sub-diffraction-limited bright or dark spots can be produced by taking advantage of the rotational ... More

Far-field Super-resolution of Thermal Electromagnetic Sources at the Quantum LimitApr 04 2016Jul 06 2016We obtain the ultimate quantum limit for estimating the transverse separation of two thermal point sources using a given imaging system with limited spatial bandwidth. Via the quantum Cramer-Rao bound, we show that, contrary to the Rayleigh limit in conventional ... More

Optomechanical parameter estimationJul 15 2013Oct 03 2013We propose a statistical framework for the problem of parameter estimation from a noisy optomechanical system. The Cram\'er-Rao lower bound on the estimation errors in the long-time limit is derived and compared with the errors of radiometer and expectation-maximization ... More

Interferometric superlocalization of two incoherent optical point sourcesDec 28 2015Jan 24 2016A novel interferometric method - SLIVER (Super Localization by Image inVERsion interferometry) - is proposed for estimating the separation of two incoherent point sources with a mean squared error that does not deteriorate as the sources are brought closer. ... More

Comment on "Resurgence of Rayleigh's curse in the presence of partial coherence"Oct 29 2018Larson and Saleh [Optica 5, 1382 (2018)] suggest that Rayeleigh's curse can recur and become unavoidable if the two sources are partially coherent. Here we show that their calculations and assertions have fundamental problems, and spatial-mode demultiplexing ... More

Magnifying perfect lens and superlens design by coordinate transformationAug 02 2007Nov 29 2007The coordinate transformation technique is applied to the design of perfect lenses and superlenses. In particular, anisotropic metamaterials that magnify two-dimensional planar images beyond the diffraction limit are designed by the use of oblate spheroidal ... More

Far-field Superresolution of Thermal Electromagnetic Sources at the Quantum LimitApr 04 2016Nov 28 2016We obtain the ultimate quantum limit for estimating the transverse separation of two thermal point sources using a given imaging system with limited spatial bandwidth. We show via the quantum Cram\'er-Rao bound that, contrary to the Rayleigh limit in ... More

Propagation of temporal entanglementMar 10 2006The equations that govern the temporal evolution of two photons in the Schr{\"o}dinger picture are derived, taking into account the effects of loss, group-velocity dispersion, temporal phase modulation, linear coupling among different optical modes, and ... More

Reflectionless evanescent-wave amplification by two dielectric planar waveguidesMar 10 2006Oct 17 2006Utilizing the underlying physics of evanescent wave amplification by a negative-refractive-index slab, it is shown that evanescent waves with specific spatial frequencies can also be amplified without any reflection simply by two dielectric planar waveguides. ... More

Optimal signal processing for continuous qubit readoutMay 28 2014Aug 06 2014The measurement of a quantum two-level system, or a qubit in modern terminology, often involves an electromagnetic field that interacts with the qubit, before the field is measured continuously and the qubit state is inferred from the noisy field measurement. ... More

Quantum Weiss-Weinstein bounds for quantum metrologyNov 29 2015Jul 26 2016Sensing and imaging are among the most important applications of quantum information science. To investigate their fundamental limits and the possibility of quantum enhancements, researchers have for decades relied on the quantum Cram\'er-Rao lower error ... More

Coherent Quantum-Noise Cancellation for Optomechanical SensorsJun 04 2010Aug 17 2010Using a flowchart representation of quantum optomechanical dynamics, we design coherent quantum-noise-cancellation schemes that can eliminate the back-action noise induced by radiation pressure at all frequencies and thus overcome the standard quantum ... More

Evading quantum mechanicsMar 11 2012Apr 02 2012Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement back action often limit the precision of conventional classical information-processing devices, such as ... More

Quantum theory of optical temporal phase and instantaneous frequencyApr 03 2008Nov 18 2008We propose a general quantum theory of optical phase and instantaneous frequency in the time domain for slowly varying optical signals. Guided by classical estimation theory, we design homodyne phase-locked loops that enable quantum-limited measurements ... More

Quantum limit for two-dimensional resolution of two incoherent optical point sourcesJun 02 2016We obtain the multiple-parameter quantum Cram\'er-Rao bound for estimating the Cartesian components of the centroid and separation of two incoherent optical point sources using an imaging system with finite spatial bandwidth. Under quite general and realistic ... More

Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous time limit and state-variable approach to phase-locked loop designFeb 18 2009May 21 2009We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [Tsang, Shapiro, and Lloyd, Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to estimation, we design ... More

