Search

The relativistic inverse stellar structure problem determines the equation of state of the stellar matter given a knowledge of suitable macroscopic observable properties (e.g. their masses and radii) of the stars composed of that material. This study determines how accurately this equation of state can be determined using noisy mass and radius observations. The relationship between the size of the observational errors and the accuracy of the inferred equation of state is evaluated, and the optimal number of adjustable equation of state parameters needed to achieve the highest accuracy is determined., Comment: 8 pages, 7 figures

Causal parametric representations of neutron-star equations of state are constructed here using Chebyshev polynomial based spectral expansions. The accuracies of these representations are evaluated for a collection of model equations of state from a variety of nuclear-theory models and also a collection of equations of state with first- or second-order phase transitions of various sizes. These tests show that the Chebyshev based representations are convergent (even for equations of state with phase transitions) as the number of spectral basis functions is increased. This study finds that the Chebyshev based representations are generally more accurate than a previously studied power-law based spectral representation, and that pressure-based representations are generally more accurate than those based on enthalpy., Comment: 7 pages, 6 figures

This paper explores the use of low-dimensional parametric representations of neutron-star equations of state that include discontinuities caused by phase transitions. The accuracies of optimal piecewise-analytic and spectral representations are evaluated for equations of state having first- or second-order phase transitions with a wide range of discontinuity sizes. These results suggest that the piecewise-analytic representations of these non-smooth equations of state are convergent, while the spectral representations are not. Nevertheless, the lower-order (2 <= N_parms <= 7) spectral representations are found to be more accurate than the piecewise-analytic representations with the same number of parameters., Comment: 9 pages, 10 figures

Neutron stars provide a unique opportunity to study strongly interacting matter under extreme density conditions. The intricacies of matter inside neutron stars and their equation of state are not directly visible, but determine bulk properties, such as mass and radius, which affect the star's thermal X-ray emissions. However, the telescope spectra of these emissions are also affected by the stellar distance, hydrogen column, and effective surface temperature, which are not always well-constrained. Uncertainties on these nuisance parameters must be accounted for when making a robust estimation of the equation of state. In this study, we develop a novel methodology that, for the first time, can infer the full posterior distribution of both the equation of state and nuisance parameters directly from telescope observations. This method relies on the use of neural likelihood estimation, in which normalizing flows use samples of simulated telescope data to learn the likelihood of the neutron star spectra as a function of these parameters, coupled with Hamiltonian Monte Carlo methods to efficiently sample from the corresponding posterior distribution. Our approach surpasses the accuracy of previous methods, improves the interpretability of the results by providing access to the full posterior distribution, and naturally scales to a growing number of neutron star observations expected in the coming years.

The effectiveness of the hyperbolic relaxation method for solving the Einstein constraint equations numerically is studied here on a variety of compact orientable three-manifolds. Convergent numerical solutions are found using this method on manifolds admitting negative Ricci scalar curvature metrics, i.e. those from the $H^3$ and the $H^2\times S^1$ geometrization classes. The method fails to produce solutions, however, on all the manifolds examined here admitting non-negative Ricci scalar curvatures, i.e. those from the $S^3$, $S^2\times S^1$, and the $E^3$ classes. This study also finds that the accuracy of the convergent solutions produced by hyperbolic relaxation can be increased significantly by performing fairly low-cost standard elliptic solves using the hyperbolic relaxation solutions as initial guesses., Comment: 7 pages, 8 figures, to appear in PRD

Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by expanding the class of suitable triangulations, significantly increasing the number of manifolds to which these methods apply. These new results show that this expanded class of triangulations is still a small subset of all possible triangulations. This demonstrates that fundamental changes to these methods are needed to further expand the collection of manifolds on which differentiable structures can be constructed numerically., Comment: 6 pages, 1 figure

We report on a new search for continuous gravitational waves from NS 1987A, the neutron star born in SN 1987A, using open data from Advanced LIGO and Virgo's third observing run (O3). The search covered frequencies from 35-1050 Hz, more than five times the band of the only previous gravitational wave search to constrain NS 1987A [B. J. Owen et al., ApJL 935, L7 (2022)]. It used an improved code and coherently integrated from 5.10 days to 14.85 days depending on frequency. No astrophysical signals were detected. By expanding the frequency range and using O3 data, this search improved on strain upper limits from the previous search and was sensitive at the highest frequencies to ellipticities of 1.6e-5 and r-mode amplitudes of 4.4e-4, both an order of magnitude improvement over the previous search and both well within the range of theoretical predictions., Comment: 7 pages, 1 figure

