Cited by 2,883stochastic dynamics and bifurcationNeural dynamics and brain functionNeuroscience and Neuropharmacology Research

Noise in the nervous system

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Faisal, A. Aldo, Selen, Luc P. J., Wolpert, Daniel M.·2008·Nature Reviews Neuroscience

Abstract

Noise--random disturbances of signals--poses a fundamental problem for information processing and affects all aspects of nervous-system function. However, the nature, amount and impact of noise in the nervous system have only recently been addressed in a quantitative manner. Experimental and computational methods have shown that multiple noise sources contribute to cellular and behavioural trial-to-trial variability. We review the sources of noise in the nervous system, from the molecular to the behavioural level, and show how noise contributes to trial-to-trial variability. We highlight how noise affects neuronal networks and the principles the nervous system applies to counter detrimental effects of noise, and briefly discuss noise's potential benefits.

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  • QuantNoise permits lower-bit precision without large accuracy loss in many vision and language models.

    “This allows lower-bit precision quantization without significant accuracy drop in many computer vision and natural language processing models.”

    From A Survey of Quantization Methods for Efficient Neural Network Inference (2022) · cites this paper as [59]

    The Cellular noise and Conclusion passages discuss noise and performance in biological nervous systems, not QuantNoise or lower-bit model quantization. Searches for QuantNoise, bit precision, quantization, and accuracy in vision and language models found no passage addressing the claim. (LLM, conf=0.78)

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  1. [1]Adrian ED Zotterman Y The impulses produced by sensory nerve endings. II. The responses of a single end-organ J. Physiol 1926 61 151 171 16993780 PMC1514782
  2. [2]Tomko GJ Crapper DR Neuronal variability: non-stationary responses to identical visual stimuli Brain Res 1974 79 405 418 4422918
  3. [3]Tolhurst DJ Movshon JA Dean AF The statistical reliability of signals in single neurons in cat and monkey visual cortex Vision Res 1983 23 775 785 6623937
  4. [4]Shadlen MN Newsome WT The variable discharge of cortical neurons: implications for connectivity, computation, and information coding J. Neurosci 1998 18 3870 3896 9570816 PMC6793166
  5. [7]Berg HC Purcell EM Physics of chemoreception Biophys. J 1977 20 193 219 911982 PMC1473391
  6. [8]Bialek W Setayeshgar S Physical limits to biochemical signaling Proc. Natl Acad. Sci. USA 2005 102 10040 10045 This paper uses a first-principle approach to show that there are noise limits to biochemical signalling, which should apply to olfaction and intracellular signalling and at the synapse 16006514 PMC1177398
  7. [9]Bialek W Physical limits to sensation and perception Annu. Rev. Biophys. Biophys. Chem 1987 16 455 478 3297091
  8. [10]Lillywhite PG Laughlin SB Transducer noise in a photoreceptor Nature 1979 277 569 572 763342
  9. [11]Barlow HB Levick WR Yoon M Responses to single quanta of light in retinal ganglion cells of the cat Vision Res 1971 11 87 101 5293890
  10. [12]Cover TM Thomas JA Elements of Information Theory 1991 Wiley-Interscience New York
  11. [13]Laughlin SBA John C O'Carroll DC de Ruyter van Steveninck RR Baddeley RHR Foldiak R Information Theory and the Brain 2000 Cambridge Univ. Press
  12. [14]Bryant HL Segundo JP Spike initiation by transmembrane current: a white-noise analysis J. Physiol 1976 260 279 314 978519 PMC1309092
