Error Control Procedures Research Articles

Application of the p-version of FEM to hierarchic rod models with reference to mechanical contact problems

The formulation of a system of hierarchic models for the simulation of the mechanical response of slender elastic bodies, such as elastic rods, is considered. The present work is concerned with aspects of implementation and numerical examples. We use a finite element formulation based on the principle of minimum potential energy. The displacement fields are represented by the product of one-dimensional field functions and two-dimensional director functions. The field functions are approximated by the p-version of the finite element method. Our objective is to control both the model form errors and the errors of discretization with a view toward the development of advanced engineering applications equipped with autonomous error control procedures. We present numerical examples that illustrate the performance characteristics of the algorithm.

A more powerful familywise error control procedure for evaluating mean equivalence

When one wishes to show no meaningful differences among group means, equivalence tests should be used, as a nonsignificant test of mean difference does not provide evidence supporting equivalence. This research proposes two modified stepwise procedures for controlling the familywise Type I error rate, based on the Bonferroni-type correction of k2/4 (where k is the number of groups to be compared) proposed by Caffo, Lauzon and Rohmel (2013 Correction to “easy multiplicity control in equivalence testing using two One-Sided tests. The American Statistician 67 (2):115–6) Bonferroni-type correction of k2/4 (where k is the number of groups to be compared). Using a Monte Carlo simulation method, we show that adopting a stepwise procedure increases power, while maintaining the familywise error rate at or below α. Implications for applied research and directions for future study are discussed.

A comprehensive error rate for multiple testing

Over the last two decades, a large variety of type I error rates and control procedures have been proposed in the field of multiple hypotheses testing. This paper proposes a framework that includes many existing proposals by investigating procedures in which the ordered p-values are compared to an arbitrary positive and non-decreasing threshold sequence. For this case, we derive the error rate being controlled under different assumptions on the p-values. Our focus will be on step-up procedures. The new formulation gives insight into the relations between existing error rates and opens new perspectives for the whole field of multiple testing.

New autonomous scheme of iterative learning control for online implementation

The purpose of this paper is to achieve the implementation of a new autonomous control scheme combining two phases: online error learning and control procedure implementation on the Arduino-Uno microcontroller. This paper presents the realisation of a real time implementation of three control algorithms applied to a resistor-capacitor (RC) circuit. Two iterative learning control schemes, proportional iterative learning control (ILC-1) and optimal iterative learning control (ILC-2) are studied and implemented and their performance results are also compared to proportional-integrator (PI) controller. The experimental results show the feasibility and the efficiency of the online autonomous control scheme.

Geometrically Uniform n-shot Subspace Codes

In [A. Khaleghi, D. Silva, and F.R. Kschischang, Subspace Codes, Lecture Notes in Computer Science, vol. 5921, pp. 1-21, 2009] it is proposed an efficient error-control procedure for use in Network Coding called subspace codes constructed from projective space of order m over a finite field Fq, denoted by P(Fqm), that is, the set of all subspaces in the vector space Fqm, [T. Etzion, and A. Vardy, Error Correcting Codes in Projective Space, Proc. of the 2008 IEEE Int. Symp. on Inf. Theory, 871-875, Toronto, Canada, 2008]. The projective space endowed with the subspace metric is a metric space. Such subspace codes are devised for the one use of the channel. An alternative to improve the rate and the error-correcting capabilities, without increasing the order of the finite field or the vector length, is to make use of the channel n times, this new code is known as the n-shot subspace code, [R. Nóbrega, and B. Uchôa-Filho, Multishot Codes for Network Coding: Bounds and a Multilevel Construction, Proc. of the 2009 IEEE Int. Symp. on Information Theory - ISIT-09, Seoul, South Korea, Jun. 2009]. In this paper we present the concept of geometrically uniform subspace codes and the new n-shot geometrically uniform subspace codes.

Dyn-ARF: a rate adaptation mechanism sensitive to the network load over 802.11 WLANs

Since the first version of the IEEE 802.11, the standard committee has included a set of transmission rates aiming to accommodate the wide variety of requirements of end-user devices and channel operating conditions. Traditionally, the sender increases the data transmission rate upon receiving various consecutive acknowledgement packets while the data transmission rate is decreased on the absence of acknowledgement packets. This error-control procedure assumes that the channel operating conditions are the main source of transmission errors and losses. However, under medium or high load conditions, transmission impairments are mainly due to channel access conflicts: collisions. Under these load conditions, reducing the data transmission based exclusively on the absence of feedback not only proves ineffective, but it actually degrades the overall network performance. In this paper, we describe a novel rate adaptation mechanism capable of mitigating the effect of collisions using the information imbedded in the received packets. Simulation results show that our proposal limits the use of the data transmission adaptation mechanism which in turn results on a significant increase of the aggregated throughput.