The interiors of neutron stars reach densities and temperatures beyond the limits of terrestrial experiments, providing vital laboratories for probing nuclear physics. While the star's interior is not directly observable, its pressure and density determine the star's macroscopic structure which affects the spectra observed in telescopes. The relationship between the observations and the internal state is complex and partially intractable, presenting difficulties for inference. Previous work has focused on the regression from stellar spectra of parameters describing the internal state. We demonstrate a calculation of the full likelihood of the internal state parameters given observations, accomplished by replacing intractable elements with machine learning models trained on samples of simulated stars. Our machine-learning-derived likelihood allows us to perform maximum a posteriori estimation of the parameters of interest, as well as full scans. We demonstrate the technique by inferring stellar mass and radius from an individual stellar spectrum, as well as equation of state parameters from a set of spectra. Our results are more precise than pure regression models, reducing the width of the parameter residuals by 11.8% in the most realistic scenario. The neural networks will be released as a tool for fast simulation of neutron star properties and observed spectra., Comment: 18 pages, 8 figures

Neutron stars provide a unique laboratory for studying matter at extreme pressures and densities. While there is no direct way to explore their interior structure, X-rays emitted from these stars can indirectly provide clues to the equation of state (EOS) of superdense nuclear matter through the inference of the star's mass and radius. However, inference of EOS directly from a star's X-ray spectra is extremely challenging and is complicated by systematic uncertainties. The current state of the art is to use simulation-based likelihoods in a piece-wise method, which first infer the star's mass and radius to reduce the dimensionality of the problem, and from those quantities infer the EOS. We demonstrate a series of enhancements to the state of the art, in terms of realistic uncertainty quantification and improved regression of physical properties with machine learning. We also demonstrate novel inference of the EOS directly from the high-dimensional spectra of observed stars, avoiding the intermediate mass-radius step. Our network is conditioned on the sources of uncertainty of each star, allowing for natural and complete propagation of uncertainties to the EOS., Comment: 24 pages, 20 figures

Numerical solutions to the Einstein constraint equations are constructed on a selection of compact orientable three-dimensional manifolds with non-trivial topologies. A simple constant mean curvature solution and a somewhat more complicated non-constant mean curvature solution are computed on example manifolds from three of the eight Thursten geometrization classes. The constant mean curvature solutions found here are also solutions to the Yamabe problem that transforms a geometry into one with constant scalar curvature., Comment: 15 pages, 6 figures, published version

We report on a search for continuous gravitational waves (GWs) from NS 1987A, the neutron star born in SN 1987A. The search covered a frequency band of 75-275 Hz, included a wide range of spin-down parameters for the first time, and coherently integrated 12.8 days of data below 125 Hz and 8.7 days of data above 125 Hz from the second Advanced LIGO observing run. We found no astrophysical signal. We set upper limits on GW emission as tight as an intrinsic strain of $2\times10^{-25}$ at 90\% confidence. The large spin-down parameter space makes this search the first astrophysically consistent one for continuous GWs from NS 1987A. Our upper limits are the first consistent ones to beat an analog of the spin-down limit based on the age of the neutron star, and hence are the first GW observations to put new constraints on NS 1987A.

Spectral representations have been shown to provide an efficient way to represent the poorly understood high-density portion of the neutron-star equation of state. This paper shows how the efficiency and accuracy of those representations can be improved by a very simple change., Comment: 5 pages, 6 figures

A method is developed here for building differentiable three-dimensional manifolds on multicube structures. This method constructs a sequence of reference metrics that determine differentiable structures on the cubic regions that serve as non-overlapping coordinate charts on these manifolds. It uses solutions to the two- and three-dimensional biharmonic equations in a sequence of steps that increase the differentiability of the reference metrics across the interfaces between cubic regions. This method is algorithmic and has been implemented in a computer code that automatically generates these reference metrics. Examples of three-manifolds constructed in this way are presented here, including representatives from five of the eight Thurston geometrization classes, plus the well-known Hantzsche-Wendt, the Poincare dodecahedral space, and the Seifert-Weber space., Comment: 37 pages, 10 figures, 12 Tables; v2 includes minor revisions and additions to agree with the final published version

The aim of this extended abstract is to introduce five examples of ethical issues in HRI that could have potential ethical implications, particularly on HRI participants. We consider these examples important to discuss in order to reach a consensus on how to handle them. Due to space limitations, this list is far from exhaustive and we hope that it can lead to a wider discussion that stimulates HRI researchers to think ethically. Previous work has shown a trend of underreporting ethical conduct in the HRI field; in this extended abstract we consider some of the ethical issues that could arise in HRI research., Comment: in TRAITS Workshop Proceedings (arXiv:2103.12679) held in conjunction with Companion of the 2021 ACM/IEEE International Conference on Human-Robot Interaction, March 2021, Pages 709-711

