We consider online stratified sampling for Monte Carlo estimation of the integral of a function given a finite budget n of noisy evaluations to the function. In this paper we address the problem of choosing the best number K of strata as a function of n. A large K provides a high quality stratification where an accurate estimate of the integral of f could be computed by an optimal oracle alloca...

The classical BGK model for describing the flow of a rarefied gas in a cylindrical tube is used as a starting point for developing an equivalent integral-equation formulation of the considered class of problems. While the problems of Poiseuille flow and thermal creep in a cylindrical tube have already been well solved in terms of a pseudo problem obtained from an integral-equation definition of...

Let u ≥ −1 be arbitrary. It has long been known that there exists a super-Euclidean nonnegative line [48]. We show that n < 0. In [8], it is shown that |k′| ∩ e = min γd→π W ′ (−∞k) . B. Bose’s derivation of integral, pseudo-countably Riemannian, multiplicative isomorphisms was a milestone in geometry.

Pseudo-spectral method is one of the most accurate techniques for simulating turbulent flows. Fast Fourier transform (FFT) is an integral part of this method. In this paper, we present a new procedure to compute FFT in which we save operations during interprocess communications by avoiding transpose of the array. As a result, our transpose-free FFT is 15% to 20% faster than FFTW.

We provide a careful analysis of the generating functional in the path integral formulation of pseudo-Hermitian and in particular PT -symmetric quantum mechanics and show how the metric operator enters the expression for the generating functional. PACS number: 03.65.-w

We introduce a τ -dependent Wigner representation, Wigτ , τ ∈ [0, 1], which permits us to define a general theory connecting time-frequency representations on one side and pseudo-differential operators on the other. The scheme includes various types of time-frequency representations, among the others the classical Wigner and Rihaczek representations and the most common classes of pseudo-differe...

Fourier integral operators, for the calculus of which I refer to Hörmander [17], have been applied in essentially two ways: as similarity transformations and in the description of the solutions of genuinely nonelliptic (pseudo-) differential equations. The first application is based on the observation of Egorov [12] that if P9 resp. g, is a pseudo-differential operator with principal symbol equ...

An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting nonlinear equation is solved via the Petviashvili iterative scheme. The computational results are compared to some existing approaches, such as Tanaka’s method and...

Importance sampling methods of wavelet products can deal with some direct rendering applications with only two functions. For multiple functions sampling that are more useful in global rendering, we present a wavelet-based factor method to simplify multiple function integral into triple function product issues. Then an optimal wavelet product representation is introduced. Major algorithms with ...