What Is Stochastic Resonance? Definitions, Misconceptions, Debates, and Its Relevance to Biology

PLoS Computational Biology - Tập 5 Số 5 - Trang e1000348
Mark D. McDonnell1, Derek Abbott2
1Institute for Telecommunications Research, University of South Australia, Mawson Lakes, South Australia, Australia
2Centre for Biomedical Engineering and School of Electrical & Electronic Engineering, University of Adelaide, Adelaide, South Australia, Australia

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R Guantes, 2006, Dynamical principles of two-component genetic oscillators., PLoS Comput Biol, 2, e30, 10.1371/journal.pcbi.0020030

US Bhalla, 2008, How to record a million synaptic weights in a hippocampal slice., PLoS Comput Biol, 4, e1000098, 10.1371/journal.pcbi.1000098

AR McIntosh, 2008, Increased brain signal variability accompanies lower behavioral variability in development., PLoS Comput Biol, 4, e1000106, 10.1371/journal.pcbi.1000106

Y Tanouchi, 2008, Noise reduction by diffusional dissipation in a minimal quorum sensing motif., PLoS Comput Biol, 4, e1000167, 10.1371/journal.pcbi.1000167

AA Faisal, 2008, Noise in the nervous system., Nature Reviews Neuroscience, 9, 292, 10.1038/nrn2258

RB Stein, 2005, Neuronal variability: noise or part of the signal?, Nature Reviews Neuroscience, 6, 389, 10.1038/nrn1668

GB Ermentrout, 2008, Reliability, synchrony and noise., Trends in Neurosciences, 31, 428, 10.1016/j.tins.2008.06.002

MW Klymkowsky, 2008, Recognizing student misconceptions through ed's tools and the biology concept inventory., PLoS Biol, 6, e3, 10.1371/journal.pbio.0060003

WJ Ma, 2006, Bayesian inference with probabilistic population codes., Nature Neuroscience, 9, 1432, 10.1038/nn1790

DC Knill, 2004, The bayesian brain: the role of uncertainty in neural coding and computation., Trends in Neuroscience, 27, 712, 10.1016/j.tins.2004.10.007

A Ghosh, 2008, Noise during rest enables the exploration of the brain's dynamic repertoire., PLoS Comput Biol, 4, e1000196, 10.1371/journal.pcbi.1000196

G Deco, 2008, The dynamic brain: From spiking neurons to neural masses and cortical fields., PLoS Comput Biol, 4, e1000092, 10.1371/journal.pcbi.1000092

C Blomberg, 2006, Fluctuations for good and bad: The role of noise in living systems., Physics of Life Reviews, 3, 133, 10.1016/j.plrev.2006.06.001

M Kaern, 2005, Stochasticity in gene expression: from theories to phenotypes., Nature Reviews Genetics, 6, 451, 10.1038/nrg1615

MD McDonnell, 2008, Stochastic Resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantisation, 10.1017/CBO9780511535239

R Benzi, 1981, The mechanism of stochastic resonance., Journal of Physics A: Mathematical and General, 14, L453, 10.1088/0305-4470/14/11/006

R Benzi, 1982, Stochastic resonance in climatic change., Tellus, 34, 10, 10.3402/tellusa.v34i1.10782

C Nicolis, 1981, Solar variability and stochastic effects on climate., Solar Physics, 74, 473, 10.1007/BF00154530

C Nicolis, 1982, Stochastic aspects of climatic transitions—response to a periodic forcing., Tellus, 34, 1, 10.3402/tellusa.v34i1.10781

P Jung, 1993, Periodically driven stochastic systems., Physics Reports—Review Section of Physics Letters, 234, 175

F Moss, 1994, Stochastic resonance—tutorial and update., International Journal of Bifurcation and Chaos, 4, 1383, 10.1142/S0218127494001118

MI Dykman, 1995, Stochastic resonance in perspective., Il Nuovo Cimento, 17, 661, 10.1007/BF02451825

K Wiesenfeld, 1995, Stochastic resonance and the benefits of noise: From ice ages to crayfish and SQUIDS., Nature, 373, 33, 10.1038/373033a0

