Parameter estimation for eutrophication models in reservoirs.

Excessive eutrophication is a major water quality issue in lakes and reservoirs worldwide. This complex biological process can lead to serious water quality problems. Although it can be adequately addressed by applying sophisticated mathematical models, the application of these tools in a reservoir management context requires significant amounts of data and large computation times. This work presents a simple primary production model and a calibration procedure that can efficiently be used in operational reservoir management frameworks. It considers four state variables: herbivorous zooplankton, algae (measured as chlorophyll-a pigment), phosphorous and nitrogen. The model was applied to a set of Portuguese reservoirs. We apply the model to 23 Portuguese reservoirs in two different calibration settings. This research work presents the results of the estimation of model parameters.

The master equation for neural interaction.

Based on neural interaction equations a random walk model for the stochastic dynamics of a single neuron is introduced. In this model the somatic potential corresponds to a state in the state space and action potentials provide the mechanism causing transitions. Time is made discrete, consisting of small finite increments delta t; assumptions are made about the transitions within such an increment and the associated probabilities are formulated. These quantities depend on delta t and on parameters derived from neural interaction equations. Moreover the model is chosen so that the sequence of somatic potentials is a Markov chain. By appropriately scaling the parameters, in the limit as delta t----0, a master equation for the probability in continuous time is obtained. Depending on the parameters, the master equation describes the evolution of a deterministic, a diffusion, or a discrete process. An interpretation for the diffusion and discrete processes is outlined. The conclusion is that the stochastic equations for neural interaction lead to a master equation representing a diffusion or a discrete process depending on the number, size of synaptic connectivity coefficients, and probability distribution of neural activity. An example is included describing how a master equation may be used to derive properties of the single neuron's output process.