UTC Dissemination to the Real-Time User: The Role of USNO

Coordinated Universal Time (UTC) is available worldwide via the Global Positioning System (GPS). The UTC disseminated by GPS is referenced to the US Naval Observatory Master Clock UTC(USNO) which is regularly steered and maintained as close as possible to UTC Bureau International des Poids et Mesures (BIPM), the international time scale. This paper will describe the role of the USNO in monitoring the time disseminated by the GPS and the steps involved to ensure its accuracy to the user. The paper will also discuss the other sources of UTC(USNO) and the process by which UTC(USNO) is steered to UTC(BIPM)

Matrix biorthogonal polynomials on the unit circle and non-Abelian Ablowitz-Ladik hierarchy

Adler and van Moerbeke \cite{AVM} described a reduction of 2D-Toda hierarchy called Toeplitz lattice. This hierarchy turns out to be equivalent to the one originally described by Ablowitz and Ladik \cite{AL} using semidiscrete zero-curvature equations. In this paper we obtain the original semidiscrete zero-curvature equations starting directly from the Toeplitz lattice and we generalize these computations to the matrix case. This generalization lead us to the semidiscrete zero-curvature equations for the non-abelian (or multicomponent) version of Ablowitz-Ladik equations \cite{GI}. In this way we extend the link between biorthogonal polynomials on the unit circle and Ablowitz-Ladik hierarchy to the matrix case.Comment: 23 pages, accepted on publication on J. Phys. A., electronic link: http://stacks.iop.org/1751-8121/42/36521

A globally efficient means of distributing UTC time and frequency through GPS

Time and frequency outputs comparable in quality to the best laboratories have been demonstrated on an integrated system suitable for field application on a global basis. The system measures the time difference between 1 pulse-per-second (pps) signals derived from local primary frequency standards and from a multi-channel GPS C/A receiver. The measured data is processed through optimal SA Filter algorithms that enhance both the stability and accuracy of GPS timing signals. Experiments were run simultaneously at four different sites. Even with large distances between sites, the overall results show a high degree of cross-correlation of the SA noise. With sufficiently long simultaneous measurement sequences, the data shows that determination of the difference in local frequency from an accepted remote standard to better than 1 x 10(exp -14) is possible. This method yields frequency accuracy, stability, and timing stability comparable to that obtained with more conventional common-view experiments. In addition, this approach provides UTC(USNO MC) in real time to an accuracy better than 20 ns without the problems normally associated with conventional common-view techniques. An experimental tracking loop was also set up to demonstrate the use of enhanced GPS for dissemination of UTC(USNO MC) over a wide geographic area. Properly disciplining a cesium standard with a multi-channel GPS receiver, with additional input from USNO, has been found to permit maintaining a timing precision of better than 10 ns between Palo Alto, CA and Washington, DC

Study of tropospheric correction for intercontinental GPS common-view time transfer

Current practice is to incorporate general empirical models of the troposphere, which depend only on the station height and the elevation of the satellite, in GPS time receivers used for common-view time transfer. Comparisons of these models with a semi-empirical model based on weather measurements show differences of several nanoseconds. This paper reports on a study of tropospheric correction during GPS common-view time transfer over a short baseline of about 700 km, and three long baselines of 6400 km, 9000 km and 9600 km. It is shown that the use of a general empirical model of the troposphere within a region where the climate is similar does not affect time transfer by more than a few hundreds of picoseconds. For the long distance links, differences between the use of a general empirical model and the use of a semi-empirical model reach several nanoseconds

Quadrature Strategies for Constructing Polynomial Approximations

Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated to this singular cause. In this paper, we begin by reviewing classical methods for finding suitable quadrature points for polynomial approximation in both the univariate and multivariate setting. Then, we categorize recent advances into those that propose a new sampling approach and those centered on an optimization strategy. The sampling approaches yield a favorable discretization of the domain, while the optimization methods pick a subset of the discretized samples that minimize certain objectives. While not all strategies follow this two-stage approach, most do. Sampling techniques covered include subsampling quadratures, Christoffel, induced and Monte Carlo methods. Optimization methods discussed range from linear programming ideas and Newton's method to greedy procedures from numerical linear algebra. Our exposition is aided by examples that implement some of the aforementioned strategies

Ensemble of heterogeneous flexible neural trees using multiobjective genetic programming

Machine learning algorithms are inherently multiobjective in nature, where approximation error minimization and model's complexity simplification are two conflicting objectives. We proposed a multiobjective genetic programming (MOGP) for creating a heterogeneous flexible neural tree (HFNT), tree-like flexible feedforward neural network model. The functional heterogeneity in neural tree nodes was introduced to capture a better insight of data during learning because each input in a dataset possess different features. MOGP guided an initial HFNT population towards Pareto-optimal solutions, where the final population was used for making an ensemble system. A diversity index measure along with approximation error and complexity was introduced to maintain diversity among the candidates in the population. Hence, the ensemble was created by using accurate, structurally simple, and diverse candidates from MOGP final population. Differential evolution algorithm was applied to fine-tune the underlying parameters of the selected candidates. A comprehensive test over classification, regression, and time-series datasets proved the efficiency of the proposed algorithm over other available prediction methods. Moreover, the heterogeneous creation of HFNT proved to be efficient in making ensemble system from the final population

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry