Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-02-05T06:36:24.615Z Has data issue: false hasContentIssue false
  • English
  • Français

Decoding neuronal firing and modelling neural networks

Published online by Cambridge University Press:  17 March 2009

L. F. Abbott
L. F. Abbott
Affiliation:
Center for Complex Systems, Brandeis University, Waltham, MA 02254
Get access Rights & Permissions [Opens in a new window]

Extract

Biological neural networks are large systems of complex elements interacting through a complex array of connexions. Individual neurons express a large number of active conductances (Connors et al. 1982; Adams & Gavin, 1986; Llinás, 1988; McCormick, 1990; Hille, 1992) and exhibit a wide variety of dynamic behaviours on time scales ranging from milliseconds to many minutes (Llinás, 1988; Harris-Warrick & Marder, 1991; Churchland & Sejnowski, 1992; Turrigiano et al. 1994).

Type
Research Article
Information
Quarterly Reviews of Biophysics , Volume 27 , Issue 3 , August 1994 , pp. 291 - 331
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abbott, L. F. (1990). Learning in neural network memories. Network: Comp. Neural Syst. 1, 105–122.CrossRefGoogle Scholar
Abbott, L. F. (1991 a). Firing-rate models for neural populations. In Neural Networks: From Biology to High-energy Physics (ed. Benhar, O., Bosio, C., Del Giudice, P. and Tabet, E.), pp. 179–196. Pisa: ETS Editrice.Google Scholar
Abbott, L. F. (1991 b). Realistic synaptic inputs for network models. Network: Comp. Neural Syst. 2, 245–258.CrossRefGoogle Scholar
Abbott, L. F. (1992). Simple diagrammatic rules for solving dendritic cable problems. Physica A 185, 343–356.CrossRefGoogle Scholar
Abbott, L. F. & Blum, K. I. (1994). Functional significance of long-term potentiation between hippocampal place cells. (Submitted.)Google Scholar
Adams, P. R. & Gavin, M. (1986). Voltage-dependent currents of vertebrate neurons and their role in membrane excitability. Adv. Neurol. 44, 37–170.Google ScholarPubMed
Altes, R. A. (1989). Ubiquity of hyperacuity. J. acoust. Soc. Am. 85, 943–952.CrossRefGoogle ScholarPubMed
Amit, D. J. (1989). Modelling Brain Function. New York: Cambridge University Press.CrossRefGoogle Scholar
Amit, D. J. & Tsodyks, M. V. (1991 a). Quantitative study of attractor neural network retrieving at low spike rates I and II. Network 2, 259–294 and Effective neurons and attractor neural networks in cortical environment. Network 3, 121–138.CrossRefGoogle Scholar
Amit, D. J. & Tsodyks, M. V. (1991 b). Effective neurons and attractor neural networks in cortical environment. Network 3, 121–138.CrossRefGoogle Scholar
Artola, A. & Singer, W. (1993). Long-term depression of excitatory synaptic transmission and its relationship to long-term potentiation. Trends Neurosci. 16, 480–487.CrossRefGoogle ScholarPubMed
Avoli, M. (1986). Inhibitory potentials in neurons of the deep layers of the in vitro neocortical slice. Brain Res. 370, 165–170.CrossRefGoogle ScholarPubMed
Bacon, J. P. & Murphey, R. K. (1984). Receptive fields of cricket (Acheta domesticus) interneurons are related to their dendritic structure. J. Physiol. Lond. 272, 779–797.Google Scholar
Baldi, P. & Heiligenberg, W. (1988). How sensory maps could enhance resolution through ordered arrangements of broadly tuned receivers. Biol. Cybern. 59, 313–318.CrossRefGoogle ScholarPubMed