The extent of genome flux and its role in the differentiation of bacterial lineages.

Horizontal gene transfer (HGT) and gene loss are key processes in bacterial evolution. However, the role of gene gain and loss in the emergence and maintenance of ecologically differentiated bacterial populations remains an open question. Here, we use whole-genome sequence data to quantify gene gain and loss for 27 lineages of the plant-associated bacterium Pseudomonas syringae. We apply an extensive error-control procedure that accounts for errors in draft genome data and greatly improves the accuracy of patterns of gene occurrence among these genomes. We demonstrate a history of extensive genome fluctuation for this species and show that individual lineages could have acquired thousands of genes in the same period in which a 1% amino acid divergence accrues in the core genome. Elucidating the dynamics of genome fluctuation reveals the rapid turnover of gained genes, such that the majority of recently gained genes are quickly lost. Despite high observed rates of fluctuation, a phylogeny inferred from patterns of gene occurrence is similar to a phylogeny based on amino acid replacements within the core genome. Furthermore, the core genome phylogeny suggests that P. syringae should be considered a number of distinct species, with levels of divergence at least equivalent to those between recognized bacterial species. Gained genes are transferred from a variety of sources, reflecting the depth and diversity of the potential gene pool available via HGT. Overall, our results provide further insights into the evolutionary dynamics of genome fluctuation and implicate HGT as a major factor contributing to the diversification of P. syringae lineages.

Integer Codes Correcting Burst Errors within a Byte

This paper presents a class of integer codes that can correct any burst of length \le l within a b-bit byte. Their main advantages lie in linear complexity of encoding and decoding procedures, as well as in the fact that a look-up table-based error control procedure requires relatively small memory resources.

Restoring coverage to the Bayesian false discovery rate control procedure

Principal among knowledge discovery tasks is recognition of insightful patterns or features from data that can inform otherwise challenging decisions. For the costly future decisions, there is little room for error. Features must provide substantial evidence to be robust for classification and dependable for important decisions. Here we seek statistical evidence for feature selection, that feature signals are of sufficient magnitude and frequency to be generalizable for classification. The Bayesian false discovery rate (bFDR) error control procedure is powerfully suited for this task. In realistic situations often encountered in practice, the bFDR procedure is biased, yielding a greater than desired FDR. In other less typical cases, the FDR is less than desired. We investigate the sources of bias in the bFDR procedure, and predict the direction of bias. A new algorithm has been developed to recover the bias in the bFDR control procedure. In simulation and real data mining examples, the new bFDR control algorithm shows promise. The strengths and limitations of the new approach are presented with examples and discussed.

Localized Glaucomatous Change Detection within the Proper Orthogonal Decomposition Framework

To detect localized glaucomatous structural changes using proper orthogonal decomposition (POD) framework with false-positive control that minimizes confirmatory follow-ups, and to compare the results to topographic change analysis (TCA). We included 167 participants (246 eyes) with ≥4 Heidelberg Retina Tomograph (HRT)-II exams from the Diagnostic Innovations in Glaucoma Study; 36 eyes progressed by stereo-photographs or visual fields. All other patient eyes (n = 210) were non-progressing. Specificities were evaluated using 21 normal eyes. Significance of change at each HRT superpixel between each follow-up and its nearest baseline (obtained using POD) was estimated using mixed-effects ANOVA. Locations with significant reduction in retinal height (red pixels) were determined using Bonferroni, Lehmann-Romano k-family-wise error rate (k-FWER), and Benjamini-Hochberg false discovery rate (FDR) type I error control procedures. Observed positive rate (OPR) in each follow-up was calculated as a ratio of number of red pixels within disk to disk size. Progression by POD was defined as one or more follow-ups with OPR greater than the anticipated false-positive rate. TCA was evaluated using the recently proposed liberal, moderate, and conservative progression criteria. Sensitivity in progressors, specificity in normals, and specificity in non-progressors, respectively, were POD-Bonferroni = 100%, 0%, and 0%; POD k-FWER = 78%, 86%, and 43%; POD-FDR = 78%, 86%, and 43%; POD k-FWER with retinal height change ≥50 μm = 61%, 95%, and 60%; TCA-liberal = 86%, 62%, and 21%; TCA-moderate = 53%, 100%, and 70%; and TCA-conservative = 17%, 100%, and 84%. With a stronger control of type I errors, k-FWER in POD framework minimized confirmatory follow-ups while providing diagnostic accuracy comparable to TCA. Thus, POD with k-FWER shows promise to reduce the number of confirmatory follow-ups required for clinical care and studies evaluating new glaucoma treatments. (ClinicalTrials.gov number, NCT00221897.).