  13. [15]Mainen ZF Sejnowski TJ Reliability of spike timing in neocortical neurons Science 1995 268 1503 1506 7770778
  14. [16]Harsch A Robinson HPC Postsynaptic variability of firing in rat cortical neurons: the roles of input synchronization and synaptic NMDA receptor conductance J. Neurosci 2000 20 6181 6192 10934268 PMC6772582
  15. [17]Schreiber S Fellous J-M Tiesinga P Sejnowski TJ Influence of ionic conductances on spike timing reliability of cortical neurons for suprathreshold rhythmic inputs J. Neurophysiol 2004 91 194 205 14507985 PMC2928819
  16. [18]de Ruyter van Steveninck RR Lewen GD Strong SP Koberle R Bialek W Reproducibility and variability in neural spike trains Science 1997 275 1805 1808 9065407
  17. [19]Berry MJ Warland DK Meister M The structure and precision of retinal spike trains Proc. Natl Acad. Sci. USA 1997 94 5411 5416 9144251 PMC24692
  18. [20]Rieke F Warland D van Steveninck R Bialek W 1997 MIT Press Cambridge, Massachusetts
  19. [21]Bair W Spike timing in the mammalian visual system Curr. Opin. Neurobiol 1999 9 447 453 10448163
  20. [22]Keat J Reinagel P Reid RC Meister M Predicting every spike: a model for the responses of visual neurons Neuron 2001 30 803 817 11430813
  21. [23]Panzeri S Petersen RS Schultz SR Lebedev M Diamond ME The role of spike timing in the coding of stimulus location in rat somatosensory cortex Neuron 2001 29 769 777 11301035
  22. [24]Kara P Reinagel P Reid RC Low response variability in simultaneously recorded retinal, thalamic and cortical neurons Neuron 2000 27 635 646 11055444
  23. [25]Billimoria CP DiCaprio RA Birmingham JT Abbott LF Marder E Neuromodulation of spike-timing precision in sensory neurons J. Neurosci 2006 26 5910 5919 16738233 PMC6675233
  24. [26]Hausser M Spruston N Stuart GJ Diversity and dynamics of dendritic signaling Science 2000 290 739 744 11052929
  25. [27]Stuart G Hausser M Dendritic coincidence detection of EPSPs and action potentials Nature Neurosci 2001 4 63 71 11135646
  26. [28]Carr CE Konishi M A circuit for detection of interaural time differences in the brain stem of the barn owl J. Neurosci 1990 10 3227 3246 2213141 PMC6570189
  27. [29]Fairhall AL Lewen GD Bialek W de Ruyter van Steveninck RR Efficiency and ambiguity in an adaptive neural code Nature 2001 412 787 792 11518957
  28. [30]Zhurov Y Brezina V Variability of motor neuron spike timing maintains and shapes contractions of the accessory radula closer muscle of aplysia J. Neurosci 2006 26 7056 7070 16807335 PMC6673911
  29. [31]Bialek W Rieke F de Ruyter van Steveninck RR Warland D Reading a neural code Science 1991 252 1854 1857 2063199
  30. [32]Softky WR Koch C The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs J. Neurosci 1993 13 334 350 8423479 PMC6576320
  31. [34]Heggelund P Albus K Response variability and orientation discrimination of single cells in striate cortex of cat Exp. Brain Res 1978 32 197 211 680039
  32. [35]Shadlen MN Newsome WT The variable discharge of cortical neurons: implications for connectivity, computation, and information coding J. Neurosci 1998 18 3870 3896 9570816 PMC6793166
  33. [36]Gur M Beylin A Snodderly DM Response variability of neurons in primary visual cortex (V1) of alert monkeys J. Neurosci 1997 17 2914 2920 9092612 PMC6573112
  34. [37]DeWeese MR Wehr M Zador AM Binary spiking in auditory cortex J. Neurosci 2003 23 7940 7949 12944525 PMC6740590
  35. [38]Berry MJ Meister M Refractoriness and neural precision J. Neurosci 1998 18 2200 2211 9482804 PMC6792934
  36. [39]Warzecha A-K Egelhaaf M Variability in spike trains during constant and dynamic stimulation Science 1999 283 1927 1930 10082467