Baudry, M. & Davis, J. L., eds. (1991). Long-Term Potentiation. Cambridge MA: MIT Press.Google Scholar
Bernander, O., Douglas, R. J., Martin, K. A. C. & Koch, C. (1991). Synaptic background activity determines spatio-temporal integration in single pyramidal cells. Proc. natn. Acad. Sci. U.S.A. 88, 11569–11573.CrossRefGoogle Scholar
Bialek, W. (1989). Theoretical physics meets experimental neurobiology. In Lectures in Complex Systems, SFI Studies in the Science of Complexity (ed. Jen, E.), vol. 2, pp. 413–595. Redwood City CA: Addison-Wesley.Google Scholar
Bialek, W.Rieke, F., De Ruyter Van Steveninck, R. R. & Warland, D. (1991). Reading a neural code. Science, N.Y. 252, 1854–1857.CrossRefGoogle Scholar
Bienenstock, E. L., Cooper, L. N. & Munro, P. W. (1982). Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. J. Neurosci. 2, 32–48.CrossRefGoogle ScholarPubMed
Bliss, T. V. P. & Collingridge, G. L. (1993). A synaptic model of memory: long-term potentiation in the hippocampus. Nature, Lond. 361, 31–39.CrossRefGoogle ScholarPubMed
Bortolotto, Z. A., Bahir, Z. I., Davies, C. H. & Collingridge, G. L. (1994). A molecular switch activated by metabotropic glutamate receptors regulates induction of long-term potentiation. Nature, Lond. 368, 740–743.CrossRefGoogle ScholarPubMed
Buhmann, J. (1989). Oscillations and low firing rates in associative memory neural networks. Phys. Rev. A 40, 4145–4151.CrossRefGoogle ScholarPubMed
Burnod, Y., Grandguillaume, P., Otto, I., Ferraina, S. & Johnson, P. B. & Camaniti, R. (1992). Visuomotor transformation underlying arm movements toward visual targets: A neural network model of cerebral cortical operations. J. Neurosci. 12, 1435–1452.CrossRefGoogle ScholarPubMed
Butz, E. G. & Cowan, J. D. (1974). Transient potentials in dendritic systems of arbitrary geometry. Biophys. J. 14, 661–689.CrossRefGoogle Scholar
Byrne, J. H. & Berry, W. O. (1989). Neural Models of Plasticity. San Diego: Academic Press.Google Scholar
Camhi, J. M. & Levy, A. (1989). The code for stimulus direction in a cell assembly in the cockroach. J. comp. Physiol. A 165, 83–97.CrossRefGoogle Scholar
Caminiti, R., Johnson, P. B., Galli, C., Ferraina, S. & Burnod, Y. (1991). Making arm movements within different parts of space: The premotor and motor cortical representations of a coordinate system for reaching to visual targets. J. Neurosci. 11, 1182–1197.CrossRefGoogle ScholarPubMed
Chen, L. L., McNaughton, B. L., Barnes, C. A. & Ortiz, E. R. (1990). Headdirectional and behavioral correlates of posterior cingulate and medial prestriate cortex neurons in freely-moving rats. Soc. Neurosci. Abst. 16, 441.Google Scholar
Churchland, P. S. & Sejnowski, T. J. (1992). The Computational Brain. Cambridge MA: MIT Press.CrossRefGoogle Scholar
Connors, B. W., Gutnick, J. M. & Prince, D. A. (1982). Electrophysiological properties of neocortical neurons in vitro. J. Neurophysiol. 48, 1302–1320.CrossRefGoogle Scholar
Connors, B. W., Malenka, R. C. & Silva, L. R. (1988). Two inhibitory postsynaptic potentials and GABAA and GABAB receptor-mediated responses in neocortex of rat and cat. J. Physiol., Lond. 406, 443–468.CrossRefGoogle ScholarPubMed
Debanne, D., Gahwiler, B. H. & Thompson, S. M. (1994). Asynchronous pre- and postsynaptic activity induces associative long-term depression in area CAi of the rat hippocampus in vitro. Proc. natn. Acad. Sci. U.S.A. 91, 1148–1152.CrossRefGoogle Scholar
