A single spike suffices: the simplest form of stochastic resonance in model neurons

References

• Abramowitz M, Stegun I A. Handbook of Mathematical Functions. National Bureau of Standards, Washington, DC 1970, Applied Mathematics Series 55
   Google Scholar
• Adrian E D. The Physical Background of Perception. Clarendon, Oxford 1946
   Google Scholar
• Ahmed B, Anderson J C, Douglas R J, Martin K A C, Nelson C. Comparison of current-discharge relationships of pyramidal neurons from the visual cortex-in vitro and in the anesthetized cat. J. Physiol. London 1995; 485P: P10–11
   Google Scholar
• Barlow H B, Levick W R. Three factors limiting the reliable detection of light by retinal ganglion cells of the cat. J. Physiol. 1969; 200: 1–24
   PubMed Web of Science ®Google Scholar
• Barron A R. Entropy and the central limit theorem. Ann. Probability 1986; 14: 336–42
   Web of Science ®Google Scholar
• Bekkers J M, Stevens C F. Presynaptic mechanism for long-term potentiation in the hippocampus. Nature 1990; 346: 724–29
   PubMed Web of Science ®Google Scholar
• Benzi R, Sutera A, Vulpiani A. The mechanism of stochastic resonance. J. Phys. A: Math. Gen. 1981; 14: L453–7
   Google Scholar
• Bialek W, DeWeese M, Rieke F, Warland D. Bits and brains: Information flow in the nervous system. Physica 1993; 200A: 581–93
   Google Scholar
• Bolshakov V Y, Siegelbaum S A. Regulation of hippocampal transmitter release during development and long-term potentiation. Science 1995; 269: 1730–4
   PubMed Web of Science ®Google Scholar
• Braun H A, Wissing H, Schafer K, Hirsch M C. Oscillation and noise determine signal-transduction in shark multimodal sensory cells. Nature 1994; 367: 270–3
   PubMed Web of Science ®Google Scholar
• Britten K H, Newsome W T, Shadlen M N, Celebrini S, Movshon J A. A relationship between behavioral choice and the visual responses of neurons in Macaque MT. J. Vis. Neurosci. 1996; 13: 87–100
   PubMed Web of Science ®Google Scholar
• Bulsara A R, Lowen S B, Rees C D. Cooperative behavior in the periodically modulated Wiener process-noise-induced complexity in a model neuron. Phys. Rev. E 1994; 49: 4989–5000
   PubMed Web of Science ®Google Scholar
• Bulsara A R, Zador A. Threshold detection of wideband signals: a noise-controlled maximum in the trans-information. Phys. Rev. E 1996; 54: 2185–8
   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
• Carandini M, Heeger D J, Movshon J A. Linearity and gain control in V1 simple cells. Cerebral Cortex, vol X Cortical Models, E G Jones, P S Ulinski. Plenum, New York 1995
   Google Scholar
• Carter G C. Coherence and time delay estimation. Les Houches 1985 Traitement du Signal, J-L Lacoume, T S Durrani, R Stora. North-Holland, Amsterdam 1985; 515–72
   Google Scholar
• Celebrini S, Thorpe S, Trotter Y, Imbert M. Dynamics of orientation coding in area V1 of the awake primate. Vis. Neurosci. 1993; 10: 811–25
   PubMed Web of Science ®Google Scholar
• Collins J J, Chow C C, Imhoff T T. Aperiodic stochastic resonance in excitable systems. Phys. Rev. E 1995a; 52: R3321–4
   PubMed Web of Science ®Google Scholar
• Collins J J, Chow C C, Imhoff T T. Stochastic resonance without tuning. Nature 1995b; 376: 236–8
   PubMed Web of Science ®Google Scholar
• Connor J A, Stevens C F. Prediction of repetitive firing behaviour from voltage clamp data on an isolated neurone soma. J. Physiol. 1971; 213: 31–53
   PubMed Web of Science ®Google Scholar
• Cover T M, Thomas J A. Elements of Information Theory. Wiley-Interscience, New York 1991
   Google Scholar
• Cox D R. Renewal Theory. Methuen, London 1962
   Google Scholar
• DeWeese M R. Optimization principles for the neural code. PhD Thesis. Princeton University. 1995
   Google Scholar
• Douglass J K, Wilkens L, Pantazelou E, Moss F. Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance. Nature 1993; 365: 337–40
   PubMed Web of Science ®Google Scholar
• Fiser J, Subramaniam S, Biederman I. The effect of changing size and spatial frequency content of gray-scale object images in RSVP identification tasks. Invest. Ophthalmol. Vision Sci. 1996; 37 S178
   Web of Science ®Google Scholar
• Gammaitoni L. Stochastic resonance and the dithering effect in threshold physical systems. Phys. Rev. E 1995; 52: 4691–8
   PubMed Web of Science ®Google Scholar
• Gammaitoni L, Marchesoni F, Santucci S. Stochastic resonance as a bona fide, resonance. Phys. Rev. Lett. 1995; 74: 1052–5
   PubMed Web of Science ®Google Scholar
• Gingl Z, Kiss L B, Moss F. Non-dynamical stochastic resonance: theory and experiments with white and arbitrarily coloured noise. Europhys. Lett. 1995; 29: 191–6
   Google Scholar
• Hessler N A, Shirke A M, Malinow R. The probability of transmitter release at a mammalian central synapse. Nature 1993; 366: 569–72
   PubMed Web of Science ®Google Scholar
• Hille B. Ionic Channels of Excitable Membranes. Sinauer Associates, Sunderland, MA 1992
