@article{sacerdote_smith_2004, title={Almost sure comparisons for first passage times of diffusion processes through boundaries}, volume={6}, ISSN={["1573-7713"]}, DOI={10.1023/B:MCAP.0000026563.27820.ff}, number={3}, journal={METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY}, author={Sacerdote, L and Smith, CE}, year={2004}, month={Sep}, pages={323–341} }
@article{sacerdote_smith_2000, title={A qualitative comparison of some diffusion models for neural activity via stochastic ordering}, volume={83}, ISSN={["0340-1200"]}, DOI={10.1007/s004220000179}, abstractNote={A number of diffusion processes have been proposed as a continuous analog of Stein's model for the subthreshold membrane potential of a neuron. Interspike intervals are then described as the first-passage-time of the corresponding diffusion model through a suitable threshold. Various biological considerations suggest the use of more sophisticated models in lieu of the Ornstein-Uhlenbeck model. However, the advantages of the additional complexity are not always clear. Comparisons among different models generally use numerical methods in specific examples without a general sensitivity analysis on the role of the model parameters. Here, we compare the distribution of interspike intervals from different models using the method of stochastic ordering. The qualitative comparison of the role of each parameter extends the results obtained from numerical simulations. One result on neurons with high positive net excitation is that the reversal potential models considered do not greatly differ from the Ornstein-Uhlenbeck model. For neurons with increased inhibition, the models give greater differences among the interspike interval distributions. In particular, when the mean trajectories are matched, the Feller model gives shorter times than the Ornstein-Uhlenbeck model but longer times than our double reversal potential model.}, number={6}, journal={BIOLOGICAL CYBERNETICS}, author={Sacerdote, L and Smith, CE}, year={2000}, month={Dec}, pages={543–551} }
@article{sacerdote_smith_2000, title={New parameter relationships determined via stochastic ordering for spike activity in a reversal potential neural model}, volume={58}, ISSN={["0303-2647"]}, DOI={10.1016/s0303-2647(00)00107-6}, abstractNote={Purpose of this work is to study the dependence of interspike interval distribution on the model parameters when use is made of the Feller diffusion process to describe the subthreshold membrane potential of a neuron. To this aim we make use of a new approach, namely the ordering of first passage times. The functional dependence among the model parameters (e.g. membrane time constant, reversal potential, etc.) resulting from the ordering criteria employed and from the study of mean trajectory plots is analyzed into detail for four different scenario.}, number={1-3}, journal={BIOSYSTEMS}, author={Sacerdote, L and Smith, CE}, year={2000}, pages={59–65} }