Dichter, M. A. & Ayala, G. F. (1987). Cellular mechanisms of epilepsy: a status report. Science, N. Y. 237, 157–164.CrossRefGoogle ScholarPubMed
Douglas, R. J. & Martin, K. A. C. (1991). A functional microcircuit for cat visual cortex. J. Physiol., Lond. 440, 735–769.CrossRefGoogle ScholarPubMed
Douglas, R. J., Martin, K. A. C. & Whitteridge, D. (1989). A canonical microcircuit for neocortex. Neural Comp. 1, 480–488.CrossRefGoogle Scholar
Eichenbaum, H. (1993). Thinking about brain cell assemblies. Science, N.Y. 261, 993–994.CrossRefGoogle ScholarPubMed
Ermentrout, G. B. (1994). Reduction of Conductance Models with Slow Synapses to Neural Nets. Neural Comp. (In the press.)CrossRefGoogle Scholar
Foldiak, P. (1991). Models of sensory coding, Ph.D. thesis. Cambridge University.Google Scholar
Foldiak, P. (1993). The ‘ideal homunculus’: statistical inference from neural population responses. In Computation and Neural Systems(ed. Eeckman, F. H. and Bower, J.), pp. 55–60. Norwell MA: Kluwer Academic Publishers.CrossRefGoogle Scholar
Fortier, P. A., Kalaska, J. F. & Smith, A. M. (1989). Cerebellar neuronal activity related to whole-arm reaching movements in the monkey. J. Neurophysiol. 62, 198–211.CrossRefGoogle ScholarPubMed
Frolov, A. A. & Medvedev, A. V. (1986). Substantiation of the ‘point approximation’ for describing the total electrical activity of the brain with the use of a simulation model. Biophysics 31, 332–335.Google Scholar
Georgopoulos, A. P., Kettner, R. E. & Schwartz, A. (1988). Primate motor cortex and free arm movements to visual targets in three-dimensional space. II. Coding of the direction of movement by a neuronal population. Neuroscience 8, 2928–2937.CrossRefGoogle ScholarPubMed
Georgopoulos, A. P., Schwartz, A. & Kettner, R. E. (1986). Neuronal population coding of movement direction. Science, N.Y. 233, 1416–1419.CrossRefGoogle ScholarPubMed
Georgopoulos, A. P., Taira, M. & Lukashin, A. (1993). Cognitive neurophysiology of the motor cortex. Science, N. Y. 260, 47–52.CrossRefGoogle ScholarPubMed
Gilbert, C. D. & Wiesel, T. N. (1990). the influence of contextual stimuli on the orientation selectivity of cells in primary visual vortex of the cat. Vision Res. 30, 1689–1701.CrossRefGoogle Scholar
Gluck, M. A. & Rumelhart, D. E. (1990). Neuroscience and Connectionist Theory. Hillsdale NJ: Lawrence Erlbaum.Google Scholar
Grossberg, S. (1988). Nonlinear neural networks: principles, mechanisms and architectures. Neural Networks 1, 17–61.CrossRefGoogle Scholar
Gozani, S. N. & Miller, J. P. (1994). Ensemble coding of information by eight primary sensory interneurons in the cricket cereal system I and II. (Submitted.)Google Scholar
Gustafsson, B. & Wigstrom, H. (1981). Shape of frequency-current curves in CA1 pyramidal cells in the hippocampus. Brain Res. 223, 417–421.CrossRefGoogle ScholarPubMed
Gustafsson, B. & Wigstrom, H. (1988). Physiological mechanisms underlying longterm potentiation. Trends Neurosci. 11, 156–162.CrossRefGoogle Scholar
Gustafsson, B. & Wigstrom, H., Abraham, W. C. & Huang, Y.-Y. (1987). Long-term potentiation in the hippocampus using depolarizing current pulses as the conditioning stimulus to single volley synaptic potentials. J. Neurosci. 7, 774–780.CrossRefGoogle ScholarPubMed