Quantum limit for two-dimensional resolution of two incoherent optical point sourcesJun 02 2016Jun 30 2017We obtain the multiple-parameter quantum Cram\'er-Rao bound for estimating the transverse Cartesian components of the centroid and separation of two incoherent optical point sources using an imaging system with finite spatial bandwidth. Under quite general ... More

Quantum-optimal detection of one-versus-two incoherent sources with arbitrary separationSep 10 2016We analyze the fundamental resolution of incoherent optical point sources from the perspective of a quantum detection problem: deciding whether the optical field on the image plane is generated by one source or two weaker sources with arbitrary separation. ... More

Quantum Theory of Superresolution for Two Incoherent Optical Point SourcesNov 02 2015Aug 29 2016Rayleigh's criterion for resolving two incoherent point sources has been the most influential measure of optical imaging resolution for over a century. In the context of statistical image processing, violation of the criterion is especially detrimental ... More

Semiclassical Theory of Superresolution for Two Incoherent Optical Point SourcesFeb 15 2016Nov 06 2016Using a semiclassical model of photodetection with Poissonian noise and insights from quantum metrology, we prove that linear optics and photon counting can optimally estimate the separation between two incoherent point sources without regard to Rayleigh's ... More

Fundamental Quantum Limit to Waveform EstimationJun 28 2010Mar 04 2011We derive a quantum Cram\'er-Rao bound (QCRB) on the error of estimating a time-changing signal. The QCRB provides a fundamental limit to the performance of general quantum sensors, such as gravitational-wave detectors, force sensors, and atomic magnetometers. ... More

Improved mirror position estimation using resonant quantum smoothingMay 13 2015Quantum parameter estimation, the ability to precisely obtain a classical value in a quantum system, is very important to many key quantum technologies. Many of these technologies rely on an optical probe, either coherent or squeezed states to make a ... More

Quantum-Limited Mirror-Motion EstimationMay 01 2013We experimentally demonstrate optomechanical motion and force measurements near the quantum precision limits set by the quantum Cram\'er-Rao bounds (QCRBs). Optical beams in coherent and phase-squeezed states are used to measure the motion of a mirror ... More

Fisher information for far-field linear optical superresolution via homodyne or heterodyne detection in a higher-order local oscillator modeJun 27 2017Dec 21 2017The distance between two point light sources is difficult to estimate if that distance is below the diffraction (Rayleigh's) resolution limit of the imaging device. A recently proposed technique enhances the precision of this estimation by exploiting ... More

The quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimationSep 28 2014We propose quantum versions of the Bell-Ziv-Zakai lower bounds on the error in multiparameter estimation. As an application we consider measurement of a time-varying optical phase signal with stationary Gaussian prior statistics and a power law spectrum ... More

Realizable classes and embedding problemsFeb 07 2016Jul 25 2016Let $K$ be a number field with ring of integers $\mathcal{O}_K$ and let $G$ be a finite group. Given a $G$-Galois $K$-algebra $K_h$, let $\mathcal{O}_h$ denote its ring of integers. If $K_h/K$ is tame, then a classical theorem of E. Noether implies that ... More

On the multiple holomorph of groups of squarefree or odd prime power orderJun 20 2019Let $G$ be a group and write $\mbox{Perm}(G)$ for its symmetric group. Define $\mbox{Hol}(G)$ to be the holomorph of $G$, regarded as a subgroup of $\mbox{Perm}(G)$, and let $\mbox{NHol}(G)$ denote its normalizer. The quotient $T(G) = \mbox{NHol}(G)/\mbox{Hol}(G)$ ... More

Linear Corotation Torques in Non-Barotropic DisksOct 31 2013Jan 13 2014I derive a fully analytic expression for the linear corotation torque to first order in eccentricity for planets in non-barotropic protoplanetary disks, taking into account the effect of disk entropy gradients. This torque formula is applicable to both ... More

Protoplanetary Disk Resonances and Type I MigrationJul 20 2011Oct 03 2011Waves reflected by the inner edge of a protoplanetary disk are shown to significantly modify Type I migration, even allowing the trapping of planets near the inner disk edge for small planets in a range of disk parameters. This may inform the distribution ... More

Video Contents Prior Storing Server for Optical Access NetworkApr 08 2015One of the most important multimedia applications is Internet protocol TV (IPTV) for next-generation networks. IPTV provides triple-play services that require high-speed access networks with the functions of multicasting and quality of service (QoS) guarantees. ... More

Hopf-Galois structures on a Galois $S_n$-extensionDec 16 2018In this paper, we shall determine the exact number of Hopf-Galois structures on a Galois $S_n$-extension, where $S_n$ denotes the symmetric group on $n$ letters.

