Effect Of Experimental Error Research Articles

A non-destructive approach to identify the stress-free state and material properties of arteries

Residual strains and stresses in arteries play a significant role in homogenizing the stress field in the arterial wall and make arteries more compliant. The stress-free state of the artery needs to be identified in order to determine the residual stresses or strains in the unloaded and loaded states of the artery. The stress-free state of an artery can be characterized by two geometric parameters of the open sector achieved after a short artery segment is cut open radially, i.e., the inner radius and the opening angle. A traditional method to determine the stress-free state of arteries is to cut a short artery segment radially and measure the inner radius and the opening angle of the open sector, which is destructive by nature. In this paper, we propose a novel non-destructive method to identify the stress-free state of arteries, i.e., its inner radius and the opening angle, without the need to make the physical cut to the artery. The essence of this method is an inverse problem to identify the inner radius and the opening angle of the stress-free state by applying optimization algorithms based on a series of loaded states of the artery under different intraluminal pressures. Numerical simulations were conducted to generate a series of deformed states of an artery from which the inner radius and the opening angle of the stress-free state were identified thereafter. In addition, the effect of experimental error was investigated, and a method to modify the experimental data with error based on the pressure-radius relation of the artery was proposed. Furthermore, a non-destructive method was proposed to identify the material parameters in Fung’s constitutive model by applying the notion of average stretch ratios and stresses, from which the stress-free state can be further identified.

Determination of volume scattering parameters that reproduce the luminance characteristics of diffusers.

The extension of a well-known inverse technique, inverse adding-doubling (IAD), is investigated for determining the volume scattering properties of diffusers for display and lighting applications. The luminance characteristics of volume scattering diffusers are vital for these applications. Through a simulation study, it is shown that fitting solely to the scattered (angular) intensity information with the extended IAD method, results in a volume scattering characterization that also reproduces the correct (spatial and angular) luminance characteristics for a wide range of samples. The gap between the simulation work and the experimental application of the investigated fitting procedure is bridged by considering the effect of experimental error in the scattered intensity distributions. This does not significantly alter the presented conclusions.

A Genetic Algorithm for Solving Combinatorial Problems and the Effects of Experimental Error – Applied to Optimizing Catalytic Materials

AbstractA new form of Genetic Algorithm (GA) is introduced which has been developed to solve combinatorial problems. A combinatorial problem involves choosing the best subset of components from a pool of possible components in order that the mixture has some desired quality. This paper concentrates on applying the new technique to the optimization of catalytic materials. The new form of GA is compared to an evolutionary algorithm developed by Wolf et al. and shown to produce faster convergence. The paper also reports on the best GA parameter values (crossover technique, parent selection etc.) for problems such as these. Finally a statistical analysis of the effects of experimental error is performed, and the effects that these errors have on the convergence of the GA are reported.

Integrated Modeling of Mixture Fluid Phase Equilibrium Experiments Using SAFT-VR Applied to Xenon + Diborane, Xenon + Cyclopropane, Xenon + Boron Trifluoride

An intermolecular parameter estimation procedure is incorporated into a model of a static cell vapor-liquid equilibrium experiment where only the total pressure and temperature are measured, so that compositions are not available experimentally. The coexistence compositions are often obtained from the raw experimental measurements by data reduction, in which a (mostly empirical) thermodynamic description must be assumed to represent the liquid and vapor phases. The molecular interaction parameters inherent in a more advanced equation of state treatment are then estimated from this pretreated data for the coexistence compositions. This can lead to a bias in the development of the mixture model and does not allow a statistical analysis to be applied to the model. To overcome these limitations, an integrated self-consistent approach is developed in this work. The pure component model parameters are used with an equation of state to calculate the amount of substance in the experimental apparatus, and the mixture parameters are obtained from parameter estimation based on a model of the experimental setup and the representation of the vapor-liquid equilibrium. This type of integrated approach, best achieved by close integration of detailed experimental information and the theoretical treatment, is tested on three well-studied and characterized binary mixtures: xenon + diborane; xenon + cyclopropane; and xenon + boron trifluoride. The statistical associating fluid theory for potentials of variable range (SAFT-VR) is the equation of state used in this work; the molecular models inherent in the approach are associating chain molecules formed from square-well segments. Excellent agreement between SAFT-VR calculations of the fluid phase equilibrium and experimental data is obtained for all three mixtures, without a priori knowledge of the compositions of the coexisting phases. In the case of xenon + boron trifluoride, the region of liquid-liquid immiscibility and the vapor-liquid-liquid three-phase line are accurately predicted. The effect of experimental error is incorporated into the parameter estimation procedure so that the confidence in the optimal parameters can be evaluated providing guidance in choosing which parameters to estimate with confidence. For comparison, SAFT-VR models are also developed using the reduced data for the coexistence compositions. The description of the fluid phase equilibrium and the values of the intermolecular parameters are found to be similar to those obtained from the integrated approach. The integrated approach presented is general and can be modified to specific static cell apparatus or applied to other types of mixtures or with other equations of state. © 2009 American Chemical Society.

Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise

The Jarzynski equality and the fluctuation theorem relate equilibrium free energy differences to nonequilibrium measurements of the work. These relations extend to single-molecule experiments that have probed the finite-time thermodynamics of proteins and nucleic acids. The effects of experimental error and instrument noise have not been considered previously. Here, we present a Bayesian formalism for estimating free energy changes from nonequilibrium work measurements that compensates for instrument noise and combines data from multiple driving protocols. We reanalyze a recent set of experiments in which a single RNA hairpin is unfolded and refolded using optical tweezers at three different rates. Interestingly, the fastest and farthest-from-equilibrium measurements contain the least instrumental noise and, therefore, provide a more accurate estimate of the free energies than a few slow, more noisy, near-equilibrium measurements. The methods we propose here will extend the scope of single-molecule experiments; they can be used in the analysis of data from measurements with atomic force microscopy, optical, and magnetic tweezers.

Posterior probability distributions for Biot parameters from experimental data

Reflectivity measurements can be used in inversion techniques to obtain estimates of the physical characteristics of seabed sediments. In addition, computation of posterior probability distributions (PPDs) [S. E. Dosso, J. Acoust. Soc. Am. 111, 129–142 (2002)] provide an uncertainty of each parameter estimate obtained by a simulated annealing inversion. In this work, PPDs are calculated for experimental reflection loss data to evaluate the sensitivities associated with the parameters in the Biot-Stoll poro-elastic model for sediments. The data comes from a lab tank experiment in which reflection loss from a sandy sediment was measured as a function of grazing angle for frequencies between 75 kHz and 150 kHz. The sampling for the PPDs is based on the least-squares error between simulated reflection coefficient data and values modeled with the reflection module of OASES. [H. Schmidt, ‘‘OASES Version 2.1 User Guide and Reference Manual,’’ Department of Ocean Engineering, Massachusetts Institute of Technology, 1997.] The PPDs resulting from the lab data are compared with those obtained for simulated data, and the effects of experimental error on the results are explored.

Using surrogate modeling in the prediction of fibrinogen adsorption onto polymer surfaces.

We present a Surrogate (semiempirical) Model for prediction of protein adsorption onto the surfaces of biodegradable polymers that have been designed for tissue engineering applications. The protein used in these studies, fibrinogen, is known to play a key role in blood clotting. Therefore, fibrinogen adsorption dictates the performance of implants exposed to blood. The Surrogate Model combines molecular modeling, machine learning and an Artificial Neural Network. This novel approach includes an accounting for experimental error using a Monte Carlo analysis. Briefly, measurements of human fibrinogen adsorption were obtained for 45 polymers. A total of 106 molecular descriptors were generated for each polymer. Of these, 102 descriptors were computed using the Molecular Operating Environment (MOE) software based upon the polymer chemical structures, two represented different monomer types, and two were measured experimentally. The Surrogate Model was developed in two stages. In the first stage, the three descriptors with the highest correlation to adsorption were determined by calculating the information gain of each descriptor. Here a Monte Carlo approach enabled a direct assessment of the effect of the experimental uncertainty on the results. The three highest-ranking descriptors, defined as those with the highest information gain for the sample set, were then selected as the input variables for the second stage, an Artificial Neural Network (ANN) to predict fibrinogen adsorption. The ANN was trained using one-half of the experimental data set (the training set) selected at random. The effect of experimental error on predictive capability was again explored using a Monte Carlo analysis. The accuracy of the ANN was assessed by comparison of the predicted values for fibrinogen adsorption with the experimental data for the remaining polymers (the validation set). The mean value of the Pearson correlation coefficient for the validation data sets was 0.54 +/- 0.12. The average root-mean-square (relative) error in prediction for the validation data sets is 38%. This is an order of magnitude less than the range of experimental values (i.e., 366%) and compares favorably with the average percent relative standard deviation of the experimental measurements (i.e., 17.9%). The effects of each of the user-defined parameters in the ANN were explored. None were observed to have a significant effect on the results. Thus, the Surrogate Model can be used to accurately and unambiguously identify polymers whose fibrinogen absorption is at the limits of the range (i.e., low or high) which is an essential requirement for assessing polymers for regenerative tissue applications.

