Error-free Values Research Articles

X-ray diffraction study, W-H plot, and Nelson-Relay function for the structural data of Ni0.7Zn0.3Fe2O4 + xwt%V2O5

In this study, we used the sol–gel method to make zinc doped nickel ferrite magnetic Ni0.7Zn0.3Fe2O4 + xwt%V2O5 (x = 0.0–1.0). The X-ray diffraction technique was used to examine the Ni0.7Zn0.3Fe2O4 + xwt%V2O5ferrite powder in order to identify Bragg's reflections and study the Miller indices (hkl). Using established formulas, the structural parameters lattice constant (a), unit cell volume (V), X-ray density (dx), porosity (P percent), and others have been calculated from XRD data. For the structural analysis, Bradley-jay (B-J) extrapolation (cos2θ) versus lattice constant (a) was employed; also, Specimen misalignment (S-M) plot was used to describe the error-free values of lattice constant (a). To review the calculated crystallite size (D) and lattice constant, the Williamson-hall extrapolation function and Nelson-relay (N-R) extrapolation function were used (a). The results of the computations revealed cubic geometry, spinel structure, and Fd3m space group formation in Ni0.7Zn0.3Fe2O4 + xwt%V2O5 ferrite. In light of the significant uses of Ni0.7Zn0.3Fe2O4 + xwt%V2O5 in energy storage devices, microwave device technology, and magnetic applications, the prepared Ni0.7Zn0.3Fe2O4 + xwt%V2O5 might be regarded for further research by the research community.

Exact Lookup Tables for the Evaluation of Trigonometric and Hyperbolic Functions

Elementary mathematical functions are pervasively used in many applications such as electronic calculators, computer simulations, or critical embedded systems. Their evaluation is always an approximation, which usually makes use of mathematical properties, precomputed tabulated values, and polynomial approximations. Each step generally combines error of approximation and error of evaluation on finite-precision arithmetic. When they are used, tabulated values generally embed rounding error inherent to the transcendence of elementary functions. In this article, we propose a general method to use error-free values that is worthy when two or more terms have to be tabulated in each table row. For the trigonometric and hyperbolic functions, we show that Pythagorean triples can lead to such tables in little time and memory usage. When targeting correct rounding in double precision for the same functions, we also show that this method saves memory and floating-point operations by up to 29 and 42 percent, respectively.

Bayesian Simultaneous Edit and Imputation for Multivariate Categorical Data

ABSTRACTIn categorical data, it is typically the case that some combinations of variables are theoretically impossible, such as a 3-year-old child who is married or a man who is pregnant. In practice, however, reported values often include such structural zeros due to, for example, respondent mistakes or data processing errors. To purge data of such errors, many statistical organizations use a process known as edit-imputation. The basic idea is first to select reported values to change according to some heuristic or loss function, and second to replace those values with plausible imputations. This two-stage process typically does not fully use information in the data when determining locations of errors, nor does it appropriately reflect uncertainty resulting from the edits and imputations. We present an alternative approach to editing and imputation for categorical microdata with structural zeros that addresses these shortcomings. Specifically, we use a Bayesian hierarchical model that couples a stochastic model for the measurement error process with a Dirichlet process mixture of multinomial distributions for the underlying, error-free values. The latter model is restricted to have support only on the set of theoretically possible combinations. We illustrate this integrated approach to editing and imputation using simulation studies with data from the 2000 U. S. census, and compare it to a two-stage edit-imputation routine. Supplementary material is available online.

Thermodynamics of protein-ligand interactions as a reference for computational analysis: how to assess accuracy, reliability and relevance of experimental data.

