Statistical methods, to determine the

There are statistical methods to determine the verisimilitude of experimental data to models. One major procedure to do this is nonlinear curve fitting to dose-response curves predicted by receptor models. 

There have been reports of electronic noses with as few as four and as many as 100 sensors in the array1718 statistical methods to determine the optimum number of sensors in an array will greatly assist in sensor selection. Statistical methods based on experimental data have been used successfully to optimize an array statistical methods may also be used with data simulated using purely computational approaches. Recent work in using neural networks for array selection in addition to analyte identification shows promise as an approach.19... 

Lubricant condition monitoring is best accomplished by the analysis of numerical data that are associated with the various fluid failure modes [2]. Numerical data can be analysed by statistical methods to determine the relationship between the various test parameters and their respective fluid and machinery failure modes. In addition, the statistical analysis can be used to determine potential data interference sources, the various alarm limits for each parameter and other criteria to be used in the daily evaluation of used oil. Note that it is important to determine all of the causes for variability in parametric data, just as it is necessary to separate changes due to interfering causes from changes with its associated relevant failure modes. 

The chain statistics method to determine the reactivity ratios is based on the fact that the P-matrix elements are related to the molar fraction of... 

Supervised neural networks that use an MSE cost function can use formal statistical methods to determine the confidence of the trained model. The MSE on a validation set can be used as an estimate for variance. This value... 

A standard statistical method to determine the coefficients of the embrittlement correlation equations is a least square method, where the... 

Based on the flame-hole dynamics [59], dynamic evolutions of flame holes were simulated to yield the statistical chance to determine the reacting or quenched flame surface under the randomly fluctuating 2D strain-rate field. The flame-hole d5mamics have also been applied to turbulent flame stabilization by considering the realistic turbulence effects by introducing fluctuating 2D strain-rate field [22] and adopting the level-set method [60]. 

Voigt-Martin, I.G., Zhang, Z.H., Kolb, U. and Gihnore, C.J. (1997) The use of maximum entropy statistics combined with simulation methods to determine the structure of 4-dimethylamino-3-cyanobiphenyl Ultramicroscopy, 68,43-59. 

Very generally, the identification of a molecule of interest by a combinatorial strategy requires (i) the random synthesis of a balanced library in which the different candidates are statistically equi-represented, (the over-representation of some compounds and the under-representation of others will bias the population and subsequently may affect the outcome of the selection) (ii) the efficient partitioning of candidates which display the desired property depends upon a carefully adjusted selection pressure combined with an effective procedure allowing the physical separation of the winners, and (iii) the identification of these winning molecules and their defined synthesis at high yield and low cost for further use. This means either a very sensitive analytical method to determine the chemical structure of the selected molecules must be used... 

Hydrogen transport. The approach that they have used to predict proton transport through complex membranes such as Nation is to use ab initio methods to determine the barriers for migration of hydrogen as a function of the donor-acceptor separation and then to employ a statistical method that is based on the ab initio results. This method allows a proton jump among water clusters when the configuration around the proton is appropriate. 

Analysis of covariance (ANCOVA) reverses drug-induced depression of the CNS. Statistical method to determine if two or more related dependent variables exposed to two or more related variables differ significantly from chance. 

Because the British group applied extensively their statistical method to determine causation of large interindividual pharmacokinetic variations without describing its strengths and weaknesses, others have attempted to assess critically the application of multiple regression analysis for this particular purpose (31,32) While this statistical method has great potential, it requires considerable modification beyond its initial applications in this area (27-29), if that potential is to be realized (H,32). Thus far, its applications in pharmacokinetics (27-29) have been disappointing because those who have employed it neither formulated nor addressed, much less demonstrated fulfillment of, several fundamental assumptions inherent in its use ( 1, 32). 

Solvent effects can significantly influence the function and reactivity of organic molecules.1 Because of the complexity and size of the molecular system, it presents a great challenge in theoretical chemistry to accurately calculate the rates for complex reactions in solution. Although continuum solvation models that treat the solvent as a structureless medium with a characteristic dielectric constant have been successfully used for studying solvent effects,2,3 these methods do not provide detailed information on specific intermolecular interactions. An alternative approach is to use statistical mechanical Monte Carlo and molecular dynamics simulation to model solute-solvent interactions explicitly.4 8 In this article, we review a combined quantum mechanical and molecular mechanical (QM/MM) method that couples molecular orbital and valence bond theories, called the MOVB method, to determine the free energy reaction profiles, or potentials of mean force (PMF), for chemical reactions in solution. We apply the combined QM-MOVB/MM method to... 