  37. [40]Azouz R Gray CM Cellular mechanisms contributing to response variability of cortical neurons in vivo J. Neurosci 1999 19 2209 2223 10066274 PMC6782570
  38. [41]Deweese MR Zador AM Shared and private variability in the auditory cortex J. Neurophysiol 2004 92 1840 1855 15115790
  39. [42]Calvin WH Stevens CF Synaptic noise and other sources of randomness in motoneuron interspike intervals J. Neurophysiol 1968 31 574 587 5709873
  40. [44]Schneidman E Freedman B Segev I Ion channel stochasticity may be critical in determining the reliability and precision of spike timing Neural Comput 1998 10 1679 1703 This paper shows that even when large numbers of stochastic ion channels are present in a neuron, fluctuations can become critical near the AP threshold 9744892
  41. [45]Hodgkin AL Huxley AF Quantitative description of membrane current and its application to conduction and excitation in nerve J. Physiol 1952 117 500 544 12991237 PMC1392413
  42. [46]Fatt P Katz B Some observations on biological noise Nature 1950 166 597 598 14780165
  43. [47]Calvin WH Stevens CF Synaptic noise as a source of variability in the interval between action potentials Science 1967 155 842 844 6018196
  44. [48]Lou X Scheuss V Schneggenburger R Allosteric modulation of the presynaptic Ca2+ sensor for vesicle fusion Nature 2005 435 497 501 15917809
  45. [49]Derksen HE Verveen AA Fluctuations of resting neural membrane potential Science 1966 151 1388 1389 5909786
  46. [50]Verveen AA Derksen HE Schick KL Voltage fluctuations of neural membrane Nature 1967 216 588 589 5583506
  47. [52]Steinmetz PN Manwani A Koch C London M Segev I Subthreshold voltage noise due to channel fluctuations in active neuronal membranes J. Comput. Neurosci 2000 9 133 148 11030518
  48. [53]White JA Rubinstein JT Kay AR Channel noise in neurons Trends Neurosci 2000 23 131 137 10675918
  49. [54]van Rossum MC O'Brien BJ Smith RG Effects of noise on the spike timing precision of retinal ganglion cells J. Neurophysiol 2003 89 2406 2419 12740401
  50. [55]Rubinstein JT Threshold fluctuations in an N sodium channel model of the node of Ranvier Biophys. J 1995 68 779 785 7756544 PMC1281801
  51. [56]Skaugen E Wallow L Firing behaviour in a stochastic nerve membrane model based upon the Hodgkin-Huxley equations Acta Physiol. Scand 1979 107 343 363 543428
  52. [57]Chow CC White JA Spontaneous action potentials due to channel fluctuations Biophys. J 1996 71 3012 3021 PMC1233790 8968572
  53. [58]Diba K Lester HA Koch C Intrinsic noise in cultured hippocampal neurons: experiment and modeling J. Neurosci 2004 24 9723 9733 15509761 PMC6730144
  54. [59]Jacobson GA Subthreshold voltage noise of rat neocortical pyramidal neurones J. Physiol 2005 564 145 160 15695244 PMC1456039
  55. [60]Dorval AD Jr White JA Channel noise is essential for perithreshold oscillations in entorhinal stellate neurons J. Neurosci 2005 25 10025 10028 This paper uses an elegant application of the dynamic-clamp technique to show that stochastic effects are required to describe CNS behaviour in vitro 16251451 PMC6725569
  56. [61]Kole MH Hallermann S Stuart GJ Single Ih channels in pyramidal neuron dendrites: properties, distribution, and impact on action potential output J. Neurosci 2006 26 1677 1687 16467515 PMC6793638
  57. [62]Schneidman E Freedman B Segev I Ion channel stochasticity may be critical in determining the reliability and precision of spike timing Neural Comput 1998 10 1679 1703 9744892
  58. [63]Faisal AA White JA Laughlin SB Ion-channel noise places limits on the miniaturization of the brain's wiring Curr. Biol 2005 15 1143 1149 This paper shows that channel noise places a universal lower limit on neuron diameter, matching anatomical data across species 15964281