Measuring polymer surface ordering differences in air and water by sum frequency generation vibrational spectroscopy.

Molecular structures of poly(n-butyl methacrylate) (PBMA) at the PBMA/air and PBMA/water interfaces have been studied by sum frequency generation (SFG) vibrational spectroscopy. PBMA surfaces in both air and water are dominated by the methyl groups of the ester side chains. The average orientation and orientation distribution of these methyl groups at the PBMA/air and PBMA/water interfaces are different, indicating that surface restructuring occurs when the PBMA sample contacts water. Analysis shows that the orientation distribution of side chain methyl groups on the PBMA surface is narrower in water than that in air, indicating that the PBMA surface can be more ordered in water. To our knowledge, this is the first time that quantitative comparisons between molecular surface structures of polymers in air and in water have been made. Two assumptions on the orientation distribution function, including a Gaussian distribution and a formula based on the maximum entropy approach, are used in the analysis. It has been found that the orientation angle distribution function deduced by the Gaussian distribution and the maximum entropy distribution are quite similar, showing that the Gaussian distribution is a good approximation for the angle distribution. The effect of experimental error on the deduced orientational distribution is also discussed.

Effect of experimental error on the efficiency of different optimization methods for bioprocess media optimization.

Four optimization methods (Simplex, Rosenbrock, iterative factorial experimental design (IFED) and genetic algorithms) for the optimization of the biotechnological media composition under conditions where the measured quantities are subjected to the experimental error were compared. The computer simulations were performed on some of the selected two- to six- parameter biotechnological models. The optimization process was modified in such a way that the experimental error was considered. The results show that the optimization efficiency increases when this new termination criteria is implemented. In addition, the method efficiency becomes independent of the experimental error. In general, Simplex and Rosenbrock methods need fewer experiments and their distribution of necessary experiments is narrower than for IFED and genetic algorithms. The increase of model parameters that need to be optimized results in a decrease in the method efficiency and in an increase of the average number of required experiments. The results were further verified on the cultivation of Saccharomyces cerevisiae and were found to be in good agreement with the results obtained from the computer simulations.

Tomographic Reconstruction of 2-D Absorption Coefficient Distributions from a Limited Set of Infrared Absorption Data

The results of infrared absorption experiments, performed on a steady, nonreacting flow of methane and argon to test a new inversion method for tomographic reconstruction of spatially nonuniform distributions, are presented. The absorption coefficient distributions to be reconstructed are expressed as a weighted sum of Karhunen-Loève eigenfunctions, formed by applying the Karhunen-Loève procedure to a training set containing a priori information regarding the distributions to be reconstructed. Reconstruction of asymmetric absorption coefficient distributions is accomplished by utilizing a set of laser absorption measurements obtained using an infrared helium neon laser. Issues pertinent to the practical application of the new inversion method, such as the construction of a training set using probe sampling, the effect of experimental error, and the precise modeling of laser absoroption paths, are discussed. Reconstruction of absorption coefficient distributions from only 42 laser absorption measurements typically achieve normalized errors of 10% or less over 80% of the domain.

A procedure for investigating the number of genotypes required to provide a stable classification of environments

Abstract The technique of classification has been used to summarise relationships among test environments, based on the way they discriminate among genotypes, in multi-environment trials. However, once environments have been grouped, at a specified truncation level, there is generally no indication of the ‘stability’ and hence validity of the grouping. Further, there is currently no way to determine whether or not an adequate number of genotypes was used to give a robust assessment of the similarities among the environments. A procedure is presented which allowed a determination of whether an adequate number of genotypes was used to assess similarities among the environments considered. The procedure also highlighted the effect of experimental error on environmental classifications. It was demonstrated using three genotype × environment data sets with pooled genetic correlations ranging from low to high. The process used for investigating the ‘stability’ of the classifications involved choosing increasing proportions of the total number of genotypes available in the data set, and classifying the environments based on each of the resultant genotypic subsets. The grouping of environments was then investigated at a particular truncation level. The process was repeated 100 times for each sub-set size and the number of different partitions of the environments, and the frequency of each partition determined. These frequencies were compared with those that were obtained, using the same procedure, but applied to data sets (of equivalent dimensions) containing random numbers. Based on the differences between the experimental and random data an assessment of the number of genotypes necessary to provide a ‘stable’ classification was made. Results indicated that a ‘stable’ classification of environments could be reached for the two data sets with moderate and high pooled genetic correlations with relatively few genotypes. However, for the data set with a low pooled genetic correlation, a ‘stable’ classification was not reached even when almost all of the genotypes were included. Based on the results for these three data sets the working hypothesis that the ‘stability’ of an environmental classification is related to the strength of the pooled genetic correlation for the data set, is advanced.

