Generation of response functions of a NaI detector by using an interpolation technic

A computer method is developed for generating response functions of a NaI detector to monoenergetic gamma-rays. The method is based on an interpolation between measured response curves by a detector. The computer programs are constructed for Heath's response spectral library. The principle of the basic mathematics used for interpolation, which was reported previously by the author, et al., is that response curves can be decomposed into a linear combination of intrinsic-component patterns, and thereby the interpolation of curves is reduced to a simple interpolation of weighting coefficients needed to combine the component patterns. This technique has some advantages of data compression, reduction in computation time, and stability of the solution, in comparison with the usual functional fitting method. The processing method of segmentation of a spectrum is devised to generate useful and precise response curves. A spectral curve, obtained for each gamma-ray source, is divided into some regions defined by the physical processes, such as the photopeak area, the Compton continuum area, the backscatter peak area, and so on. Each segment curve then is processed separately for interpolation. Lastly the estimated curves to the respective areas are connected on one channel scale. The generation programs are explained briefly. It is shown that the generated curve represents the overall shape of a response spectrum including not only its photopeak but also the corresponding Compton area, with a sufficient accuracy.     

Detection and visualisation of elemental components in various ambient species by synchrotron microbeam technique

This study introduces the application of the synchrotron radiation induced X-ray fluorescence (SR-XRF) microprobe installed at the Super Photon ring-8 GeV (SPring-8), which is the world's largest third-generation synchrotron radiation facility, to the specification of chemical properties of various atmospheric samples. The combination of visual elemental mapping and XRF spectral analyses allows for the interpretation of the nature and composition of individual particles. Individually collected droplets by the replication technique were also irradiated by X-ray microbeam to carry out visual reconstruction of elemental maps for their multiple components. The multielemental peaks corresponding to X-ray energy were also successfully resolved. Because the chemical contents of solute for individual droplets can be definitely clarified in this study, we can describe the mechanisms involved in droplet formation and pollutant scavenging. The point analysis of sand dust collected from the local desert in China confirmed that the fine fragments of sand, which may be lifted and transported over a long distance, are considerably inhomogeneous in elemental component.     

An analytical consistent pseudo-component delumping procedure for equations of state with non-zero binary interaction parameters

For mixtures with many components, some or most of the components are grouped into pseudo-components in order to reduce the dimensionality of the problem for phase equilibrium calculations, and therefore the computational effort. However, knowing the detailed fluid phase split may be important for a variety of applications. The detailed phase compositions resulting from a flash calculation performed on a lumped mixture can be predicted using a delumping (inverse lumping) procedure [C.F. Leibovici, E.H. Stenby, K. Knudsen, Fluid Phase Equilibr. 117 (1997) 225–232].If the mixture parameters of an equation of state (EoS) can be expressed as a linear combination of pure component parameters and the phase mole fractions, then the component fugacity coefficients can also be expressed as a linear combination of pure component parameters with coefficients only depending on mixture properties. As a result, the equilibrium coefficients are related only to component properties and EoS coefficients, independently on phase compositions.In this work, we show using a reduction method how to effectively obtain such an expression of the equilibrium constants even for non-zero binary interaction parameters (BIPs) in the EoS, and based on these results, we propose a totally consistent analytical procedure for the estimation of equilibrium constants of detailed mixtures from lumped information, which is an extension of Leibovici's delumping method.For several examples with non-zero BIPs between hydrocarbon components and classical contaminants, phase mole fractions and the vapor mole fraction of the delumped mixture are in excellent agreement with the exact values obtained by flashing the original mixture. The delumping procedure has multiple applications, mainly for reservoir simulation and distillation problems.     

Efficient computation of root mean square deviations under rigid transformations

The computation of root mean square deviations (RMSD) is an important step in many bioinformatics applications. If approached naively, each RMSD computation takes time linear in the number of atoms. In addition, a careful implementation is required to achieve numerical stability, which further increases runtimes. In practice, the structural variations under consideration are often induced by rigid transformations of the protein, or are at least dominated by a rigid component. In this work, we show how RMSD values resulting from rigid transformations can be computed in constant time from the protein's covariance matrix, which can be precomputed in linear time. As a typical application scenario is protein clustering, we will also show how the Ward‐distance which is popular in this field can be reduced to RMSD evaluations, yielding a constant time approach for their computation. © 2014 Wiley Periodicals, Inc.     

