Improved error estimate for extraordinary Catmull–Clark subdivision surface patches

Based on an optimal estimate of the convergence rate of the second order norm, an improved error estimate for extraordinary Catmull–Clark subdivision surface (CCSS) patches is proposed. If the valence of the extraordinary vertex of an extraordinary CCSS patch is even, a tighter error bound and, consequently, a more precise subdivision depth for a given error tolerance, can be obtained. Furthermore, examples of adaptive subdivision illustrate the practicability of the error estimation approach.     

Determining error bounds for spectral filtering based reconstruction methods in privacy preserving data mining

Additive randomization has been a primary tool for hiding sensitive private information. Previous work empirically showed that individual data values can be approximately reconstructed from the perturbed values, using spectral filtering techniques. This poses a serious threat of privacy breaches. In this paper we conduct a theoretical study on how the reconstruction error varies, for different types of additive noise. In particular, we first derive an upper bound for the reconstruction error using matrix perturbation theory. Attackers who use spectral filtering techniques to estimate the true data values may leverage this bound to determine how close their estimates are to the original data. We then derive a lower bound for the reconstruction error, which can help data owners decide how much noise should be added to satisfy a given threshold of the tolerated privacy breach.

Analytic-numerical solutions with a priori error bounds for time-dependent mixed partial differential problems

The aim of this paper is double. First, we point out that the hypothesis D(t₁)D(t₂) = D(t₂)D(t₁) imposed in [1] can be removed. Second, a constructive method for obtaining analytic-numerical solutions with a prefixed accuracy in a bounded domain Ω(t₀,t₁) = [0,p] × [t₀,t₁], for mixed problems of the type u_t(x,t) − D(t)u_xx(x,t) = 0, 0 < x < p, t> 0, subject to u(0,t) = u(p,t) = 0 and u(x,0) = F(x) is proposed. Here, u(x,t) and F(x) are r-component vectors, D(t) is a C^{r × r} valued analytic function and there exists a positive number δ such that every eigenvalue z of (1/2) (D(t) + D(t)^H) is bigger than δ. An illustrative example is included.     

Exact error bounds for the reconstruction processes using interpolating wavelets

It is known that a multiresolution scheme without control on the infinity norm can produce numerical artifacts. This work is intended to provide explicit error bounds for the reconstruction process associated with the interpolating wavelets introduced by Donoho [D. Donoho, Interpolating Wavelet Transforms, Preprint, Department of Statistics, Stanford University, 1992]. The stability constants related to the interpolatory wavelets defined by the use of the Daubechies filters [I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992], also called the Deslaurier–Dubuc wavelets, are tabulated. Our study present two important facts: The first is that the obtained stability constants are much better approximated than those given by other approaches motivated by [S. Amat, J. Liandrat, On the stability of the PPH multiresolution algorithm, Appl. Comp. Harmon. Anal. 18 (2005) 198–206] and the second is that our analysis uses basic rules easily understood by a wide part of the scientific community interested in this kind of explicit numerical results.     

Computable explicit bounds for the discretization error of variable stepsize multistep methods

This paper deals with the achievement of explicit computable bounds for the global discretization error of variable stepsize multistep methods which are perturbation of strongly stable fixed stepsize methods. The approach is based on the study of the growth of solutions of certain variable coefficient difference equations satisfied by the global discretization error.     

Estimating the error variance after a pre-test for an interval restriction on the coefficients

This paper considers the estimation of the error variance after a pre-test of an interval restriction on the coefficients. We derive the exact finite sample risks of the interval restricted and pre-test estimators of the error variance, and examine the risk properties of the estimators to model misspecification through the omission of relevant regressors. It is found that the pre-test estimator performs better than the interval restricted estimator in terms of the risk properties in a large region of the parameter space; moreover, its risk performance is more robust with respect to the degrees of model misspecification. Furthermore, we propose a bootstrap procedure for estimating the risks of the estimators, to overcome the difficulty of computing the exact risks.     

LP-oriented upper bounds for the weighted stability number of a graph

Upper bounds for the weighted stability number of a graph are considered that are based on the approximation of its stable set polytope by linear inequalities for odd cycles and p-wheels in the graph. Algorithms are developed for finding upper bounds on the basis of solution of LP problems with a finite number of inequalities produced by the shortest path algorithm for a special graph. The results of test experiments are given for graphs with several hundred or thousand vertices. This work was partially financially supported by the CRDF Cooperative Grants Program under grant UKM2-2812-KV-06. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 157–170, January–February 2009.     

An experimental study on estimating human error probability (HEP) parameters for PSA/HRA by using human model simulation

A framework of Human Error Probability (HEP) parameters, which is needed for Human Reliability Analysis (HRA) within a practice of Probabilistic Safety Assessment (PSA) of Nuclear Power Plant is first proposed. Then a laboratory experiment was conducted in order to construct a computer simulation model (human model) that describes human cognitive behaviour on detecting and diagnosing plant anomaly causes. An inter-comparison between experimental data and human model simulation was performed to estimate Human Cognitive Reliability (HCR) curves, in order to confirm the applicability of a human model for estimating these HEP parameters for PSA/HRA practice.