Finding an effective medical treatment often requires a search by trial and error. Making this search more efficient by minimizing the number of unnecessary trials could lower both costs and patient suffering. We formalize this problem as learning a policy for finding a near-optimal treatment in a minimum number of trials using a causal inference framework. We give a model-based dynamic programming algorithm which learns from observational data while being robust to unmeasured confounding. To reduce time complexity, we suggest a greedy algorithm which bounds the near-optimality constraint. The methods are evaluated on synthetic and real-world healthcare data and compared to model-free reinforcement learning. We find that our methods compare favorably to the model-free baseline while offering a more transparent trade-off between search time and treatment efficacy.

We describe directed searches for continuous gravitational waves from twelve well localized non-pulsing candidate neutron stars in young supernova remnants using data from Advanced LIGO's second observing run. We assumed that each neutron star is isolated and searched a band of frequencies from 15 to 150\,Hz, consistent with frequencies expected from known young pulsars. After coherently integrating spans of data ranging from 12.0 to 55.9 days using the F-statistic and applying data-based vetoes, we found no evidence of astrophysical signals. We set upper limits on intrinsic gravitational wave amplitude in some cases stronger than 10^{-25}, generally about a factor of two better than upper limits on the same objects from Advanced LIGO's first observing run., Comment: v2 updated to version accepted for publication in Physical Review D

We investigate the role of relativity in photo ionization of hydrogen-like ions by a laser pulse. For hydrogen, the wavelengths of the laser resides in the weakly ultra violet region. For higher nuclear charges, the laser parameters are scaled in a manner which renders the time-dependent Schr{\"o}dinger equation in the dipole approximation independent of nuclear charge. The ionization potentials of these highly charged ions are strongly modified by relativistic effects. In an earlier work, Ivanova et al., Phys. Rev. A {\bf 98}, 063402 (2018), it is demonstrated how this explains most of the relativistic correction to the ionization probability. Here we investigate to what extent remaining discrepancies can be attributed to relativistic effects stemming from the strong external field. To this end, we solve semi-relativistic formulations of both the Schr{\"o}dinger and the Dirac equations; the former accounts for increased inertia due to the external laser field, while the latter features a non-relativistic interaction term.

Observations suggest that our universe is spatially flat on the largest observable scales. Exactly six different compact orientable three-dimensional manifolds admit flat metrics. These six manifolds are therefore the most natural choices for building cosmological models based on the present observations. This paper briefly describes these six manifolds and the harmonic basis functions previously developed for representing arbitrary scalar fields on them. The principal focus of this paper is the development of new harmonics for representing arbitrary vector and second-rank tensor fields on these manifolds. These new harmonics are designed to be useful tools for analyzing the dynamics of electromagnetic and gravitational fields on these spaces., Comment: 12 pages; version 2 to match JCAP accepted draft

The purpose of this note is to clarify the conditions under which the first-order generalize-harmonic representation of the vacuum Einstein evolution system is linearly degenerate.

A semi-relativistic formulation of light-matter interaction is derived using the so called propagation gauge and the relativistic mass shift. We show that relativistic effects induced by a super-intense laser field can, to a surprisingly large extent, be accounted for by the Schr{\"o}dinger equation, provided that we replace the rest mass in the propagation gauge Hamiltonian by the corresponding time-dependent field-dressed mass. The validity of the semi-relativistic approach is tested numerically on a hydrogen atom exposed to an intense XUV laser pulse strong enough to accelerate the electron towards relativistic velocities. It is found that while the results obtained from the ordinary (non-relativistic) Schr{\"o}dinger equation generally differ from those of the Dirac equation, merely demonstrating that relativistic effects are significant, the semi-relativistic formulation provides results in quantitative agreement with a fully relativistic treatment.