Harris-Warrick, R. M. & Marder, E. (1991). Modulation of neural networks for behavior. Ann. Rev. Neurosci. 14, 39–57.CrossRefGoogle Scholar
Hawkins, R. D., Kandel, E. R. & Siegelbaum, S. A. (1993). Learning to modulate transmitter release: Themes and variations in synaptic plasticity. Ann. Rev. Neurosci. 16, 625–665.CrossRefGoogle ScholarPubMed
Hebb, D. O. (1949). The Organization of Behavior: A Neuropsychological Theory. New York: Wiley.Google Scholar
Hertz, J., Krough, A. & Palmer, R. G. (1990). Introduction to the Theory of Neural Computation. New York: Addison-Wesley.Google Scholar
Hessler, N. A., Shirke, A. M. & Malinow, R. (1993). The probability of transmitter release at a mammalian central synapse. Nature, Lond. 366, 569–572.CrossRefGoogle Scholar
Hille, B. (1992). Ionic Channels of Excitable Membranes. Sunderland, MA: Sinauer Assoc.Google Scholar
Hopfield, J. J. (1982). Neural networks and systems with emergent selective computational abilities. Proc. natn. Acad. Sci. U.S.A. 79, 2554–2558.CrossRefGoogle Scholar
Hopfield, J. J. (1984). Neurons with graded response have collective computational properties like those of two-state neurons. Proc. natn. Acad. Sci. U.S.A. 81, 3088–3092.CrossRefGoogle ScholarPubMed
Jack, J. J. B., Noble, D. & Tsien, R. W. (1974). Electrical Current Flow in Excitable Cells. Oxford: Oxford University Press.Google Scholar
Jagadeesh, B., Wheat, H. S. & Ferster, D. (1993). Linearity of summation of synaptic potentials underlying direction selectivity in simple cells of the cat visual cortex. Science, N.Y. 262, 1901–1904.CrossRefGoogle ScholarPubMed
Jahr, C. E. & Stevens, C. F. (1990). A quantitative description of NMDA receptor channel kinetic behavior. J. Neurosci. 10, 1830–1837.CrossRefGoogle ScholarPubMed
Kalaska, J. F., Caminiti, R. & Georgopoulos, A. P. (1983). Cortical mechanisms related to the direction of two-dimensional arm movements: relations in parietal area 5 and comparison with motor cortex. Expl Brain Res. 51, 247–260.CrossRefGoogle Scholar
Knudsen, E., DuLac, S. & Esterly, S. D. (1987). Computational maps in the brain. Ann. Rev. Neurosci. 10, 41–65.CrossRefGoogle ScholarPubMed
Knudsen, E. & Konishi, M. (1978). A neural map of auditory space in the owl. Science, N. Y. 200, 795–797.CrossRefGoogle ScholarPubMed
Koch, C. & Poggio, T. (1985). A simple algorithm for solving the cable equation in dendritic trees of arbitrary geometry. J. Neurosci. Meth. 12, 303–315.CrossRefGoogle ScholarPubMed
Koch, C., Poggio, T. & Torre, V. (1983). Nonlinear interactions in a dendritic tree: localization, timing and role in information processing. Proc. natn. Acad. Sci. U.S.A. 80, 2799–2802.CrossRefGoogle Scholar
Kohonen, T. (1984). Self Organization and Associative Memory. Berlin: Springer Verlag.Google Scholar
Kohonen, T. (1988). An introduction to neural computing. Neural Networks 1, 3–16.CrossRefGoogle Scholar
Konishi, M. (1987). Centrally synthesized maps of sensory space. Trends Neurosci. 9, 163–168.CrossRefGoogle Scholar
Konishi, M. (1991). Deciphering the brain's codes. Neural Comp. 3, 1–18.CrossRefGoogle ScholarPubMed
Lanthorn, T., Storm, J. & Andersen, P. (1984). Current-to-frequency transduction in CA1 hippocampal pyramidal cells: Slow prepotentials dominate the primary firing range. Expl Brain Res. 53, 431–443.CrossRefGoogle Scholar
Lee, C., Rohrer, W. H. & Sparks, D. L. (1988). Population coding of saccadic eye movements by neurons in the superior colliculus. Nature, Lond. 332, 357–360.CrossRefGoogle ScholarPubMed
