Controlling activity fluctuations in large, sparsely connected random networks

References

• Amaral D G, Ishizuka N, Claiborne B. Neurons, numbers and hippocampal networks. Understanding the Brain through the Hippocampus: The Hippocampal Region as a Model for Studying Brain Structure and Function (Progress in Brain Research vol 83), J Storm-Mathisen, et al. Elsevier, Amsterdam 1990; 1–11
   Google Scholar
• Amaral, Witter. Hippocampal formation. The Rat Nervous System2nd edn, G Paxinos. Academic, San Diego, CA 1995; 443–93
   Google Scholar
• Amari S-I. Characteristics of randomly connected threshold-element networks and networks systems. Proc. IEEE 1972; 59: 35–47
   Google Scholar
• Amarasingham A, Levy W B. Predicting the distribution of synaptic strength and cell firing correlations in a self-organizing, sequence prediction model. Neural Comput. 1998; 10: 25–57
   PubMed Web of Science ®Google Scholar
• Amit D J, Brunel N. Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cerebral Cortex 1997; 7: 237–52
   PubMed Web of Science ®Google Scholar
• Andersen P, Trommald M, Jensen V. Low synaptic convergence of CA3 collaterals on CA1 pyramidal cells suggests few release sites. Molecular and Cellular Mechanisms of Neurotransmitter Release, L Stjarne, et al. Raven, New York 1994; 341–51
   Google Scholar
• Buckingham J, Willshaw D. On setting unit thresholds in an incompletely connected associative net. Netw., Comput. Neural Syst. 1993; 4: 441–59
   PubMed Web of Science ®Google Scholar
• Carandini M, Heeger D J. Summation and division by neurons in primate visual-cortex. Science 1994; 264: 1333–6
   PubMed Web of Science ®Google Scholar
• Derrida B, Gardner E, Zippelius A. An exactly solvable asymmetric neural network model. Europhy. Lett. 1987; 4: 167–73
   Google Scholar
• Dusek J A, Eichenbaum H. The hippocampus and memory for orderly stimulus relations. Proc. Natl Acad. Sci. USA 1997; 94: 7109–14
   PubMed Web of Science ®Google Scholar
• Furman G G. Comparison of models for subtractive and shunting lateral-inhibition in receptor-neuron fields. Kybernetik 1965; 2: 257–74
   PubMedGoogle Scholar
• Geman S, Geman D. Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 1984; 6: 721–41
   PubMed Web of Science ®Google Scholar
• Ginzburg I, Sompolinsky H. Theory of correlations in stochastic neural networks. Phys. Rev. E 1994; 50: 3171–91
   PubMed Web of Science ®Google Scholar
• Grossberg S. Nonlinear neural networks: principles, mechanisms, and architectures. Neural Netw. 1988; 1: 17–61
   Web of Science ®Google Scholar
• Hale J, Koçak H. Dynamics and Bifurcations. Springer, New York 1991
   Google Scholar
• Hasselmo M E, Schnell E, Barkai E. Dynamics of learning and recall at excitatory recurrent synapses and cholinergic modulation in rat hippocampal region CA3. J. Neurosci. 1995; 15: 5249–62
   PubMed Web of Science ®Google Scholar
• Hendin O, Horn D, Tsodyks M V. The role of inhibition in an associative memory model of the olfactory bulb. J. Comput. Neurosci. 1997; 4: 173–82
   PubMed Web of Science ®Google Scholar
• Herrmann M, Ruppin E, Usher M. A neural model of the dynamic activation of memory. Biol. Cybern. 1993; 68: 455–63
   PubMed Web of Science ®Google Scholar
• Hinton G E, Sejnowski T J (1983) Optimal perceptual interference. Proc. IEEE Conf. on Computer Vision and Pattern Recognition, Washington, 1983. IEEE, New York, 448–53
   Google Scholar
• Holt G R, Koch C. Shunting inhibition does not have a divisive effect on firing rates. Neural Comput. 1997; 9: 1001–13
   PubMed Web of Science ®Google Scholar
• Hopfield J J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl Acad. Sci. USA 1982; 79: 2554–8
   PubMed Web of Science ®Google Scholar
• Kirkpatrick S, Gelatt C D, Jr, Vecchi M P. Optimization by simulated annealing. Science 1983; 220: 671
   PubMed Web of Science ®Google Scholar
• Lansner A, Fransén E. Modelling Hebbian cell assemblies comprised of cortical neurons. Netw., Comput. Neural Syst. 1992; 3: 105–19
   Web of Science ®Google Scholar
• Levy W B. A computational approach to hippocampal function. Computational Models of Learning in Simple Neural Systems, The Psychology of Learning and Motivation, R D Hawkins, G H Bower. Academic, San Diego, CA 1989; 23: 243–305
   Google Scholar
• Levy W B. A sequence predicting CA3 is a flexible associator that learns and uses context to solve hippocampal-like tasks. Hippocampus 1996; 6: 579–90
   PubMed Web of Science ®Google Scholar
• Levy W B, Wu X B. Controlling performance by controlling activity levels in a model of hippocampal region CA3. II: Memory capacity comes at the expense of context cell firing and compressed coding. INNS World Congress on Neural Networks 1995; 1: 582–6
   Google Scholar
• Levy W B, Wu X B. The relationship of local context codes to sequence length memory capacity. Netw., Comput. Neural Syst. 1996; 7: 371–84
   PubMed Web of Science ®Google Scholar
• Levy W B, Wu X B (1997) A simple, biologically motivated neural network solves the transitive inference problem. Proc. IEEE Int. Conf. on Neural Networks. 1997, 368–71
   Google Scholar
• Levy W B, Wu X B. Some randomness benefits a model of hippocampal function disorder versus order in brain function—essays in theoretical neurobiology. P Århem, et al. World Scientific, Singapore 1999, at press
   Google Scholar
• Levy W B, Sederburg P B, August D. Sequence compression by a hippocampal model: a functional dissection. Computational Neuroscience: Trends in Research, 1998, J M Bower. Plenum, New York 1998; 435–9
   Google Scholar
• Levy W B, Wu X B, Baxter R A. Unification of hippocampal function via computational/coding considerations. Int. J. Neural Systems 1995; 6: 71–80, (suppl.)