Gravitational wave detectors in the LIGO/Virgo frequency band are able to measure the individual masses and the composite tidal deformabilities of neutron-star binary systems. This paper demonstrates that high accuracy measurements of these quantities from an ensemble of binary systems can in principle be used to determine the high density neutron-star equation of state exactly. This analysis assumes that all neutron stars have the same thermodynamically stable equation of state, but does not use simplifying approximations for the composite tidal deformability or make additional assumptions about the high density equation of state., Comment: 6 pages, 4 figures; v2 updated to version accepted for publication in Phys. Rev. D

Parameterized representations of the equation of state play an important role in efforts to measure the properties of the matter in the cores of neutron stars using astronomical observations. New representations are presented here that are capable of representing any equation of state to any desired level of accuracy, while automatically imposing causality and thermodynamic stability constraints. Numerical tests are presented that measure how accurately and efficiently these new parameterizations represent a collection of causal nuclear-theory model equations of state., Comment: 10 pages, 8 figures; v2 updated with minor modifications to form accepted for publication in Phys. Rev. D

We discuss magnetic field enhancement by unstable r-modes (driven by the gravitational radiation reaction force) in rotating stars. In the absence of a magnetic field, gravitational radiation exponentially increases the r-mode amplitude $\alpha$, and accelerates differential rotation (secular motion of fluid elements). For a magnetized star, differential rotation enhances the magnetic field energy. Rezzolla et al. (2000--2001) argued that if the magnetic energy grows faster than the gravitational radiation reaction force pumps energy into the r-modes, then the r-mode instability is suppressed. Chugunov (2015) demonstrated that without gravitational radiation, differential rotation can be treated as a degree of freedom decoupled from the r-modes and controlled by the back reaction of the magnetic field. In particular, the magnetic field windup does not damp r-modes. Here we discuss the effect of the back reaction of the magnetic field on differential rotation of unstable r-modes, and show that it limits the generated magnetic field and the magnetic energy growth rate preventing suppression of the r-mode instability by magnetic windup at low saturation amplitudes, $\alpha \ll 1$, predicted by current models., Comment: 5 pages; Contribution to the proceedings of the Physics of Neutron Stars - 2017 (Saint Petersburg, July 10-14, 2017), associated with a talk by A.I. Chugunov

Molecular dynamics (MD) simulations are used in biochemistry, physics, and other fields to study the motions, thermodynamic properties, and the interactions between molecules. Computational limitations and the complexity of these problems, however, create the need for approximations to the standard MD methods and for uncertainty quantification and reliability assessment of those approximations. In this paper, we exploit the intrinsic two-scale nature of MD to construct a class of large-scale dynamics approximations. The reliability of these methods are evaluated here by measuring the differences between full, classical MD simulations and those based on these large-scale approximations. Molecular dynamics evolutions are non-linear and chaotic, so the complete details of molecular evolutions cannot be accurately predicted even using full, classical MD simulations. This paper provides numerical results that demonstrate the existence of computationally efficient large-scale MD approximations which accurately model certain large-scale properties of the molecules: the energy, the linear and angular momenta, and other macroscopic features of molecular motions., Comment: 16 pages, 12 figures

Scalar, vector and tensor harmonics on the three-sphere were introduced originally to facilitate the study of various problems in gravitational physics. These harmonics are defined as eigenfunctions of the covariant Laplace operator which satisfy certain divergence and trace identities, and ortho-normality conditions. This paper provides a summary of these properties, along with a new notation that simplifies and clarifies some of the key expressions. Practical methods are described for accurately and efficiently computing these harmonics numerically, and test results are given that illustrate how well the analytical identities are satisfied by the harmonics computed numerically in this way., Comment: 14 pages, 9 figures, to appear in General Relativity and Gravitation

At second order in perturbation theory, the unstable r-mode of a rotating star includes growing differential rotation whose form and growth rate are determined by gravitational-radiation reaction. With no magnetic field, the angular velocity of a fluid element grows exponentially until the mode reaches its nonlinear saturation amplitude and remains nonzero after saturation. With a background magnetic field, the differential rotation winds up and amplifies the field, and previous work where large mode amplitudes were considered suggests that the amplification may damp out the instability. A background magnetic field, however, turns the saturated time-independent perturbations corresponding to adding differential rotation into perturbations whose characteristic frequencies are of order the Alfv\'en frequency. As found in previous studies, we argue that magnetic- field growth is sharply limited by the saturation amplitude of an unstable mode. In contrast to previous work, however, we show that if the amplitude is small, i.e., of order 10^(-4), then the limit on the magnetic-field growth is stringent enough to prevent the loss of energy to the magnetic field from damping or significantly altering an unstable r-mode in nascent neutron stars with normal interiors and in cold stars whose interiors are type II superconductors. We show this result first for a toy model, and we then obtain an analogous upper limit on magnetic field growth using a more realistic model of a rotating neutron star. Our analysis depends on the assumption that there are no marginally unstable perturbations, and this may not hold when differential rotation leads to a magnetorotational instability., Comment: This is essentially the published version

