Proceedings Volume 2010 (format .pdf) - SimpBTH

AN APPLICATION OF STOCHASTIC APPROXIMATION TO APROBLEM OF VITICULTURE1 Faculty of Biotechnology, USAMV BucharestVARGA M 1 , VIŞAN L. 1ABSTRACTIn this paper, we discussed about an application of stochastic approximation to a problem ofviticulture. We presented some fundamental concepts and then, we considered a simple model ofcompetitive antagonism to determine the optimal quantities of two factors: Atonik and Ronilan, so themain shoots reach a well-balanced growth obviously influencing on the grape yield. We solve thisproblem applaying the stochastic approximation technique and we discuss its comparison with aNewton-Raphson method.Keywords: stochastic approximation, random variable, distribution function, regression function.1. INTRODUCTIONMultidimensional techniques of stochastic approximation have become verypopular due to their practical utility and simplicity.There are experimentalsituations where the stochastic approximation may be applied, but those might besolved also by using statistical methods or techniques of numerical analysis. In theconstruction of systems there are many problems which often force one to besatisfied with a design that is less than optimum and the effects of certain factorsmay not be known and so forth. Under these conditions, it is often desired, once areasonable system has been built, to attempt to optimize its performance byexperimenting with the values of its adjustable parameters.We presented in [5] some advantages of the stochastic approximation whencompared to other methods: first of all, it consists in the fact that it is not necessaryto know x value (that value which the experiment depends on) at the initialmoment, but only its value at the final moment, that one being easily measured inpractice. Moreover, it is not necessary to know the form of the regression function,or to estimate the unknown parameters; therefore, the stochastic approximation is anon-parametric technique that often generates a stochastic process, which is not aMarkov process.2. MATERIAL AND METHODThe following genuine data come from the results of several analyses, whichthe Research & Development Institute for Viticulture and Enology, ValeaCalugareasca made available for us.For a better rooting and a successful joining of the grafting partners used inthe grapevine grafting (an European grapevine susceptible to phylloxera was usedas a scion; an American grapevine resistant to phylloxera was used as a rootstock),Atonik was used as a growth regulator. This product stimulates plant growth andfruit development in case of all the crops by activating the cytoplasm flow, by a328