Fitting models to correlated data II (small samples, large correlations, and wrong models)

The estimation of experimental error, data correlation and model error by the analysis of the fit residuals in an ordered sequence of data [J. Mol. Spectrosc. 224 (2004) 73] is improved by a better insight in the calculation of the statistical relevant quantities. The biases previously observed for too small samples of data, very wrong models or highly correlated data, are partially corrected and this leads to better estimates in some extreme cases provided these unfavourable conditions are not combined. However, such results are always obtained with a decrease in accuracy.     

An improved gridding method for spiral MRI using nonuniform fast Fourier transform

The algorithm of Liu and Nguyen [IEEE Microw. Guided Wave Lett. 8 (1) (1998) 18; SIAM J. Sci. Comput. 21 (1) (1999) 283] for nonuniform fast Fourier transform (NUFFT) has been extended to two dimensions to reconstruct images using spiral MRI. The new gridding method, called LS_NUFFT, minimizes the reconstruction approximation error in the Least Square sense by generated convolution kernels that fit for the spiral k-space trajectories. For analytical comparison, the LS_NUFFT has been fitted into a consistent framework with the conventional gridding methods using Kaiser-Bessel gridding and a recently proposed generalized FFT (GFFT) approach. Experimental comparison was made by assessing the performance of the LS_NUFFT with that of the standard direct summation method and the Kaiser-Bessel gridding method, using both digital phantom data and in vivo experimental data. Because of the explicitly optimized convolution kernel in LS_NUFFT, reconstruction results showed that the LS_NUFFT yields smaller reconstruction approximation error than the Kaiser-Bessel gridding method, but with the same computation complexity.     

Flexible statistical modelling detects clinical functional magnetic resonance imaging activation in partially compliant subjects

Clinical functional magnetic resonance imaging (fMRI) occasionally fails to detect significant activation, often due to variability in task performance. The present study seeks to test whether a more flexible statistical analysis can better detect activation, by accounting for variance associated with variable compliance to the task over time. Experimental results and simulated data both confirm that even at 80% compliance to the task, such a flexible model outperforms standard statistical analysis when assessed using the extent of activation (experimental data), goodness of fit (experimental data), and area under the operator characteristic curve (simulated data). Furthermore, retrospective examination of 14 clinical fMRI examinations reveals that in patients where the standard statistical approach yields activation, there is a measurable gain in model performance in adopting the flexible statistical model, with little or no penalty in lost sensitivity. This indicates that a flexible model should be considered, particularly for clinical patients who may have difficulty complying fully with the study task.     

Development and exploration of a new methodology for the fitting and analysis of XAS data

A new data analysis methodology for X‐ray absorption near‐edge spectroscopy (XANES) is introduced and tested using several examples. The methodology has been implemented within the context of a new Matlab‐based program discussed in a companion related article [Delgado‐Jaime et al. (2010), J. Synchrotron Rad. 17 , 132–137]. The approach makes use of a Monte Carlo search method to seek appropriate starting points for a fit model, allowing for the generation of a large number of independent fits with minimal user‐induced bias. The applicability of this methodology is tested using various data sets on the Cl K‐edge XAS data for tetragonal CuCl₄^2?, a common reference compound used for calibration and covalency estimation in M—Cl bonds. A new background model function that effectively blends together background profiles with spectral features is an important component of the discussed methodology. The development of a robust evaluation function to fit multiple‐edge data is discussed and the implications regarding standard approaches to data analysis are discussed and explored within these examples.     

A new approach to determine accurately minority-carrier lifetime

Electron or proton irradiations introduce recombination centers, which tend to affect solar cell parameters by reducing the minority-carrier lifetime (MCLT). Because this MCLT plays a fundamental role in the performance degradation of solar cells, in this work we present a new approach that allows us to get accurate values of MCLT. The relationship between MCLT in p-region and n-region both before and after irradiation has been determined by the new method. The validity and accuracy of this approach are justified by the fact that the degradation parameters that fit the experimental data are the same for both short-circuit current and the open-circuit voltages. This method is applied to the p⁺/n-InGaP solar cell under 1 MeV electron irradiation.     

Blueprint XAS: a Matlab‐based toolbox for the fitting and analysis of XAS spectra

Blueprint XAS is a new Matlab‐based program developed to fit and analyse X‐ray absorption spectroscopy (XAS) data, most specifically in the near‐edge region of the spectrum. The program is based on a methodology that introduces a novel background model into the complete fit model and that is capable of generating any number of independent fits with minimal introduction of user bias [Delgado‐Jaime & Kennepohl (2010), J. Synchrotron Rad. 17 , 119–128]. The functions and settings on the five panels of its graphical user interface are designed to suit the needs of near‐edge XAS data analyzers. A batch function allows for the setting of multiple jobs to be run with Matlab in the background. A unique statistics panel allows the user to analyse a family of independent fits, to evaluate fit models and to draw statistically supported conclusions. The version introduced here (v0.2) is currently a toolbox for Matlab. Future stand‐alone versions of the program will also incorporate several other new features to create a full package of tools for XAS data processing.     