This paper derives accuracy standards for model gravitational waveforms required to ensure proper use of the Allen $\chi^2$ discriminator in gravitational wave (GW) data analysis. These standards are different from previously established requirements for detection and waveform parameter measurement based on signal-to-noise optimization. We present convenient formulae for evaluating and interpreting the contribution of model errors to measured values of this $\chi^2$ statistic. The new accuracy standards derived here are needed to ensure the reliability of measured values of the Allen $\chi^2$ statistic, both in their traditional role as vetoes and in their current role as elements in evaluating the significance of candidate detections., Comment: 5 pages, v2 revised to version to appear in Phys. Rev. D

At second order in perturbation theory, the $r$-modes of uniformly rotating stars include an axisymmetric part that can be identified with differential rotation of the background star. If one does not include radiation-reaction, the differential rotation is constant in time and has been computed by S\'a. It has a gauge dependence associated with the family of time-independent perturbations that add differential rotation to the unperturbed equilibrium star: For stars with a barotropic equation of state, one can add to the time-independent second-order solution arbitrary differential rotation that is stratified on cylinders (that is a function of distance $\varpi$ to the axis of rotation). We show here that the gravitational radiation-reaction force that drives the $r$-mode instability removes this gauge freedom: The expontially growing differential rotation of the unstable second-order $r$-mode is unique. We derive a general expression for this rotation law for Newtonian models and evaluate it explicitly for slowly rotating models with polytropic equations of state., Comment: Published (2016) version, but with two updated references

Reference metrics are used to define the differential structure on multicube representations of manifolds, i.e., they provide a simple and practical way to define what it means globally for tensor fields and their derivatives to be continuous. This paper introduces a general procedure for constructing reference metrics automatically on multicube representations of manifolds with arbitrary topologies. The method is tested here by constructing reference metrics for compact, orientable two-dimensional manifolds with genera between zero and five. These metrics are shown to satisfy the Gauss-Bonnet identity numerically to the level of truncation error (which converges toward zero as the numerical resolution is increased). These reference metrics can be made smoother and more uniform by evolving them with Ricci flow. This smoothing procedure is tested on the two-dimensional reference metrics constructed here. These smoothing evolutions (using volume-normalized Ricci flow with DeTurck gauge fixing) are all shown to produce reference metrics with constant scalar curvatures (at the level of numerical truncation error)., Comment: 37 pages, 16 figures; additional introductory material added in version accepted for publication

The observable macroscopic properties of relativistic stars (whose equations of state are known) can be predicted by solving the stellar structure equations that follow from Einstein's equation. For neutron stars, however, our knowledge of the equation of state is poor, so the direct stellar structure problem can not be solved without modeling the highest density part of the equation of state in some way. This talk will describe recent work on developing a model independent approach to determining the high-density neutron-star equation of state by solving an inverse stellar structure problem. This method uses the fact that Einstein's equation provides a deterministic relationship between the equation of state and the macroscopic observables of the stars which are composed of that material. This talk illustrates how this method will be able to determine the high-density part of the neutron-star equation of state with few percent accuracy when high quality measurements of the masses and radii of just two or three neutron stars become available. This talk will also show that this method can be used with measurements of other macroscopic observables, like the masses and tidal deformabilities, which can (in principle) be measured by gravitational wave observations of binary neutron-star mergers., Comment: Talk given at the Fifth Leopoldo Garcia-Colin Mexican Meeting on Mathematical and Experimental Physics

This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational procedures that make it possible to explore the never before studied properties of solutions to Einstein's equation on manifolds with arbitrary toplogical structures. A new covariant, first-order symmetric-hyperbolic representation of Einstein's equation is developed for this purpose, along with the needed boundary conditions at the interfaces between adjoining cubic regions. Numerical tests are presented that demonstrate the long-term numerical stability of this method for evolutions of a complicated, time-dependent solution of Einstein's equation coupled to a complex scalar field on a manifold with spatial topology S^3. The accuracy of these numerical test solutions is evaluated by performing convergence studies and by comparing the full non-linear numerical results to the analytical perturbation solutions, which are also derived here., Comment: 20 pages, 12 figures, 1 table; v2 minor revisions to agree with published version