L Gammaitoni, 1998, Stochastic resonance., Reviews of Modern Physics, 70, 223, 10.1103/RevModPhys.70.223

K Wiesenfeld, 1998, Minireview of stochastic resonance., Chaos, 8, 539, 10.1063/1.166335

VS Anishchenko, 1999, Stochastic resonance: Noise enhanced order., Uspekhi Fizicheskikh Nauk, 169, 7, 10.3367/UFNr.0169.199901c.0007

T Wellens, 2004, Stochastic resonance., Reports on Progress in Physics, 67, 45, 10.1088/0034-4885/67/1/R02

V Shatokhin, 2004, The noise makes the signal: What a small fry should know about stochastic resonance., Journal of Modern Optics, 51, 851, 10.1080/09500340408233602

DG Luchinsky, 1999, Stochastic resonance in electrical circuits—I: Conventional stochastic resonance., IEEE Transactions on Circuits and Systems—II: Analog and Digital Signal Processing, 46, 1205, 10.1109/82.793710

DG Luchinsky, 1999, Stochastic resonance in electrical circuits—II: Nonconventional stochastic resonance., IEEE Transactions on Circuits and Systems—II: Analog and Digital Signal Processing, 46, 1215, 10.1109/82.793711

B Andò, 2000, Stochastic Resonance: Theory and Applications, 10.1007/978-1-4615-4391-6

GP Harmer, 2002, A review of stochastic resonance: Circuits and measurement., IEEE Transactions on Instrumentation and Measurement, 51, 299, 10.1109/19.997828

LM Ward, 2002, Dynamical Cognitive Science

P Hänggi, 2002, Stochastic resonance in biology: How noise can enhance detection of weak signals and help improve biological information processing., Chemphyschem, 3, 285, 10.1002/1439-7641(20020315)3:3<285::AID-CPHC285>3.0.CO;2-A

F Moss, 2004, Stochastic resonance and sensory information processing: a tutorial and review of application., Clinical Neurophysiology, 115, 267, 10.1016/j.clinph.2003.09.014

F Moss, 1995, The benefits of background noise., Scientific American, 273, 50, 10.1038/scientificamerican0895-66

AR Bulsara, 1996, Tuning in to noise., Physics Today, 49, 39, 10.1063/1.881491

HC von Baeyer, 2003, Information: The New Language of Science

B Kosko, 2006, Noise., Viking

C Rouvas-Nicolis, 2007, Stochastic resonance., Scholarpedia, 2, 1474, 10.4249/scholarpedia.1474

S Fauve, 1983, Stochastic resonance in a bistable system., Physics Letters A, 97A, 5, 10.1016/0375-9601(83)90086-5

VS Anishchenko, 1994, Stochastic resonance in Chua&apos;s circuit driven by amplitude or frequency-modulated signals., International Journal of Bifurcation and Chaos, 4, 441, 10.1142/S0218127494000290

R Benzi, 1985, Stochastic resonance in the Landau-Ginzburg equation., Journal of Physics A: Mathematical and General, 18, 2239, 10.1088/0305-4470/18/12/022

G Hu, 1990, Periodically forced Fokker-Planck equation and stochastic resonance., Physical Review A, 42, 2030, 10.1103/PhysRevA.42.2030

B McNamara, 1988, Observation of stochastic resonance in a ring laser., Physical Review Letters, 60, 2626, 10.1103/PhysRevLett.60.2626

JM Iannelli, 1994, Stochastic resonance in a semiconductor distributed feedback laser., Applied Physics Letters, 65, 1983, 10.1063/1.112838

A Bulsara, 1991, Stochastic resonance in a single neuron model—theory and analog simulation., Journal of Theoretical Biology, 152, 531, 10.1016/S0022-5193(05)80396-0

A Longtin, 1991, Time-interval sequences in bistable systems and the noise-induced transmission of information by sensory neurons., Physical Review Letters, 67, 656, 10.1103/PhysRevLett.67.656

JK Douglass, 1993, Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance., Nature, 365, 337, 10.1038/365337a0

JE Levin, 1996, Broadband neural encoding in the cricket cercal sensory system enhanced by stochastic resonance., Nature, 380, 165, 10.1038/380165a0

