We describe a novel approach to quadrature for ratios of probabilistic integrals, such as are used to compute posterior probabilities. This approach offers performance superior to Monte Carlo methods by exploiting a Bayesian quadrature framework. We improve upon previous Bayesian quadrature techniques by explicitly modelling the nonnegativity of our integrands, and the correlations that exist b...

This paper presents technology for the suppression of the mechanical coupling errors for an improved decoupled dual-mass micro-gyroscope (DDMG). The improved micro-gyroscope structure decreases the moment arm of the drive decoupled torque, which benefits the suppression of the non-ideal decoupled error. Quadrature correction electrodes are added to eliminate the residual quadrature error. The s...

In this paper we examine the computation of the potential generated by space-time BIE representations associated with Dirichlet and Neumann problems for the 2D wave equation. In particular, we consider the efficient evaluation of the (convolution) time integral that appears in the potential representation. For this, we propose two simple quadrature rules which appear more efficient than the cur...

We investigate the use of sparse grid methods in computing polynomial chaos (PC) proxies for forward stochastic problems associated with numerically-expensive simulators. These are problems where some input parameters are random with known distributions, and stochastic properties of the simulator output are desired. The bottleneck for PC proxy construction is the estimation of the coefficients,...

and Applied Analysis 3 The class of Runge-Kutta methods with CQ formula has been applied to delay-integro-differential equations by many authors (c.f. [18, 19]). For the CQ formula (9), we usually adopt the repeated trapezoidal rule, the repeated Simpson’s rule, or the repeated Newton-cotes rule, and so forth, denote η = max{?̃? 0 , ?̃? 1 , . . . , ?̃? m }. It should be pointed out that the adopte...

This paper presents a Wireless-USB/WiMedia-compliant fast-hopping frequency synthesizer architecture with quadrature outputs based on sub-harmonic injection-locking. The synthesizer features a cross-coupled quadrature digitally-controlled oscillator, that is injection-locked to a sub-harmonic frequency. An intuitive closed-form expression for the dynamics of the quadrature injection-locked osci...