Goodness of fit: analysis of residuals

The goodness-of-fit problem is addressed and two among the more efficient tests presently available are revisited and discussed: the autocorrelation method and the sign test recently proposed by Paolo Minguzzi [J. Mol. Spectrosc. 209, (2001) 169], both based on residual analysis. A mathematical proof of the empirical relations needed in the sign test is proposed; it allows more insight in the comparison of both methods and shows that more information may be available from the sign test. Some differences of efficiency are pointed out in special cases, but finally these methods prove to be closely related. A general procedure is deduced that takes advantage of the practical usefulness of both approaches, of their efficiency and of the statistical information each of them can provide.     

Quantification of intervertebral displacement with a novel MRI-based modeling technique: Assessing measurement bias and reliability with a porcine spine model

The purpose of this study was to develop a novel magnetic resonance imaging (MRI)-based modeling technique for measuring intervertebral displacements. Here, we present the measurement bias and reliability of the developmental work using a porcine spine model. Porcine lumbar vertebral segments were fitted in a custom-built apparatus placed within an externally calibrated imaging volume of an open-MRI scanner. The apparatus allowed movement of the vertebrae through pre-assigned magnitudes of sagittal and coronal translation and rotation. The induced displacements were imaged with static (T₁) and fast dynamic (2D HYCE S) pulse sequences. These images were imported into animation software, in which these images formed a background ‘scene’. Three-dimensional models of vertebrae were created using static axial scans from the specimen and then transferred into the animation environment. In the animation environment, the user manually moved the models (rotoscoping) to perform model-to-‘scene’ matching to fit the models to their image silhouettes and assigned anatomical joint axes to the motion-segments. The animation protocol quantified the experimental translation and rotation displacements between the vertebral models. Accuracy of the technique was calculated as ‘bias’ using a linear mixed effects model, average percentage error and root mean square errors. Between-session reliability was examined by computing intra-class correlation coefficients (ICC) and the coefficient of variations (CV). For translation trials, a constant bias (β₀) of 0.35 (± 0.11) mm was detected for the 2D HYCE S sequence (p = 0.01). The model did not demonstrate significant additional bias with each mm increase in experimental translation (β₁Displacement = 0.01 mm; p = 0.69). Using the T₁ sequence for the same assessments did not significantly change the bias (p > 0.05). ICC values for the T₁ and 2D HYCE S pulse sequences were 0.98 and 0.97, respectively. For rotation trials, a constant bias (β₀) of 0.62 (± 0.12)° was detected for the 2D HYCE S sequence (p < 0.01). The model also demonstrated an additional bias (β₁Displacement) of 0.05° with each degree increase in the experimental rotation (p < 0.01). Using T₁ sequence for the same assessments did not significantly change the bias (p > 0.05). ICC values for the T₁ and 2D HYCE S pulse sequences were recorded 0.97 and 0.91, respectively. This novel quasi-static approach to quantifying intervertebral relationship demonstrates a reasonable degree of accuracy and reliability using the model-to-image matching technique with both static and dynamic sequences in a porcine model. Future work is required to explore multi-planar assessment of real-time spine motion and to examine the reliability of our approach in humans.     

Interpolation of experimental data without a theoretical model

A new approach is proposed for the interpolation of experimental data when a theoretical model is unavailable. The method is based on the minimization of a modified likelihood function incorporating a generalized smoothness test of the theoretical curve. The conditions for applicability of the method are a sufficiently accurate estimate of the statistical errors of the experimental data (assuming that the results fit a Gaussian distribution in accordance with the resulting rms deviations) and smoothness of the theoretical curve. A FORTRAN 77 program for the interpolation of experimental data has been written to implement the proposed algorithm. The computing time and roundoff error are determined as functions of the number of experimental points. Zh. éksp. Teor. Fiz. 116, 760–776 (September 1999)     

A functional-group-based approach to modeling real-fuel combustion chemistry – III: Application to biodiesels

