Variables interrelated

The central idea of PCA is to reduce the dimensionality of a data set that may consist of a large number of interrelated variables while retaining as much as possible of the variation present in the data set [317-320]. 

Which of the two types of processes depicted above will preponderate u presumably governed by a number of interrelated variables. 

The development of the chromatographic separation conditions was approached in terms of three interrelated variables the column, the chromatographic separation... 

While possible to obtain satisfactory products with the pneumatic nebuliser, the experimental difficulties due to clogging and the strong dependence on many interrelated variables indicated that another type of atomiser should be investigated. An ultrasonic nozzle, in which high frequency electrical energy is converted into vibratory mechanical motion at the same frequency, was therefore examined. The ultrasonic nozzle was chosen because the average droplet size was small, about 25 microns, and... 

Aside from the continuity assumption and the discrete reality discussed above, deterministic models have been used to describe only those processes whose operation is fully understood. This implies a perfect understanding of all direct variables in the process and also, since every process is part of a larger universe, a complete comprehension of how all the other variables of the universe interact with the operation of the particular subprocess under study. Even if one were to find a real-world deterministic process, the number of interrelated variables and the number of unknown parameters are likely to be so large that the complete mathematical analysis would probably be so intractable that one might prefer to use a simpler stochastic representation. A small, simple stochastic model can often be substituted for a large, complex deterministic model since the need for the detailed causal mechanism of the latter is supplanted by the probabilistic variation of the former. In other words, one may deliberately introduce simplifications or errors in the equations to yield an analytically tractable stochastic model from which valid statistical inferences can be made, in principle, on the operation of the complex deterministic process. 

Probably, the very long time used in most cases could be significantly reduced by using a multivariate optimization approach focusing on interrelated variables. Figure 5.4 shows a surface response from a central composite design for [HCI]-ultrasound exposure for the determination of tin in coal acidified slurries [6]. 

In this chapter we summarize the complex issues that are involved in the analysis of sizing DNA by capillary electrophoresis (CE), and how chemomet-ric methods can help to optimize a high number of interrelated variables. It is impressive to observe how diverse is the obtainable biological information despite the size of the double-stranded DNA molecule. We also briefly introduce some typical genetic assays that rely on sizing DNA molecules, and how some chemometric approaches are used to correlate sizes of DNA with population and or evolution of species. 

The behavior of RNA polymerases at sites of DNA damage can best be understood by using site-specific, modified DNA templates in which the precise location, base linkage site, and stereochemistry of the lesion is known. Studies using this approach have collectively shown that the capacity of a DNA lesion to block transcription is a function of several interrelated variables, which have been summarized in prior articles and still hold true [11, 12, 33, 34]. These parameters include the structure of the specific RNA polymerase s active site, the size and shape of the DNA adduct, the stereochemistry of the adduct, the particular base incorporated into the growing transcript at the site of the damage, and the local DNA sequence. 

As the properties of ceramics monoliths are examined, it s important to note that changes or improvements in melting temperature, thermal shock resistance, strength, back pressure and/or catalyst surface area each have an effect on other properties. The present ceramic monolith design is the result of a compromise of these interrelated variables. 

As described above, electrokinetic remediation has many interrelated variables determining overall remediation efficiency These include pH, ionic strength, soil... 

Recently, a nonlinear version of PLS analysis was described [616]. The CARSO (computer-aided response surface optimization) procedure [617, 618] aims at obtaining response surfaces for non-designed data sets. Quadratic terms and interaction terms are generated for each independent variable and PLS analysis is used to model the data, due to the fact that regression analysis will fail for data sets with many highly interrelated variables in the X block. 

Principal components are linear combinations of random or statistical variables, which have special properties in terms of variances. The central idea of PCA is to reduce the dimensionality of a data set that may consist of a large number of interrelated variables while retaining as much as possible of the variation present in the data set. This is achieved by transforming the PCs which are uncorrelated into a new set of variables which are ordered so that the first few retain most of the variation present in all of the original variables [292-295]. 

I created the inclusion equation to help depict the interrelated variables necessary to create and sustain inclusive cultures (see Figure 7.1). There are two broad components of the inclusion model it depicts macro and micro inclusion practices. The two macro aspects focus on organizational culture and organizational systems. At the micro level, the model identifies individual cultural competence and emotional intelligence as the two core requirements to create and sustain inclusion. The components of the model are interdependent and work synergistically. When any one aspect is weak or absent, it severely inhibits the ability of an organization to effectively practice inclusion. 

The complexity of the flow in twin-screw extruders, as well as the large number of parameters and interrelated variables that affect the flow, make this process difficult to understand, control, and optimise. 

The purpose of this paper is to describe, briefly, several interrelated variables that affect the course of methyl pentene pyrolysis Initially, mechanistic aspects are described for the decomposition of methyl substituted pentenes to isoprene. Next, the high temperature degradation of isoprene and related by-product dienes will be discussed. Finally, the heterogeneous effects associated with reactor metallurgy are detailed. 

Because water management in PEM fuel cells involve a number of interrelated local variables, e.g. gas composition, temperatures, flow velocity, current density, and phenomena such as local occurrence of water flooding, test equipment for the measiuement of several local interrelated variables would be preferred, for simultaneous acquisition of data indicating on the state - or the change in state -of the cell. 

Another general characteristic of multistage columns is that they usually require controUing several interrelated variables using a number of interrelated manipulated variables. This is a multiple-input, multiple-output (MMO) problem as compared with the basic control action in a single-input, singleoutput (SISO) problem. In a multiple variable process each manipulated variable may affect more than one controlled variable due to process interactions. The multiple variable control problem in multistage columns may be handled either by multiple control loops or by a multivariable controller. 

Answer by Author A good discussion of this problem appears in R. M. Bozorth s Ferromagnetism, D. Van Nostrand and Co.. Princeton, New Jersey (1956) p. 146. Temperature and cold-work are interrelated variables in that both lowered tempera-mres and cold-work promote the transformation of paramagnetic austenite to ferromagnetic martensite (also called "alpha" or ferrite by other investigators). In this sense, magnetic permeability depends on both variables. 

---