Lehky, S. R. & Sejnowski, T. J. (1990). Neural model of stereoacuity and depth interpolation based on a distributed representation of stereo disparity. J. Neurosci. 10, 2281–2299.CrossRefGoogle ScholarPubMed
Levy, W. B. (1989). A computational approach to hippocampal function. In Computational Models of Learning in Simple Neural Systems. (ed. Hawkins, R. D. and Bower, G. H.), pp. 243–305. N.Y.: Academic Press.CrossRefGoogle Scholar
Levy, W. B., Colbert, C. M. & Desmond, N. L. (1990). Elemental adaptive processes of neurons and synapses: a statistical/computational perspective. In Neuroscience and Connectionist Theory (ed. Gluck, M. A. and Rumelhart, D. E.), pp. 187–236. New York: Lawrence Erlbaum, Hillsboro.Google Scholar
Levy, W. B. & Steward, D. (1983). Temporal contiguity requirements for long-term associative potentiation/depression in the hippocampus. Neurosci. 8, 791–797.CrossRefGoogle ScholarPubMed
Linkser, R. (1986). From basic network principles to neural architecture. Proc. natn. Acad. Sci. U.S.A. 83, 7508–7512, 8390–8394 and 8770–8783.Google Scholar
Linsker, R. (1988). Self-organization in a perceptual network. Computer 21, 105–117.CrossRefGoogle Scholar
Linsker, R. (1993). Local synaptic learning rules suffice to maximize mutual information in a linear network. Neural Comp. 4, 691–702.CrossRefGoogle Scholar
Lisman, J. E. (1989). A mechanism for the Hebb and the anti-Hebb processes underlying learning and memory. Proc. natn. Acad. Sci. U.S.A. 86, 9574–9578.CrossRefGoogle ScholarPubMed
Lisman, J. E. & Goldring, M. A. (1988). Feasibility of long-term storage of graded information by the Ca2+/calmodulin-dependent protein kinase molecules of the postsynaptic density. Proc. natn. Acad. Sci. U.S.A. 85, 5320–5324.CrossRefGoogle ScholarPubMed
Llinás, R. R. (1988). Intrinsic electrophysiological properties of mammalian neurons: insights into central nervous system function. Science, N. Y. 242, 1654–1664.CrossRefGoogle Scholar
Lukashin, A. V. (1990). A learned neural network that simulates properties of the neural population vector. Biol. Cybern. 63, 377–382.CrossRefGoogle Scholar
Lynch, G., Larson, J., Kelson, S., Barrionuevo, G. & Schottler, F. (1983). Intracellular injections of EGTA block induction of hippocampal long-term potentiation. Nature, Lond. 305, 719–721.CrossRefGoogle ScholarPubMed
Madison, D. V., Malenka, R. C. & Nicoll, R. A. (1991). Mechanisms underlying long-term potentiation of synaptic transmission. Ann. Rev. Neurosci. 124, 379–397.CrossRefGoogle Scholar
Malenka, R. C. & Nicoll, R. A. (1993). MBDA-receptor-dependent synaptic plasticity: Multiple forms and mechanisms. Trends Neurosci. 16, 521–527.CrossRefGoogle ScholarPubMed
Malsburg, C. v. D. (1971). Self-organization of orientation sensitive cells in the striate cortex. Kybernetik 14, 85–100.CrossRefGoogle Scholar
Malsburg, C. V. D. (1979). Development of ocularity domains and growth behavior of axon terminals. Biol. Cybern. 32, 49–62.CrossRefGoogle ScholarPubMed
Marr, D. (1971). Simple memory: A theory for archicortex. Phil. Trans. R. Soc. Lond. B 262, 21–81.Google ScholarPubMed
Maunsell, J. H. R. & Newsome, W. T. (1987). Visual processing in monkey extrastriate cortex. Ann. Rev. Neurosci. 10, 363.CrossRefGoogle ScholarPubMed