Metabolic control analysis

This paper illustrates a method to calculate the sensitivities of control coefficients to the elasticities which determine their values and it is shown that these sensitivities are systemic properties. We show, both theoretically and with a practical example, how they can be used to investigate: (a) the relative importance of a particular elasticity in the determination of the value of a control coefficient; (b) the effect of experimental error on the values of the control coefficients and (c) the construction of confidence limits around the values of the control coefficients.

Information content of the multibreath nitrogen washout: effects of experimental error

Methods that recover a continuous distribution of specific ventilation (ventilation-to-volume ratio, VA/V) from the multibreath N2 washout curve theoretically can resolve up to four modes of ventilation and reveal the major characteristics of the underlying distribution if experimental error is absent. This paper quantitatively assesses the effects of experimental error on resolution. The washout curves from five typical distributions were studied using linear programming and Monte Carlo methods. A measurement error of 0.1% was assumed in the mixed-expired N2 signal. Only 7 of the first 17 breaths contribute independent information about the underlying distribution, and only rough resolution of the underlying distribution is possible in the presence of error. Only two modes of ventilation plus an estimate of dead space can be confidently resolved. It is not possible to separate VA/V greater than 10 from dead space. A 10-fold reduction in experimental error will not greatly improve resolution. Experimental error, by reducing the linear independence of the defining kernels, significantly limits the information content and resolution of the multibreath N2 washout.

Ozone/Precursor Relationships in the Detroit Metropolitan Area Derived from Captive-Air Irradiations and an Empirical Photochemical Model

The ozone generating potential of ambient Detroit air was characterized using transparent bags as outdoor smog chambers. Air samples gathered in downtown Detroit on 12 sunny days during the summer of 1981 were irradiated and ozone production was measured throughout the day. Morning additions of nonmethane organic compounds (NMOC), nitrogen oxides (NO x ), or clean air were made to some bags to assess their effects and determine how different emission control strategies will perturb the ozone formation process. The results show that the photochemical process is hydrocarbon limited and the most effective ozone reduction strategy is one that reduces NMOC while leaving NO x unchanged. Reductions in NO x will likely increase maximum ozone in the Detroit area since NO x additions were found to suppress ozone formation in the outdoor smog chambers. The smog chamber results were compared to predictions of the EPA EKMA model that was used by the State of Michigan to forecast the effects of NMOC and NO x controls. The model provided a reasonable approximation for the ozone maxima in the chambers and predicted the relative changes in ozone due to changes in NMOC or NO x . The observed NO x -inhibition and NMOC-enhancement effects on the ozone maxima in the bags were correctly described by the model. However, the model underpredicted ozone formation for the limited number of mixtures diluted initially with clean air. Finally, the effects of experimental error in a key input to EKMA (the early morning NMOC-to-NO x ratio in the downtown area) were small enough that they had a minimal impact on the results. Thus, our analyses support the use of EKMA in Michigan's State Implementation Plan.

On the determination of deoxyribonucleic acid-protein interaction parameters using the nitrocellulose filter-binding assay.

We examine the effects of filter efficiency on DNA-protein binding data obtained by the popular nitrocellulose filter-binding assay. Graphical procedures for determining the efficiency parameter epsilon (for the efficiency of retention of DNA on the filter, per bound protein molecule) are established. Filter efficiency modified formulas for determining thermodynamic binding parameters are derived for four simple prototypes of DNA-protein binding systems. The effects of experimental error on discrimination between models are considered. Finally, we discuss conceptual errors often made in calculating binding stoichiometry from filter-binding experiments and suggest a general protocol for the analysis of filter-binding data.

