We investigate Gaussian spherical quadrature as a method for calculating orientational averages in solid-state NMR. For the case of magic-angle-spinning sideband amplitudes of isolated spins-1/2, we demonstrate the superiority of Gaussian spherical quadrature over other orientational averaging methods. Depending on the shift anisotropy parameters and the desired accuracy, the computation speed ...

Multiple integrals encountered when evaluating posterior densities in Bayesian estimation were approximated using Multivariate Gaussian Quadrature (MGQ). Experimental results for a linear regression model suggest MGQ provides better approximations to unknown parameters and error variance than simple Monte Carlo based approximations. The authors are Graduate Research Assistant, Professor and Gra...

This paper compares different types of simulated draws over a range of number of draws in generating Bayesian efficient designs for stated choice (SC) studies. The paper examines how closely pseudo Monte Carlo, quasi Monte Carlo and Gaussian quadrature methods are able to replicate the true levels of Bayesian efficiency for SC designs of various dimensions. The authors conclude that the predomi...

Most continuous-variable quantum key distribution schemes are based on the Gaussian modulation of coherent states followed by continuous quadrature detection using homodyne detectors. In all previous schemes, the Gaussian modulation has been carried out in conjugate quadratures thus requiring two independent modulators for their implementations. Here, we propose and experimentally test a largel...

We consider error estimates for optimal and Gaussian quadrature for-mulae if the integrand is analytic and bounded in a certain complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented. This method is applied to Szegg o-type weight functions and ellipses as regions of analyticity. In this situation, the error constants for the Gau...

3 INFN, Sezione di Pisa, Largo Pontecorvo, 3, Ed. C, 56127 Pisa, Italy 4 Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56100 Pisa, Italy 5 Department of Physics, Keio University, Hiyoshi, Yokohama, Kanagawa 223-8521, JAPAN 6 Department of Physics, Tokyo Institute of Technology Tokyo 152-8551, JAPAN 7 Theoretical Physics Laboratory, The Institute of Physical and Chemical Research (RIKEN), 2...

We propose the adaptive multicarrier quadrature division–multiuser quadrature allocation (AMQD-MQA) multiple access technique for continuous-variable quantum key distribution (CVQKD). The MQA scheme is based on the AMQD modulation, which granulates the inputs of the users into Gaussian subcarrier continuous-variables (CVs). The subcarrier coherent states formulate Gaussian sub-channels from the...

The aim of this contribution is to show how the Ftransform technique can be generalized from the case of constant components to the case of polynomial components. For this purpose, we choose complete functional spaces with inner products. After a general presentation of Fm-transform where m ≥ 0, a detailed characterization of the F -transform is given. We applied a technique of numeric integrat...

Szegő quadrature rules are commonly applied to integrate periodic functions on the unit circle in the complex plane. However, often it is difficult to determine the quadrature error. Recently, Spalević introduced generalized averaged Gauss quadrature rules for estimating the quadrature error obtained when applying Gauss quadrature over an interval on the real axis. We describe analogous quadrat...

in this paper, we show that the conditional transform with respect to the gaussian process involving the first variation can be expressed in terms of the conditional transform without the first variation. we then use this result to obtain various integration formulas involving the conditional $diamond$-product and the first variation.