McCormick, D. A. (1990). Membrane properties and neurotransmitter actions. In The Synaptic Organization of the Brain (ed. Shepherd, G. M.), pp. 32–66. New York: Oxford University Press.Google Scholar
McCulloch, W. S. & Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5, 115–133.CrossRefGoogle Scholar
MacKay, D. J. C. & Miller, K. D. (1990). Analysis of Linsker's application of Hebian rules to linear networks. Network 1, 257–299.CrossRefGoogle Scholar
Middlebrooks, J. C., Clock, A. E., Xu, L. & Green, D. M. (1994). A panoramic code for sound location by cortical neurons. Science, N. Y. 264, 842–844.CrossRefGoogle ScholarPubMed
Miles, R. & Wong, R. K. S. (1987). Inhibitory control of local excitatory circuits in the guinea-pig hippocampus. J. Physiol. Lond. 388, 611–629.CrossRefGoogle ScholarPubMed
Miller, J. P., Jacobs, G. A. & Theunissen, F. (1991). Representation of sensory information in the cricket cereal sensory system. I. Response properties of the primary interneurons. J. Neurophysiol. 66, 1680–1689.CrossRefGoogle Scholar
Miller, K. D. (1990). Correlation-based models of neural development. In Neuroscience and Connectionist Theory (ed. Gluck, M. A. and Rumelhart, D. E.), pp. 267–354. New York: Lawrence Erlbaum, Hillsdale.Google Scholar
Miller, K. D. (1992). Models of activity-dependent neural development. Seminars in Neurosci. 4, 61–73.CrossRefGoogle Scholar
Miller, K. D. (1994). A model for the development of simple cell receptive fields and the ordered arrangement of orientation columns through activity-dependent competition between on- and off-center inputs. J. Neurosci. 14, 409–441.CrossRefGoogle Scholar
Miller, K. D. & MacKay, D. J. C. (1994). The role of constraints in Hebbian learning. Neural Comp. 6, 100–126.CrossRefGoogle Scholar
Morris, R. G. M., Anderson, E., Lunch, G. S. & Baudry, M. (1986). Selective impairment of learning and blockade of long-term potentiation by an N-methyl-D-aspartate receptor antagonist, AP5. Nature, Lond. 319, 774–776.CrossRefGoogle ScholarPubMed
Oja, E. (1982). A simplified neuron model as a principal component analyzer. J. Math. Biol. 15, 267–273.CrossRefGoogle ScholarPubMed
O'Keefe, J. (1979). A review of the hippocampal place cells. Prog. Neurobiol. 13, 419–439.CrossRefGoogle ScholarPubMed
O'Keefe, J. & Dostovsky, J. (1971). The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely moving rat. Brain Res. 34, 171–175.CrossRefGoogle ScholarPubMed
O'Keefe, J. & Nadel, L. (1978). The Hippocampus as a Cognitive Map. Oxford: Clarendon.Google Scholar
O'Neill, W. E. & Suga, N. (1982). Encoding of target range information and its representation in the auditory cortex of the mustache bat. J. Neurosci. 2, 17–31.CrossRefGoogle Scholar
Optican, L. M. & Richmond, B. J. (1987). Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. III. Information theoretic analysis. J. Neurophysiol. 57, 163–178.CrossRefGoogle ScholarPubMed
Orban, G. A. (1984). Neuronal Operations in the Visual Cortex. Berlin: Springer.CrossRefGoogle Scholar
Paradiso, M. A. (1988). A theory for the use of visual orientation information which exploits the columnar structure of striate cortex. Biol. Cybern. 58, 35–49.CrossRefGoogle ScholarPubMed
Rall, W. (1962). Theory of physiological properties of dendrites. Ann. N. Y. Acad. Sci. 96, 1071–1092.CrossRefGoogle ScholarPubMed