   Google Scholar
• Hines M. NEURON-a program for simulation of nerve equations. Neural Systems: Analysis and Modeling, F Eeckman. Kluwer, Dordrecht 1993; 127–36
   Google Scholar
• Hodgkin A L, Huxley A F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 1952; 117: 500–44
   PubMed Web of Science ®Google Scholar
• Hopfield J J. Neurons, dynamics, and computation. Phys. Today 1994; 47: 40–6
   Web of Science ®Google Scholar
• Jung P. Stochastic resonance and optimal design of threshold detectors. Phys. Lett. 1995; 207A: 93–104
   Google Scholar
• Knight B. Dynamics of encoding in a population of neurons. J. Gen. Physiol. 1972; 59: 734–66
   PubMed Web of Science ®Google Scholar
• Koch C, Bernander Ö, Douglas R J. Do neurons have a voltage or a current threshold for action potential initiation?. J. Comput. Neurosci. 1995; 2: 63–82
   PubMed Web of Science ®Google Scholar
• Levin J, Miller J P. Stochastic resonance in the cricket cercal system. Nature 1996; 380: 165–8
   PubMed Web of Science ®Google Scholar
• Longtin A, Bulsara A, Moss F. Time-interval sequences in bistable systems and the noise-induced transmission of information by sensory neurons. Phys. Rev. Lett. 1991; 67: 656–9
   PubMed Web of Science ®Google Scholar
• Longtin A, Hinzer K. Encoding with bursting, subthreshold oscillations, and noise in mammalian cold receptors. Neural Computat. 1996; 8: 215–55
   PubMed Web of Science ®Google Scholar
• Lukes T. Sequences of stochastic pulses. Proc. Phys. Soc. 1961; 78: 153–68
   Google Scholar
• Mason A, Larkman A. Correlations between morphology and electrophysiology of pyramidal neurons in slices of rat visual cortex. J. Neurosci. 1990; 10: 1415–28
   PubMed Web of Science ®Google Scholar
• McCullough W S, Pitts W. A logical calculus of ideas immanent in nervous activity. Bull. Math. Biophys. 1943; 5: 115–33
   Google Scholar
• McNamara B, Wiesenfeld K. Theory of stochastic resonance. Phys. Rev. A 1989; 39: 4854–69
   PubMed Web of Science ®Google Scholar
• Miller J C P. A method for the determination of converging factors, applied to the asymptotic expansions for the parabolic cylinder functions. Proc. Camb. Phil. Soc. 1952; 48: 243–54
   Google Scholar
• Moss F, Pierson D, O'Gorman D. Stochastic resonance: tutorial and update. Int. J. Bifurc. Chaos 1994; 4: 1383–98
   Web of Science ®Google Scholar
• Newsome W T, Britten K H, Movshon J A. Neuronal correlates of a perceptual decision. Nature 1989; 341: 52–4
   PubMed Web of Science ®Google Scholar
• Paradiso M A. A theory for the use of visual orientation information which exploits the columnar structure of striate cortex. Biol. Cybern. 1988; 58: 35–49
   PubMed Web of Science ®Google Scholar
• Riani M, Simonotto E. Stochastic resonance in the perceptual interpretation of ambiguous figures: a neural network model. Phys. Rev. Lett. 1994; 72: 3120–3
   PubMed Web of Science ®Google Scholar
• Ricciardi L. Diffusion Processes and Related Problems. Springer, Berlin 1977
   Google Scholar
• Seung H S, Sompolinsky H. Simple models for reading neuronal population codes. Proc. Natl Acad. Sci. USA 1993; 90: 10749–53
   PubMed Web of Science ®Google Scholar
• Siegert A J F. On the first passage time probability problem. Phys. Rev. 1951; 81: 617–23
   Web of Science ®Google Scholar
• Softky W R, Koch C. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 1993; 13: 334–50
   PubMed Web of Science ®Google Scholar
• Stein R B. The information capacity of nerve cells using a frequency code. Biophys. J. 1967; 7: 797–826
   PubMed Web of Science ®Google Scholar
• Stemmler M, Usher M, Niebur E. Lateral interactions in primary visual cortex: a model bridging physiology and psychophysics. Science 1995; 269: 1877–80
   PubMed Web of Science ®Google Scholar
• Strogatz S H. Nonlinear Dynamics and Chaos. Addison-Wesley, Reading, MA 1991
   Google Scholar
• Subramaniam S, Biederman I, Kalocsai P, Madigan S F. Accurate identification, but chance recognition memory, of RSVP object pictures. Invest. Ophthalmol. Vision Sci. 1995; 36 S377
   Web of Science ®Google Scholar
• Tovée M J. How fast is the speed of thought?. Curr. Biol. 1994; 4: 1125–7
   PubMed Web of Science ®Google Scholar
• Tovée M J, Rolls E T, Treves A. Information encoding and the responses of single neurons in the primate temporal visual-cortex. J. Neurophysiol. 1993; 70: 640–54
   PubMed Web of Science ®Google Scholar
• Wan F Y M, Tuckwell H C. Neuronal firing and input variability. J. Theor. Neurobiol. 1982; 1: 197–218
   Google Scholar
• Wiesenfeld K, Benz S P, Booi P A A. Phase-locked oscillator optimization for arrays of Josephson junctions. J. Appl. Phys. 1994; 76: 3835–46
   Web of Science ®Google Scholar
• Wiesenfeld K, Moss F. Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs. Nature 1995; 373: 33–6
   PubMed Web of Science ®Google Scholar