About this Journal Submit a Manuscript Table of Contents 
Advances in Artificial Neural Systems
Volume 2012 (2012), Article ID 713581, 16 pages
doi:10.1155/2012/713581
Research Article

A Radial Basis Function Spike Model for Indirect Learning via Integrate-and-Fire Sampling and Reconstruction Techniques

X. Zhang,1 G. Foderaro,1 C. Henriquez,2 A. M. J. VanDongen,3 and S. Ferrari1

1Laboratory for Intelligent Systems and Control (LISC), Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708, USA
2Department of Biomedical Engineering and Department of Computer Science, Duke University Durham, NC 27708, USA
3Program in Neuroscience & Behavioral Disorders, Duke-NUS Graduate Medical School, Singapore, Singapore

Received 17 February 2012; Accepted 21 May 2012

Academic Editor: Olivier Bastien

Copyright © 2012 X. Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. J. B. Jack, D. Nobel, and R. Tsien, Electric Current Flow in Excitable Cells, Oxford University Press, Oxford, UK, 1st edition, 1975.
  2. A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” The Journal of Physiology, vol. 117, no. 4, pp. 500–544, 1952. View at Scopus
  3. W. Maass, “Noisy spiking neurons with temporal coding have more computational power than sigmoidal neurons,” Advances in Neural Information Processing Systems, vol. 9, pp. 211–217, 1997.
  4. C. M. A. Pennartz, “Reinforcement learning by Hebbian synapses with adaptive thresholds,” Neuroscience, vol. 81, no. 2, pp. 303–319, 1997. View at Publisher · View at Google Scholar · View at Scopus
  5. S. Ferrari, B. Mehta, G. Di Muro, A. M. J. VanDongen, and C. Henriquez, “Biologically realizable reward-modulated hebbian training for spiking neural networks,” in Proceedings of the International Joint Conference on Neural Networks (IJCNN '08), pp. 1780–1786, Hong Kong, June 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. R. Legenstein, C. Naeger, and W. Maass, “What can a neuron learn with spike-timing-dependent plasticity?” Neural Computation, vol. 17, no. 11, pp. 2337–2382, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. J. P. Pfister, T. Toyoizumi, D. Barber, and W. Gerstner, “Optimal spike-timing-dependent plasticity for precise action potential firing in supervised learning,” Neural Computation, vol. 18, no. 6, pp. 1318–1348, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. R. V. Florian, “Reinforcement learning through modulation of spike-timing-dependent synaptic plasticity,” Neural Computation, vol. 19, no. 6, pp. 1468–1502, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. S. G. Wysoski, L. Benuskova, and N. Kasabov, “Adaptive learning procedure for a network of spiking neurons and visual pattern recognition,” in Proceedings of the 8th International Conference on Advanced Concepts for Intelligent Vision Systems (ACIVS '06), vol. 4179 of Lecture Notes in Computer Science, pp. 1133–1142, Antwerp, Belgium, September 2006. View at Scopus
  10. S. H. Jo, T. Chang, I. Ebong, B. B. Bhadviya, P. Mazumder, and W. Lu, “Nanoscale memristor device as synapse in neuromorphic systems,” Nano Letters, vol. 10, no. 4, pp. 1297–1301, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. A. M. VanDongen, “Vandongen laboratory,” http://www.vandongen-lab.com/.
  12. T. J. Van De Ven, H. M. A. VanDongen, and A. M. J. VanDongen, “The nonkinase phorbol ester receptor α1-chimerin binds the NMDA receptor NR2A subunit and regulates dendritic spine density,” Journal of Neuroscience, vol. 25, no. 41, pp. 9488–9496, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. P. Dayan and L. F. Abbott, Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, MIT Press, Cambridge, Mass, USA, 2001.
  14. W. Gerstner and W. Kistler, Spiking Neuron Models: Single Neurons, Populations, Plasticity, Cambridge University Press, Cambridge, UK, 2006.
  15. G. Foderaro, C. Henriquez, and S. Ferrari, “Indirect training of a spiking neural network for flight control via spike-timing-dependent synaptic plasticity,” in Proceedings of the 49th IEEE Conference on Decision and Control (CDC '10), pp. 911–917, Atlanta, Ga, USA, December 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. A. Aldroubi and K. Gröchenig, “Nonuniform sampling and reconstruction in shift-invariant spaces,” SIAM Review, vol. 43, no. 4, pp. 585–620, 2001. View at Scopus
  17. A. A. Lazar and L. T. Toth, “A toeplitz formulation of a real-time algorithm for time decoding machines,” in Proceedings of the Telecommunication Systems, Modeling and Analysis Conference, 2003.
  18. E. M. Izhikevich, “Which model to use for cortical spiking neurons?” IEEE Transactions on Neural Networks, vol. 15, no. 5, pp. 1063–1070, 2004. View at Publisher · View at Google Scholar · View at Scopus
  19. E. M. Izhikevich, “Simple model of spiking neurons,” IEEE Transactions on Neural Networks, vol. 14, no. 6, pp. 1569–1572, 2003. View at Publisher · View at Google Scholar · View at Scopus
  20. A. N. Burkitt, “A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input,” Biological Cybernetics, vol. 95, no. 1, pp. 1–19, 2006. View at Publisher · View at Google Scholar · View at Scopus
  21. S. Song, K. D. Miller, and L. F. Abbott, “Competitive Hebbian learning through spike-timing-dependent synaptic plasticity,” Nature Neuroscience, vol. 3, no. 9, pp. 919–926, 2000. View at Publisher · View at Google Scholar · View at Scopus
  22. P. Sjostrom, G. Turrigiano, and S. Nelson, “Rate, timing, and cooperativity jointly determine cortical synaptic plasticity,” Neuron, vol. 32, no. 6, pp. 1149–1164, 2001.
  23. S. Ferrari and R. Stengel, “Model-based adaptive critic designs,” in Learning and Approximate Dynamic Programming, J. Si, A. Barto, and W. Powell, Eds., John Wiley & Sons, 2004.
  24. R. E. Bellman, Dynamic Programming, Princeton University Press, Princeton, NJ, USA, 1957.
  25. R. Howard, Dynamic Programming and Markov Processes, MIT Press, Cambridge, Mass, USA, 1960.
  26. A. M. J. VanDongen, J. Codina, J. Olate et al., “Newly identified brain potassium channels gated by the guanine nucleotide binding protein G(o),” Science, vol. 242, no. 4884, pp. 1433–1437, 1988. View at Scopus
  27. J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM, Englewood Cliffs, NJ, USA, 1996.
  28. H. G. Feichtinger, J. C. Príncipe, J. L. Romero, A. Singh Alvarado, and G. A. Velasco, “Approximate reconstruction of bandlimited functions for the integrate and fire sampler,” Advances in Computational Mathematics, vol. 36, no. 1, pp. 67–78, 2012. View at Publisher · View at Google Scholar · View at Scopus
  29. R. F. Stengel, Optimal Control and Estimation, Dover Publications, Inc., 1986.