Using the concept of $\mathcal {I}$-convergence we provide a Korovkin type approximation theorem by means of positive linear operators defined on an appropriate weighted space given with any interval of the real line. We also study rates of convergence by means of the modulus of continuity and the elements of the Lipschitz class.
Functioning of plant-aphid-natural enemy interactions may be associated with the structure and composition of withinfield vegetation, neighborhood fields and field borders, and the regional plant community of cropped and noncropped areas. Farmand region-scale vegetation in the wheat-growing area of the North American Great Plains was hypothesized to effect the abundance of two hymenopteran parasitoids, that differ in physiological and behavioral attributes, of the key pest aphid of wheat, Diuraphis noxia (Mordvilko). The parasitoids had greater sensitivity to farm-scale vegetation (wheat strip rotation with or without spring-sown sunflower) than region-scale vegetation (degree of diversification with other crops and wheat fields converted to conservation grasslands). A two-way factorial design of scale (farm- and region-scale) revealed that parasitoid abundance in grass-dominant (homogeneous) areas especially benefited from adding sunflower to the wheat-fallow strip crop rotation. Considerable sensitivity of the analysis was added when adjusting for seasonality of vegetation, revealing that the region-scale effects were most prominent late season. From a management viewpoint, adding sunflower into the wheat production system, especially in relatively homogeneous vegetation regions, tends to promote local parasitoid populations during the summer when spring-sown plants are maturing and wheat is not in cultivation. Contrasting results for A. albipodus and L. testaceipes were consistent with expectations based on behavioral and physiological attributes of the two aphid parasitoid families they represent. Still, the general management interpretation seems robust for the two parasitoids and has relevance to both farm- and region-scale management schemes that are occurring in the wheat production zone of North American Great Plains.
In this paper, a learning algorithm for a novel neural network architecture motivated by Integrate-and-Fire Neuron Model (IFN) is proposed and tested for various applications where a multilayer perceptron (MLP) neural network is conventionally used. It is observed that inclusion of a few more biological phenomenon in the formulation of artificial neural networks make them more prevailing. Several benchmark and real-life problems of classification and function-approximation are illustrated.