The inverse stellar structure problem determines the equation of state of the matter in stars from a knowledge of their macroscopic observables (e.g. their masses and radii). This problem was solved in a previous paper by constructing a spectral representation of the equation of state whose stellar models match a prescribed set of macroscopic observables. This paper improves and extends that work in two significant ways: i) The method is made more robust by accounting for an unexpected feature of the enthalpy based representations of the equations of state used in this work. After making the appropriate modifications, accurate initial guesses for the spectral parameters are no longer needed so Monte-Carlo techniques can now be used to ensure the best fit to the observables. ii) The method is extended here to use masses and tidal deformabilities (which will be measured by gravitational wave observations of neutron-star mergers) as the macroscopic observables instead of masses and radii. The accuracy and reliability of this extended and more robust spectral method is evaluated in this paper using mock data for observables from stars based on 34 different theoretical models of the high density neutron-star equation of state. In qualitative agreement with earlier work, these tests suggest the high density part of the neutron-star equation of state could be determined at the few-percent accuracy level using high quality measurements of the masses and radii (or masses and tidal deformabilities) of just two or three neutron stars., Comment: 16 pages, 5 figures, 2 tables; v2 updated to published version, includes expanded discussion section, v3 corrected typo in Eq. (C7)

We studied current-voltage characteristics of long one dimensional Josephson junction chains with Josephson energy much larger than charging energy, $E_J \gg E_C$. In this regime, typical IV curves of the samples consist of a supercurrent branch at low bias voltages followed by a voltage-independent chain current branch, $I_{Chain}$ at high bias. Our experiments showed that $I_{Chain}$ is not only voltage-independent but it is also practically temperature-independent up to $T_C$. We have successfully model the transport properties in these chains using a capacitively shunted junction model with nonlinear damping.

A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as a set of non-overlapping cubic regions, plus a set of maps to identify the faces of adjoining regions. The differential structure on these manifolds is fixed by specifying a smooth reference metric tensor. Matching conditions that ensure the appropriate levels of continuity and differentiability across region boundaries are developed for arbitrary tensor fields. Standard numerical methods are then used to solve the equations with the appropriate boundary conditions, which are determined from these inter-region matching conditions. Numerical examples are presented which use pseudo-spectral methods to solve simple elliptic equations on multi-cube representations of manifolds with the topologies T^3, S^2 x S^1 and S^3. Examples are also presented of numerical solutions of simple hyperbolic equations on multi-cube manifolds with the topologies R x T^3, R x S^2 x S^1 and R x S^3., Comment: 36 pages, 11 figures, 9 tables

We study the two-user multiple-input single-output (MISO) Gaussian interference channel where the transmitters have perfect channel state information and employ single-stream beamforming. The receivers are capable of performing successive interference cancellation, so when the interfering signal is strong enough, it can be decoded, treating the desired signal as noise, and subtracted from the received signal, before the desired signal is decoded. We propose efficient methods to compute the Pareto-optimal rate points and corresponding beamforming vector pairs, by maximizing the rate of one link given the rate of the other link. We do so by splitting the original problem into four subproblems corresponding to the combinations of the receivers' decoding strategies - either decode the interference or treat it as additive noise. We utilize recently proposed parameterizations of the optimal beamforming vectors to equivalently reformulate each subproblem as a quasi-concave problem, which we solve very efficiently either analytically or via scalar numerical optimization. The computational complexity of the proposed methods is several orders-of-magnitude less than the complexity of the state-of-the-art methods. We use the proposed methods to illustrate the effect of the strength and spatial correlation of the channels on the shape of the rate region., Comment: Accepted for publication in IEEE Transactions on Signal Processing

A new method for solving the relativistic inverse stellar structure problem is presented. This method determines a spectral representation of the unknown high density portion of the stellar equation of state from a knowledge of the total masses M and radii R of the stars. Spectral representations of the equation of state are very efficient, generally requiring only a few spectral parameters to achieve good accuracy. This new method is able, therefore, to determine the high density equation of state quite accurately from only a few accurately measured [M,R] data points. This method is tested here by determining the equations of state from mock [M,R] data computed from tabulated "realistic" neutron-star equations of state. The spectral equations of state obtained from these mock data are shown to agree on average with the originals to within a few percent (over the entire high density range of the neutron-star interior) using only two [M,R] data points. Higher accuracies are achieved when more data are used. The accuracies of the equations of state determined in these examples are shown to be nearly optimal, in the sense that their errors are comparable to the errors of the best-fit spectral representations of these realistic equations of state., Comment: 12 pages; 1 table; v2 minor changes to version accepted in Phys. Rev. D

We consider the slow-fading two-user multiple-input single-output (MISO) interference channel. We want to understand which rate points can be achieved, allowing a non-zero outage probability. We do so by defining four different outage rate regions. The definitions differ on whether the rates are declared in outage jointly or individually and whether the transmitters have instantaneous or statistical channel state information (CSI). The focus is on the instantaneous CSI case with individual outage, where we propose a stochastic mapping from the rate point and the channel realization to the beamforming vectors. A major contribution is that we prove that the stochastic component of this mapping is independent of the actual channel realization., Comment: Accepted for publication in IEEE Wireless Communications Letters

