Deconvolution function

To process the LC/MS data more efficiently, we have automated this deconvolution functionality using a Visual Basic macro (termed AutoME or Automated Maximum... 

FSD assumes that the experimental spectrum consists of well-resolved narrow peaks, which have been convoluted with the same sort of LBF. If the shape and width of this LBF are known, its effect can be mathematically removed from the spectrum. This is done in the interferogram space where removal of the LBF simply corresponds to multiplication by a deconvolution function being the inverse of the Fourier transformation of the LBF. 

In other words, the deconvolution corresponds to a multiplication of the interferogram 7(x) by the deconvolution function exp(ux) for a Lorentzian shape and exp(ax ) in the case of a Gaussian shape. The deconvolution factor is the maximum value of this function at the end of the x-interval used. 

KIN Corrects total admittance for effects of heterogeneous charge transfer as described.85 Uses observed cot< data to calculate deconvolution function. 

Figure 15. Deconvolution procedure representation where function to be deconvoluted and deconvolution function are identical (simulated data), n = = 2.

A Lorentzian LBF was used in the deconvolution. A deconvolution factor of 100 was chosen in order to achieve a net amplification of 3.4. This value was chosen after trials with deconvolution factors of 50,100 and 1000 in the manner recommended by Kauppinen et al. (52). With a factor of 50, underdeconvolution is observed, while a factor of 1000 results in over-deconvolution and negative side lobes. The deconvolution function amplifies the noise as well, and in order to reduce the noise, apodisation with a Blackman function is performed in conjunction with the deconvolution over the fraction of the interferogram specified by a noise reduction factor. A noise reduction factor of 0.5 was chosen. While the intensities of the deconvolved peaks are higher than those in the original spectra, the relative peak intensities in the deconvolved spectra remain the same as in the original (57). 

Fig. 2. Deconvolution of TPD profile from 17%Ga203/Ga-M0R-115 (a) by using a profile from Ga203/Si02 (c) and two Gaussian functions (d and e). Profile b is the sum of c, dande.

It is still possible to enhance the resolution also when the point-spread function is unknown. For instance, the resolution is improved by subtracting the second-derivative g x) from the measured signal g x). Thus the signal is restored by ag x) - (7 - a)g Xx) with 0 < a < 1. This llgorithm is called pseudo-deconvolution. Because the second-derivative of any bell-shaped peak is negative between the two inflection points (second-derivative is zero) and positive elsewhere, the subtraction makes the top higher and narrows the wings, which results in a better resolution (see Fig. 40.30). Pseudo-deconvolution methods can correct for sym-... 

This key paper was followed by a flurry of activity in this area, spanning several years." " "" A variety of workers reported attempts to deconvolute the temperature dependence of carbene singlet/triplet equilibria and relative reactivities from the influence of solid matrices. Invariably, in low-temperature solids, H-abstraction reactions were found to predominate over other processes. Somewhat similar results were obtained in studies of the temperature and phase dependency of the selectivity of C-H insertion reactions in alkanes. While, for example, primary versus tertiary C-H abstraction became increasingly selective as the temperature was lowered in solution, the reactions became dramatically less selective in the solid phase as temperatures were lowered further. Similar work of Tomioka and co-workers explored variations of OH (singlet reaction) versus C-H (triplet reaction) carbene insertions with alcohols as a function of temperature and medium. Numerous attempts were made in these reports to explain the results based on increases in triplet carbene population... 

The analysis of absorption data in humans has moved away from the more traditional modeling and data fitting techniques [35]. Absorption processes are now more often characterized by a mean absorption (or input) time (i.e., the average amount of time that the drug molecules spend at the absorption site) or by a process called deconvolution. The former analysis results in a single value (similar to absorption half-life) and the latter results in a profile of the absorption process as a function of time (e.g., absorption rate or cumulative amount absorbed vs. time). These approaches offer additional ways of interpreting the absorption process. 

Experimentally, the EMD function p(q) can be reconstructed from a set of Compton profiles J qz ) s, and B( r) from the EMD. However, A Air) is not a direct experimental product. By combining the experimental B(r) with theoretical B aik (r), we need to derive a semiexperimental AB(r). Since the atomic image is very weak, many problems must be cleared in experimental resolution, in reconstruction (for example, selection of a set of directions and range of qzs), in various deconvolution procedures and so on. First of all, high resolution experiments are desirable. 

Figure 7.6. Purification of protein from pooled yeast strains. Each yeast ORF was cloned as a fusion to glutathione-S-transferase in a protein expression vector to create 6144 yeast strains. The individual strains were pooled in groups of 96 to create a set of 64 pools. Each pool was grown and the 96 fusion proteins are purified in batch. Each pool was then assayed for a biochemical function (Martzen et al., 1999). Pools positive for function were then deconvoluted using smaller pools consisting of strains from rows and columns of a 96-well plate.

System analysis techniques have been used to generate input functions for PB-PK models. Oral administration of carbon tetrachloride in different vehicles was successfully described by absorption input functions obtained by deconvolution and disposition decomposition methods [25,26],... 

After H0bs has properly been extracted (cf. Sect. 2.2.2), the effect of instrumental broadening can be eliminated by numerical deconvolution (see p. 38). If the peaks shall be modeled by analytical functions (Sects. 8.2.5.7-8.2.5.8), the consideration... 

In the presented form Eq. (8.13) is only valid, if Hj (s) is, indeed, constant over the whole angular range required for analysis. If this is not the case and numerical deconvolution is aimed at, the standard algorithm may be adapted by consideration of the fact that, in any case, the broadening is a slowly varying function of 29. 

There is significant debate about the relative merits of frequency and time domain. In principle, they are related via the Fourier transformation and have been experimentally verified to be equivalent [9], For some applications, frequency domain instrumentation is easier to implement since ultrashort light pulses are not required, nor is deconvolution of the instrument response function, however, signal to noise ratio has recently been shown to be theoretically higher for time domain. The key advantage of time domain is that multiple decay components can, at least in principle, be extracted with ease from the decay profile by fitting with a multiexponential function, using relatively simple mathematical methods. 

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