The computer is an excellent tool for statistical analysis of data and for solving mathematical problems. Commercial software packages (Table 1) are generally used for statistical analysis. The scientist often works with the statistician to design an experiment and determine the most appropriate statistical method to analyze the... 

The results of acute toxicity tests are reported as the LC50 and EC50 (concentration that reduces growth 50%) values and their 95% confidence intervals. Probit analysis is the most commonly used statistical method to determine LC50 values. Graphical interpolation can be used to estimate the LC50 value where the proportion of deaths versus the test concentration is plotted for each observation time. 

For yes/no tests, the evaluation model is different. The analyte concentration at which 50% of the observers consider the test positive must be determined. The performance of the test can be described in teems of the percentage of tests recorded as positive by the trial participants at a series of concentrations below and above the threshold. The heavy line in Figure 1 is a hypothetical plot of the percentage of positive results at a series of concentration points. Unlike the quantitative test in which 50% of the sanples at concentration T were positive, in the case illustrated by the heavy line, only about 20% of the samples of concentration T are positive. If the yes/no or positive/negative decision is made visually by a comparison with colored standards and the line does not cross the threshold concentration at or near the 50% positive point, cme could adjust the standards to correct the concentration at which the 50% point occurs. Statistical methods for determining the concentration corresponding to the 50% point, the number of sanples required at each concentration, and the behavior of the response curve belcw and above the 50% point have not been standardized. This is under consideration by an Association of Official Analytical Chemists (AQAC) Task Force on Test Kits. 

In any case, the simulated profiles must be compared with the measured data to check the validity of the determined data as well as the assumed model. Statistical methods to quantify the goodness of the fit are given, for example, in Lapidus (1962), Barns (1994), Korns (2000) and Press et al. (2002). 

Another approach to obtain a parameter that describes the dissolution rate is to use statistical moments to determine the mean dissolution time (MDT) (von Hattingberg 1984). This method has the advantage of being applicable to all types of dissolution profiles, and it does not require fitting to any model. The only prerequisite is that data points are available close to the final plateau level. The MDT can be interpreted as the most likely time for a molecule to be dissolved from a solid dosage form. In the case of zero- and first-order dissolution processes, the MDT corresponds to the time when 50 and 63.2 percent have been released, respectively. The MDT is determined from ... 

The recommended error estimation methods for high volatility compounds from the reference are reviewed in this section of the report after describing the test protocol procedures. A Monte Carlo simulation of experimental results was then performed followed by statistical analyses to determine the distribution and amount of error associated with estimation of volatilization from water for a high volatility compound. 

In either approach, if the goal is to compare close titer values (such as eightfold difference between titers of two ADA samples), it is important to apply the interpolation method to determine the titers, or if a noninterpolation method is used, the serial dilutions should be narrowly spaced (ideally twofold or less). In addition, an objective method is needed for determining the ability of the assay to differentiate titers (titer precision). This titer precision is defined by the minimum significant ratio (MSR), which is the smallest fold change between the titers of any two ADA-positive samples that can be considered as significant. For example, MSR = 5 means that at least a fivefold difference in the titer results between any two positive samples will be required to conclude that they are statistically different. Evaluation of MSR is mostly relevant when comparison of samples with close titers is of interest. 

The high-Z atomic column positions at a grain boundaries can therefore be determined directly from the image during the experiment. However, on completion of the microscopy, a more accurate statistical method to obtain the column positions is to recover the Z-contrast object function through maximum entropy image analysis [11.12]. Maximum entropy image analysis is based on... 

The previous discussions have dealt with statistical methods to estimate the reliability of analyses at specific confidence levels, these being ultimately determined... 

The battery industry developed a statistical method for determining the concentration of mercury in the waste stream at any point in time, and used this to predict the future date by which all of the mercury within primary batteries will have passed through the waste stream. This method, which uses date code analysis was developed over a period of many years through stockpile analyses in Germany, Sweden, Belgium and The Netherlands. It is employed annually in Europe to forecast the decline of residual... 

In general one can decide how many independent decay components are needed to describe the observed kinetics by closely inspecting the residuals (difference between measured and fitted curves). The singular value decomposition (SVD) method is a statistical tool to determine the maximum number of components that can be extracted with confidence from the experimental traces. 

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