A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

The statistical theory of relative errors in floating-point computation /

Thesis (M. S.)--University of Illinois at Urbana-Champaign.

A priori prediction of roundoff error accumulation in the solution of a super-large geodetic normal equation system /

"June 1980."

Methods for automatic error analysis of numerical algorithms /

Vita.

Solving triangular systems on a parallel computer /

Includes bibliographical references.

Gaussian elimination and numerical instability /

"UILU-ENG 77 1714."

An error analysis of solutions to sparse linear programming problems,

"Supported in part by the Advanced Research Projects Agency ... contract no. US AF 30(602) 4144."

QRT: A Qr-based tridiagonalization algorithm for nonsymmetric matrices

The stable similarity reduction of a nonsymmetric square matrix to tridiagonal form has been a long-standing problem in numerical linear algebra. The biorthogonal Lanczos process is in principle a candidate method for this task, but in practice it is confined to sparse matrices and is restarted periodically because roundoff errors affect its three-term recurrence scheme and degrade the biorthogonality after a few steps. This adds to its vulnerability to serious breakdowns or near-breakdowns, the handling of which involves recovery strategies such as the look-ahead technique, which needs a careful implementation to produce a block-tridiagonal form with unpredictable block sizes. Other candidate methods, geared generally towards full matrices, rely on elementary similarity transformations that are prone to numerical instabilities. Such concomitant difficulties have hampered finding a satisfactory solution to the problem for either sparse or full matrices. This study focuses primarily on full matrices. After outlining earlier tridiagonalization algorithms from within a general framework, we present a new elimination technique combining orthogonal similarity transformations that are stable. We also discuss heuristics to circumvent breakdowns. Applications of this study include eigenvalue calculation and the approximation of matrix functions.

Prevalence of refractive errors and ocular disorders in preschool and school children of Ibiporã - PR, Brazil (1989 to 1996)

Purpose: To establish the prevalence of refractive errors and ocular disorders in preschool and schoolchildren of Ibiporã, Brazil. Methods: A survey of 6 to 12-year-old children from public and private elementary schools was carried out in Ibiporã between 1989 and 1996. Visual acuity measurements were performed by trained teachers using Snellen's chart. Children with visual acuity <0.7 in at least one eye were referred to a complete ophthalmologic examination. Results: 35,936 visual acuity measurements were performed in 13,471 children. 1.966 children (14.59%) were referred to an ophthalmologic examination. Amblyopia was diagnosed in 237 children (1.76%), whereas strabismus was observed in 114 cases (0.84%). Cataract (n=17) (0.12%), chorioretinitis (n=38) (0.28%) and eyelid ptosis (n=6) (0.04%) were also diagnosed. Among the 614 (4.55%) children who were found to have refractive errors, 284 (46.25%) had hyperopia (hyperopia or hyperopic astigmatism), 206 (33.55%) had myopia (myopia or myopic astigmatism) and 124 (20.19%) showed mixed astigmatism. Conclusions: The study determined the local prevalence of amblyopia, refractive errors and eye disorders among preschool and schoolchildren.

Knowledge acquisition by networks of interacting agents in the presence of observation errors

In this work we investigate knowledge acquisition as performed by multiple agents interacting as they infer, under the presence of observation errors, respective models of a complex system. We focus the specific case in which, at each time step, each agent takes into account its current observation as well as the average of the models of its neighbors. The agents are connected by a network of interaction of Erdos-Renyi or Barabasi-Albert type. First, we investigate situations in which one of the agents has a different probability of observation error (higher or lower). It is shown that the influence of this special agent over the quality of the models inferred by the rest of the network can be substantial, varying linearly with the respective degree of the agent with different estimation error. In case the degree of this agent is taken as a respective fitness parameter, the effect of the different estimation error is even more pronounced, becoming superlinear. To complement our analysis, we provide the analytical solution of the overall performance of the system. We also investigate the knowledge acquisition dynamic when the agents are grouped into communities. We verify that the inclusion of edges between agents (within a community) having higher probability of observation error promotes the loss of quality in the estimation of the agents in the other communities.

The impact of measurement errors in the identification of regulatory networks

Background: There are several studies in the literature depicting measurement error in gene expression data and also, several others about regulatory network models. However, only a little fraction describes a combination of measurement error in mathematical regulatory networks and shows how to identify these networks under different rates of noise. Results: This article investigates the effects of measurement error on the estimation of the parameters in regulatory networks. Simulation studies indicate that, in both time series (dependent) and non-time series (independent) data, the measurement error strongly affects the estimated parameters of the regulatory network models, biasing them as predicted by the theory. Moreover, when testing the parameters of the regulatory network models, p-values computed by ignoring the measurement error are not reliable, since the rate of false positives are not controlled under the null hypothesis. In order to overcome these problems, we present an improved version of the Ordinary Least Square estimator in independent (regression models) and dependent (autoregressive models) data when the variables are subject to noises. Moreover, measurement error estimation procedures for microarrays are also described. Simulation results also show that both corrected methods perform better than the standard ones (i.e., ignoring measurement error). The proposed methodologies are illustrated using microarray data from lung cancer patients and mouse liver time series data. Conclusions: Measurement error dangerously affects the identification of regulatory network models, thus, they must be reduced or taken into account in order to avoid erroneous conclusions. This could be one of the reasons for high biological false positive rates identified in actual regulatory network models.

