Simulated spectra

The simulated data containing three classes were previously generated by [14] as follows  

For this data we believe that the basic shape of the data will be useful for classification and the scaling band will therefore be considered as a possible candidate. Indeed, the scaling band produced the largest CVQPM of 0.9353 at initialization (see Fig. 4(a)). Thus, t = 0 was selected. A marginally smaller CVQPM was produced for band(2,l) at initialization followed by band(2,3) and then band(2,2). Upon termination of the algorithm, the discriminant measure for band(2,0) has further increased to 0.9641 and clearly produces a larger CVQPM than the remaining bands. 

To test the classification performance of the adaptive wavelet, the coefficients from each of the bands (at level 2) at initialization and at termination of the algorithm were used as inputs to the classifier. The results are summarized for both the training and test data in Table I. At initialization the coefficients in band(2,0) gave the best classification rates closely followed by band(2,l). At completion the classification performance of band(2,0) has further improved. 

Since band(2,l) produced quite a competitive CVQPM at initialization, and promising classification results in the previous analysis, optimization over 

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Figure 9.2. Carbon Is photoelectron spectrum Is core-hole-state spectra for the 2-norbornyl cation of tert-butyl cation and Clark s simulated spectra for the classical and nonclassical ions.

Fig. 3.64. H depth profile of an H-im-planted Si sample obtained with 6-MeV C projectile ions for different recoil angles 9. q gives the charge ofthe incident ions. The experimental depth profiles (full line) are compared with simulated spectra (dashed line-SIMNRA, dotted line - DEPTH) [3.177].

As a second example, results from a TOP ERDA measurement for a multi-element sample are shown in Fig. 3.65 [3.171]. The sample consists of different metal-metal oxide layers on a boron silicate glass. The projectiles are 120-MeV Kr ions. It can be seen that many different recoil ions can be separated from the most intense line, produced by the scattered projectiles. Figure 3.66 shows the energy spectra for O and Al recoils calculated from the measured TOF spectra, together with simulated spectra using the SIMNRA code. The concentration and thickness of the O and Al layers are obtained from the simulations. 

Our data will simulate spectra collected on mixtures that contain 4 different components dissolved in a spectrally inactive solvent. We will suppose that we have measured the concentrations of 3 of the components with referee methods. The 4th component will be present in varying amounts in all of the samples, but we will not have access to any information about the concentrations of the 4th component. 

Our synthetic data simulate spectra that are measured at 100 discrete wavelengths. But, we only have 15 spectra in our training set. Thus, before we can perform ILS on our data, we must first condense our training set data to no... 

The program will be demonstrated with poly(vinyl alcohol) for tacticity analysis and with copolymer vinylidene chloride isobutylene for monomer sequence analysis. Peak assignments in C-13 spectra were obtained independently by two-dimensional NMR techniques. In some cases, assignments have been extended to longer sequences and confirmed via simulation of the experimental data. Experimental and "best-fit" simulated spectra will be compared. 

Several options are now available to the user in the main menu of the program. Probabilities can be calculated using an iterative method. Brown s modified version of the Levenberg-Marquardt algorithm (14-16). by substi futing values for P1-P4 in Equation 1 to calculate the peak integral which are then used in Equation 2 to simulate spectra until a good match between experimental and simulated data is achieved. 

Optimum values for the probabilities may not be obtained in the case that experimental llnewidths in the spectrum are very different since only a single linewidth is used for the simulated spectra. The calculated probabilities may be stored in the database and hard copy reports may be printed-... 

Simulated spectra can be created by another option in the main menu of the program. Probabilities (P1-P4) are prompted from the user, depending on the model, if vaiues other than those stored with the data base are desired and a single linewidth is entered. Equation 1 and 2 are then used to simulate a spectrum which can be saved, compared to the experimental spectrum (including overlaying spectra, spectral subtractions, additions, etc.) or plotted. 

Figure 4 shows zoomed regions of the experimental and simulated spectra. The methine region was simulated separately using the same optimized probability but with a linewidth of 8.0 Hz. At this point the user may wish to use the spectral manipulation options (overlay, subtraction, etc.), repeat the calculation, or do further simulations. 

A portion of the database for this polymer is shown in Figure 6. Literature reports that this polymer follows second-order Markov statistics ( 21 ). And, in fact, probabilities that produced simulated spectra comparable to the experimental spectrum could not be obtained with Bernoullian or first-order Markov models. Figure 7 shows the experimental and simulated spectra for these ten pentads using the second-order Markov probabilities Pil/i=0.60, Piv/i=0.35, Pvi/i=0.40, and Pvv/i=0.55 and a linewidth of 14.8 Hz. 

In the direct standardization introduced by Wang et al. [42] one finds the transformation needed to transfer spectra from the child instrument to the parent instrument using a multivariate calibration model for the transformation matrix = ZgF. The transformation matrix F (qxq) translates spectra Zg that are actually measured on the child instrument B into spectra Z that appear as if they were measured on instrument A. Predictions are then obtained by applying the old calibration model to these simulated spectra Z ... 

C.B.M. Didden and H.N.J. Poulisse. On the determination of the number of components from simulated spectra using Kalman filtering. Anal. Lett., 13 (1980) 921-935. 

