Spline adaptive

The Bell/Boeing V22 Osprey tilt-rotor aircraft uses carbon fiber-reinforced polyether etherketone (PEEK) for doors and housings of the engine air particle separator and for fuel vent tanks (Figure 6.44). TP polyimide (TPI) forms the basis for an injection-molded spline adapter in the drive train which tilts the rotors. Costs were reduced some 22%. The parts were developed by RTP Company with Bell Helicopter and molder RAM Inc., Texas. The tanks are molded by the lost core process. 

J- Friedman, Multivariate Adaptive Regression Splines, Technical Report No. 102. Stanford University, CA,... 

A generalized partial differential equation solver which handles simultaneous parabolic, one dimensional elliptic, ordinary and integral equations and uses B-splines with an adaptive grid was written to solve the model. Further details on the model and solution method can be found in Reference 14. 

Stener and co-workers [59] used an alternative B-spline LCAO density functional theory (DFT) method in their PECD investigations [53, 57, 60-63]. In this approach a normal LCAO basis set is adapted for the continuum by the addition of B-spline radial functions. A large single center expansion of such... 

TMARS two-step multivariate adaptive regression splines... 

The %HIA, on a scale between 0 and 100%, for the same dataset was modeled by Deconinck et al. with multivariate adaptive regression splines (MARS) and a derived method two-step MARS (TMARS) [38]. Among other Dragon descriptors, the TMARS model included the Tig E-state topological parameter [25], and MARS included the maximal E-state negative variation. The average prediction error, which is 15.4% for MARS and 20.03% for TMARS, shows that the MARS model is more robust in modeling %H1A. 

Coomans, D., Massart, D. L Vander Heyden, Y. Prediction of gastro-intestinal absorption using multivariate adaptive regression splines. J. Pharm. Biomed. Anal. 2005, 39,1021-1030. 

Multivariate adaptive regression Input partition Adaptive shape, spline [0, t], minimum output prediction error... 

Multivariable smart transmitters, 20 664 Multivariate Adaptive Regression Splines (MARS), 6 53... 

Xu, Q. S., Massart, D. L., Liang, Y. Z., Fang, K. T. J. Chromatogr. A 998, 2003, 155-167. Two-step multivariate adaptive regression splines for modeling a quantitative relationship between gas chromatographic retention indices and molecular descriptors. 

Testing the Accuracy of a Calibration Spline Function. Of primary concern in calibration is the freedom from systematic errors introduced by fitting the wrong model. For judging the accuracy of the cubic spline functions, it is therefore desirable to start with a curve of known shape. Particularly difficult to adapt by ordinary polynomial expressions are... 

Friedman, J. [November 1988 (revised August 1990)] Multivariate adaptive regression splines, technical report number 102. Laboratory for Computational Statistics, Department of Statistics, Stanford University, Stanford, CA. 

Fig. 4. (A) Parametrization of a shaped pulse envelope with the help of a cubic spline interpolation between a small number of anchor points (circles). (B) Approximation of the smooth pulse envelope by rectangular pulses with piecewise constant rf amplitude. (Adapted from Ewing et al., 1990, p. 123, with kind permission from Elsevier Science—NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.)...

Nguyen-Cong, V., Vandang, G. and Rode, B.M. (1996b). Using Multivariate Adaptive Regression Splines to QSAR Studies of Dihydroartemisinin Derivatives. Eur.J.Med.Chem., 31, 797-803. 

Fig. 7. Vertical resolution in the upper mantle of model S16B30 of Masters et al. (1996). The input velocity anomaly is a linear combination of three natural B-splines in radius and spherical harmonics laterally. The continuous curve shows the amplitude of the input anomaly as a function of depth, normalized to unit amplitude. The dashed curve is the peak recovered value. The data inversion tends to smear the anomaly c. 200 km radially. Adapted from Masters et al, (1996).

Exploration of the linear modeling techniques and their combination with multivariate adaptive regression splines to predict gastrointestinal absorption of drugs... 

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