Least squares, Parameter estimation, Simulated annealing (Mathematics)
In this thesis, a weighted least squares approach is initially presented to estimate the parameters of an adaptive quadratic neuronal model. By casting the discontinuities in the state variables at the spiking instants as an impulse train driving the system dynamics, the neuronal output is represented as a linearly parameterized model that depends on filtered versions of the input current and the output voltage at the cell membrane. A prediction errorbased weighted least squares method is formulated for the model. This method allows for rapid estimation of model parameters under a persistently exciting input current injection. Simulation results show the feasibility of this approach to predict multiple neuronal firing patterns. Results of the method using data from a detailed ion-channel based model showed issues that served as the basis for the more robust resonate-and-fire model presented. A second method is proposed to overcome some of the issues found in the adaptive quadratic model presented. The original quadratic model is replaced by a linear resonateand-fire model -with stochastic threshold- that is both computational efficient and suitable for larger network simulations. The parameter estimation method presented here consists of different stages where the set of parameters is divided in to two. The first set of parameters is assumed to represent the subthreshold dynamics of the model, and it is estimated using a nonlinear least squares algorithm, while the second set is associated with the threshold and iii reset parameters as its estimated using maximum likelihood formulations. The validity of the estimation method is then tested using detailed Hodgkin-Huxley model data as well as experimental voltage recordings from rat motoneurons.
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Master of Science in Electrical Engineering (M.S.E.E.)
College of Engineering and Computer Science
Electrical Engineering and Computer Science
Length of Campus-only Access
Masters Thesis (Open Access)
Dissertations, Academic -- Engineering and Computer Science, Engineering and Computer Science -- Dissertations, Academic
Suarez, Jose, "Data-true Characterization Of Neuronal Models" (2011). Electronic Theses and Dissertations. 1798.