  59. [64]Rall W Time constants and electrotonic length of membrane cylinders and neurons Biophys. J 1969 9 1483 1508 5352228 PMC1367649
  60. [65]Faisal AA Laughlin SB Stochastic simulations on the reliability of action potential propagation in thin axons PLoS Comput. Biol 2007 3 e79 This paper uses stochastic simulations to show that the many thin axons in the CNS are a source of spike-time variability that had been overlooked experimentally. It demonstrated that noise acts in a context-dependent manner and allows for a previously unknown mode of AP conduction 17480115 PMC1864994
  61. [66]Cecchi GA Noise in neurons is message dependent Proc. Natl Acad. Sci. USA 2000 97 5557 5561 10792057 PMC25867
  62. [67]Fellous J-M Tiesinga PHE Thomas PJ Sejnowski TJ Discovering spike patterns in neuronal responsess J. Neurosci 2004 24 2989 3001 15044538 PMC2928855
  63. [68]Horikawa Y Noise effects on spike propagation in the stochastic Hodgkin-Huxley models Biol. Cybern 1991 66 19 25 1768709
  64. [69]Kandel ER Schwartz JH Jessell TM Principles of Neural Science 2000 McGraw–Hill/Appleton & Lange New York
  65. [70]Debanne D Information processing in the axon Nature Rev. Neurosci 2004 5 304 316 15034555
  66. [71]Debanne D Guerineau NC Gahwiler BH Thompson SM Action-potential propagation gated by an axonal IA-like K+ conductance in hippocampus Nature 1997 389 286 289 9305843
  67. [72]Lecar H Nossal R Theory of threshold fluctuations in nerves. II. Analysis of various sources of membrane noise Biophys. J 1971 11 1068 1084 5167401 PMC1484102
  68. [73]Manwani A Koch C Detecting and estimating signaals in noisy cable structures. I. Neuronal noise sources Neural Comput 1999 11 1797 1829 10578033
  69. [74]Jefferys JG Nonsynaptic modulation of neuronal activity in the brain: electric currents and extracellular ions Physiol. Rev 1995 75 689 723 7480159
  70. [75]Szapiro G Barbour B Multiple climbing fibers signal to molecular layer interneurons exclusively via glutamate spillover Nature Neurosci 2007 10 735 742 17515900
  71. [76]Katz B Miledi R Membrane noise produced by acetylcholine Nature 1970 226 962 963 5445879
  72. [77]Kleppe IC Robinson HPC Correlation entropy of synaptic input-output dynamics Phys. Rev. E Stat. Nonlin. Soft Matter Phys 2006 74 041909 17155098
  73. [78]Faure P Kaplan D Korn H Synaptic efficacy and the transmission of complex firing patterns between neurons J. Neurophysiol 2000 84 3010 3025 11110828
  74. [79]Steriade M McCormick DA Sejnowski TJ Thalamocortical oscillations in the sleeping and aroused brain Science 1993 262 679 685 8235588
  75. [80]Cowan RL Wilson CJ Spontaneous firing patterns and axonal projections of single corticostriatal neurons in the rat medial agranular cortex J. Neurophysiol 1994 71 17 32 8158226
  76. [81]Metherate R Ashe JH Ionic flux contributions to neocortical slow waves and nucleus basalis-mediated activation: whole-cell recordings in vivo J. Neurosci 1993 13 5312 5323 8254377 PMC6576427
  77. [82]Destexhe A Rudolph M Fellous JM Sejnowski TJ Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons Neuroscience 2001 107 13 24 11744242 PMC3320220
  78. [84]Stuart GJ Sakmann B Active propagation of somatic action potentials into neocortical pyramidal cell dendrites Nature 1994 367 69 72 8107777
  79. [85]Wehr M Zador AM Balanced inhibition underlies tuning and sharpens spike timing in auditory cortex Nature 2003 426 442 446 14647382
  80. [86]Stevens CF Zador AM Input synchrony and the irregular firing of cortical neurons Nature Neurosci 1998 1 210 217 10195145
  81. [88]Conti R Tan Y Llano I Action potential-evoked and ryanodine-sensitive spontaneous Ca2+ transients at the presynaptic terminal of a developing CNS inhibitory synapse J. Neurosci 2004 24 6946 6957 15295030 PMC6729609
