Distance Measurements to Centres of Gravity

This method can be used for muLticategory classifications application to binary encoded infrared spectra gave however poorer results than distance measurements to centres of gravity C3563. 

Classification by distance measurements to centres of gravity requires compact clusters which are often not present in chemical applications. Usually, other classification methods give better results. Nevertheless, this simple and evident method serves as a standard for comparisons with more sophisticated pattern recognition methods. 

Interpretation of mass spectra by distance measurement to centres of gravity has been reported by Justice and Isenhour C133, 1353, Mathews... 

Less satisfactory results have been obtained by distance measurement to centres of gravity, learning machine or other methods. Some sequences of methods with decreasing quality have been reported ... 

Recognition of carboxylic acids by the KNN-method and distance measurements to centres of gravity were investigated by Woodruff and Munk C3543. Predictive abilities for binary encoded infrared spectra were 64 - 70 % and could be improved to 70 - 88 % by consideration of shoulders in the spectra. However a computer program based on chemical interpretation rules yielded significantly better results (91 % correct). 

The analysis of the data of PS I gave quite accurate information on the distance of the spin centres (25.4 0.3 A)301 that compared well with the crystal structure data.68 A problem is the extended it-spin density distribution in the donor and acceptor. For a solid comparison a centre of gravity for the spin must be calculated from experimental or theoretical spin density distributions of the two radicals. Similar data with almost unaltered distances were obtained for PS I with other quinones substituted into the Ai site.147-302This work has been extended to other electron acceptors,303 which show a larger heterogeneity in distances. It has been shown that the lifetime of the RP can also be measured and can even be controlled in the experiments by an additional mw pulse prior to the 2-pulse echo sequence.302 This pulse transfers population to triplet levels which cannot directly recombine to the singlet ground state. This has earlier been shown for the bRC.304,305 The OOP-ESEEM technique has also been applied to various mutants of PS I to characterize them by the measured distances between fixed donor and variable acceptors.254 256-263-264... 

The most important peak parameters are the peak area, the elution time of the centre of the peak and the peak variance. The peak area is proportional to the mass of the eluted compound and is usually used as the basis of quantitation. The elution time of the centre of gravity of the chromatographic peak is the elution (retention) time, fR, or the elution (retention) volume, Vr. of the compound. It is controlled by the distribution constant of the compound between the stationary and the mobile pha.ses and can be used for identification of the individual sample components. Finally, the peak variance, o (in time units) or a (in volume units) is a measure of peak broadening and can be used for the evaluation of the efficiency of the chromatographic column. For a truly Gaussian peak, the distance between the two inflection points (at 0.607 peak height) corresponds to 2(7. The peak width, u>, equals 4a and can be determined as the distance between the intersection points of the baseline with tangents drawn to the inflection points of the peak. 

The fully extended length of the chain is equal to nl so that the maximum extensibility of a random coil with r = Zrms is from n l to nl, i.e. a factor of rfi. The value of Znns also gives a measure of the spatial extent of a chain. A second useful measure of this is the radius of gyration, r, which is the RMS distance of the atoms of the chain from the centre of gravity of the chain. Debye showed that, provided that n is very large, Zg = r /s/6. 

In tissue samples from 17 anatomic regions in pig hearts, the concentrations of 13 trace elements have been determined by emission spectroscopy. By using distance measurements to 17 centres of gravity, 65 % of the specimens were classified correctly with respect to their anatomic region C3253. Concentrations of trace elements in the human brain of normal persons and of persons with various diseases have been utilized for a multivariate analysis. Sick persons could be correctly classified, however, the data set used was very small C643. 

It is essential to understand that an ensemble of random chains can only be described by means of a spatial distribution function. Two different measures of the random chain are commonly used (a) the end-to-end distance (r) and (b) the radius of gyration (s). The former is simply the distance between the chain ends. The radius of gyration is defined as the root-mean-square distance of the collection of atoms from their common centre of gravity ... 

An equivalent measure of the dimensions of a simple chain is the RMS radius of gyration s Y which is the RMS distance of the elements of the cham from its centre of gravity. It can be shown that s Y is related simply to r Y through the equation... 

---