P Cordo, 1996, Noise in human muscle spindles., Nature, 383, 769, 10.1038/383769a0

BJ Gluckman, 1996, Stochastic resonance in a neuronal network from mammalian brain., Physical Review Letters, 77, 4098, 10.1103/PhysRevLett.77.4098

DS Leonard, 1994, Stochastic resonance in a chemical-reaction., Physical Review E, 49, 1734, 10.1103/PhysRevE.49.1734

SM Bezrukov, 1995, Noise-induced enhancement of signal transduction across voltage-dependent ion channels., Nature, 378, 362, 10.1038/378362a0

AD Hibbs, 1995, Stochastic resonance in a superconducting loop with a Josephson-junction., Journal of Applied Physics, 77, 2582, 10.1063/1.358720

DF Russell, 1999, Use of behavioural stochastic resonance by paddle fish for feeding., Nature, 402, 291, 10.1038/46279

PE Greenwood, 2000, Stochastic resonance enhances the electrosensory information available to paddlefish for prey capture., Physical Review Letters, 84, 4773, 10.1103/PhysRevLett.84.4773

JA Freund, 2002, Behavioral stochastic resonance: How the noise from a daphnia swarm enhances individual prey capture by juvenile paddlefish., Journal of Theoretical Biology, 214, 71, 10.1006/jtbi.2001.2445

A Blarer, 1999, Resonance effects and outbreaks in ecological time series., Ecology Letters, 2, 167, 10.1046/j.1461-0248.1999.00067.x

J Paulsson, 2000, Random signal fluctuations can reduce random fluctuations in regulated components of chemical regulatory networks., Physical Review Letters, 84, 5447, 10.1103/PhysRevLett.84.5447

J Paulsson, 2000, Stochastic focusing: Fluctuation-enhanced sensitivity of intracellular regulation., Proceedings of the National Academy of Sciences of the USA, 97, 7148, 10.1073/pnas.110057697

XM Mao, 2002, Stochastic resonance in a financial model., Chinese Physics, 11, 1106, 10.1088/1009-1963/11/11/303

JJ Collins, 1996, Noise-enhanced tactile sensation., Nature, 383, 770, 10.1038/383770a0

E Simonotto, 1997, Visual perception of stochastic resonance., Physical Review Letters, 78, 1186, 10.1103/PhysRevLett.78.1186

LM Ward, 2002, Stochastic resonance in psychophysics and in animal behavior., Biological Cybernetics, 87, 91, 10.1007/s00422-002-0328-z

LM Ward, 2004, Psychophysics of stochastic resonance., Fluctuation and Noise Letters, 4, L11, 10.1142/S0219477504001616

IY Lee, 2003, Nanosignal processing: Stochastic resonance in carbon nanotubes that detect subthreshold signals., Nano Letters, 3, 1683, 10.1021/nl0348239

I Lee, 2006, Noise-enhanced detection of subthreshold signals with carbon nanotubes., IEEE Transactions on Nanotechnology, 5, 613, 10.1109/TNANO.2006.883476

RL Badzey, 2005, Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance., 10.1038/nature04124

AR Bulsara, 2005, No-nuisance noise., Nature, 437, 962, 10.1038/437962a

C Tao, 2008, Dynamic interfaces in an organic thin film., Proceedings of the National Academy of Sciences of the USA, 105, 16418, 10.1073/pnas.0805811105

R Wallace, 1997, AIDS, tuberculosis, violent crime, and low birthweight in eight US metropolitan areas: Public policy, stochastic resonance, and the regional diffusion of inner-city markers., Environment and Planning A, 29, 525, 10.1068/a290525

L Gammaitoni, 1995, Stochastic resonance and the dithering effect in threshold physical systems., Physical Review E, 52, 4691, 10.1103/PhysRevE.52.4691

CR Doering, 1995, Randomly rattled ratchets., Il Nuovo Cimento, 17, 685, 10.1007/BF02451826

JA Paradiso, 2005, Energy scavenging for mobile and wireless electronics., IEEE Pervasive Computing, 4, 18, 10.1109/MPRV.2005.9

L Schuchman, 1964, Dither signals and their effect on quantization noise., IEEE Transactions on Communications, COM-12, 162, 10.1109/TCOM.1964.1088973