Error Analysis for Matrix Factorizations Using Non-Overlapped Localizing Basis Functions

Local-global solution (LOGOS) modes provide a computationally efficient framework for developing error controllable, fast, direct solution methods for electromagnetic simulations. This communication provides an error control analysis for the non-overlapped localizing LOGOS factorization procedure. The error analysis indicates how to control the error in the factored representation of the system matrix. Numerical examples demonstrate that the proposed error control procedure provides factorizations with controllably small errors for a number of PEC scattering problems while maintaining the efficiency of the LOGOS factorization.

Error control variability in pathway-based microarray analysis

Motivation: The decision to commit some or many false positives in practice rests with the investigator. Unfortunately, not all error control procedures perform the same. Our problem is to choose an error control procedure to determine a P-value threshold for identifying differentially expressed pathways in high-throughput gene expression studies. Pathway analysis involves fewer tests than differential gene expression analysis, on the order of a few hundred. We discuss and compare methods for error control for pathway analysis with gene expression data.Results: In consideration of the variability in test results, we find that the widely used Benjamini and Hochberg's (BH) false discovery rate (FDR) analysis is less robust than alternative procedures. BH's error control requires a large number of hypothesis tests, a reasonable assumption for differential gene expression analysis, though not the case with pathway-based analysis. Therefore, we advocate through a series of simulations and applications to real gene expression data that researchers control the number of false positives rather than the FDR.Availability: Our R package, EPath.omg is available at http://sphhp.buffalo.edu/biostat/research/software.Contact: dlgold@buffalo.eduSupplementary information: Supplementary data are available at Bioinformatics online.

Obtaining accurate solutions using reduced chemical kinetic models: a new model reduction method for models rigorously validated over ranges

Reduced chemical kinetics models are often used to lessen the computational cost of reacting flow simulations. However, because a reduced model is usually validated only for a nominal set of reaction conditions, unknown errors are introduced if the reduced model is used at new reaction conditions. In a previous paper, we introduced a method that, given a reduced model as input, identifies a rigorous range over which the model remains valid. However, this procedure is backwards: in most cases one starts with a known range of reaction conditions and one desires a reduced model that can be used over this range. Here we present the first automatic procedure that constructs a reduced chemistry model that is guaranteed to be valid everywhere in any user-specified range. The rigorousness of the model reduction method enables rigorous statements about the difference between the solution obtained using the reduced model and the solution that would have been obtained using the original full-chemistry model. By appropriate choice of error tolerances, the reduced-model solution can be made arbitrarily close to the full-model solution. This is demonstrated with adaptive chemistry simulations of one- and two-dimensional steady state laminar methane/air flames. As guaranteed by the error control procedure, the solutions of the reduced models are just as accurate as those obtained using the full-chemistry model, but they require significantly less CPU time.

High Throughput Screening of Co-Expressed Gene Pairs with Controlled False Discovery Rate (FDR) and Minimum Acceptable Strength (MAS)

Many exploratory microarray data analysis tools such as gene clustering and relevance networks rely on detecting pairwise gene co-expression. Traditional screening of pairwise co-expression either controls biological significance or statistical significance, but not both. The former approach does not provide stochastic error control, and the later approach screens many co-expressions with excessively low correlation. We have designed and implemented a statistically sound two-stage co-expression detection algorithm that controls both statistical significance (false discovery rate, FDR) and biological significance (minimum acceptable strength, MAS) of the discovered co-expressions. Based on estimation of pairwise gene correlation, the algorithm provides an initial co-expression discovery that controls only FDR, which is then followed by a second stage co-expression discovery which controls both FDR and MAS. It also computes and thresholds the set of FDR p-values for each correlation that satisfied the MAS criterion. Using simulated data, we validated asymptotic null distributions of the Pearson and Kendall correlation coefficients and the two-stage error-control procedure; we also compared our two-stage test procedure with another two-stage test procedure using the receiver operating characteristic (ROC) curve. We then used yeast galactose metabolism data to illustrate the advantage of our method for clustering genes and constructing a relevance network. The method has been implemented in an R package "GeneNT" that is freely available from the Comprehensive R Archive Network (CRAN): www.cran.r-project.org/.

