Heuristic Elements Research Articles

EXPERIMENTAL SYSTEMATICS—LA DUKE'S REFRESHING COUNTERPOINT OF VIEW

John La Duke (1987) brings up many worthwhile points in his counterpoint of view of Gilmartin (1986). The crux of my paper, however was to support a concept sensu lato of experimental research, i.e., one dependent upon the essential element of hypothesis-testing rather than upon manipulation of organisms as implied in Hagen (1983). Whether or not a given research paper deals with hypothesis-testing implicitly or explicitly is another interesting question. La Duke has done us a favor also by cogently emphasizing the importance of carefully distinguishing: (1) the heuristic element of research (hypothesis-generation) from (2) hypothesis-testing. Both of these may occur and usually do occur in such rapid succession that they are difficult to distinguish but as La Duke points out, experiments need to be planned that explicitly attempt to falsify the hypothesis. Certainly, it is true that the latter effort is NOT evident in the majority of plant systematics papers, and I might add, it need not be so in every paper. Nonetheless, the more plant systematic research that is carried out with the world view of La Duke and others whom he cites, the richer will be the area of plant systematics, an already highly rewarding subdiscipline.

Adaptive step adjustment for a stochastic optimization algorithm

The quasigradient algorithm of stochastic optimization is considered. The conditions to be imposed on the step multiplier, for Cesaro convergence of the algorithms with probability 1, are studied. Adaptive step adjustment is proposed, and the convergence of the corresponding algorithm is proved. A numerical algorithm containing heuristic elements is described. The results of numerical experiments are quoted.