Rall, W. (1964). Theoretical significance of dendritic trees for neuronal input-output relations. In Neural Theory and Modeling (ed. Reiss, R.), pp. 73–97. Stanford CA: Stanford University Press.Google Scholar
Rall, W. (1977). Core conductor theory and cable properties of neurons. In Handbook of Physiology, vol. 1 (ed. Kandel, E. R.), pp. 39–97. Amer. Physiol. Soc, Bethesda.Google Scholar
Rapp, M., Yarom, Y. & Segev, I. (1992). The impact of parallel background activity on the cable properties of cerebellar Purkinje cells. Neural. Comp. 4, 518–533.CrossRefGoogle Scholar
Reike, F. M. (1991). Physical Principles Underlying Sensory Processing and Computation. Ph.D. thesis. University of California Berkeley.Google Scholar
Rinzel, J. & Ermentrout, G. G. (1989). Analysis of neural excitability and oscillations. In Methods in Neuronal Modeling (ed. Koch, C. and Segev, I.). Cambridge MA: MIT Press.Google Scholar
Rolls, E. T. (1989). Parallel distributed processing in the brain: Implications of the functional architecture of neuronal networks in the hippocampus. In Parallel Distributed Processing: Implications for Psychology and Neuroscience (ed. Morris, R. G. M.), pp. 286–308. Oxford: Oxford University Press.Google Scholar
Rosenmund, C., Clements, J. D. & Westbrook, G. L. (1993). Nonuniform probability of glutamate release at a hippocampal synapse. Science, N. Y. 262, 754–758.CrossRefGoogle Scholar
Salinas, E. & Abbott, L. F. (1994). Vector reconstruction from firing rates. J. Comp. Neurosci. 1, 89–107.CrossRefGoogle ScholarPubMed
Salzman, C. D. & Newsome, W. T. (1994). Neural mechanisms for forming a perceptual decision. Science, N. Y. 264, 231–237.CrossRefGoogle ScholarPubMed
Schwartz, A., Kettner, R. E. & Georgopoulos, A. P. (1988). Primate motor cortex and free arm movements to visual targets in three-dimensional space. I. Relations between single cell discharge and direction of movement. Neurosci. 8, 2913–2927.CrossRefGoogle ScholarPubMed
Segev, I. & Parnas, I. (1989). Synaptic integration mechanisms: a theoretical and experimental investigation of temporal postsynaptic interaction between excitatory and inhibitory input. Biophys. J. 41, 41–50.CrossRefGoogle Scholar
Sejnowski, T. J. (1977). Storing covariance with nonlinearly interacting neurons. J. Math. Biol. 4, 303–321.CrossRefGoogle Scholar
Sejnowski, T. J. (1988). Neural populations revealed. Nature, Lond. 332, 308.CrossRefGoogle Scholar
Seung, H. S. & Sompolinsky, H. (1993). Simple models for reading neuronal population codes. Proc. natn. Acad. Sci. U.S.A. 90, 10749–10753.CrossRefGoogle ScholarPubMed
Shatz, J. C. (1990). Impulse activity and the patterning of connections during CNS development. Neuron 5, 745–756.CrossRefGoogle ScholarPubMed
Shor, R. H., Miller, A. D. & Tomko, D. L. (1984). Responses to head tilt in cat central vestibular neurons. I. Direction of maximum sensitivity. J. Neurophysiol. 51, 136–146.CrossRefGoogle Scholar
Smetters, D. K. & Nelson, S. B. (1993). Estimates of functional synaptic convergence in rat and cat visual cortical neurons. Neurosci. Abstr. 16, 263.Google Scholar
Snippe, H. P. & Koenderink, J. J. (1992). Discrimination thresholds for channel-coded systems. Biol. Cybern. 66, 543–551.CrossRefGoogle Scholar
Steinmetz, M. A., Motter, B.C., Duffy, C. J. & Mountcastle, V. B. (1987). Functional properties of parietal visual neurons: Radial organization of directionalities with the visual field. J. Neurosci. 7, 177–191.CrossRefGoogle ScholarPubMed
