Abstract
The research work outlined in the present note highlights the essential role played by the simulation procedures implemented by us on CINECA supercomputers to complement the mathematical investigations concerning neuronal activity modeling, carried within our group over the past several years. The ultimate target of our research is the understanding of certain crucial features of the information processing and transmission by single neurons embedded in complex networks. More specifically, here we provide a bird’s eye look of some analytical, numerical and simulation results on the asymptotic behavior of first passage time densities for Gaussian processes, both of a Markov and of a non-Markov type. Significant similarities or diversities between computational and simulated results are pointed out.
Keywords
- Gaussian Process
- Neuronal Modeling
- Stationary Gaussian Process
- Wiener Model
- Kind Integral Volterra Equation
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Buonocore, A., Nobile, A.G., Ricciardi, L.M.: A new integral equation for the evaluation of first-passage-time probability densities. Adv. Appl. Prob. 19, 784–800 (1987)
Di Crescenzo, A., Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: On some computational results for single neurons’ activity modeling. BioSystems 58, 19–26 (2000)
Di Nardo, E., Pirozzi, E., Ricciardi, L.M., Rinaldi, S.: Vectorized simulations of normal processes for first crossing-time problems. In: Moreno-Díaz, R., Pichler, F. (eds.) EUROCAST 1997. LNCS, vol. 1333, pp. 177–188. Springer, Heidelberg (1997)
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M., Rinaldi, S.: Simulation of Gaussian processes and first passage time densities evaluation. In: Kopacek, P., Moreno-Díaz, R., Pichler, F. (eds.) EUROCAST 1999. LNCS, vol. 1798, pp. 319–333. Springer, Heidelberg (2000)
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: On a non-Markov neuronal model and its approximation. BioSystems 48, 29–35 (1998)
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: Evaluation of upcrossing first passage time densities for Gaussian processes via a simulation procedure. In: Atti della Conferenza Annuale della Italian Society for Computer Simulation, pp. 95–102 (1999)
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: Parallel simulations in FPT problems for Gaussian processes. In: Report 2001, Science and Supercomputing at CINECA, pp. 405–412 (2001)
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: A computational approach to first-passage-time problem for Gauss-Markov processes. Adv. Appl. Prob. 33, 453–482 (2001)
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: Computer-aided simulations of gaussian processes and related asymptotic properties. In: Moreno-Díaz Jr., R., Buchberger, B., Freire, J.-L. (eds.) EUROCAST 2001. LNCS, vol. 2178, pp. 67–78. Springer, Heidelberg (2001)
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: Gaussian processes and neuronal models: an asymptotic analysis. In: Trappl, R. (ed.) Cybernetics and Systems 2002, vol. 1, pp. 313–318. Austrian Society for Cybernetics Studies, Vienna (2002)
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: On the asymptotic behavior of first passage time densities for stationary Gaussian processes and varying boundaries. Methodology and Computing in Applied Probability 5, 211–233 (2003)
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: Computational methods for the evaluation of neuron’s firing densities. In: Moreno-Díaz Jr., R., Pichler, F. (eds.) EUROCAST 2003. LNCS, vol. 2809, pp. 394–403. Springer, Heidelberg (2003)
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: Towards the Modeling of Neuronal Firing by Gaussian Processes. Scientiae Mathematicae Japonicae 58(2), 255–264 (2003) (e8, 497-506)
Giorno, V., Nobile, A.G., Ricciardi, L.M.: On the asymptotic behavior of first-passage-time densities for one-dimensional diffusion processes and varying boundaries. Adv. Appl. Prob. 22, 883–914 (1990)
Franklin, J.N.: Numerical simulation of stationary and non stationary gaussian random processes. SIAM Review 7, 68–80 (1965)
Kostyukov, A.I., Ivanov, Y.N., Kryzhanovsky, M.V.: Probability of Neuronal Spike Initiation as a Curve-Crossing Problem for5445 Gaussian Stochastic Processes. Biological Cybernetics 39, 157–163 (1981)
Nobile, A.G., Ricciardi, L.M., Sacerdote, L.: Exponential trends of Ornstein-Uhlenbeck first passage time densities. J. Appl. Prob. 22, 360–369 (1985)
Nobile, A.G., Ricciardi, L.M., Sacerdote, L.: Exponential trends of first-passage-time densities for a class of diffusion processes with steady-state distribution. J. Appl. Prob. 22, 611–618 (1985)
Ricciardi, L.M., Sato, S.: On the evaluation of first-passage-time densities for Gaussian processes. Signal Processing 11, 339–357 (1986)
Ricciardi, L.M.: Diffusion Processes and Related Topics in Biology. Springer, New York (1977)
Stratonovich, R.L.: Topics in Theory of Random Noise, vol. 1. Gordon and Breach, New York (1963)
Yaglom, A.M.: Correlation Theory of Stationary Related Random Functions, Basic Results, vol. I. Springer, New York (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M. (2005). Gaussian Processes and Neuronal Modeling. In: Mira, J., Álvarez, J.R. (eds) Mechanisms, Symbols, and Models Underlying Cognition. IWINAC 2005. Lecture Notes in Computer Science, vol 3561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499220_19
Download citation
DOI: https://doi.org/10.1007/11499220_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26298-5
Online ISBN: 978-3-540-31672-5
eBook Packages: Computer ScienceComputer Science (R0)