Correlations, computer

Once the descriptors have been computed, is necessary to decide which ones will be used. This is usually done by computing correlation coelficients. Correlation coelficients are a measure of how closely two values (descriptor and property) are related to one another by a linear relationship. If a descriptor has a correlation coefficient of 1, it describes the property exactly. A correlation coefficient of zero means the descriptor has no relevance. The descriptors with the largest correlation coefficients are used in the curve fit to create a property prediction equation. There is no rigorous way to determine how large a correlation coefficient is acceptable. 

The AeroSizer, manufactured by Amherst Process Instmments Inc. (Hadley, Massachusetts), is equipped with a special device called the AeroDisperser for ensuring efficient dispersal of the powders to be inspected. The disperser and the measurement instmment are shown schematically in Figure 13. The aerosol particles to be characterized are sucked into the inspection zone which operates at a partial vacuum. As the air leaves the nozzle at near sonic velocities, the particles in the stream are accelerated across an inspection zone where they cross two laser beams. The time of flight between the two laser beams is used to deduce the size of the particles. The instmment is caUbrated with latex particles of known size. A stream of clean air confines the aerosol stream to the measurement zone. This technique is known as hydrodynamic focusing. A computer correlation estabUshes which peak in the second laser inspection matches the initiation of action from the first laser beam. The equipment can measure particles at a rate of 10,000/s. The output from the AeroSizer can either be displayed as a number count or a volume percentage count. 

The mechanism of boiling is essentially nucleate pool hoiling. In hoth styles of rehoiler the liquid velocity is relatively low compared to thermosiphon units. Jacobs provides an extensive comparison of advantages and disadvantages of essentially all the reboiler types used in industrial plants. Palen and Taborek conducted extensive studies of available data and proposed nucleate boiling equations to correlate various data from the available 14 equations down to a selected 6 for detailed study. The study was limited to various hydrocarbons and hydrocarbon mixtures. Their conclusions after computer correlations of the results from several equations were as follows. 

The details of computing correlated coordinates (x, y) in spaces WEG, FAN, and PAR are of marginal interest to most of the readers. They are reported in Appendix 3A. 

An alternative approach to the calculation of accurate thermochemical data is to scale the computed correlation energy with multiplicative parameters determined by fitting to the experimental data. Pioneering methods using such an approach include the scaling all correlation (SAC) method of Gordon and Truhlar [32], the parameterized correlation (PCI-X) method of Siegbahn et al. [33], and the multi-coefficient correlation methods (MCCM) of Truhlar et al. [34-36]. Such methods can be used... 

Finally, Levchenko and Krylov (2004) have defined spin-flip versions of coupled cluster theories along lines similar to those previously described for SF-CISD. Applications to date have primarily been concerned with the accurate computation of electronically excited states, but the models are equally applicable to computing correlation energies for ground states. 

A wide range of bituminous coals, representing most of the major U. S. coal fields, were microscopically and chemically analyzed in this study. The samples tested, approximately 200 in all, were obtained through various coal producers. However, analytical data were not available for all samples carbonization, chemical, and by-product gas data for these subject coals were assumed to be the same as those reported previously in published sources (7, 9910,11,17,18). Only those carbonization data obtained from tests conducted in 18-inch pilot coke ovens at 900°C. are included. The remaining analytical data, approximately one-tenth of the total test results, were obtained from full scale commercial coke oven tests. Because these latter data were not sufficiently represented in the study, they were not considered in computing correlation coefficients (r). 

Petrographic analysis of the separated macerals, density determinations, and elemental analyses were performed at Argonne National Laboratories. The ash content of these samples is less than 1%. The oxygen levels reported here are obtained by difference. Computer correlations of the resulting parameters were done using the Statistical Analysis System on the VS/CMS system at the ER E-Linden site. Linear-regression analyses are also performed with that system. In the correlation plots which follow, samples will be identified by coal rank and maceral group. 

Reprinted from Computer Correlations to Estimate High Temperature Hydrogen Sulfide Corrosion in Refinery Streams," Materials Protection, January 1971.)... 

For subsequent computer correlation studies, the lb/acre data were converted to moles/acre. Herbicidal formulations corresponding to different... 

An automated retrieval system which benefits from the frame type representation has been developed to easily and rapidly access any data in a transparent way for the user. He only needs to indicate his choice among the propositions suggested by the system. The program has been designed so that constraints can be put on any parameter in order to select distinct experiments. For example, to analyze which zeolite is the most suitable for a given chemical reaction at given reaction conditions, the user will put successive constraints on the kind of reaction, the type of zeolite, the limits of conversion and selectivity, and on the reaction conditions. After each selection, the system displays the number of experiments which satisfy these constraints. Hence, the user can decide to i) list the selected experiments, ii) impose a new selection by entering an additional constraint, iii) plot the retained data, iv) compute correlations, or v) quit the application. One can then easily access the characteristics of the listed experiments so that the user can check and compare all the parameters and verify which one(s) could influence the observed conversion, selectivity, and yield, and maybe have a track for further analyses. 

One way to qualitatively check and/or discover some possible relations between the considered parameters (reaction conditions, zeolite characteristics) and the reaction efficiency (conversion of reactants, selectivity and yield of products), is to plot these parameters from selected experiments and to compute correlation coefficients. 

To assess the analyses, it is useful to have a more accurate and quantitative idea of those relations. Therefore, the program is able to compute correlation coefficients. In the near future, it will also be able to search for possible classes in a set of points using cluster analysis methods. 

In principle, attractor reconstruction can distinguish low-dimensional chaos from noise as we increase the embedding dimension, the computed correlation dimension levels off for chaos, but keeps increasing for noise (see Eckmann and Ruelle (1985) for examples). Armed with this technique, many optimists have asked questions like. Is there any evidence for deterministic chaos in stock market prices, brain waves, heart rhythms, or sunspots If so, there may be simple laws waiting to be discovered (and in the case of the stock market, fortunes to be made). Beware Much of this research is dubious. For a sensible discussion, along with a state-of-the-art method for distinguishing chaos from noise, see Kaplan and Glass (1993). 

The correlation between observations made at different times (autocorrelation) is described mathematically by computing the autocorrelation function, the degree of correlation between observations made k time units apart k = 1,2, ). The correlation coefficient is a measure of the linear association between two variables. It does not describe a cause-and-effect relation. The autocorrelation depends on sampling interval. Most statistical and mathematical software packages include routines for computing correlation and autocorrelation. 

Couper, A.S., and J.W. Gorman. Computer Correlations to Estimate High Temperature H2S Corrosion in Refinery Streams. Materials Protection and Performance 10(1) (1971) 31-37. 

Typically, the problem of correctly computing correlation effects comes into play with properties like nuclear spin-spin coupling constants, which are "second-order one-electron properties. A perturbation study of the role of correlation in this case shows that the terms contributing to energy are not the same as those contributing to other properties. The important moral of the story is that conclusions about the importance of correlation should be drawn only by considering at the same time properties of different types, because effects on one property may be important while those on other properties are not, and viceversa. 

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