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The ability of such a mathematical function is usually quantified by exploring its capability to represent experimental data.
A mathematical function is evolved through Genetic Programming according to the known direct kinematic model to determine an analytical expression which approximates the joint variable solution for a given end-effector configuration.
Assuming the hepatic glycerol permeability as depending on the protein levels of AQP9, a mathematical function is designed describing the time course of the involvement of AQP9 in mouse hepatic glycerol metabolism in different nutritional states.
For each type of behaviour a mathematical function is derived that expresses β as function of average particle conversion, maximum attainable conversion (with regard to pore plugging) and a new-defined expansion factor, which is a measure for the expansion (or shrinking) of the reacting solid during conversion.
Calculating the coordinates of the critical point through the first derivative of the mathematical function is possible which describes the response surface and equates it to zero (Myers and Montgomery 1995).
From these choices, a mathematical function is estimated that describes numerically the value that respondents attach to different choice options.
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Epistatic effects were evaluated, ultimately, according to an intuitive fitness criterion represented by a mathematical function, being this dependent on phenotypic discrepancies between mutant and reference spatio-temporal expression trajectories.
Using the receptor competition model together with the preclinical data on vabicaserin (see above) in combination with published data on the effect of 5-HT2C monulation on DA activity, a mathematical function was derived to describe the effect of 5-HT 2C receptor activation on dopamine firing frequency and therefore the effects on striatal D1 and D2 receptor activation.
A set of 11 mathematical functions is used to validate the proposed approach.
Firstly, a set of 19 mathematical functions is employed to test different characteristics of ALO.
For waveshaping, use the function partials->polynomial. Abramowitz and Stegun, "A Handbook of Mathematical Functions" is a treasure-trove of interesting polynomials.
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