On the multiple holomorph of a finite almost simple groupApr 22 2019Let $G$ be a group and write $\mbox{Perm}(G)$ for its symmetric group. The holomorph $\mbox{Hol}(G)$ of $G$ is defined to be the normalizer of the subgroup of left translations in $\mbox{Perm}(G)$. Its normalizer $\mbox{NHol}(G)$ in $\mbox{Perm}(G)$ in ... More

On the multiple holomorph of a finite almost simple groupApr 22 2019May 29 2019Let $G$ be a group. Let $\mathrm{Perm}(G)$ denote its symmetric group and write $\mathrm{Hol}(G)$ for the normalizer of the subgroup of left translations in $\mathrm{Perm}(G)$. The multiple holomorph $\mathrm{NHol}(G)$ of $G$ is in turn defined to be ... More

Non-existence of Hopf-Galois structures and bijective crossed homomorphismsMay 28 2018Sep 15 2018By work of C. Greither and B. Pareigis as well as N. P. Byott, the enumeration of Hopf-Galois structures on a Galois extension of fields with Galois group $G$ may be reduced to that of regular subgroups of $\mbox{Hol}(N)$ isomorphic to $G$ as $N$ ranges ... More

On the self-duality of rings of integers in tame and abelian extensionsMar 09 2017Dec 06 2018Let $L/K$ be a tame and Galois extension of number fields with group $G$. It is well-known that any ambiguous ideal in $L$ is locally free over $\mathcal{O}_KG$ (of rank one), and so it defines a class in the locally free class group of $\mathcal{O}_KG$, ... More

Shattering Flares During Close Encounters of Neutron StarsJul 12 2013We demonstrate that resonant shattering flares can occur during close passages of neutron stars in eccentric or hyperbolic encounters. We provide updated estimates for the rate of close encounters of compact objects in dense stellar environments, which ... More

On the Galois module structure of the square root of the inverse different in abelian extensionsJul 16 2014Jun 09 2015Let $K$ be a number field with ring of integers $\mathcal{O}_K$ and $G$ a finite group of odd order. If $K_h$ is a weakly ramified $G$-Galois $K$-algebra, then its square root $A_h$ of the inverse different is a locally free $\mathcal{O}_{K}G$-module ... More

Hopf-Galois structures on a Galois $S_n$-extensionDec 16 2018May 20 2019In this paper, we shall determine the exact number of Hopf-Galois structures on a Galois $S_n$-extension, where $S_n$ denotes the symmetric group on $n$ letters.

Galois module structure of the square root of the inverse different over maximal ordersJul 25 2016Let $K$ be a number field with ring of integers $\mathcal{O}_K$ and let $G$ be a \mbox{finite group of} odd order. Given a $G$-Galois $K$-algebra $K_h$, let $A_h$ be the square root of the inverse different of $K_h/K$, which exists by Hilbert's formula. ... More

N derivatives are necessary for order N+1 convergence in quadrature: a converse resultJan 28 2014Results on the error bounds of quadrature methods are well known - most state that if the method has degree N, and the integrand has N derivatives, then the error is order N+1. We prove here a converse: that if the integrand fails to have N derivatives, ... More

Spectrum analysis with quantum dynamical systemsMar 07 2016Measuring the power spectral density of a stochastic process, such as a stochastic force or magnetic field, is a fundamental task in many sensing applications. Quantum noise is becoming a major limiting factor to such a task in future technology, especially ... More

On the realizable classes of the square root of the inverse different in the unitary class groupSep 21 2015Dec 08 2015Let $K$ be a number field with ring of integers $\mathcal{O}_K$ and let $G$ be a finite abelian group of odd order. Given a $G$-Galois $K$-algebra $K_h$, let $A_h$ denote its square root of the inverse different, which exists by Hilbert's formula. If ... More

Hopf-Galois structures of isomorphic type on a non-abelian characteristically simple extensionNov 28 2018Mar 15 2019Let $L/K$ be a finite Galois extension whose Galois group $G$ is non-abelian and characteristically simple. Using tools from graph theory, we shall give a closed formula for the number of Hopf-Galois structures on $L/K$ with associated group isomorphic ... More

On the solvability of regular subgroups in the holomorph of a finite solvable groupJan 30 2019In this paper, we shall exhibit an infinite family of non-solvable numbers $n$ for which the holomorph of any solvable group of order $n$ has no insolvable regular subgroup.