Application of two preconditioned generalizedconjugate gradient methods to three-dimensional neutron and photon transport equations

In this paper the preconditioned generalized conjugate gradient methods are applied to solve the linear system of equations that arise in three-dimensional neutron and photon transport equations. These generalized conjugate gradient methods are the CGS (conjugate gradient square) algorithm and the Bi-CGSTAB (bi-conjugate gradient stabilized) algorithm. Several subroutines are developed from these preconditioned generalized conjugate gradient methods for use in time-independent multi-group three-dimensional neutron and photon transport equations. These subroutines are connected to the computer program TORT. The reason for choosing the preconditioned generalized conjugate gradient methods is that these methods have good residual error control procedures during computation and have good convergence rates. We test a problem having an 8 set of matrix equations with 24255 unknowns each, in a personal computer with an AMD Athlon-XP1600+ central processing unit (CPU) and using Mandrake Linux 6.3 as the operating system. The point-wise incomplete LU factorization (ILU) and modified point-wise incomplete LU factorization (MILU) are the preconditioning techniques used in the test problem. We find that the preconditioned CGS and Bi-CGSTAB methods with the preconditioner ILU are more efficient than with the preconditioner MILU in the test problem. The numerical solution of flux by the preconditioned Bi-CGSTAB and CGS methods produces the same results as those obtained bythe successive over relaxation method (SOR) in the TORT program which is usually used for the calculation of radiation shielding in nuclear power plant and nuclear spent fuel storage.

Error Control in Residue Number Systems

This paper introduces an alternate approach to error control in residue number systems which utilizes sets of moduli that include pairs with non-trivial common factors. Necessary and sufficient conditions for achieving a specified capacity for error detection or correction are derived by considering the minimum Hamming distance of an associated linear code. Effective error-control procedures are developed based on a syndrome matrix whose entries are obtained directly from the residue digits. The potential of a priori bounds on the magnitude of measurement errors to increase the efficiency of the control process is analyzed.

Error norm estimation and stopping criteria in preconditioned conjugate gradient iterations

AbstractSome techniques suitable for the control of the solution error in the preconditioned conjugate gradient method are considered and compared. The estimation can be performed both in the course of the iterations and after their termination.The importance of such techniques follows from the non‐existence of some reasonable a priori error estimate for very ill‐conditioned linear systems when sufficient information about the right‐hand side vector is lacking. Hence, some a posteriori estimates are required, which make it possible to verify the quality of the solution obtained for a prescribed right‐hand side. The performance of the considered error control procedures is demonstrated using real‐world large‐scale linear systems arising in computational mechanics. Copyright © 2001 John Wiley & Sons, Ltd.

Hybrid solution for the laminar flow of power-law fluids inside rectangular ducts

The so-called generalized integral transform technique (GITT) is employed in the hybrid numerical–analytical solution of two-dimensional fully-developed laminar flow of non-Newtonian power-law fluids inside rectangular ducts. The characteristic of the automatic and straightforward global error control procedure inherent to this approach, permits the determination of fully converged benchmark results to assess the performance of purely numerical techniques. Therefore, numerical results for the product Fanning friction factor-generalized Reynolds number are computed for different values of power-law index and aspect ratio, which are compared with previously reported results in the literature, providing critical comparisons among them as well as illustrating the powerfulness of the integral transform approach. The resulting velocity profiles computed by using this methodology are also compared with those calculated by approximated methods for power-law fluids, within the range of governing parameters studied.

A posteriori error estimation and error control for finite element approximations of the time-dependent Navier–Stokes equations

We present an approach to estimate numerical errors in finite element approximations of the time-dependent Navier–Stokes equations along with a strategy to control these errors. The error estimators and the error control procedure are based on the residuals of the Navier–Stokes equations, which are shown to be comparable to error components in the velocity variable. The present methodology applies to the estimation of numerical errors due to the spatial discretization only. Its performance is demonstrated for two-dimensional channel flows past a cylinder in the periodic regime.

New embedded explicit methods with minimal phase-lag for the numerical integration of the Schrödinger equation

A new family of explicit two-step Numerov-type methods with minimal phase-lag is developed for the numerical integration of the Schrödinger equation. Based on this family of methods and on the phase-lag error-control procedure, an embedded method is developed. An application to the phase shift problem of the radial Schrödinger equation and to the coupled differential equations arising from the Schrödinger equation, indicates that these new methods are generally more efficient than other previously developed finite difference methods.