RM Gray, 1993, Dithered quantizers., IEEE Transactions on Information Theory, 39, 805, 10.1109/18.256489

RA Wannamaker, 2000, A theory of non-subtractive dither., IEEE Transactions on Signal Processing, 48, 499, 10.1109/78.823976

AS Pikovsky, 1997, Coherence resonance in a noise-driven excitable system., Physical Review Letters, 78, 775, 10.1103/PhysRevLett.78.775

SG Lee, 1998, Coherence resonance in a Hodgkin-Huxley neuron., Physical Review E, 57, 3292, 10.1103/PhysRevE.57.3292

GP Harmer, 1999, Losing strategies can win by Parrondo&apos;s paradox., Nature, 402, 864, 10.1038/47220

DJ Watts, 1998, Collective dynamics of “small-world” networks., Nature, 393, 440, 10.1038/30918

X Yu, 1989, Studies with spike initiators: Linearization by noise allows continuous signal modulation in neural networks., IEEE Transactions on Biomedical Engineering, 36, 36, 10.1109/10.16447

MI Dykman, 1994, Noise-induced linearisation., Physics Letters A, 193, 61, 10.1016/0375-9601(94)91001-4

GK Basak, 2001, Stabilization of dynamical systems by adding a colored noise., IEEE Transactions on Automatic Control, 46, 1107, 10.1109/9.935065

A Neiman, 1994, Synchronization-like phenomena in coupled stochastic bistable systems., Physical Review E, 49, 3484, 10.1103/PhysRevE.49.3484

K Matsumoto, 1985, Information theoretical approach to noisy dynamics., Journal of Physics A: Mathematical and General, 18, 3561, 10.1088/0305-4470/18/18/017

J von Neumann, 1944, Theory of Games and Economic Behaviour.

A Allison, 2000, Some benefits of random variables in switched control systems., Microelectronics Journal, 31, 515, 10.1016/S0026-2692(00)00024-0

N Gershenfeld, 1999, The Nature of Mathematical Modeling

S Kirkpatrick, 1983, Optimisation by simulated annealing., Science, 220, 671, 10.1126/science.220.4598.671

RM Narayanan, 2005, Implementation of fully polarimetric random noise radar., IEEE Antennas and Wireless Propagation Letters, 4, 125, 10.1109/LAWP.2005.844653

GP Harmer, 2001, Motion detection and stochastic resonance in noisy environments., Microelectronics Journal, 32, 959, 10.1016/S0026-2692(01)00094-5

D Abbott, 2001, Overview: Unsolved problems of noise and fluctuations., Chaos, 11, 526, 10.1063/1.1398543

S Zozor, 2005, Noise-aided processing: revisiting dithering in a sigma-delta quantizer., IEEE Transactions on Signal Processing, 53, 3202, 10.1109/TSP.2005.851119

AR Bulsara, 1996, Threshold detection of wideband signals: A noise induced maximum in the mutual information., Physical Review E, 54, R2185, 10.1103/PhysRevE.54.R2185

C Heneghan, 1996, Information measures quantifying aperiodic stochastic resonance., Physical Review E, 54, R2228, 10.1103/PhysRevE.54.R2228

JJ Collins, 1996, Aperiodic stochastic resonance., Physical Review E, 54, 5575, 10.1103/PhysRevE.54.5575

M Stemmler, 1996, A single spike suffices: The simplest form of stochastic resonance in model neurons., Network: Computation in Neural Systems, 7, 687, 10.1088/0954-898X_7_4_005

L Gammaitoni, 1995, Stochastic resonance as a bona fide resonance., Physical Review Letters, 74, 1052, 10.1103/PhysRevLett.74.1052

MH Choi, 1998, Quantifying stochastic resonance in bistable systems: Response vs residence-time distribution functions., Physical Review E, 57, 6335, 10.1103/PhysRevE.57.6335

G Giacomelli, 1999, Stochastic and bona fide resonance: An experimental investigation., Physical Review Letters, 82, 675, 10.1103/PhysRevLett.82.675