Real biodiesel fuels are mixtures comprising many high molecular weight components, making it a challenge to predict their combustion chemistry with detailed kinetic models. Our group previously proposed a functional-group approach (FGMech) to model the combustion chemistry of real gasoline and jet fuels; this approach has now been extended to model real biodiesel combustion and mixtures with petroleum fuels. As in our previous work, a decoupling philosophy is adopted for construction of the model. A lumped reaction mechanism describes the (oxidative) pyrolysis of fuels, while a detailed base chemistry model represents the oxidation of key pyrolysis intermediates. However, due to the presence of the ester group, several oxygenated species are identified as additional primary products and incorporated into the lumped reaction steps. In addition to the lumped reactions initiated by unimolecular decomposition and H-atom abstraction reactions, a lumped H-atom addition-elimination reaction is also incorporated as a new reaction class to account for the presence of double bonds. Stoichiometric parameters are obtained based on a multiple linear regression (MLR) model, which establishes relationships between the fuel's functional group distributions and the stoichiometric parameters of the lumped reactions. Global rate constants are developed from consistent rate rules obtained from pure fuels. New pyrolysis experimental data for methyl pentanoate/methyl nonanoate and methyl heptanoate/n-heptane mixtures (50%/50% in mol) are obtained in a jet-stirred reactor at atmospheric pressure. In general, kinetic models developed using the FGMech approach can reasonably reproduce all the validation targets obtained in this work, as well as those in the literature, confirming that functional-group-modeling is a promising approach to simulate combustion behavior of diesel/biodiesel surrogate fuels and real biodiesels.     

Fitting models to correlated data III: A comparison between residual analysis and other methods

Applications of the χ² test, the F test, the Durbin-Watson d test, and the f (or Sign) test, to examples of correlated data treatment, show important drawbacks with the d test and (apparently) with the f test. An analytical approach based on residual analysis suggests an improvement in their use that leads to better results at lowest order; it also points out a distinction between goodness-of-fit tests, as the f test, and goodness-of-modeling tests, as the χ² and F tests. The residual analysis method is applied to the same examples; it looks faster, simpler, and often more accurate than the classical ones.     

拟合参量计算跃迁概率

根据光谱线相对强度和跃迁特性参数值,通过线性拟合一次函数,得到两个拟合参量.借助于这些参量,计算得到特殊激发态或高激发态谱线的跃迁概率.目前在对NⅡ光谱分析的基础上,得到了一条对耦合激发组态谱线的跃迁概率.为求取一些在理论计算中很难处理的特殊组态或高激发态谱线的跃迁概率,提供了一种最新的、简单可行的半经典计算方法. 关键词： 拟合 跃迁概率 对耦合     

Gear transmission dynamic: Effects of tooth profile deviations and support flexibility

In this work a non-linear dynamic model of spur gear transmissions previously developed by the authors is extended to include both desired (relief) and undesired (manufacture errors) deviations in the tooth profile. The model uses a hybrid method for the calculation of meshing forces, which combines FE analysis and analytical formulation, so that it enables a very straightforward implementation of the tooth profile deviations. The model approach handles well non-linearity due to the variable meshing stiffness and the clearances involved in gear dynamics, also including the same phenomena linked to bearings. In order to assess the ability of the model to simulate the impact of the deviations on the transmission dynamics, an example is presented including profile deviations under different values of transmitted torque. Several results of this example implementation are presented, showing the model’s effectiveness.     

Integrating artificial neural networks and empirical correlations for the prediction of water-subcooled critical heat flux

The critical heat flux (CHF) is an important parameter for the design of nuclear reactors, heat exchangers and other boiling heat transfer units. Recently, the CHF in water-subcooled flow boiling at high mass flux and subcooling has been thoroughly studied in relation to the cooling of high-heat-flux components in thermonuclear fusion reactors. Due to the specific thermal-hydraulic situation, very few of the existing correlations, originally developed for operating conditions typical of pressurized water reactors, are able to provide consistent predictions of water-subcooled-flow-boiling CHF at high heat fluxes. Therefore, alternative predicting techniques are being investigated. Among these, artificial neural networks (ANN) have the advantage of not requiring a formal model structure to fit the experimental data; however, their main drawbacks are the loss of model transparency (‘black-box’ character) and the lack of any indicator for evaluating the accuracy and reliability of the ANN answer when ‘never-seen’ patterns are presented. In the present work, the prediction of CHF is approached by a hybrid system which couples a heuristic correlation with a neural network. The ANN role is to predict a datum-dependent parameter required by the analytical correlation; this parameter was instead set to a constant value obtained by usual best-fitting techniques when a pure analytical approach was adopted. Upper and lower boundaries can be possibly assigned to the parameter value, thus avoiding the case of unexpected and unpredictable answer failure. The present approach maintains the advantage of the analytical model analysis, and it partially overcomes the ‘black-box’ character typical of the straight application of ANNs because the neural network role is limited to the correlation tuning. The proposed methodology allows us to achieve accurate results and it is likely to be suitable for thermal-hydraulic and heat transfer data processing.     