  82. [89]Wang SQ Song LS Lakatta EG Cheng H Ca2+ signalling between single L-type Ca2+ channels and ryanodine receptors in heart cells Nature 2001 410 592 596 11279498
  83. [90]Bekkers JM Richerson GB Stevens CF Origin of variability in quantal size in cultured hippocampal neurons and hippocampal slices Proc. Natl Acad. Sci. USA 1990 87 5359 5362 2371276 PMC54323
  84. [91]Zucker RS Regehr WG Short-term synaptic plasticity Annu. Rev. Physiol 2002 64 355 405 11826273
  85. [92]Sulzer D Edwards R Vesicles: equal in neurotransmitter concentration but not in volume Neuron 2000 28 5 7 11086975
  86. [93]Wu X-S The origin of quantal size variation: vesicular glutamate concentration plays a significant role J. Neurosci 2007 27 3046 3056 17360928 PMC6672571
  87. [95]Nimchinsky EA Yasuda R Oertner TG Svoboda K The number of glutamate receptors opened by synaptic stimulation in single hippocampal spines J. Neurosci 2004 24 2054 2064 14985448 PMC6730404
  88. [96]Nusser Z Cull-Candy S Farrant M Differences in synaptic GABAA receptor number underlie variation in GABA mini amplitude Neuron 1997 19 697 709 9331359
  89. [97]Lim R Alvarez FJ Walmsley B Quantal size is correlated with receptor cluster area at glycinergic synapses in the rat brainstem J. Physiol 1999 516 505 512 10087348 PMC2269264
  90. [98]Paulsson J Summing up the noise in gene networks Nature 2004 427 415 418 14749823
  91. [99]Abbott LF Regehr WG Synaptic computation Nature 2004 431 796 803 15483601
  92. [100]Miller P Zhabotinsky AM Lisman JE Wang XJ The stability of a stochastic CaMKII switch: dependence on the number of enzyme molecules and protein turnover PLoS Biol 2005 3 e107 15819604 PMC1069645
  93. [101]Henneman E Relation between size of neurons and their susceptibility to discharge Science 1957 126 1345 1347 13495469
  94. [102]Schmidt R Zelaznik H Hawkins B Frank J Quinn J Jr. Motor-output variability: a theory for the accuracy of rapid motor acts Psychol. Rev 1979 47 415 451 504536
  95. [103]Jones KE Hamilton AF Wolpert DM Sources of signal-dependent noise during isometric force production J. Neurophysiol 2002 88 1533 1544 This paper provides experimental and theoretical evidence that the linear scaling of force variability (signal-dependent noise) is a natural by-product of the organization of motor neurons and muscle fibres (the size principle) 12205173
  96. [104]Hamilton AF Jones KE Wolpert DM The scaling of motor noise with muscle strength and motor unit number in humans Exp. Brain Res 2004 157 417 430 15014922
  97. [105]Selen LP Beek PJ van Dieen JH Can co-activation reduce kinematic variability? A simulation study Biol. Cybern 2005 93 373 381 16249892
  98. [106]Moritz CT Barry BK Pascoe MA Enoka RM Discharge rate variability influences the variation in force fluctuations across the working range of a hand muscle J. Neurophysiol 2005 93 2449 2459 15615827
  99. [107]Christakos CN Papadimitriou NA Erimaki S Parallel neuronal mechanisms underlying physiological force tremor in steady muscle contractions of humans J. Neurophysiol 2006 95 53 66 16162838
  100. [108]Moffitt MA McIntyre CC Grill WM Prediction of myelinated nerve fiber stimulation thresholds: limitations of linear models IEEE Trans. Biomed. Eng 2004 51 229 236 14765695
  101. [109]Mino H Grill WM Jr. Effects of stochastic sodium channels on extracellular excitation of myelinated nerve fibers IEEE Trans. Biomed. Eng 2002 49 527 532 12046697
  102. [110]Frank TD Friedrich R Beek PJ Stochastic order parameter equation of isometric force production revealed by drift-diffusion estimates Phys. Rev. E Stat. Nonlin. Soft Matter Phys 2006 74 051905 17279937
