PubMed · 8171095
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L E Cunningham. 1994. Overpopulation.. https://pubmed.ncbi.nlm.nih.gov/8171095/
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We study the (Ito) stochastic differential equation [equation: see text] as a model for population growth in a stochastic environment with finite carrying capacity K > 0. Here r and alpha are constants and Bt denotes Brownian motion. If r > or = 0, we show that this equation has a unique strong global solution for all x > 0 and we study some of its properties. Then we consider the following problem: What harvesting strategy maximizes the expected total discounted amount harvested (integrated over all future times)? We formulate this as a stochastic control problem. Then we show that there exists a constant optimal "harvest trigger value" x* epsilon (0, K) such that the optimal strategy is to do nothing if Xt < x* and to harvest Xt-x* if Xt > x*. This leads to an optimal population process Xt being reflected downward at x*. We find x* explicitly.
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Orientation selectivity is a basic property of neurones in the visual cortex of higher vertebrates. Such neurones can be seen to act as 'feature detectors', which provide an efficient cortical representation of the outside world. More recently, the removal of correlations between the signals of cortical neurones has been suggested as suitable theoretical concept for explaining the development of receptive fields. Corresponding neural network simulations yielded oriented 'receptive field' structures resembling those observed by neurophysiologists. The findings suggest that the 'decorrelation approach' can provide a causal relationship between characteristics of the physical world and brain function. However, we were able to reveal a basic deficit of the decorrelation approach which we illustrate by the construction of two artificial 'worlds', a 'Gaussian' one and an 'orientation-only' one. We show that, according to the decorrelation approach, oriented environmental features would be neither necessary nor sufficient for the development of oriented receptive fields. Thus the link between environmental structure and cortical orientation selectivity still awaits a theoretical explanation.