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Biological Cybernetics

, Volume 83, Issue 6, pp 543–551 | Cite as

A qualitative comparison of some diffusion models for neural activity via stochastic ordering

  • Laura Sacerdote
  • Charles E. Smith

Abstract.

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.

Keywords

Stein Diffusion Model Neural Activity Additional Complexity Qualitative Comparison 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Laura Sacerdote
    • 1
  • Charles E. Smith
    • 2
  1. 1. Dept. of Mathematics, University of Torino, V.C. Alberto 10, I-10123 Torino, ItalyIT
  2. 2. Dept. of Statistics, North Carolina State University, Raleigh NC 27695-8203, USAUS

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