F Marchesoni, 2000, Numerical verification of bona fide stochastic resonance., Physical Review E, 62, 146, 10.1103/PhysRevE.62.146

Z Gingl, 1995, Non-dynamical stochastic resonance: Theory and experiments with white and arbitrarily coloured noise., Europhysics Letters, 29, 191, 10.1209/0295-5075/29/3/001

RA Wannamaker, 2000, Stochastic resonance as dithering., Physical Review E, 61, 233, 10.1103/PhysRevE.61.233

B McNamara, 1989, Theory of stochastic resonance., Physical Review A, 39, 4854, 10.1103/PhysRevA.39.4854

JJ Collins, 1995, Aperiodic stochastic resonance in excitable systems., Physical Review E, 52, R3321, 10.1103/PhysRevE.52.R3321

JJ Collins, 1996, Noise-enhanced information transmission in rat SA1 cutaneous mechanoreceptors via aperiodic stochastic resonance., Journal of Neurophysiology, 76, 642, 10.1152/jn.1996.76.1.642

K Wiesenfeld, 1991, Amplification by globally coupled arrays—coherence and symmetry., Physical Review A, 44, 3543, 10.1103/PhysRevA.44.3543

JF Lindner, 1995, Array enhanced stochastic resonance and spatiotemporal synchronization., Physical Review Letters, 75, 3, 10.1103/PhysRevLett.75.3

NG Stocks, 2000, Suprathreshold stochastic resonance in multilevel threshold systems., Physical Review Letters, 84, 2310, 10.1103/PhysRevLett.84.2310

MD McDonnell, 2002, A characterization of suprathreshold stochastic resonance in an array of comparators by correlation coefficient., Fluctuation and Noise Letters, 2, L205, 10.1142/S0219477502000786

T Hoch, 2003, Optimal noise-aided signal transmission through populations of neurons., Physical Review E, 68, 011911, 10.1103/PhysRevE.68.011911

D Rousseau, 2003, Suprathreshold stochastic resonance and noise-enhanced Fisher information in arrays of threshold devices., Physical Review E, 68, 031107, 10.1103/PhysRevE.68.031107

CJ Tessone, 2005, System size stochastic resonance in a model for opinion formation., Physica A—Statistical Mechanics and Its Applications, 351, 106, 10.1016/j.physa.2004.12.012

A Lopera, 2006, Ghost stochastic resonance with distributed inputs in pulse-coupled electronic neurons., Physical Review E, 73, 021101, 10.1103/PhysRevE.73.021101

CJ Tessone, 2006, Diversity-induced resonance., Physical Review Letters, 97, 194101, 10.1103/PhysRevLett.97.194101

AR Bulsara, 1991, Single neuron dynamics: Noise-enhanced signal processing., 420

J Maddox, 1991, Towards the brain-computer&apos;s code?, Nature, 352, 469, 10.1038/352469a0

A Longtin, 1993, Stochastic resonance in neuron models., Journal of Statistical Physics, 70, 309, 10.1007/BF01053970

DR Chialvo, 1993, Modulated noisy biological dynamics—three examples., Journal of Statistical Physics, 70, 375, 10.1007/BF01053974

A Bulsara, 1993, Single effective neuron: Dendritic coupling effect and stochastic resonance., Biological Cybernetics, 70, 145, 10.1007/BF00200828

A Longtin, 1994, Bistability and the dynamics of periodically forced sensory neurons., Biological Cybernetics, 70, 569, 10.1007/BF00198810

L Emberson, 2007, Endogenous neural noise and stochastic resonance. SPIE Noise and Fluctuations in Biological, Biophysical, and Biomedical Systems; 21–23 May 2007; Florence, Italy., Proceedings SPIE Noise and Fluctuations in Biological, Biophysical, and Biomedical Systems, 6602, 66020T(1–12)

JM Fellous, 2003, Synaptic background noise controls the input/output characteristics of single cells in an in vitro model of in vivo activity., Neuroscience, 122, 811, 10.1016/j.neuroscience.2003.08.027

H Lecar, 1971, Theory of threshold fluctuations in nerves. I. Relationships between electrical noise and fluctuations in axon firing., Biophysical Journal, 11, 1048