Theory of light scattering from vesicles

The scattering and depolarization of light from spherical membrane systems, vesicles, is calculated in a new succinct formalism appropriate to spherical systems and the rotations of anisotropic elements composing them. The results of Tinker (1972) and Mishima (1980, 1981) are readily derived within this formalism and there is a considerable saving in numerical computation. The problem of fluctuations in the molecular packing of the component phospholipid molecules is also addressed.     

A fast polygon inflation algorithm to compute the area of feasible solutions for three‐component systems. I: concepts and applications

The multicomponent factorization of multivariate data often results in nonunique solutions. The so‐called rotational ambiguity paraphrases the existence of multiple solutions that can be represented by the area of feasible solutions (AFS). The AFS is a bounded set that may consist of isolated subsets. The numerical computation of the AFS is well understood for two‐component systems and is an expensive numerical process for three‐component systems. In this paper, a new fast and accurate algorithm is suggested that is based on the inflation of polygons. Starting with an initial triangle located in a topologically connected subset of the AFS, an automatic extrusion algorithm is used to form a sequence of growing polygons that approximate the AFS from the interior. The polygon inflation algorithm can be generalized to systems with more than three components. The efficiency of this algorithm is demonstrated for a model problem including noise and a multicomponent chemical reaction system. Further, the method is compared with the recent triangle‐boundary‐enclosing scheme of Golshan, Abdollahi, and Maeder (Anal. Chem. 2011, 83, 836–841). Copyright © 2013 John Wiley & Sons, Ltd.     

Analysis of gamma-ray spectra by using fast Fourier transform (author's transl)]

In order to simplify the mass data processing in a response matrix method for gamma-ray spectral analysis, a method using a Fast Fourier Transform devised. The validity of the method was confirmed by a computer simulation for spectra of a NaI detector. The method uses the fact that spectral data can be represented by Fourier series with reduced number of terms. The estimation of intensities of gamma-ray components is performed by a matrix operation using the compressed data of an observation spectrum and standard spectra in Fourier coefficients. The identification of gamma-ray energies is also easy. Several features in the method and a general problem to be solved in a response matrix method are described.     

Applications of Haar basis method for solving some ill-posed inverse problems

In this paper a numerical method consists of combining Haar basis method and Tikhonov regularization method for solving some ill-posed inverse problems using noisy data is presented. By using a sensor located at a point inside the body and measuring the u(x, t) at a point x?=?a, 0?<?a?<?1, and applying Haar basis method to the inverse problem, we determine a stable numerical solution to this problem. Results show that an excellent estimation on the unknown functions of the inverse problem can be obtained within a couple of minutes CPU time at pentium IV-2.4?GHz PC.     

Non-invasive identification of chemical compounds by energy dispersive X-ray fluorescence spectrometry, combined with chemometric methods of data evaluation

Chemicals from customers’ returns have to be analyzed before they can be reused as raw materials in production. A procedure for non-invasive qualitative analysis of compounds in a closed container based on energy dispersive X-ray fluorescence (EDXRF) spectrometry is described. EDXRF was chosen as method for non-invasive analysis of chemicals through PE bottle walls without opening the bottle. This analysis aims for a quick proof of correspondence between the declaration of a reagent on the label of the bottle and its content. This analytical result cannot be achieved by a mere evaluation of characteristic element lines in EDXRF-spectra in combination with the method of matrix correction or the method of mean atomic number. These methods take into account only a small part of the total information available in an X-ray spectrum. It is shown here that valuable additional information is extractable from the spectral ranges of the Compton-scattering and Rayleigh-scattering areas by the use of methods of multivariate data analysis, especially by principle component analysis (PCA). Regularized discriminant analysis (RDA) was employed to establish a classification scheme for unknown samples.     

