Auxiliary parameter detection

How to discover which parameters are aiailiary parameters Problems such as efface 3, insert 3, member , partition , and plateau 3 have auxiliary parameters unless this is stated somewhere, considerable design effort may go into detecting this. The logic algorithms listed above for these problems actually are versions for which the detection was not done. 

Heuristic 13-4 If parameter T is not an auxiliary parameter (see Section 14.2.2 on how to detect auxiliary parameters), then it is irrelevant for discrimination, and its equality atom may be deleted from the body of every discriminant. 

How to detect that recursion is useless in some non-minimal sub-cases Step 4 (Syntactic introduction of the recursive atoms) creates a non-recursive case if at least one example Ej leads to a non-admissible procComp(,,yp atom. Howto invent or re-use appropriate predicates How to implement invented predicates The predicate invention problem is tackled at four points during the synthesis. At Steps 2 and 3, the Database Method re-uses predefined predicates this amounts to using domain knowledge. At Step 6, the Synthesis Method (see Section 14.2.4 below) invents new composition operators. As of now, there is no method yet of re-using common composition operators. At Step 7, the PaP Method synthesizes discriminants that are in terms of predicates other than rfn. How to discover which parameters are auxiliary parameters Due to our restriction to version 3 of the divide-and-conquer schema, auxiliary parameters are not taken into account. See Section 14.2.2 below on how to achieve this. 

At Task U , the entire synthesis mechanism is used to synthesize LA pcPermiitation) from EP pcPermutation) as generated by the two previous tasks. Supposing an induction on the second parameter and an intrinsic decomposition thereof, plus a detection that the first parameter necessarily is an auxiliary parameter, the result is pcPermutation (E, L, R) <=>... 

Again, this sub-synthesis needs to be done in totally automatic mode. Hence, the fact that L2 actually also is an auxiliary parameter of pcSort/3, just like A, cannot be declared, and is only detected as such after this sub-synthesis has been completed. 

The computation of the PRESS residuals e-k k) using Equation (3.24) only requires the orthogonal matrix W and the auxiliary parameter vector g. Hence, the value of the PRESS can be used to detect the significance of each additional term in the original model without actually having to compute 6. This is a result of the structure of the T matrix and the relationship between g and 9. 

Optical detection methods have a suite of attractive features for many in situ monitoring and reaction optimization applications. These features include nondestructive measurement capabilities, fast response, low detection limit, means to analyze materials with no sample preparation, ease of multiplexing for parallel measurements of multiple compounds in the library, and spatial-mapping capabilities. One or several lightwave parameters (amplitude, wavelength, polarization, phase, and temporal property) can be measured and related to a material property of interest. Complementing direct measurements, in which the spectroscopic features of the material are measured, an indirect material determination can be used in which an auxiliary reagent is employed. ... 

After deposition of elemental arsenic, 2.0 ml of the carrier solution are pumped through the detection cell at a flow rate of 30.0 ml min-i. The elemental arsenic is then stripped off in stop flow mode using the CS as clean medium under the SWASV parameters mentioned above. The exchange of the sample solution by the CS electrolyte solution minimizes the interference produced by the chlorine generated at the auxiliary electrode (Billing et al., 2002). 

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