Fig. 3.23 Left-. Calculated relationship between the thickness of an alteration rind and/or dust coating on a rock and the amount of 15.0-keV radiation absorbed in the rind/coating for densities of 0.4, 2.4, and 4.0 g cm [57]. The bulk chemical composition of basaltic rock was used in the calculations, and the 15.0 keV energy is approximately the energy of the 14.4 keV y-ray used in the Mossbauer experiment. The stippled area between densities of 2.4 and 4.0 g cm is the region for dry bulk densities of terrestrial andesitic and basaltic rocks [58]. The stippled area between densities of 0.1 and 0.4 g cm approximates the range of densities possible for Martian dust. The density of 0.1 g cm is the density of basaltic dust deposited by air fall in laboratory experiments [59]. Right Measured spectra obtained on layered laboratory samples and the corresponding simulated spectra, from top to bottom 14.4 keV measured (m) 14.4 keV simulated (s) 6.4 keV measured (m) and 6.4 keV simulated (s). All measurements were performed at room temperature. Zero velocity is referenced with respect to metallic iron foil. Simulation was performed using a Monte Carlo-based program (see [56])...

In the low-field condition, the quantization axis is defined by the EFG main component In this situation, and rj can both be determined from powder spectra when recorded in an externally applied field. Figure 4.14 shows simulated spectra as is often encountered in practice such as in applied-field measurements of diamagnetic compounds or fast-relaxing paramagnetic compounds at high temperatures. The simulated traces differ in detail from a single-crystal spectrum as shown in Fig. 4.13, but their features still correlate in a unique manner with rj and the sign of... 

Simulation spectra were generated using parameters that describe the ion beam, target and detector geometry, beam and detector resolution, and sample characteristics. The sample parameters, which include the number of layers and the areal density and atomic composition of each layer were then varied until the simulation conformed to the experimental data. The HIBS spectra were analysed using a modified version of the RBS analysis program. 

Carotenoid neutral radicals are also formed under irradiation of carotenoids inside molecular sieves. Davies and Mims ENDOR spectra of lutein (Lut) radicals in Cu-MCM-41 were recorded and then compared with the simulated spectra using the isotropic and anisotropic hfcs predicted by DFT. The simulation of lutein radical cation, Lut +, generated the Mims ENDOR spectrum in Figure 9.7a. Its features at B through E could not account for the experimental spectrum by themselves, so contribution from different neutral radicals whose features coincided with those of the experimental... 

All programs use input and output files (experimental and simulated spectra) consisting of 1024 amplitude values in a single column in ASCII format. If you have experimental files in a different format, then you must first modify them. A program is included to change from n to 1024 points. 

While I am no longer working in this field, and cannot easily do simulations, I think that a 2 factor PCR or PLS model would fully model the simulated spectra. At any wavelength in your simulation, a second degree power series applies, which is linear in coefficients, and the coefficients of a 2 factor PCR or PLS model will be a linear function of the coefficients of the power series. (This assumes an adequate number of calibration spectra, that is, at least as many spectra as factors and a sufficient number of wavelength, which the full spectrum method assures.) The PCR or PLS regression should find the linear combination of these PCR/PLS coefficients that is linear in concentration. 

While I am no longer working in this field, and cannot easily do simulations, I think that a 2 factor PCR or PLS model would fully model the simulated spectra. (Fred Cahn)... 

Figure 5 29Si NMR of a silicalite-1 precursor solution with a molar ratio of 25 TEOS 9 TPAOH 152 H20 a) experimental spectrum, b), c), and d) simulated spectra of large components, narrow lines and all components respectively.

Fig. 12 C -detected C CSA patterns of the SHPrP109 i22 fibril sample. The upper and lower traces correspond to the experimental and simulated spectra, respectively. Simulations correspond to the evolution of a one-spin system under the ROCSA sequence. The only variables are the chemical shift anisotropy and the asymmetry parameter. A Gaussian window function of 400 Hz was applied to the simulated spectmm before the Fourier transformation. (Figure and caption adapted from [164], Copyright (2007), with permission from Elsevier)...

The simulated spectra of 7,7-diphenyl-6,7-dihydro[l,2,5]thiadiazolo[3,4-/]-quinoline-6-oxyl 36 gave a small value of 0.81 mT for the N-O site (typical hfcc s for dialkyl Ar-oxyl-localizcd radical is ca. 1.4-1.5 mT) and small but... 

Initially in this chapter, the various features of the PHIP phenomenon, of the apparatus to enrich parahydrogen and orthodeuterium, and of the computer-based analysis or simulations of the PHIP spectra to be observed under specific assumptions will be outlined. In the following sections, comparisons of the experimentally obtained and of the simulated spectra reveal interesting details and mechanistic information about the hydrogenation reactions and their products. 

This section deals with the quantitative description of the proton transfer processes (denoted by Eqs. (4) and (6) in Scheme 1), identified by the qualitative NMR experiments on the acid/base behavior of the Mo(IV), W(IV), Re(V), Tc(V), and Os(VI) systems as described in Section II. The data obtained on the signal behavior from these similar complexes were used to simulate spectra and model the proton exchange processes to finally obtain rate constants associated therewith. 

In Fig. 4, we show simulations of the vibrational absorption bands V2V 0 (u2 < 4) for The simulated spectra are drawn as stick diagrams... 

To assess the quality of the simulated spectra, we compare in Fig. 5 the simulated 2v2 and V4 bands of with stick spectra drawn with... 

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