Reduction of data

In describing the various mechanical properties of polymers in the last chapter, we took the attitude that we could make measurements on any time scale we chose, however long or short, and that such measurements were made in isothermal experiments. Most of the experimental results presented in Chap. 3 are representations of this sort. In that chapter we remarked several times that these figures were actually the result of reductions of data collected at different temperatures. Now let us discuss this technique our perspective, however, will be from the opposite direction taking an isothermal plot apart. 

All data recorded in the data base have been acquired from plant records. Statistical reductions of data for generation of reports or specific end use are available. Data are currently collected from four operating plants (eight units). Time clocks have been installed on components, to record actual exposure time. Event data are available on a broad variety of safety and commercial grade components including pumps, valves, transformers, diesels, filters, tanks (vessels), and heat exchangers. 

Conf) S) W.H. Snyder C.R. Hoggatt, Performance of Testing Services on High Explosive Devices and the Reduction of Data , DRI-4350-7004-F (1970) (Conf)... 

This presentation demonstrates that a small minicomputer can be used to provide a full range of functions for collection and interactive reduction of data from a size-exclusion liquid chromatograph. A number of different users have collected in excess of 5000 chromatograms using this equipment. The experience gained with this system has influenced our approach to the automation of other analytical instruments. Careful attention to control paths, provision of "user friendly" access to the system functions, and careful management of the data archiving functions are crucial to the success of such efforts. 

Four levels of pattern recognition have been defined by Albano (2). Levels I and II are most frequently used to determine the similarity of objects, or to characterize clusters of samples and to classify unknown objects. Level III takes advantage of the reduction of data dimensions resulting from SIMCA and seeks to establish a correlation of sample scores with independent variables... 

A principal component analysis is reasonable only when the intrinsic dimensionality is much smaller than the dimensionality of the original data. This is the case for features related by high absolute values of the correlation coefficients. Whenever correlation between features is small, a significant direction of maximum variance cannot be found (Fig. 3.7) all principal components participate in the description of the data structure hence a reduction of data by principal component analysis is not possible. 

Values of parameters for the Margules, van Laar, Wilson, NRTL, and UNIQUAC equations are given for many binary pairs by Gmehling et al.t in a summary collection of the world s published VLE data for low to moderate pressures. These values are based on reduction of data through application of Eq. (11.74). On the other hand, data reduction for determination of parameters in the UNIFAC method (App. D) is carried out with Eq. (12.1). 

Note Equation 4 in Ref. 11 has a typographical error resulting in a numerator—denominator interchange error.] Statistical reduction of data from multiple samples was accomplished by a non-linear least squares computer program (16). 

An alternate arrangement that would relocate the force gage from the shaker armature to the driven sample block could be advantageous, provided that the force gage sensitivity remains constant over the required temperature range. This relocation would eliminate the need to take account of the mass correction term, in the reduction of data. Instead, this mass loading... 

The true instrumental method of analysis requires no reduction of data to normal pressure and temperature, no corrections or computations, no reference to correction factors nor interpolation on nomographic charts. It indicates the desired information directly on a dial or counter and if it is desired to have the answer printed on paper—that can be had for the asking. (Muller, 1947, pp. 23A-24A)... 

Simplification of the equation and reduction of data requirement have been achieved in newer equations by addressing binary molecular interactions only. Interactions of clusters of greater than two molecules are not explicitly addressed, but their constituent molecular pairs are included as binary interactions. In this way only binary interaction parameters appear in all activity coefficient equations—for binary solutions as well as for multi-component solutions. By fitting binary solution data all solution parameters can be obtained, for multi-component solutions as well. The need for experimental data on multi-component solutions is eliminated, as all required parameters can be determined by fitting binary solution data. 

Corresponding to the dimension d = 2, the poset shown in Fig. 19 can alternatively be visualized by a two-dimensional grid as is shown in Fig. 22. Both visualizations have their advantages. Structures within a Hasse diagram, e.g., successor sets, or sets of objects separated from others by incomparabilities, can be more easily disclosed by a representation like that of Fig. 19. In multivariate statistics reduction of data is typically performed by principal components analysis or by multidimensional scaling. These methods minimize the variance or preserve the distance between objects optimally. When order relations are the essential aspect to be preserved in the data analysis, the optimal result is a visualization of the sediment sites within a two-dimensional grid. 

The large amount of data generated with Ge(Li) or HP-Ge radiation detector systems makes it very useful to have a computer for information processing. The equipment can be programmed to compare the areas of specified peaks in the spectra of samples and standards and, thus, to calculate the elemental levels. For additional information, the reader is referred to publications focusing on analysis of gamma spectra and reduction of data (Harpers, 1986 Op de Beeck and Hoste, 1976 Perlman, 1981 and Yule, 1981). 

Figure 5. Values of 9Ga k versus reciprocaffemperature as calculated by the NRTL equation with Equation 9. Reduction of data set ---------, 1iquidus temperature --------, 1iquidus temperature and Ga activity ------------, 1iquidus temperature and...

Data Reduction and Background Correction Reduction of data points is important if, for example, further processing of a spectrum is only feasible if the number of data points is decreased. For reduction of measurements in the original data vector, the data are transformed by means of FT or HT. After that, back transformation is performed on the basis of a limited number of Fourier or Hadamard coefficients. For back transformation, the coefficients are sorted according to importance, and the effect of less important coefficients is thus eUminated (cf. Zupan, Section 3.3). Practically, the number of coefficients is not changed, but unimportant coefficients are set to zero. 

Moment analysis [11] refers to the reduction of data to statistical properties such as the mean and variance of the distribution of measured values. If a quantity, x, has a mean value (or expectation value) given by,... 

Reduction of data preparation efforts JT data helps to reduce data preparation efforts on supplier side in company with native CAD-data. 

Reduction of Data from the Automated Gas-Liquid Chromatographic Analysis of Complex Extracts from Human Biological Fluids Using a Digital Electronic Integrator and on Off-Line Computer Programs... 

J. L. Cross, Reduction of Data for Piston Gauge Pressure Measurements , NBS Monograph 65, U.S. Department of Commerce, Washington, D.C., 1964. 

MCTDH therefore takes a different route. The basis functions that are used to represent the wavefunction are chosen variationally optimal and typically span a few (one to four) physical DOF. Numerically, this corresponds to combining a subset of the indices in Eq. (5.1) into one single index and subsequently finding an optimal basis to describe this subset of DOF. In this way only a few most important basis functions and their expansion coefficients on the primitive grid as well as the expansion coefficients of the wavefunction in this optimal basis have to be stored. This leads to an enormous reduction of data. 

In practically all cases, composite functions are utilized, obtained by reduction of data from experiments at various temperatures as described in the preceding chapter. Most of the data refer to uncross-linked polymers of quite high molecular weight, but since moderate cross-linking affects the transition zone only to a minor degree, a few cross-linked systems are included. Polymers of low molecular weight are discussed in Section D. 

It is once again important to stress that this segmentation does not lead to a reduction of data, like binning does, but it provides an overall picture of the relevant information in different spectral subdivisions, focusing on important spectral regions [7]. /PLS models shown in this section were carried out in Matlab using the open source /PLS toolbox available at http //www.models. life.ku.dk/algorithms. 

Lee, J.A., Verleysen, M. Nonlinear dimensionality reduction of data manifolds with essential loops. Neurocomputing 67, 29-53 (2005)... 

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