  103. [111]Capogrossi MC Stern MD Spurgeon HA Lakatta EG Spontaneous Ca2+ release from the sarcoplasmic reticulum limits Ca2+-dependent twitch potentiation in individual cardiac myocytes. A mechanism for maximum inotropy in the myocardium J. Gen. Physiol 1988 91 133 155 3343586 PMC2216123
  104. [112]Khatib M Hilaire G Monteau R Excitatory interactions between phrenic motoneurons in the cat Exp. Brain Res 1986 62 273 280 3709712
  105. [113]Chen H Tourtellotte W Frank E Muscle spindle-derived neurotrophin 3 regulates synaptic connectivity between muscle sensory and motor neurons J. Neurosci 2002 22 3512 3519 11978828 PMC6758400
  106. [114]Furness J The excitatory input to a single smooth muscle cell Pflugers Arch 1970 314 1 13 4391451
  107. [115]Morris LG Hooper SL Muscle response to changing neuronal input in the lobster (Panulirus interruptus) stomatogastric system: spike number-versus spike frequency-dependent domains J. Neurosci 1997 17 5956 5971 9221792 PMC6573197
  108. [116]Lum CS Zhurov Y Cropper EC Weiss KR Brezina V Variability of swallowing performance in intact, freely feeding aplysia J. Neurophysiol 2005 94 2427 2446 15944235 PMC1224712
  109. [117]Hooper SL Guschlbauer C von Uckermann G Buschges A Natural neural output that produces highly variable locomotory movements J. Neurophysiol 2006 96 2072 2088 16775206
  110. [118]Ludlow CL Central nervous system control of the laryngeal muscles in humans Respir. Physiol. Neurobiol 2005 147 205 222 15927543 PMC1351146
  111. [120]Harris CM Wolpert DM The main sequence of saccades optimizes speed-accuracy trade-off Biol. Cybern 2006 95 21 29 16555070 PMC2637438
  112. [121]van Beers RJ The sources of variability in saccadic eye movements J. Neurosci 2007 27 8757 8 17699658 PMC6672172
  113. [122]Hamilton AF Wolpert DM Controlling statistics of action: obstacle avoidance J. Neurophysiol 2002 87 2434 2440 11976380
  114. [123]van Beers RJ Haggard P Wolpert DM The role of execution noise in movement variability J. Neurophysiol 2004 91 1050 1063 14561687
  115. [124]Kozlov AS Risler T Hudspeth AJ Coherent motion of stereocilia assures the concerted gating of hair-cell transduction channels Nature Neurosci 2007 10 87 92 17173047 PMC2174432
  116. [126]Glowatzki E Fuchs PA Transmitter release at the hair cell ribbon synapse Nature Neurosci 2002 5 147 154 11802170
  117. [127]Barlow H Rosenblith WA Sensory Communication 1961 217 234 MIT Press Cambridge, Massachusetts
  118. [128]Laughlin S A simple coding procedure enhances a neuron's information capacity Z. Naturforsch. [C] 1981 36 910 912 7303823
  119. [129]Field D Relations between the statistics of natural images and the response properties of cortical cells J. Opt. Soc. Am. A 1987 4 2379 2394 3430225
  120. [130]Adelman TL Bialek W Olberg RM The information content of receptive fields Neuron 2003 40 823 833 14622585
  121. [131]Turin G An introduction to matched filters IEEE Trans. Information Theory 1960 6 311 329
  122. [133]Ernst MO Banks MS Humans integrate visual and haptic information in a statistically optimal fashion Nature 2002 415 429 433 11807554
  123. [134]Alais D Burr D The ventriloquist effect results from near-optimal bimodal integration Curr. Biol 2004 14 257 262 14761661
  124. [135]Jacobs RA Optimal integration of texture and motion cues to depth Vision Res 1999 39 3621 3629 This was one of the first studies to demonstrate statistically optimal weighting (weighted averaging) of sensory cues 10746132
  125. [136]Knill DC Mixture models and the probabilistic structure of depth cues Vision Res 2003 43 831 854 12639607
  126. [138]Beers RJ Sittig AC Denier JJ How humans combine simultaneous proprioceptive and visual position information Exp. Brain Res 1996 111 253 261 8891655