Antimicrobial drug administration errors identified in Brazilian multicentric study

Medication administration errors (MAE) are the most frequent kind of medication errors. Errors with antimicrobial drugs (AD) are relevant because they may interfere inpatient safety and in the development of microbial resistance. The aim of this study is to analyze the AD errors detected in a Brazilian multicentric study of MAE. It was a devcriptive and explorotory study carried out in clinical units in five Brazilian teaching hospitals. The hospitals were investigated during 30 days. MAE were detected by observation technique. MAE were classified in categories: wrong route(WR), wrong patient(WP), wrong dose(WD) wrong time (WT) and unordered drug (UD). AD with MA E were classified by Anatomical-Therapeutical-Chemical Classification System. AD with narrow therapeutic index (NTI) wet-e identified A descriptive statistical analysis was performed using SPSS version 11.5 software. A total of 1500 errors were observed, 277 (18.5%) of them were error with AD. The hopes of AD error were: WT87.7%, QD 6.9%, WR 1.5%, UD 3.2% and WP 0.7%. The number of AD found was 36. The mostly ATC class were fluoroquinolones 13.9%, combinations of penicillin 13.9%, macrolides 8.3% and third-generation cephalosporines 5.6%. The parenteral drug dosage form was associated with 55.6% of AD. 16.7% of AD were NTI. 47.4% of WD and 21.8% WT were with NTI drugs. This study shows that these errors should be considered potential areas for improvement in the medication process and patient safety plus there is requirement to develop rational drug use of AD.

Offline Detection, Identification, and Correction of Branch Parameter Errors Based on Several Measurement Snapshots

This paper proposes a three-stage offline approach to detect, identify, and correct series and shunt branch parameter errors. In Stage 1 the branches suspected of having parameter errors are identified through an Identification Index (II). The II of a branch is the ratio between the number of measurements adjacent to that branch, whose normalized residuals are higher than a specified threshold value, and the total number of measurements adjacent to that branch. Using several measurement snapshots, in Stage 2 the suspicious parameters are estimated, in a simultaneous multiple-state-and-parameter estimation, via an augmented state and parameter estimator which increases the V - theta state vector for the inclusion of suspicious parameters. Stage 3 enables the validation of the estimation obtained in Stage 2, and is performed via a conventional weighted least squares estimator. Several simulation results (with IEEE bus systems) have demonstrated the reliability of the proposed approach to deal with single and multiple parameter errors in adjacent and non-adjacent branches, as well as in parallel transmission lines with series compensation. Finally the proposed approach is confirmed on tests performed on the Hydro-Quebec TransEnergie network.

Robot measuring form errors

This work presents an automated system for the measurement of form errors of mechanical components using an industrial robot. A three-probe error separation technique was employed to allow decoupling between the measured form error and errors introduced by the robotic system. A mathematical model of the measuring system was developed to provide inspection results by means of the solution of a system of linear equations. A new self-calibration procedure, which employs redundant data from several runs, minimizes the influence of probes zero-adjustment on the final result. Experimental tests applied to the measurement of straightness errors of mechanical components were accomplished and demonstrated the effectiveness of the employed methodology. (C) 2007 Elsevier Ltd. All rights reserved.

Diagnostic errors and repetitive sequential classifications in on-line process control by attributes

The procedure of on-line process control by attributes, known as Taguchi`s on-line process control, consists of inspecting the mth item (a single item) at every m produced items and deciding, at each inspection, whether the fraction of conforming items was reduced or not. If the inspected item is nonconforming, the production is stopped for adjustment. As the inspection system can be subject to diagnosis errors, one develops a probabilistic model that classifies repeatedly the examined item until a conforming or b non-conforming classification is observed. The first event that occurs (a conforming classifications or b non-conforming classifications) determines the final classification of the examined item. Proprieties of an ergodic Markov chain were used to get the expression of average cost of the system of control, which can be optimized by three parameters: the sampling interval of the inspections (m); the number of repeated conforming classifications (a); and the number of repeated non-conforming classifications (b). The optimum design is compared with two alternative approaches: the first one consists of a simple preventive policy. The production system is adjusted at every n produced items (no inspection is performed). The second classifies the examined item repeatedly r (fixed) times and considers it conforming if most classification results are conforming. Results indicate that the current proposal performs better than the procedure that fixes the number of repeated classifications and classifies the examined item as conforming if most classifications were conforming. On the other hand, the preventive policy can be averagely the most economical alternative rather than those ones that require inspection depending on the degree of errors and costs. A numerical example illustrates the proposed procedure. (C) 2009 Elsevier B. V. All rights reserved.