Entropy Minimization

To a significant extent, the theoretical basis of modern communication theory arose from the work of Claude Shannon at Bell Labs. [80]. In these seminal works, the concept of the information entropy associated with an arbitrary signal arose. In 1981, Watanabe realised the close association between entropy minimization and pattern recognition [81]. An association between entropy minimization and the principle of simplicity is also recognized [82]. The basic mathematical form of signal 

1) PCA techniques have been applied to various data sets. From the open literature, I have been unable to find reference to their application to homogeneous catalytic systems. Having said that, it is important to note that the new ReactIR system by Mettler Toledo contains a program ConcIRT. It is a proprie- 

In 1983, Sasaki et al. obtained rough first approximations of the mid-infrared spectra of o-xylene, p-xylene and m-xylene from multi-component mixtures using entropy minimization [83-85] However, in order to do so, an a priori estimate of the number S of observable species present was again needed. The basic idea behind the approach was (i) the determination of the basis functions/eigenvectors V,xv associated with the data (three solutions were prepared) and (ii) the transformation of basis vectors into pure component spectral estimates by determining the elements of a transformation matrix TsXs- The simplex optimization method was used to optimize the nine elements of Tixi to achieve entropy minimization, and the normalized second derivative of the spectra was used as a measure of the probability distribution. 

At least two complications are immediately apparent. First, the separation of highly overlapping pure component spectra may be problematic. Second, for systems with more than three components, many local solutions (minima) should exist for Eq. (15). 

The second problem can be overcome by using a stochastic search. Thus Corana s simulating annealing SA [89], a sophisticated global search method arising from the Metropolis algorithm [90] was employed. A synthetic seven species problem was constructed and the elements in T-jx were correctly determined using SA. The recovered spectra are essentially identical to the synthetic 7 pure component spectra. [91] 

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Kamimura, R. D-Entropy Minimization. In Proceedings of the International Conference on Neural Networks. Houston (1997). 

Since a larger sample volume is presumed to be probed, the use of transmission mode has led to simpler, more accurate models requiring fewer calibration samples [50]. Scientists at AstraZeneca found that with a transmission Raman approach as few as three calibration samples were required to obtain prediction errors nearly equivalent to their full model [42]. For a fixed 10-s acquisition time, the transmission system had prediction errors as much as 30% less than the WAI system, though both approaches had low errors. It is hoped that this approach in combination with advanced data analysis techniques, such as band target entropy minimization (BTEM) [51], might help improve Raman s quantitative sensitivity further. 

E. Widjaja and M. Garland, Use of Raman microscopy and band-target entropy minimization analysis to identify dyes in a commercial stamp. Implications for authentication and counterfeit detection. Anal. Chem., 80, 729-733 (2008). 

E. Widjaja, Y.Y. Tan and M. Garland, Application of band-target entropy minimization to on-line Raman monitoring of an organic synthesis. An example of new technology for process analytical technology, Org. Process Res. Dev., 11, 98-103 (2007). 

BTEM band target entropy minimization DAQ data acquisition... 

Figure 4.2 The pure component reference spectra of hexane (a), dissolved carbon monoxide (b), dissolved cyclooctene (c) and dissolved Rh4(CO),2 obtained after entropy minimization.

Figure 4.10 Spectral reconstruction progression of Rli4 (a-CO)9(p-CO)3 during entropy minimization process by simulated annealing optimization ...

E. Widjaja, Devdopment of Band-Target Entropy Minimization (BTEM) and Associated Software Tools, PhD Thesis, National University of Singapore, 2002. 

Garland et al. have developed a powerful method for the reconstruction of individual pure component spectra from complex catalytic mixtures [20]. Using this band-target entropy minimization (BTEM) protocol, he was able to identify the mononuclear rhodium acyl intermediate in the hydroformylation reaction of 3,3-dimethylbut-l-ene starting from Rh4(a-CO)9(p-CO)3 as catalyst precursor [21]. In addition to the catalyst precursor and the more stable decomposition product... 

Finlayson GD, Drew MS and Lu C 2004 Intrinsic images by entropy minimization In Proceedings of the 8th European Conference on Computer Vision, Part III, Prague, Czech Republic, May, 2004 (eds. Pajdla T and Matas J), pp. 582-595. Springer-Verlag, Berlin. 

Zudkevitch, D. and Wenzel, L. A., "The Economic Role of Entropy Minimization ip Chemical Process Design," AIChE Annual Meeting, Chicago, IL, Nov. (1980). 

Tan et al. [166] present the potential of a new chemometric method (band target entropy minimization combined with multilinear regression, BTEM-MLR) for estimating the concentration maps of four significant components associated with cellular water, a-helical proteins, lipids, and spectral aberration in FPA images [166]. 

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