Non-invasive identification of chemical compounds by energy dispersive X-ray fluorescence spectrometry, combined with chemometric methods of data evaluation

Chemicals from customers' returns have to be analyzed before they can be reused as raw materials in production. A procedure for non-invasive qualitative analysis of compounds in a closed container based on energy dispersive X-ray fluorescence (EDXRF) spectrometry is described. EDXRF was chosen as method for noninvasive analysis of chemicals through PE bottle walls without opening the bottle. This analysis aims for a quick proof of correspondence between the declaration of a reagent on the label of the bottle and its content. This analytical result cannot be achieved by a mere evaluation of characteristic element lines in EDXRF-spectra in combination with the method of matrix correction or the method of mean atomic number. These methods take into account only a small part of the total information available in an X-ray spectrum. It is shown here that valuable additional information is extractable from the spectral ranges of the Compton-scattering and Rayleigh-scattering areas by the use of methods of multivariate data analysis, especially by principle component analysis (PCA). Regularized discriminant analysis (RDA) was employed to establish a classification scheme for unknown samples.     

Generic solvent sites in a crystal

A numerical procedure is described and tested for the determination of solvent sites in a crystal hydrate from computer simulation results. The method does not require the computation of density distributions.     

Sequential imputation for missing values

As missing values are often encountered in gene expression data, many imputation methods have been developed to substitute these unknown values with estimated values. Despite the presence of many imputation methods, these available techniques have some disadvantages. Some imputation techniques constrain the imputation of missing values to a limited set of genes, whereas other imputation methods optimise a more global criterion whereby the computation time of the method becomes infeasible. Others might be fast but inaccurate. Therefore in this paper a new, fast and accurate estimation procedure, called SEQimpute, is proposed. By introducing the idea of minimisation of a statistical distance rather than a Euclidean distance the method is intrinsically different from the thus far existing imputation methods. Moreover, this newly proposed method can be easily embedded in a multiple imputation technique which is better suited to highlight the uncertainties about the missing value estimates. A comparative study is performed to assess the estimation of the missing values by different imputation approaches. The proposed imputation method is shown to outperform some of the existing imputation methods in terms of accuracy and computation speed.     

Thermodynamic characterization of weak association equilibria accompanied with spectral overlapping by a SVD-based chemometric method

A singular value decomposition (SVD)-based chemometric method is used for deconvolution of spectral information obtained from a single sample containing an equilibrium system with spectral overlapping at different temperatures. The output of analysis is the association constants at each temperature, thermodynamic parameters and the component spectral profiles. Thermodynamic characterization of charge-transfer complex formation between chloranil and some aromatic hydrocarbons are used as a model system for weak association equilibria and strong component spectral overlapping. The approach can be successfully applied for studying equilibrium systems, which cannot be treated with classical methods like Benesi-Hildebrand method due to the presence of systematic errors.     

天然植物复杂化学模式特征的分步提取法

在运用神经元计算技术对高维小样本复杂化学模式进行分类时,通过模式特征提取,降低输入变量维数,能使复杂的模式分类问题比较容易解决。根据模式类别相关分步分析思路,提出复杂化学模式特征分步提取法,可将原始模式数据中与类别指标相关较大的特征量有效地提取出来。应用于天然植物组效关系辨识结果表明,这种化学模式特征提取方法比经典主成分分析法更为实用可靠。     

Estimation of individual ultraviolet spectra in incomplete two-component separations by high-performance liquid chromatography

A method is described for the estimation of spectral features in a two-component chromatographic peak by means of a u.v. diode-array detector. The calculation relies on the assumption that the front of a fused chromatographic peak contains a single pure component. The spectrum of this component is used in calculating the concentration profile of the other component, thus allowing the determination of a solution band for the spectrum of the second component. The boundaries of the solution band are based on non-negativity restrictions of chromatographic and spectral features. The method does not require the use of principal components analysis.     