Methods are developed for constructing spectral representations of cold (barotropic) neutron-star equations of state. These representations are faithful in the sense that every physical equation of state has a representation of this type, and conversely every such representation satisfies the minimal thermodynamic stability criteria required of any physical equation of state. These spectral representations are also efficient, in the sense that only a few spectral coefficients are generally required to represent neutron-star equations of state quiet accurately. This accuracy and efficiency is illustrated by constructing spectral fits to a large collection of "realistic" neutron-star equations of state., Comment: 10 pages, 8 figures, 2 tables; updated to accepted Phys. Rev. D version

Model gravitational waveforms must be accurate enough to be useful for detection of signals and measurement of their parameters, so appropriate accuracy standards are needed. Yet these standards should not be unnecessarily restrictive, making them impractical for the numerical and analytical modelers to meet. The work of Lindblom, Owen, and Brown [Phys. Rev. D 78, 124020 (2008)] is extended by deriving new waveform accuracy standards which are significantly less restrictive while still ensuring the quality needed for gravitational-wave data analysis. These new standards are formulated as bounds on certain norms of the time-domain waveform errors, which makes it possible to enforce them in situations where frequency-domain errors may be difficult or impossible to estimate reliably. These standards are less restrictive by about a factor of 20 than the previously published time-domain standards for detection, and up to a factor of 60 for measurement. These new standards should therefore be much easier to use effectively., Comment: 10 pages, 5 figures

Several improvements in numerical methods and gauge choice are presented that make it possible now to perform simulations of the merger and ringdown phases of "generic" binary black-hole evolutions using the pseudo-spectral evolution code SpEC. These improvements include the use of a new damped-wave gauge condition, a new grid structure with appropriate filtering that improves stability, and better adaptivity in conforming the grid structures to the shapes and sizes of the black holes. Simulations illustrating the success of these new methods are presented for a variety of binary black-hole systems. These include fairly ``generic'' systems with unequal masses (up to 2:1 mass ratios), and spins (with magnitudes up to 0.4 M^2) pointing in various directions., Comment: 16 pages, 16 figures

Accuracy standards have been developed to ensure that the waveforms used for gravitational-wave data analysis are good enough to serve their intended purposes. These standards place constraints on certain norms of the frequency-domain representations of the waveform errors. Examples are given here of possible misinterpretations and misapplications of these standards, whose effect could be to vitiate the quality control they were intended to enforce. Suggestions are given for ways to avoid these problems., Comment: v2: updated to version published in Phys. Rev. D; 10 pages, 7 figures

Calibration errors in the response function of a gravitational wave detector degrade its ability to detect and then to measure the properties of any detected signals. This paper derives the needed levels of calibration accuracy for each of these data-analysis tasks. The levels derived here are optimal in the sense that lower accuracy would result in missed detections and/or a loss of measurement precision, while higher accuracy would be made irrelevant by the intrinsic noise level of the detector. Calibration errors affect the data-analysis process in much the same way as errors in theoretical waveform templates. The optimal level of calibration accuracy is expressed therefore as a joint limit on modeling and calibration errors: increased accuracy in one reduces the accuracy requirement in the other., Comment: v2: minor changes, updated to version accepted in Phys. Rev. D

A new gauge driver is introduced for the generalized harmonic (GH) representation of Einstein's equation. This new driver allows a rather general class of gauge conditions to be implemented in a way that maintains the hyperbolicity of the combined evolution system. This driver is more stable and effective, and unlike previous drivers, allows stable evolutions using the dual-frame evolution technique. Appropriate boundary conditions for this new gauge driver are constructed, and a new boundary condition for the ``gauge'' components of the spacetime metric in the GH Einstein system is introduced. The stability and effectiveness of this new gauge driver are demonstrated through numerical tests, which impose a new damped-wave gauge condition on the evolutions of single black-hole spacetimes., Comment: v2: final version to be published in PRD; 15 pages, 5 figures

Model waveforms are used in gravitational wave data analysis to detect and then to measure the properties of a source by matching the model waveforms to the signal from a detector. This paper derives accuracy standards for model waveforms which are sufficient to ensure that these data analysis applications are capable of extracting the full scientific content of the data, but without demanding excessive accuracy that would place undue burdens on the model waveform simulation community. These accuracy standards are intended primarily for broad-band model waveforms produced by numerical simulations, but the standards are quite general and apply equally to such waveforms produced by analytical or hybrid analytical-numerical methods., Comment: 11 pages, 5 figures; Final version accepted in Phys. Rev. D

