63
Views
63
CrossRef citations to date
0
Altmetric
Research Article

Population density methods for large-scale modelling of neuronal networks with realistic synaptic kinetics: cutting the dimension down to size

, &
Pages 141-174 | Published online: 04 Aug 2009

References

  • Abbott L F and van Vreeswijk C 1993 Asynchronous states in networks of pulse-coupled oscillators Phys. Rev. E 48 1483–90
  • Adorja´n P, Barna G, E´rdi P and Obermayer K 1999 A statistical neural field approach to orientation selectivity Neurocomputing at press
  • Barna G, Gro¨bler T and E´rdi P 1998 Statistical model of the hippocampal ca3 region, ii. the population framework: model of rhythmic activity in ca3 slice Biol. Cybern. 79 309–21
  • Bressloff P C and Coombes S 2000 Dynamics of strongly coupled spinking neurons Neural Comput. 12 91–129
  • Brunel N and Hakim V 1999 Fast global oscillations in networks of integrate-and-fire neurons with low firing rates Neural Computation 11 1621–71
  • Chawanya T, Aoyagi A, Nishikawa I, Okuda K and Kuramoto Y 1993 A model for feature linking via collective oscillations in the primary visual cortex Biol. Cybern. 68 483–90
  • Fain GL 1999 Molecular and Cellular Physiology of Neurons (Cambridge, MA: Harvard University Press)
  • Gerstner W 1995 Time structure of the activity in neural network models Phys. Rev. E 51 738–58
  • Gerstner W 1999 Population dynamics of spiking neurons: fast transients, asynchronous states, and locking Neural Comput. 12 43–90
  • Gerstner W and van Hemmen J 1994 Coding and information processinginneural networksModels of Neural Networks vol 2, ed E Domany, J van Hemmen and K Schulten (New York: Springer) pp 1–93
  • Grzywacz N M, Hillman P and Knight BW 1988 The quantal source of area supralinearity of flash responses in Limulus photoreceptors J. Gen. Physiol. 91 659–84
  • Hansel D, Mato G, Meunier C and Neltner L 1998 On numerical simulations of integrate-and-fire neural networks Neural Comput. 10 467–83
  • Knight B, Omurtag A and Sirovich L 2000 The approach of a neuron population firing rate to a new equilibrium: an exact theoretical result Neural Comput. 12 1045–55
  • Knight B W 1972a Dynamics of encoding in a population of neurons J. Gen. Physiol. 59 734–66
  • Knight B W 1972b Therelationship between thefiring rateofasingle neuron and the levelofactivityinapopulationofneurons. experimental evidence for resonant enhancement in the population response J. Gen. Physiol. 59 767–78
  • Knight BW 2000 Dynamics of encoding in neuron populations: some general mathematical features Neural Comput. 12 473–518
  • Knight B W, Manin D and Sirovich L 1996 Dynamical models of interacting neuron populations Symposium on
  • Robotics and Cybernetics: Computational Engineering in Systems Applications ed EC Gerf (France: Cite Scientifique)
  • Koch C 1999 Biophysics of Computation: Information Processing in Single Neurons (New York: Oxford University Press)
  • Kuramoto Y 1991 Collective synchronization of pulse-coupled oscillators and excitable units Physica D 50 15–30
  • Nykamp D Q and Tranchina D 2000 A population density approach that facilitates large-scale modelling of neural networks: Analysis and an application to orientation tuning J. Comput. Neurosci. 8 19–50
  • Nykamp D Q and Tranchina D 2001 A population density approach that facilitates large-scale modelling of neural networks: extension to slow inhibitory synapses Neural Comput. 13 511–46
  • Omurtag A, Knight B W and Sirovich L 2000 On the simulation of large populations of neurons J. Comput. Neurosci. 8 51–63
  • Pham J, Pakdaman K, Champagnat J and Vibert J 1998 Activity in sparsely connected excitatory neural networks: effect of connectivity Neural Networks 11 415–34
  • Sirovich L, Knight B and Omurtag A 2000 Dynamics of neuronal populations: the equilibrium solution SIAM at press
  • Somers D C, Nelson S B and Sur M 1995 An emergent model of orientation selectivity in cat visual cortical simple cells J. Neurosci. 15 5448–65
  • Strogatz S H and Mirollo RE 1991 Stability of incoherence in a population of coupled oscillators J. Stat. Phys. 63 613–35
  • Treves A 1993 Mean-field analysis of neuronal spike dynamics Network 4 259–84
  • Tuckwell HC 1988 Introduction to Theoretic Neurobiology vol 2 (New York: Cambridge University Press) pp 111–89
  • Wang XJ 1999 Synaptic basis of cortical persistent activity: the importance of NMDA receptors to working memory J. Neurosci. 19 9587–603
  • Wilbur W and Rinzel J 1982 An analysis of stein’s model for stochastic neural excitation Biol. Cyber. 45 107–14
  • Wilbur W and Rinzel J 1983 A theoretical basis for large coefficient of variation and bimodality in neuronal interspike interval distributions J. Theor. Biol. 105 345–68

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.