Estimation of source infrared spectra profiles of acetylspiramycin active components from troches using kernel independent component analysis

Kernel independent component analysis (KICA), a kind of independent component analysis (ICA) algorithms based on kernel, was preliminarily investigated for blind source separation (BSS) of source spectra profiles from troches. The robustness of different ICA algorithms (KICA, FastICA and Infomax) was first checked by using them in the retrieval of source infrared (IR), ultraviolet (UV) and mass spectra (MS) from synthetic mixtures. It was found that KICA is the most robust method for retrieval of source spectra profiles. KICA algorithm is subsequently adopted in the analysis of diffuse reflection IR of acetylspiramycin (ASPM) troches. It is observed that KICA is able to isolate the theoretically predicted spectral features corresponding to the ASPM active components, excipients and other minor components as different independent (spectral) component. A troche can be authenticated and semi-quantified using the estimated ICs. KICA is an useful method for estimation of source spectral features of molecules with different geometry and stoichiometry, while features belonging to very similar molecules remain grouped.     

Repetitive spectral subtraction method for the spectrophotometric determination of rare earth elements

Summary A new multiwavelength data-analysis method for the determination of multicomponent mixtures, the repetitive spectral subtraction method (RSSM), is proposed. In RSSM, spectral data are obtained at evenly spaced wavelengths in the range of interest, and the analysis of the spectrum is performed as repetitive determination-subtraction cycle. In the determination step, the series of data in the narrow wavelength range is used, which is specified as to include the most characteristic or the largest peak for each component. Assuming a linear background, the target component, which can be a small group of components, is simultaneously determined together with co-existing components. In the next subtraction step, the calculated contribution of the component is subtracted from the spectral data in the whole measured wavelength range, and the component is assigned as determined and is excluded from the following analysis. This determination-subtraction cycle is repeated until all the components are determined.With RSSM, a mixture of many components can be precisely determined by the use of most information contained in the spectrum. The accuracy of determination can be improved by automatic estimation of the background and the gradual decrease of interferences. In order to demonstrate the usefulness of RSSM, the 8 rare earth elements (Pr, Nd, Sm, Eu, Dy, Ho, Er, Tm) in the model mixtures were determined by spectrophotometry, and the results were compared with those of the usual correction factor method and the derivative method. Furthermore, the 8 rare earth elements were determined in ores, monazite and xenotime.

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Spektralphotometrische Bestimmung von Seltenen Erden mit Hilfe eines Verfahrens der wiederholten Subtraktion

     

Computation of molecular weight distributions by polynomial approximation with complete adaptation procedures

The choice of appropriate reference functions is still the major drawback for collocation techniques to be used during the computation of molecular weight distributions (MWDs) in polymerization reactions and other problems constituted by systems of differential‐difference equations. Complete adaptation procedures provide significant improvement of numerical approximations obtained, but convergence to the real solution is not assured and oscillatory numerical approximations may be obtained when the actual solution experiences large variations during time integration. An alternative method to compute the reference function in an adaptative manner, called here the integration of the reference function procedure, is presented. The technique is used to allow the computation of MWDs in two polymerization problems: the metallocene‐based propene polymerization and the methyl methacrylate/butyl acrylate emulsion polymerization. The integration of the reference function procedure allowed the proper computation of broad, bimodal and fast changing distributions with polynomials of very low order (below 4), where other approximation techniques failed. The method may be easily implemented and does not require any pre‐processing before implementation.     

Three-dimensional modeling of EXAFS spectral mixtures by combining Monte Carlo simulations and target transformation factor analysis

We have developed a new method for the three-dimensional modeling of extended X-ray absorption fine structure (EXAFS) spectra which enables the extraction of the local structure of aqueous metal complexes from spectral mixtures of several components. The new method combines two techniques: Monte Carlo simulation and target transformation factor analysis (TFA). Monte Carlo simulation is used to create random arrangements between the X-ray absorbing metal ion and the ligand atoms, and to calculate the theoretical EXAFS spectrum of each arrangement. The theoretical EXAFS spectrum is then introduced as test spectrum in the TFA procedure, to test whether or not the test spectrum is likely to be a component of the spectral mixtures. This coupled procedure is repeated until the error in the test spectrum is minimized. The new method can thus be used to isolate and refine the structure of complexes from spectral mixtures and to determine their relative concentrations, solely on the basis of an estimate of a ligand structure. The performance of the proposed method is validated using uranium Liii-edge EXAFS spectra of binary mixtures of two uranium(VI) 3,4-dihydroxybenzoic acid complexes.