  127. [140]Sober S Sabes P Flexible strategies for sensory integration during motor planning Nature Neurosci 2005 8 490 497 15793578 PMC2538489
  128. [141]Haruno M Wolpert DM Optimal control of redundant muscles in step-tracking wrist movements J. Neurophysiol 2005 94 4244 4255 16079196
  129. [142]Georgopoulos A Schwartz A Kettner R Neuronal population coding of movement direction Science 1986 233 1416 1419 3749885
  130. [143]Lee C Rohrer WH Sparks DL Population coding of saccadic eye movements by neurons in the superior colliculus Nature 1988 332 357 360 3352733
  131. [144]Deneve S Latham P Pouget A Efficient computation and cue integration with noisy population codes Nature Neurosci 2001 4 826 831 11477429
  132. [145]Zohary E Shadlen MN Newsome WT Correlated neuronal discharge rate and its implications for psychophysical performance 1994 370 140 143 8022482
  133. [146]Osborne LC Bialek W Lisberger SG Time course of information about motion direction in visual area MT of macaque monkeys J. Neurosci 2004 24 3210 3222 15056700 PMC2553809
  134. [147]Romo R Hernandez A Zainos A Salinas E Correlated neuronal discharges that increase coding efficiency during perceptual discrimination Neuron 2003 38 649 657 12765615
  135. [148]Jaynes ET Bretthorst GL Probability Theory: The Logic of Science 2003 Cambridge Univ. Press
  136. [149]Kording KP Wolpert DM Bayesian integration in sensorimotor learning Nature 2004 427 244 247 This was the first paper to demonstrate that subjects use task statistics (prior knowledge) and knowledge of their sensory variability to produce estimates that are Bayes optimal 14724638
  137. [150]Stocker AA Simoncelli EP Noise characteristics and prior expectations in human visual speed perception Nature Neurosci 2006 9 578 585 This paper provides a framework for testing how experimental variability can be used to infer prior probabilities as well as the internal noise characteristics directly from experimental data 16547513
  138. [151]Barlow HB Pattern recognition and the responses of sensory neurons Ann. NY Acad. Sci 1969 156 872 881 5258022
  139. [152]Barlow H Single units and sensation: a neuron doctrine for perceptual psychology Perception 1972 1 371 394 4377168
  140. [153]Paradiso M A theory for the use of visual orientation information which exploits the columnar structure of striate cortex Biol. Cybern 1988 58 35 49 3345319
  141. [155]Hartwell LH Hopfield JJ Leibler S Murray AW From molecular to modular cell biology Nature 1999 402 C47 C42 10591225
  142. [156]van Hateren JH Laughlin SB Membrane parameters, signal transmission, and the design of a graded potential neuron J. Comp. Physiol. A 1990 166 437 448 2159070
  143. [157]Niven JE The contribution of Shaker K+ channels to the information capacity of Drosophila photoreceptors Nature 2003 421 630 634 12571596
  144. [158]Gold JI Shadlen MN Representation of a perceptual decision in developing oculomotor commands Nature 2000 404 390 394 10746726
  145. [160]Wolpert DM Ghahramani Z Jordan MI An internal model for sensorimotor integration Science 1995 269 1880 1882 7569931
  146. [161]Kuo A An optimal control model for analyzing human postural balance IEEE Trans. Biomed. Eng 1995 42 87 101 7851935
  147. [163]Todorov E Optimality principles in sensorimotor control Nature Neurosci. sci 2004 7 907 915 PMC1488877 15332089
  148. [164]Diedrichsen J Optimal task-dependent changes of bimanual feedback control and adaptation Curr. Biol 2007 17 1675 1679 17900901 PMC2230536
  149. [165]Liu D Todorov E Evidence for the flexible sensorimotor strategies predicted by optimal feedback control J. Neurosci 2007 27 9354 9368 17728449 PMC6673117