Light scattering characterization of thermodynamic interaction of polymers in dilute solution. Effect of experimental error and temperature

Interaction between non-identical polymer molecules in a dilute solution of a mixture of two polymers is quantitatively characterized by the interaction parameter A 24, which is the second virial coefficient for interaction of unlike species. The value of A 24 may be experimentally obtained by light scattering. The determination of A 24 is very sensitive to experimental error in the input data, particularly for mixtures in which one polymer is greatly in excess, and for mixtures of polymers having molecular weights differing by orders of magnitude. A slight rise in A 24 with temperature has been observed for solutions of mixtures of polystyrene and poly(methyl methacrylate) in diethyl malonate in the range 25–100 C. This change in A 24 reflects the increased mutual miscibility of the polymers in solution at elevated temperatures.

Hydrodynamic properties of a rigid molecule: rotational and linear diffusion and fluorescence anisotropy.

AbstractThe fluorescence anisotropy of a general rigid body is formally the sum of five exponentials. We show that, to a high degree of approximation, there are relationships between the five time constants. As we define the time constants here, τ1 ≅ τ5, τ2 ≅ τ3, and τ1−1 + 3τ4−1 ≅ 4τ2−1. In practical cases, at most only three exponentials will be observed, and, of these, only two are independent.Using a numerical integration procedure, Perrin's equations for the rotational and translational diffusion of a general ellipsoid are solved. Rotational friction coefficients, frictional ratio, rotational relaxation times, and the five exponential terms in the fluorescence anisotropy are tabulated as functions of the axial ratios of the ellipsoid.In principle, the three axes of a general ellipsoid may be determined by a simultaneous measurement of the anisotropy and the linear diffusion constant. We examine, and illustrate, the effect of experimental error on such a determination.

A recycle flow flotation machine model: Response of model to parameter changes

The fraction of solid tracer retained in a laboratory flotation machine is measured as a function of time, simulating semi-batch testing. Observed departures from ideal mixing in which the ratio mean retention time/mean residence time exceeds unity can be accounted for by a recycle model of pulp circulation around the impeller region. Solutions of the system differential equations are recast into forms allowing calculation of the system parameters from the retention time ratio and an initial value, both obtained from tracer experiment data. The effect of changing the parameter values on the model response is discussed. Some special cases, applications, and alternative models are mentioned, and an example is provided. The effects of experimental error on estimated parameter values, and relationships between tracer concentration in the exit stream and the fraction retained formulations, are discussed in appendices.

On the effect of experimental error on the calculation of the number of stages for a given distillation separation

Earlier work on the effect of experimental error is re-examined, certain limitations are brought out and some of the formulae are re-derived. A method of direct evaluation is also presented which overcomes the former limitations, is of universal applicability and involves no greater computational effort.

Conductivity Models and Banks' Data

Summary The magnetic response data of Banks has been used to determine an ensemble of conductivity models. Each model consists of a uniformly conducting thick shell surrounding a perfectly conducting inner sphere. The conductivity and thickness of the shell are found for each observed response measurement in the frequency range. The results show that the data leads to inconsistencies, and confirms the conclusions by Parker concerning this data. It is also found here that the low frequency response measurements, in particular, are unreliable. It is concluded that, neglecting the low frequency measurements, Banks’ data requires the conductivity to be low for the first 550km, or so, from the surface, followed by a gradual rise. The thickness of the transition region is uncertain, but could be as great as 300 km. Geomagnetic response measurements are used to determine the global distribution of electrical conductivity within the mantle. Measurements are available at a number of discrete frequencies corresponding to; the quiet day daily variation (Sq), the 27-day variation and its principal harmonics, the semi-annual, and annual variations. In addition, estimates of the response at close intervals in the range 0.01 to 0-225cpd, have been derived (Banks 1969), and published in tabular form (Banks 1972). References to earlier work are contained in a review of the subject by Price (1 970). Parker (1970) has used the continuum response estimates to determine a conductivity profile for the mantle. The general method of Backus & Gilbert (1967, 1968, 1970) was used to invert the data, and it was found that whatever conductivity model was used as an initial approximation, the iterative scheme failed to converge. Assuming that the initial starting model was accurate enough, Parker concluded that no conductivity model exists that satisfies Banks’ data. A further application of Backus-Gilbert inversion theory to Banks’ data was made recently by Parker (1972). The self-consistency of data pairs were examined with the use of two simple models. One consists of an infinitesimally thin surface shell of conductor surrounding a non-conducting inner core, the other consists of a non-conducting thick layer surrounding a perfectly conducting inner core. Parker found that, ignoring the effects of experimental error in the data, the consistency conditions are not satisfied by several pairs of data values. Because of the importance to the problem of conductivity modelling in the mantle, of accurate response measurements in the same frequency range as Banks’ data, these data are further examined here, by using a model which is physically more realistic