Unfolding SPECTRA method

Equation 9.10 is an integral equation with the source spectrum S E) being the unknown. The procedure by which S E) is obtained, after R E, E ) and M(E) have been determined, is called unfolding of the measured spectrum. Methods of unfolding are discussed in Chaps. 11-14. 

Experience has shown that the proper values of w depend on both the shape of the neutron spectrum and the statistical errors of M, and that small changes in the Wj cause large changes in the errors of the result.This effect has been mitigated in the code FORIST, " which is a modification of FERDOR. In FORIST, the value of is obtained by an iterative process in terms of the desired statistical error of the result 5. Choosing the widths w by this method improves the resolution of the unfolded spectrum, for a fixed desired statistical error. 

In view of this apparent contradictory outcome from the transport and magnetic properties, we were motivated to investigate the dynamics of the charge excitation spectrum by optical methods. In fact, the optical measurement is a powerful contactless experimental tool which should in principle allow to unfold the disagreement between and p(7 since the optical response of a metal... 

The MCR-ALS decomposition method applied to three-way data can also deal with nontrilinear systems [81]. Whereas the spectrum of each compound of the columnwise augmented matrix is considered to be invariant for all of the matrices, the unfolded C matrix allows the profile of each compound in the concentration direction to be different for each appended data matrix. This freedom in the shape of the C profiles is appropriate for many problems with a nontrilinear structure. The least-squares problems solved by MCR-ALS, when applied to a three-way data set, are the same as those in Equation 11.11 and Equation 11.12 the only difference is that D and C are now augmented matrices. The operating procedure of the MCR-ALS method has already been described in Section 11.5.4, but some particulars regarding the treatment of three-way data sets deserve further comment. 

This section discusses methods of unfolding, assuming that an energy spectrum is measured with a multichannel analyzer or any other device that divides the measured spectrum into energy bins. As stated at the beginning of Sec. 11.5, unfolding means to solve the Fredholm-type integral equation... 

There are several iteration methods. The method presented here is useful for slowly varying spectra and has been used successfully to unfold beta spectra. The source spectrum S(E) is approximated over any interval AEj by the expression... 

The task of neutron spectroscopy is to obtain the neutron energy spectrum general methods used to unfold this equation are discussed next. 

The calculation of (.E) based on Eq. 14.41 is another case of unfolding. Usually the flux is expressed in terms of a number of energy groups G. If G < n, unfolding of Eq. 14.41 is a simple case of least-squares fit. Unfortunately, in most cases of practical interest, G > n, and the only way to obtain E) is to assume a certain a priori form for it and then try to improve upon this initial guess. The result depends on the choice of the input spectrum, the set of threshold reactions chosen, the errors of the measured activities, and the uncertainties of the cross sections involved. The several unfolding codes that are used differ mainly in the choice of the input spectrum. A brief description of four such codes, SAND-II, SPECTRA, relative deviation minimization method (RDMM)," and LSL-M2 is given next. 

Guimet et al. used two potential multiway methods for the discrimination between virgin olive oils and pure olive oils the unfold principal component analysis (U-PCA) and parallel factor analysis (PARAFAC), for the exploratory analysis of these two types of oils. Both methods were applied to the excitation-emission fluorescence matrices (EEM) of olive oils and followed the comparison of the results with the ones obtained with multivariate principal component analysis (PCA) based on a fluorescence spectrum recorded at only one excitation wavelength. 

In practice, the (F) function in a given point inside the sample is determined by the unfolding method using a set of activation threshold detector foils. The most commonly used dosimetry reactions are also summarized in Sect. 36.3 of the Appendix of this Volume. With the knowledge of the 0(F) and [Pg.1677]

The results obtained from viscosity to characterize the unfolded state are presented in Chapter 5. In the present section, the data obtained by optical methods currently used in the study of the transition between native and denatured proteins are briefly discussed. Various reviews describe spectrophotometric methods and their use in the conformational studies of proteins (Wetlaufer, 1962 Hermans, 1965 Herskovits, 1967 Donovan, 1969b, 1973 Yon, 1969 Chen, 1967 Weber and Teale, 1965 Chen et ai, 1969 Lehrer and Fasman, 1967). Ultraviolet difference spectroscopy is the most current method used to study conformational transitions of proteins. When a protein undergoes a conformational transition from the native to the unfolded state, several chromophoric groups are transferred from the interior of the protein to the solvent. The alteration of their environment is accompanied by a small variation of the absorption spectrum, which is shifted in wavelength (A>1) and in intensity (As). The variation of intensity is in first approximation given by the first derivative of the absorption spectrum... 

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