Corotational Damping of Diskoseismic C-modes in Black Hole Accretion DiscsOct 07 2008Nov 14 2008Diskoseismic c-modes in accretion discs have been invoked to explain low-frequency variabilities observed in black-hole X-ray binaries. These modes are trapped in the inner-most region of the disc and have frequencies much lower than the rotation frequency ... More

On the solvability of regular subgroups in the holomorph of a finite solvable groupJan 30 2019Mar 20 2019In this paper, we shall exhibit an infinite family of non-solvable numbers $n$ for which the holomorph of any solvable group of order $n$ has no insolvable regular subgroup.

Third Order Intermodulation Power Estimation for N Sinusoidal ChannelsNov 23 2013In this paper analysis is given to find the third order intermodulation power given sinusoids are fed into a nonlinear device. A simple expression of the third order intermodulation power is given for the case that the center frequencies of the input ... More

Corotational Instability of Inertial-Acoustic Modes in Black Hole Accretion Discs and Quasi-Periodic OscillationsOct 01 2008Nov 14 2008We study the global stability of non-axisymmetric p-modes (also called inertial-acoustic modes) trapped in the inner-most regions of accretion discs around black holes. We show that the lowest-order (highest-frequency) p-modes, with frequencies $\omega=(0.5-0.7) ... More

Schwinger Generating Functional Derivation of LHC Elastic Proton-Proton Scattering AmplitudesNov 12 2018Nov 30 2018A recent Schwinger Generating Functional based formulation, by H.M.Fried,Y.Gabellini,T.Grandou and Y-M.Sheu and P.H.Tsang provided gauge-invariant, exact, non-perturbative solutions for QCD. After choosing a renormalization scheme and assuming a simpler ... More

Taking all positive eigenvectors is suboptimal in classical multidimensional scalingFeb 12 2014It is hard to overstate the importance of multidimensional scaling as an analysis technique in the broad sciences. Classical, or Torgerson multidimensional scaling is one of the main variants, with the advantage that it has a closed-form analytic solution. ... More

Super-Reflection in Fluid Discs: Corotation Amplifier, Corotation Resonance, Rossby Waves, and Overstable ModesOct 11 2007May 16 2008In differentially rotating discs with no self-gravity, density waves cannot propagate around the corotation, where the wave pattern rotation speed equals the fluid rotation rate. Waves incident upon the corotation barrier may be super-reflected (commonly ... More

An index for regular expression queries: Design and implementationAug 04 2011Aug 15 2011The like regular expression predicate has been part of the SQL standard since at least 1989. However, despite its popularity and wide usage, database vendors provide only limited indexing support for regular expression queries which almost always require ... More

Non-universal velocity probability densities in two-dimensional turbulence: the effect of large-scale dissipationMar 20 2017We show that some statistical properties of forced two-dimensional turbulence have an important sensitivity to the form of large-scale dissipation which is required to damp the inverse cascade. We consider three models of large-scale dissipation: linear ... More

Black Magic Investigation Made Simple: Monte Carlo Simulations and Historical Back Testing of Momentum Cross-Over Strategies Using FRACTI PatternsAug 23 2018To promote economic stability, finance should be studied as a hard science, where scientific methods apply. When a trading strategy is proposed, the underlying model should be transparent and defined robustly to allow other researchers to understand and ... More

Interface Modes and Their Instabilities in Accretion Disc Boundary LayersDec 20 2008We study global non-axisymmetric oscillation modes trapped near the inner boundary of an accretion disc. Observations indicate that some of the quasi-periodic oscillations (QPOs) observed in the luminosities of accreting compact objects (neutron stars, ... More

Corotational Instability of Inertial-Acoustic Modes in Black-Hole Accretion Discs: Non-Barotropic FlowsJun 24 2009May 08 2010We study the effect of corotation resonance on the inertial-acoustic oscillations (p-modes) of black-hole accretion discs. Previous works have shown that for barotropic flows (where the pressure depends only on the density), wave absorption at the corotation ... More