H Lecar, 1971, Theory of threshold fluctuations in nerves. II. Analysis of various sources of membrane noise., Biophysical Journal, 11, 1068, 10.1016/S0006-3495(71)86278-1

W Horsthemke, 1980, Voltage-noise–induced transitions in electrically excitable membranes., Biophysical Journal, 35, 415, 10.1016/S0006-3495(81)84799-6

HA Braun, 1994, Oscillation and noise determine signal transduction in shark multimodal sensory cells., Nature, 367, 270, 10.1038/367270a0

G Buzsáki, 2004, Neuronal oscillations in cortical networks., Science, 304, 1926, 10.1126/science.1099745

TJ Sejnowski, 2006, Network oscillations: Emerging computational principles., The Journal of Neuroscience, 26, 1673, 10.1523/JNEUROSCI.3737-05d.2006

N Brunel, 2003, What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation–inhibition balance., Journal of Neurophysiology, 90, 415, 10.1152/jn.01095.2002

MD McDonnell, 2008, Maximally informative stimuli and tuning curves for sigmoidal rate-coding neurons and populations., Physical Review Letters, 101, 058103, 10.1103/PhysRevLett.101.058103

P Lansky, 2007, Optimal signal in sensory neurons under an extended rate coding concept., BioSystems, 89, 10, 10.1016/j.biosystems.2006.04.010

J Tougaard, 2000, Stochastic resonance and signal detection in an energy detector—implications for biological receptor systems., Biological Cybernetics, 83, 471, 10.1007/s004220000176

J Tougaard, 2002, Signal detection theory, detectability and stochastic resonance effects., Biological Cybernetics, 87, 79, 10.1007/s00422-002-0327-0

M DeWeese, 1995, Information flow in sensory neurons., Il Nuovo Cimento, 17, 733, 10.1007/BF02451830

MD McDonnell, 2009, Suprathreshold stochastic resonance., Scholarpedia

MD McDonnell, 2006, Optimal information transmission in nonlinear arrays through suprathreshold stochastic resonance., Physics Letters A, 352, 183, 10.1016/j.physleta.2005.11.068

MD McDonnell, 2009, Stochastic pooling networks., Journal of Statistical Mechanics: Theory and Experiment: Art. No. P01012

MI Dykman, 1998, What can stochastic resonance do?, Nature, 391, 344, 10.1038/34812

ME Inchiosa, 2000, Information-theoretic stochastic resonance in noise-floor limited systems: The case for adding noise., Physical Review Letters, 85, 3369, 10.1103/PhysRevLett.85.3369

S Kay, 2000, Can detectability be improved by adding noise?, IEEE Signal Processing Letters, 7, 8, 10.1109/97.809511

P Hänggi, 2000, Nonlinear stochastic resonance: The saga of anomalous output–input gain., Physical Review E, 62, 6155, 10.1103/PhysRevE.62.6155

S Zozor, 2003, Stochastic resonance in locally optimal detectors., IEEE Transactions on Signal Processing, 51, 3177, 10.1109/TSP.2003.818905

S Zozor, 2007, On pooling networks and fluctuation in suboptimal detection framework., Fluctuation and Noise Letters, 7, L39, 10.1142/S0219477507003684

H Chen, 2007, Theory of the stochastic resonance effect in signal detection: Part I: fixed detectors., IEEE Transactions on Signal Processing, 55, 3172, 10.1109/TSP.2007.893757

F Chapeau-Blondeau, 2007, Injecting noise to improve performance of optimal detector., Electronics Letters, 43, 897, 10.1049/el:20070502

F Martorell, 2008, Cell architecture for nanoelectronic design., Microelectronics Journal, 39, 1041, 10.1016/j.mejo.2007.10.008

A Priplata, 2002, Noise-enhanced human balance control., Physical Review Letters, 89, 238101, 10.1103/PhysRevLett.89.238101

AA Priplata, 2003, Vibrating insoles and balance control in elderly people., Lancet, 362, 1123, 10.1016/S0140-6736(03)14470-4

JJ Collins, 2003, Noise-enhanced human sensorimotor control., IEEE Engineering in Medicine and Biology Magazine, 22, 76, 10.1109/MEMB.2003.1195700

