Empirical modeling and prediction of neuronal dynamics.

Mathematical modeling of neuronal dynamics has experienced a fast growth in the last decades thanks to the biophysical formalism introduced by Hodgkin and Huxley in the 1950s. Other types of models (for instance, integrate and fire models), although less realistic, have also contributed to understand neuronal dynamics. However, there is still a vast volume of data that have not been associated with a mathematical model, mainly because data are acquired more rapidly than they can be analyzed or because it is difficult to analyze (for instance, if the number of ionic channels involved is huge). Therefore, developing new methodologies to obtain mathematical or computational models associated with data (even without previous knowledge of the source) can be helpful to make future predictions. Here, we explore the capability of a wavelet neural network to identify neuronal (single-cell) dynamics. We present an optimized computational scheme that trains the ANN with biologically plausible input currents. We obtain successful identification for data generated from four different neuron models when using all variables as inputs of the network. We also show that the empiric model obtained is able to generalize and predict the neuronal dynamics generated by variable input currents different from those used to train the artificial network. In the more realistic situation of using only the voltage and the injected current as input data to train the network, we lose predictive ability but, for low-dimensional models, the results are still satisfactory. We understand our contribution as a first step toward obtaining empiric models from experimental voltage traces.

Optimising the extraction rate of a non-durable non-renewable resource in a monopolistic market: a mathematical programming approach.

We assume a monopolistic market for a non-durable non-renewable resource such as crude oil, phosphates or fossil water. Stating the problem of obtaining optimal policies on extraction and pricing of the resource as a non-linear program allows general conclusions to be drawn under diverse assumptions about the demand curve, discount rates and length of the planning horizon. We compare the results with some common beliefs about the pace of exhaustion of this kind of resources.