   Google Scholar
• Li X G, Somogyi P, Ylinen A, Buzsaki G. The hippocampal CA3 network: an in vivo intracellular labelling study. J. Comput. Neurol. 1994; 339: 181–208
   PubMed Web of Science ®Google Scholar
• Marr D. Simple memory: a theory for archicortex. Phil. Trans. R. Soc. 1971; 262: 23–81
   PubMed Web of Science ®Google Scholar
• McNaughton B L. Cognitive cartography. Nature 1996; 381: 368–9
   PubMed Web of Science ®Google Scholar
• Miles R, Wong R K S. Excitatory synaptic interactions between CA3 neurones in the guinea-pig hippocampus. J. Physiol. 1986; 373: 397–418
   PubMed Web of Science ®Google Scholar
• Milton S J, Arnold J C. Introduction to Probability and Statistics. McGraw-Hill, New York 1990
   Google Scholar
• Minai A A, Levy W B. Predicting complex behaviour in sparse asymmetric networks. Neural Information Processing Systems 5: Natural and Synthetic 1993a; 556–63
   Google Scholar
• Minai A A, Levy W B. The dynamics of sparse random networks. Biol. Cybern. 1993b; 70: 177–87
   PubMed Web of Science ®Google Scholar
• Minai A A, Levy W B. Activity level in random networks. Neural Comput. 1994; 6: 85–99
   Web of Science ®Google Scholar
• Polyn S, Wu X B, Levy W B. Entorhinal/dentate excitation of CA3: a critical variable in hippocampal models. Neurocomputing 1999, at press
   PubMed Web of Science ®Google Scholar
• Simmen M W, Treves A, Rolls E T. Pattern retrieval in threshold linear associative nets. Netw., Comput. Neural Syst. 1996; 7: 109–22
   PubMed Web of Science ®Google Scholar
• Tamamaki N, Nojyo Y. Disposition of the slab-like modules formed by axon branches originating from single CA1 pyramidal neurons in the rat hippocampus. J. Comput. Neurol. 1990; 291: 509–19
   PubMed Web of Science ®Google Scholar
• Tamamaki N, Nojyo Y. Projection of the entorhinal layer II neurons in the rat as revealed by intracellular pressure-injection of neurobiotin. Hippocampus 1993; 3: 471–80
   PubMed Web of Science ®Google Scholar
• Thompson L T, Best E T. Place cells and silent cells in the hippocampus of freely-behaving rats. J. Neurosci. 1989; 9: 2382–90
   PubMed Web of Science ®Google Scholar
• Tsodyks M V, Sejnowski T. Rapid state switching in balanced cortical network models. Netw., Comput. Neural Syst. 1995; 6: 111–24
   Web of Science ®Google Scholar
• Wallenstein G V, Hasselmo M E. GABAergic modulation of hippocampal population activity: sequence learning, place field development, and the phase precession effect. J. Neurophys. 1997; 78: 393–408
   PubMed Web of Science ®Google Scholar
• Wilson H R, Cowan J D. Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 1972; 12: 1–24
   PubMed Web of Science ®Google Scholar
• Wolfram S. Mathematica. Cambridge University Press, Cambridge 1996
   Google Scholar
• Wu X B, Levy W B. Controlling performance by controlling activity levels in a model of hippocampal region CA3. I: overcoming the effect of noise by adjusting network excitability parameters. INNS World Congress on Neural Networks 1995; 1: 577–81
   Google Scholar
• Wu X B, Levy W B. A hippocampal-like neural network model solves the transitive inference problem. Computational Neuroscience: Trends in Research, 1998, J M Bower. Plenum, New York 1998; 567–72
   Google Scholar
• Wu X B, Levy W B. Enhancing the performance of a hippocampal model by increasing variability early in learning. Neurocomputing 1999; 26–27: 601–7
   Web of Science ®Google Scholar