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

Network: Computation in Neural Systems

Volumn 12, Issue 2, 2001, Pages 141-174

  Haskell, Evan ^a,b   Nykamp, Duane Q ^a,c   Tranchina, Daniel ^a  

^a NEW YORK UNIVERSITY   (United States)

^b SISSA   (Italy)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ARTIFICIAL NEURAL NETWORK; CELL COUNT; CELL MEMBRANE POTENTIAL; EXCITATORY POSTSYNAPTIC POTENTIAL; FOURIER ANALYSIS; KINETICS; METHODOLOGY; MONTE CARLO METHOD; NERVE CELL; PHYSIOLOGY; POISSON DISTRIBUTION; SYNAPSE;

CELL COUNT; EXCITATORY POSTSYNAPTIC POTENTIALS; FOURIER ANALYSIS; KINETICS; MEMBRANE POTENTIALS; METHODS; MONTE CARLO METHOD; NEURAL NETWORKS (COMPUTER); NEURONS; PHYSIOLOGY; POISSON DISTRIBUTION; SYNAPSES;

EID: 0042736230     PISSN: 0954898X     EISSN: None     Source Type: Journal    
DOI: 10.1088/0954-898X/12/2/304     Document Type: Article

References (31)

1. Abbott L F and van Vreeswijk C 1993 Asynchronous states in networks of pulse-coupled oscillators Phys. Rev. E 48 1483-90
2. Adorján P, Barna G, Érdi P and Obermayer K 1999 A statistical neural field approach to orientation selectivity Neurocomputing at press
3. Barna G, Gröbler T and Érdi 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
4. Bressloff P C and Coombes S 2000 Dynamics of strongly coupled spinking neurons Neural Comput. 12 91-129
5. 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
6. 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
7. Fain G L 1999 Molecular and Cellular Physiology of Neurons (Cambridge, MA: Harvard University Press)
8. Gerstner W 1995 Time structure of the activity in neural network models Phys. Rev. E 51 738-58
9. _1999 Population dynamics of spiking neurons: fast transients, asynchronous states, and locking Neural Comput. 12 43-90
10. Gerstner W and van Hemmen J 1994 Coding and information processing in neural networks Models of Neural Networks vol 2, ed E Domany, J van Hemmen and K Schulten (New York: Springer) pp 1-93
11. Grzywacz N M, Hillman P and Knight B W 1988 The quantal source of area supralinearity of flash responses in Limulus photoreceptors J. Gen. Physiol. 91 659-84
12. Hansel D, Mato G, Meunier C and Neltner L 1998 On numerical simulations of integrate-and-fire neural networks Neural Comput. 10 467-83
13. 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
14. Knight B W 1972a Dynamics of encoding in a population of neurons J. Gen. Physiol. 59 734-66
15. _1972b The relationship between the firing rate of a single neuron and the level of activity in a population of neurons. experimental evidence for resonant enhancement in the population response J. Gen. Physiol. 59 767-78
16. _2000 Dynamics of encoding in neuron populations: some general mathematical features Neural Comput. 12 473-518
17. 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 E C Gerf (France: Cite Scientifique)
18. Koch C 1999 Biophysics of Computation: Information Processing in Single Neurons (New York: Oxford University Press)
19. Kuramoto Y 1991 Collective synchronization of pulse-coupled oscillators and excitable units Physica D 50 15-30
20. 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
21. 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
22. Omurtag A, Knight B W and Sirovich L 2000 On the simulation of large populations of neurons J. Comput. Neurosci. 8 51-63
23. 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
24. Sirovich L, Knight B and Omurtag A 2000 Dynamics of neuronal populations: the equilibrium solution SIAM at press
25. 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
26. Strogatz S H and Mirollo R E 1991 Stability of incoherence in a population of coupled oscillators J. Stat. Phys. 63 613-35
27. Treves A 1993 Mean-field analysis of neuronal spike dynamics Network 4 259-84
28. Tuckwell H C 1988 Introduction to Theoretic Neurobiology vol 2 (New York: Cambridge University Press) pp 111-89
29. Wang X J 1999 Synaptic basis of cortical persistent activity: the importance of NMDA receptors to working memory J. Neurosci. 19 9587-603
30. Wilbur W and Rinzel J 1982 An analysis of stein's model for stochastic neural excitation Biol. Cyber. 45 107-14
31. _1983 A theoretical basis for large coefficient of variation and bimodality in neuronal interspike interval distributions J. Theor. Biol. 105 345-68