F Moss, 2003, Balancing the unbalanced., Nature, 425, 911, 10.1038/425911a

JD Harry, 2005, Balancing act (noise based sensory enhancement technology)., IEEE Spectrum, 42, 36, 10.1109/MSPEC.2005.1413729

AA Priplata, 2006, Noise-enhanced balance control in patients with diabetes and patients with stroke., Annals of Neurology, 59, 4, 10.1002/ana.20670

JM Hijmans, 2007, Development of vibrating insoles., International Journal of Rehabilitation Research, 30, 343, 10.1097/MRR.0b013e3282f14469

RP Morse, 1996, Enhancement of vowel coding for cochlear implants by addition of noise., Nature Medicine, 2, 928, 10.1038/nm0896-928

MF Dorman, 2004, The design and function of cochlear implants., American Scientist, 92, 436, 10.1511/2004.49.942

N Hohn, 2001, Shot noise in the leaky integrate-and-fire neuron., Physical Review E, 63, 031902, 10.1103/PhysRevE.63.031902

NG Stocks, 2002, The application of suprathreshold stochastic resonance to cochlear implant coding., Fluctuation and Noise Letters, 2, L169, 10.1142/S0219477502000774

M Chatterjee, 2001, Noise enhances modulation sensitivity in cochlear implant listeners: Stochastic resonance in a prosthetic sensory system?, Journal of the Association for Research in Otolaryngology, 2, 159, 10.1007/s101620010079

RP Morse, 2007, The effect of Gaussian noise on the threshold, dynamic range, and loudness of analogue cochlear implant stimuli., J Assoc Res Otolaryngol, 8, 42, 10.1007/s10162-006-0064-5

AJ Hudspeth, 1989, How the ear&apos;s works work., Nature, 341, 397, 10.1038/341397a0

ER Lewis, 2000, Essential roles of noise in neural coding and in studies of neural coding., Biosystems, 58, 109, 10.1016/S0303-2647(00)00113-1

RP Morse, 2002, An information-theoretic approach to cochlear implant coding., UPoN 2002. Proceedings of the Third International Conference on Unsolved Problems of Noise and Fluctuations in Physics, Biology, and High Technology; Washington, D.C.; 3–6 September 2002. Am Inst Phys Conf Proc, 665, 125

JT Rubinstein, 2003, Signal coding in cochlear implants: exploiting stochastic effects of electrical stimulation., Ann Otol Rhinol Laryngol, 112, 14, 10.1177/00034894031120S904

RP Morse, 2007, Stochastic beamforming for cochlear implant coding. SPIE Noise and Fluctuations in Biological, Biophysical, and Biomedical Systems; 21–23 May 2007; Florence, Italy., Proc SPIE Noise Fluct Biological Biophysical Biomedical Sys, 6602, 66020U

GR Lefevre, 1996, Improved arterial oxygenation after oleic acid lung injury in the pig using a computer-controlled mechanical ventilator., Am Respir Crit Care Med, 154, 1567, 10.1164/ajrccm.154.5.8912782

B Suki, 1998, Life-support system benefits from noise., Nature, 393, 127, 10.1038/30130

JF Brewster, 2005, Convexity, Jensen&apos;s inequality and benefits of noisy mechanical ventilation., J Royal Society Interface, 2, 393, 10.1098/rsif.2005.0043

ME Inchiosa, 1995, Nonlinear dynamic elements with noisy sinusoidal forcing: Enhancing response via nonlinear coupling., Phys Rev E, 52, 327, 10.1103/PhysRevE.52.327

V Galdi, 1998, Evaluation of stochastic-resonance–based detectors of weak harmonic signals in additive white Gaussian noise., Phys Rev E, 57, 6470, 10.1103/PhysRevE.57.6470

BA Olshausen, 1996, Emergence of simple-cell receptive field properties by learning a sparse code for natural images., Nature, 381, 607, 10.1038/381607a0

EC Smith, 2006, Efficient auditory coding., Nature, 439, 978, 10.1038/nature04485

PE Greenwood, 2004, Soft threshold stochastic resonance., Phys Rev E, 70, 051110, 10.1103/PhysRevE.70.051110