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Abstract Background Hepatic steatosis (HS) can cause substantial problems for both donors and recipients in living donor liver transplantation. The controlled attenuation parameter (CAP) is a noninvasive method of measuring HS using a process based on transient elastography. Aim To evaluate the accuracy of CAP in quantifying HS during living donor liver transplantation. Methods A total of 54 liver donors who received CAP and intraoperative liver biopsy (LB) were enrolled in this study. The performance of CAP compared with LB for diagnosing HS was assessed using areas under receiver operating characteristic curves. HS was defined by the presence of steatosis in >5% of hepatocytes. Results No HS was found in 47 donors, while the remaining 7 donors showed HS ranging from 10% to 30%. Using CAP, the area under receiver operating characteristic curve was 0.96 (95% CI, 0.91–1; P <.001) for HS; the optimal cutoff value for HS was 257 dB/m (sensitivity: 100%, specificity: 89.4%, positive predictive value: 58.3%, negative predictive value: 100%). Among the 42 candidates with CAP <257 dB/m, none had HS, while of the 12 candidates with CAP ≥257 dB/m, 7 had HS. In a multivariate linear regression analyses, body mass index (β = 0.71, P <.001) was found to be independently associated with CAP in those without HS. Conclusions CAP might be a promising tool to exclude HS in East Asian living liver donors. Body mass index was found to be independently associated with CAP values in those without HS. Highlights • Steatosis can cause problems for both donors and recipients in liver transplantation. • Controlled attenuation parameter (CAP) is a noninvasive method of measuring steatosis. • CAP might be a promising tool to exclude steatosis in East Asian living liver donors. [ABSTRACT FROM AUTHOR]

We further develop the Multivariate Decomposition Method (MDM) for the Lebesgue integration of functions of infinitely many variables x 1 , x 2 , x 3 , … with respect to a corresponding product of a one dimensional probability measure. The method is designed for functions that admit a dominantly convergent decomposition f = ∑ u f u , where u runs over all finite subsets of positive integers, and for each u = { i 1 , … , i k } the function f u depends only on x i 1 , … , x i k . Although a number of concepts of infinite-dimensional integrals have been used in the literature, questions of uniqueness and compatibility have mostly not been studied. We show that, under appropriate convergence conditions, the Lebesgue integral equals the ‘anchored’ integral, independently of the anchor. For approximating the integral, the MDM assumes that point values of f u are available for important subsets u , at some known cost. In this paper, we introduce a new setting, in which it is assumed that each f u belongs to a normed space F u , and that bounds B u on ‖ f u ‖ F u are known. This contrasts with the assumption in many papers that weights γ u , appearing in the norm of the infinite-dimensional function space, are somehow known. Often such weights γ u were determined by minimizing an error bound depending on the B u , the γ u and the chosen algorithm, resulting in weights that depend on the algorithm. In contrast, in this paper, only the bounds B u are assumed to be known. We give two examples in which we specialize the MDM: in the first case, F u is the | u | -fold tensor product of an anchored reproducing kernel Hilbert space; in the second case, it is a particular non-Hilbert space for integration over an unbounded domain. [ABSTRACT FROM AUTHOR]

We consider a ϱ -weighted L q approximation in the space of univariate functions f : R + → R with finite ‖ f ( r ) ψ ‖ L p . Let α = r − 1 / p + 1 / q and ω = ϱ / ψ . Assuming that ψ and ω are non-increasing and the quasi-norm ‖ ω ‖ L 1 / α is finite, we construct algorithms using function/derivatives evaluations at n points with the worst case errors proportional to ‖ ω ‖ L 1 / α n − r + ( 1 / p − 1 / q ) + . In addition we show that this bound is sharp; in particular, if ‖ ω ‖ L 1 / α = ∞ then the rate n − r + ( 1 / p − 1 / q ) + cannot be achieved. Our results generalize known results for bounded domains such as [ 0 , 1 ] and ϱ = ψ ≡ 1 . We also provide a numerical illustration. [ABSTRACT FROM AUTHOR]

Abstract: We devise and implement quasi-Monte Carlo methods for computing the expectations of nonlinear functionals of solutions of a class of elliptic partial differential equations with random coefficients. Our motivation comes from fluid flow in random porous media, where relevant functionals include the fluid pressure/velocity at any point in space or the breakthrough time of a pollution plume being transported by the velocity field. Our emphasis is on situations where a very large number of random variables is needed to model the coefficient field. As an alternative to classical Monte Carlo, we here employ quasi-Monte Carlo methods, which use deterministically chosen sample points in an appropriate (usually high-dimensional) parameter space. Each realization of the PDE solution requires a finite element (FE) approximation in space, and this is done using a realization of the coefficient field restricted to a suitable regular spatial grid (not necessarily the same as the FE grid). In the statistically homogeneous case the corresponding covariance matrix can be diagonalized and the required coefficient realizations can be computed efficiently using FFT. In this way we avoid the use of a truncated Karhunen–Loève expansion, but introduce high nominal dimension in parameter space. Numerical experiments with 2-dimensional rough random fields, high variance and small length scale are reported, showing that the quasi-Monte Carlo method consistently outperforms the Monte Carlo method, with a smaller error and a noticeably better than convergence rate, where N is the number of samples. Moreover, the rate of convergence of the quasi-Monte Carlo method does not appear to degrade as the nominal dimension increases. Examples with dimension as high as 106 are reported. [Copyright &y& Elsevier]

It is known from the analysis by Sloan and Woz´niakowski that under appropriate conditions on the weights, the optimal rate of convergence for multivariate integration in weighted Korobov spaces is O(n−α/2+δ) where α>1 is some parameter of the spaces, δ is an arbitrary positive number, and the implied constant in the big O notation depends only on δ, and is independent on the number of variables. Similarly, the optimal rate for weighted Sobolev spaces is O(n−1+δ). However, their work did not show how to construct rules achieving these rates of convergence. The existing theory of the component-by-component constructions developed by Sloan, Kuo and Joe for the Sobolev case yields the rules achieving O(n−1/2) error bounds. Here we present theorems which show that those lattice rules constructed by the component-by-component algorithms in fact achieve the optimal rate of convergence under appropriate conditions on the weights. [Copyright &y& Elsevier]

Shifted rank-1 lattice rules, a special class of quasi-Monte Carlo methods, have recently been proposed by the present authors for the integration of functions belonging to certain "weighted" Sobolev spaces. The shifts in these rules were generated in a deterministic manner. In contrast, in this paper we generate these shifts randomly. This allows probabilistic estimates for the error in a given integral. It also reduces the number of operations required to find the generating vectors for the underlying lattice rules component-by-component. The rules thus constructed achieve a worst-case strong tractability error bound in an average or probabilistic sense. [ABSTRACT FROM AUTHOR]