Related papers: Pulsar timing array analysis in a Legendre polynom…
We obtain robust and computationally efficient estimators for learning several linear models that achieve statistically optimal convergence rate under minimal distributional assumptions. Concretely, we assume our data is drawn from a…
A generalization of associated Legendre functions is proposed and used to describe the scattering states of the Rosen-Morse potential. The functions are then given explicit formulas in terms of the hypergeometric function, their asymptotic…
A pulsar timing array is a Galactic-scale detector of nanohertz gravitational waves (GWs). Its target signals contain two components: the `Earth term' and the `pulsar term' corresponding to GWs incident on the Earth and pulsar respectively.…
We present a new algorithm for the computation of the inverse Abel transform, a problem which emerges in many areas of physics and engineering. We prove that the Legendre coefficients of a given function coincide with the Fourier…
Pulsar timing experiments require high fidelity template profiles in order to minimize the biases in pulse time-of-arrival (TOA) measurements and their uncertainties. Efforts to acquire more precise TOAs given fixed effective area of…
The analysis of pulsar timing array data has provided evidence for a gravitational wave background in the nanohertz band. This raises the question of what is the source of the signal, is it astrophysical or cosmological in origin? If the…
Pulsar timing array (PTA) searches for a gravitational-wave background (GWB) typically include time-correlated "red" noise models intrinsic to each pulsar. Using a simple simulated PTA dataset with an injected GWB signal we show that the…
Many traditional algorithms applied in gravitational-wave astronomy rely on the assumption of Gaussian noise, a condition not always met. To meet this need, this study extends a robust statistical framework, advancing previous work on…
We formulate a framework of polynomial diagrams, which are a generalisation of power diagrams (PDs) and anisotropic power diagrams (APDs) allowing for boundaries between cells to be algebraic curves of a prescribed degree. We show that they…
A new method of polarimetric calibration is presented in which the instrumental response is derived from regular observations of PSR J0437-4715 based on the assumption that the mean polarized emission from this millisecond pulsar remains…
Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a…
We define sets of orthogonal polynomials satisfying the additional constraint of a vanishing average. These are of interest, for example, for the study of the Hohenberg-Kohn functional for electronic or nucleonic densities and for the study…
The noise in millisecond pulsar (MSP) timing data can include contributions from observing instruments, the interstellar medium, the solar wind, solar system ephemeris errors, and the pulsars themselves. The noise environment must be…
Pulsar timing experiments are reaching sufficient sensitivity to detect a postulated stochastic gravitational wave background generated by merging supermassive black hole systems in the cores of galaxies. We describe the techniques behind…
A low frequency stochastic background of gravitational waves may be detected by pulsar timing experiments in the next five to ten years. Using methods developed to analyze interferometric gravitational wave data, in this paper we lay out…
The article is devoted to comparative analysis of the efficiency of application of Legendre polynomials and trigonometric functions to the numerical integration of Ito stochastic differential equations in the framework of the method of…
Pulsar timing array projects measure the pulse arrival times of millisecond pulsars for the primary purpose of detecting nanohertz-frequency gravitational waves. The measurements include contributions from a number of astrophysical and…
Pulsar Timing Arrays (PTA) provide a powerful framework to measure low-frequency gravitational waves, but accuracy and robustness of the results are challenged by complex noise processes that must be accurately modeled. Standard PTA…
Long-term precise timing of Galactic millisecond pulsars holds great promise for measuring the long-period (months-to-years) astrophysical gravitational waves. Several gravitational-wave observational programs, called Pulsar Timing Arrays…
Sparse linear regression is one of the classic problems in the field of statistics, which has deep connections and high intersections with optimization, computation, and machine learning. To address the effective handling of…