Base variables

Bevin, K. J. and Kirkby, M. J. (1979). A physically based variable contributing area model of basin hydrology. Hydrolog. Sci. Bull. 23,419-437. 

In an s-dimensional space, s vectors at most can be independent. At equilibrium, a rock made of s elements cannot consist of more than s minerals, which implies that at least p—s of the p mole numbers are zero. In order to find the set of independent vectors that minimize the energy, we first rearrange the order of variables and split the vector n into two parts. The first part is the vector nB made of s base variables, and the second part is the vector F of (p —s) free variables. Provided the base variables are non-negative, the non-negativity constraints can be satisfied by setting the free variables to zero. For the vector n to be a feasible solution, it should also satisfy the recipe equation, i.e.,... 

For nF = 0, we immediately get the relationship between nB and q. We now want to change both uB and nF in a direction that decreases G. More precisely, we will exchange one free for one base variable at a time as long as the Gibbs free energy can be decreased. The last equation can be differentiated as... 

The most negative component is i=4, so the merwinite mole number will be moved from the status of a free variable to that of a base variable. The fourth row k4t of fiFZJb-1 is [2,1,3] and the components of B/ 4 are 0.45/2=0.225, 0.45/1=0.45, 0.10/3 = 0.03. The third component (fc=3, lime) of nB is first to reach zero upon increase of merwinite. We therefore exchange the rows assigned to lime and merwinite in the matrix B and the vector g as... 

The reduction of latent variables is an effective method to reduce the number of possible models, yet in PLS, variable reduction is not needed. The reduction of the number of variables in traditional regression techniques will lead to models with improved predictive ability and, in the case of PLS, a model that is easier to understand. The attempts to reduce the number of variables for PLS have only resulted in simpler models that fit the Training Set better yet do not have the predictive abilities of the complete PLS model (111). The reduction of latent variables with respect to the descriptors is possible with no apparent decrease in the model s ability to predict bioactivities, yet the remaining descriptor-based variables are considered to be more important before reduction and thus introduces bias (111). 

Ho vever this approach does not address inter-individual variability in CYP expression nor the apparent substrate specificity of RAFs. This may be overcome through the use of intersystem extrapolation factors (ISEFs) vhich compare the intrinsic activities of rCYP versus liver microsomes and provide CYP abundance scaling by mathematical means. This employs the RAF approach and adjusts for the actual amount of liver microsomes CYP present (measured by immunochemistry) rather than a theoretical amount (Equation 8.4). Such corrections can be made using nominal specific contents of individual CYP proteins in liver microsomes or more appropriately employ modeling and simulation software (e.g., SIMCYP www.simcyp.com) which takes into account population-based variability in CYP content. 

Equations (12.14) and (12.16) retain their validity even when X, Y and Z do not belong to a single set of base variables and conjugates. (For example, each might be expressed as a linear combination of two other base variables.) In such cases, one may select the complementary variables rather arbitrarily. For example, it is often convenient to define X and Y to be complementary variables ... 

Two-Phase State of a Pure Substance (p = 2 c = / = 1) In this case, we may choose the usual c + 2 base variables as... 

Cun-dinuclear, multidentate Schiff bases variable temperature magnetism 817... 

Warren-Hicks W, ParkhurstB. 2003. Whole effluent toxicity tests using Bayesian methods to calculate model-based variability. SETAC 24th Annual Meeting, Austin, Texas. 

A name, which should capture the meaning of the base variable involved... 

A base variable with its range of values (a closed interval of real numbers)... 

A set of linguistic terms that refer to values of the base variable... 

With respect to CoMFA, the Compass method effectively reduces the number of descriptors, performing a physicochemically based - variable reduction and overcomes the problem of guessing the best conformation and alignmet of the molecules. 

Platt number total edge adjacency index -> edge adjacency matrix PLS-based variable selection - variable selection P matrix -> bond order indices (O graphical bond order)... 

A number of variable selection techniques were also suggested for the Partial Least Squares (PLS) regression method [Lindgren et al, 1994]. The different strategies for PLS-based variable selection are usually based on a rotation of the standard solution by a manipulation of the PLS weight vector w or of the regression coefficient vector b of the PLS closed form. 

This equation for whole blood base excess (Icnown as the Van Slyke equation ), together with the Henderson-Hasselbalch equation, provides the simplest algorithm for calculation of the various acid-base variables. The buffer... 

Other specific PLS-based variable selection methods were proposed and presented below. 

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