Stevens, C. F. (1989). How cortical interconnectedness varies with network size. Neural Comp. 1, 473–479.CrossRefGoogle Scholar
Suzuki, I., Timerick, J. B. & Wilson, V. J. (1985). Body position with respect to the head or body position in space is coded in lumbar interneurons. J. Neurophysiol. 54, 123–133.CrossRefGoogle Scholar
Swindale, N. V. (1980). A model for the formation of ocular dominance stripes. Proc. R. Soc. Lond. B 208, 243–264.Google Scholar
Taube, J. S., Muller, R. I. & Ranck, J. B. J. (1990). Head direction cells recorded from the postsubicullum in freely moving rats. I. Description and quantitative analysis. J. Neurosci. 10, 420–435.CrossRefGoogle Scholar
Theunissen, F. (1993). An Investigation of Sensory Coding Principles Using Advanced Statistical Techniques. Berkeley Ph.D. thesis. University of California.Google Scholar
Theunissen, F. & Miller, J. P. (1991). Representation of sensory information in the cricket cereal sensory system. II. Information theoretic calculation of system accuracy and optimal tuning-curve widths of four primary interneurons. J. Neurophysiol. 66, 1690–1703.CrossRefGoogle Scholar
Touretzky, D. S., Redish, A. D. & Wan, H. S. (1993). Neural representation of space using sinusoidal arrays. Neural Comp. 5, 869–884.CrossRefGoogle Scholar
Tuckwell, H. C. (1988). Introduction to Theoretical Neurobiology. Cambridge: Cambridge University Press.Google Scholar
Turrigiano, G., Abbott, L. F. & Marder, E. (1994). Activity-dependent changes in the intrinsic properties of cultured neurons. Science, N. Y. 264, 974–977.CrossRefGoogle ScholarPubMed
Van Gisbergen, J. A. M., Van Opstal, A. J. & Tax, A. M. M. (1987). Collicular ensemble coding of saccades based on vector summation. Neuroscience 21, 541–555.CrossRefGoogle ScholarPubMed
Van Opstal, A. J. & Kappen, H. (1993). A two-dimensional ensemble coding model for spatial-temporal transformation of saccades in monkey superior colliculus. Network 4, 19–38.CrossRefGoogle Scholar
Vogels, R. (1990). Population coding of stimulus orientation by cortical cells. J. Neurosci. 10, 3543–3558.CrossRefGoogle Scholar
Warland, D., Landolfa, M. A., Miller, J. P. & Bialek, W. (1991). Reading between the spikes in the cereal filiform hair receptors of the cricket. In Analysis and Modeling of Neural Systems (ed. Eeckman, F. and Bower, J.). Norwell, MA: Kluwer Academic Publishers.Google Scholar
Wilson, H. R. & Cowan, J. D. (1972). Excitatory and inhibitory interactions. in localized populations of model neurons. Biophys. J. 12, 1–24.CrossRefGoogle ScholarPubMed
Wilson, H. R. & Cowan, J. D. (1973). A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybern. 13, 55–80.CrossRefGoogle ScholarPubMed
Wilson, M. A. & McNaughton, B. (1993). Dynamics of the hippocampal ensemble code for space. Science, N.Y. 261, 1055–1058.CrossRefGoogle ScholarPubMed
Young, M. P. & Yamane, S. (1992). Sparse population coding of faces in the inferotemporal cortex. Science, N. Y. 256, 1327–1331.CrossRefGoogle Scholar
Zhang, J. & Miller, J. P. (1991). A mathematical model for resolution enhancement in layered sensory systems. Biol. Cybern. 64, 357–364.CrossRefGoogle ScholarPubMed
Zohary, E. (1992). Population coding of visual stimuli by cortical neurons tuned to more than one dimension. Biol. Cybern. 66, 265–272.CrossRefGoogle ScholarPubMed