For a conscientious interpretation of thermodynamic parameters (Gibbs free energy, enthalpy and entropy) obtained by isothermal titration calorimetry (ITC), it is necessary to first evaluate the experimental setup and conditions at which the data were measured. The data quality must be assessed and the precision and accuracy of the measured parameters must be estimated. This information provides the basis at which level discussion of the data is appropriate, and allows insight into the significance of comparisons with other data. The aim of this article is to provide the reader with basic understanding of the ITC technique and the experimental practices commonly applied, in order to foster an appreciation for how much measured thermodynamic parameters can deviate from ideal, error-free values. Particular attention is paid to the shape of the recorded isotherm (c-value), the influence of the applied buffer used for the reaction (protonation reactions, pH), the chosen experimental settings (temperature), impurities of protein and ligand, sources of systematic errors (solution concentration, solution activity, and device calibration) and to the applied analysis software. Furthermore, we comment on enthalpy-entropy compensation, heat capacities and van't Hoff enthalpies.

Reliability, repeatability and reproducibility: analysis of measurement errors in continuous variables

Reliability, repeatability and reproducibility: analysis of measurement errors in continuous variables

Verification of helical tomotherapy delivery using autoassociative kernel regressiona)

Quality assurance (QA) is a topic of major concern in the field of intensity modulated radiation therapy (IMRT). The standard of practice for IMRT is to perform QA testing for individual patients to verify that the dose distribution will be delivered to the patient. The purpose of this study was to develop a new technique that could eventually be used to automatically evaluate helical tomotherapy treatments during delivery using exit detector data. This technique uses an autoassociative kernel regression (AAKR) model to detect errors in tomotherapy delivery. AAKR is a novel nonparametric model that is known to predict a group of correct sensor values when supplied a group of sensor values that is usually corrupted or contains faults such as machine failure. This modeling scheme is especially suited for the problem of monitoring the fluence values found in the exit detector data because it is able to learn the complex detector data relationships. This scheme still applies when detector data are summed over many frames with a low temporal resolution and a variable beam attenuation resulting from patient movement. Delivery sequences from three archived patients (prostate, lung, and head and neck) were used in this study. Each delivery sequence was modified by reducing the opening time for random individual multileaf collimator (MLC) leaves by random amounts. The errof and error-free treatments were delivered with different phantoms in the path of the beam. Multiple autoassociative kernel regression (AAKR) models were developed and tested by the investigators using combinations of the stored exit detector data sets from each delivery. The models proved robust and were able to predict the correct or error-free values for a projection, which had a single MLC leaf decrease its opening time by less than 10 msec. The model also was able to determine machine output errors. The average uncertainty value for the unfaulted projections ranged from 0.4% to 1.8% of the detector signal. The low model uncertainty indicates that the AAKR model is extremely accurate in its predictions and also suggests that the model may be able to detect errors that cause the fluence to change by less than 2%. However, additional evaluation of the AAKR technique is needed to determine the minimum detectable error threshold from the compressed helical tomotherapy detector data. Further research also needs to explore applying this technique to electronic portal imaging detector data.

EVOLVING AN EMPIRICAL METHODOLOGY DOR DETERMINING APPROPRIATE INTERVAL FOR REMOTE SENSING OF A FOREST ENVIRONMENT

The phenomenon of deforestation has been an environmental threat, and some concerted efforts have been made by researchers to tackle the problem. These generally include mapping of the areas affected, using remote sensing and GIS to display information on the spatial and temporal distributions of the processes. It is however, observed that little or no attempt has been made on the conceptualization of deforestation for better understanding of the problem scenario which can be applied to any forest for effective planning and management. It is in this light that the paper attempted to evolve an innovative mathematical model for establishing appropriate interval for remote sensing of a forest environment, using Afaka Forest Reserve as a case study. The methodology consists of conceptualizing Afaka Forest Reserve as a tightly stretched string under tension of human - induced deforestation; deriving a mathematical model; and testing it with the assumed error free values of the rate of deforestation computed in each period, using remote sensing imageries of 1962 aerial photographs (B-W); Landsat MSS (1970); Landsat TM (1987); and SPOT (XS) of 1994. The results show that the proper interval for mapping is eight years under ideal condition, followed by nine years interval, irrespective of imageries used. The uniqueness of this approach, is that it can be applied to any forest or dynamic feature on the earth, and can enjoy universal application as well. KEY WORDS: Evolving empirical methodology, innovative mathematical model, appropriate interval, remote sensing, forest environment planning and management. Global Jnl Geological Sciences . Vol.2(1) 2004: 91-99