MCMCINLA Estimation of Missing Data and Its Application to Public Health Development in China in the Post-Epidemic Era

Medical data are often missing during epidemiological surveys and clinical trials. In this paper, we propose the MCMCINLA estimation method to account for missing data. We introduce a new latent class into the spatial lag model (SLM) and use a conditional autoregressive specification (CAR) spatial model-based approach to impute missing values, making the model fit into the integrated nested Laplace approximation (INLA) framework. Combining the advantages of both the Markov chain Monte Carlo (MCMC) and INLA frameworks, the MCMCINLA algorithm is used to implement imputation of the missing data and fit the model to derive estimates of the parameters from the posterior margins. Finally, the economic data and the hemorrhagic fever with renal syndrome (HFRS) disease data of mainland China from 2016–2018 are used as examples to explore the development of public health in China in the post-epidemic era. The results show that compared with expectation maximization (EM) and full information maximum likelihood estimation (FIML), the predicted values of the missing data obtained using our method are closer to the true values, and the spatial distribution of HFRS in China can be inferred from the imputation results with a southern-heavy and northern-light distribution. It can provide some references for the development of public health in China in the post-epidemic era.     

Spectral response of (CH)x-CdZnS heterojunction: Application of Onsager's theory of geminate recombination

The Onsager's theory of geminate recombination is used to fit experimental photoresponse of (CH)_x-CdZnS heterojunctions. This model, which depends upon three adjustable parameters, gives good agreement between experimental and calculated spectral response in zero bias conditions and lead to a simple interpretation of the change of spectral response under reverse bias.     

Direct fit of experimental ro-vibrational intensities to the dipole moment function: Application to HCl

A dipole moment function (DMF) for hydrogen chloride (HCl) has been obtained using a direct fit approach that fits the best available and appropriately weighted experimental data for individual ro-vibrational transitions. Combining wavefunctions derived from the Rydberg-Klein-Rees (RKR) numerical method and a semi-empirical DMF, line intensities were calculated numerically for bands with Δv=0, 1, 2, 3, 4, 5, 6, 7 up to v′=7. The results have demonstrated the effectiveness of inclusion of rotational dipole moment matrix elements and appropriate weighting of the experimental data in the DMF fitting. The new method is shown to be superior to the common method of fitting only the rotationless dipole moment elements, while at the same time being simple to implement.     

Hadrons from a hard wall AdS/QCD model

We review a recent work on masses of mesons and nucleons within a hard wall model of holographic QCD in a unified approach.In order to treat meson and nucleon properties on the same footing,we introduced the same infrared(IR)cut for both sectors.In framework of present approach,the best fit to the experimental data is achieved introducing the anomalous dimension for baryons.     

Determination of Protolytic Constants by Trilinear Fluorescence Spectroscopy

Protolytic equilibria often have profound effects on chemical activity, since protolytic species usually behave quite differently. It is therefore important to characterize the protolytic properties of important chemicals. Here we present a new approach to study protolytic equilibria of fluorescent species that is extremely accurate and relies on minimum assumptions. We show that by measuring 2-dimensional excitation/emission scans of samples at different pH. the 3-dimensional experimental data set, I(lambda(ex), lambda(em), C(pH)), can be unambiguously decomposed into the spectral responses of the protolytic species present as well as their concentration. The approach is demonstrated on the protolytic equilibrium of fluorescein. Although the fluorescein monoanion cannot be obtained in pure form, the spectra and concentrations of both fluorescein species, as well as the protolytic constant, are determined with excellent accuracy. The proposed method is general and can be applied not only for studies of protolytic equilibria, but on any chemical equilibria and chemical reactions involving fluorescent species.     

A generalised approach for active control of structural–interior global noise: Practical implementation

The experimental validation of a generalised approach to the sensing of orthogonal contributors to the global error (acoustic potential energy) within a coupled structural–acoustic cavity is presented. The goal is the measurement and control of the global error without any knowledge of the structural dynamics of the noise source, based on an acoustic centric decomposition approach that is applicable to any noise source. Two sensing approaches are attempted, structural and acoustic sensing, to measure the global error within the coupled enclosure. Once estimates of the global error are obtained, minimisation with an adaptive feedforward controller is implemented. The level of achieved attenuation in the global error is compared. The achieved level of attenuation is also compared to the maximum level of attenuation of the global error that can be achieved based on the disturbance/secondary source arrangement. The maximum level of attenuation is evaluated from experimental data, rather than pure theoretical methods.