The generalized harmonic representation of Einstein's equation is manifestly hyperbolic for a large class of gauge conditions. Unfortunately most of the useful gauges developed over the past several decades by the numerical relativity community are incompatible with the hyperbolicity of the equations in this form. This paper presents a new method of imposing gauge conditions that preserves hyperbolicity for a much wider class of conditions, including as special cases many of the standard ones used in numerical relativity: e.g., K-freezing, Gamma-freezing, Bona-Masso slicing, conformal Gamma-drivers, etc. Analytical and numerical results are presented which test the stability and the effectiveness of this new gauge driver evolution system., Comment: 17 pages, 9 figures

Various methods of treating outer boundaries in numerical relativity are compared using a simple test problem: a Schwarzschild black hole with an outgoing gravitational wave perturbation. Numerical solutions computed using different boundary treatments are compared to a `reference' numerical solution obtained by placing the outer boundary at a very large radius. For each boundary treatment, the full solutions including constraint violations and extracted gravitational waves are compared to those of the reference solution, thereby assessing the reflections caused by the artificial boundary. These tests use a first-order generalized harmonic formulation of the Einstein equations. Constraint-preserving boundary conditions for this system are reviewed, and an improved boundary condition on the gauge degrees of freedom is presented. Alternate boundary conditions evaluated here include freezing the incoming characteristic fields, Sommerfeld boundary conditions, and the constraint-preserving boundary conditions of Kreiss and Winicour. Rather different approaches to boundary treatments, such as sponge layers and spatial compactification, are also tested. Overall the best treatment found here combines boundary conditions that preserve the constraints, freeze the Newman-Penrose scalar Psi_0, and control gauge reflections., Comment: Modified to agree with version accepted for publication in Class. Quantum Grav

Binary black hole simulations starting from quasi-circular (i.e., zero radial velocity) initial data have orbits with small but non-zero orbital eccentricities. In this paper the quasi-equilibrium initial-data method is extended to allow non-zero radial velocities to be specified in binary black hole initial data. New low-eccentricity initial data are obtained by adjusting the orbital frequency and radial velocities to minimize the orbital eccentricity, and the resulting ($\sim 5$ orbit) evolutions are compared with those of quasi-circular initial data. Evolutions of the quasi-circular data clearly show eccentric orbits, with eccentricity that decays over time. The precise decay rate depends on the definition of eccentricity; if defined in terms of variations in the orbital frequency, the decay rate agrees well with the prediction of Peters (1964). The gravitational waveforms, which contain $\sim 8$ cycles in the dominant l=m=2 mode, are largely unaffected by the eccentricity of the quasi-circular initial data. The overlap between the dominant mode in the quasi-circular evolution and the same mode in the low-eccentricity evolution is about 0.99., Comment: 27 pages, 9 figures; various minor clarifications; accepted to the "New Frontiers" special issue of CQG

The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the KST representation of the Einstein evolution equations. The basic "Mexico City Tests" widely adopted by the numerical relativity community are adapted here for codes based on spectral methods. Exponential convergence of the spectral code is established, apparently limited only by numerical roundoff error. A general expression for the growth of errors due to finite machine precision is derived, and it is shown that this limit is achieved here for the linear plane-wave test. All of these tests are found to be stable, except for simulations of high amplitude gauge waves with nontrivial shift., Comment: Final version, as published in Phys. Rev. D; 13 pages, 16 figures

A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the way fields are projected onto an orthonormal tetrad basis. These field components are then determined as functions of a second independent coordinate system. The transformation to the second coordinate system can be thought of as a mapping from the original ``inertial'' coordinate system to the computational domain. This dual-coordinate method is used to perform stable numerical evolutions of a black-hole spacetime using the generalized harmonic form of Einstein's equations in coordinates that rotate with respect to the inertial frame at infinity; such evolutions are found to be generically unstable using a single rotating coordinate frame. The dual-coordinate method is also used here to evolve binary black-hole spacetimes for several orbits. The great flexibility of this method allows comoving coordinates to be adjusted with a feedback control system that keeps the excision boundaries of the holes within their respective apparent horizons., Comment: Updated to agree with published version

A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially suppresses all small short-wavelength constraint violations. Physical and constraint-preserving boundary conditions are derived for this system, and numerical tests that demonstrate the effectiveness of the constraint suppression properties and the constraint-preserving boundary conditions are presented., Comment: Updated to agree with published version