  150. [166]Gribble PL Mullin LI Cothros N Mattar A Role of cocontraction in arm movement accuracy J. Neurophysiol 2003 89 2396 2405 12611935
  151. [167]Selen LP Beek PJ van Dieen JH Impedance is modulated to meet accuracy demands during goal-directed arm movements Exp. Brain Res 2006 172 129 138 This paper provided the first experimental evidence that subjects increase joint stiffness when confronted with higher accuracy demands in goal-directed movements. The increase in joint stiffness results in less kinematic variability 16372169
  152. [168]Selen LP van Dieen JH Beek PJ Impedance modulation and feedback corrections in tracking targets of variable size and frequency J. Neurophysiol 2006 96 2750 2759 16899639
  153. [169]Lametti DR Houle G Ostry DJ Control of movement variability and the regulation of limb impedance J. Neurophysiol 2007 98 3516 3524 17913978
  154. [170]Attwell D Laughlin SB An energy budget for signaling in the grey matter of the brain J. Cereb. Blood Flow Metab 2001 21 1133 1145 11598490
  155. [171]Balasubramanian V Kimber D Berry MJ Metabolically efficient information processing Neural Comput 2001 13 799 815 11255570
  156. [172]de Polavieja GG Errors drive the evolution of biological signalling to costly codes J. Theor. Biol 2002 214 657 664 11851374
  157. [176]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 67 656 659 10044954
  158. [177]Douglass JK Wilkens L Pantazelou E Moss F Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance 1993 365 337 340 8377824
  159. [178]Braun HA Wissing H Schafer K Hirsch MC Oscillation and noise determine signal transduction in shark multimodal sensory cells 1994 367 270 273 11407413
  160. [179]Levin JE Miller JP Broadband neural encoding in the cricket cereal sensory system enhanced by stochastic resonance 1996 380 165 168 8600392
  161. [180]Cordo P Noise in human muscle spindles 1996 383 769 770 8892999
  162. [181]Russell DF Wilkens LA Moss F Use of behavioural stochastic resonance by paddle fish for feeding 1999 402 291 294 This paper provided the first demonstration of stochastic resonance effects at the behavioural level 10580499
  163. [182]Priplata AA Niemi JB Harry JD Lipsitz LA Collins JJ Vibrating insoles and balance control in elderly people Lancet 2003 362 1123 1124 14550702
  164. [185]Kirkpatrick S Gelatt CD Jr Vecchi MP Optimization by simulated annealing Science 1983 220 671 680 17813860
  165. [186]Tuckwell HC Rodriguez R Analytical and simulation results for stochastic Fitzhugh-Nagumo neurons and neural networks J. Comput. Neurosci 1998 5 91 113 9540051
  166. [188]Turrigiano GG Leslie KR Desai NS Rutherford LC Nelson SB Activity-dependent scaling of quantal amplitude in neocortical neurons Nature 1998 391 892 896 9495341
  167. [189]Prinz A Bucher D Marder E Similar network activity from disparate circuit parameters Nature Neurosci 2004 7 1345 1352 15558066
  168. [190]Marsalek P Koch C Maunsell J On the relationship between synaptic input and spike output jitter in individual neurons Proc. Natl Acad. Sci. USA 1997 94 735 740 9012854 PMC19583
  169. [191]Poliakov AV Powers RK Binder MD Functional identification of the input-output transforms of motoneurones in the rat and cat J. Physiol 1997 504 401 424 9365914 PMC1159920
  170. [192]Sarpeshkar R Analog versus digital: extrapolating from electronics to neurobiology Neural Comp 1998 9 1601 1638 9744889
  171. [193]Laughlin S van Steveninck RR Anderson J The metabolic cost of neural information Nature Neurosci 1998 1 36 41 10195106
  172. [194]Laughlin SB Sejnowski TJ Communication in neuronal networks Science 2003 301 1870 1874 14512617 PMC2930149
  173. [195]Laughlin SB Bock G Good J Complexity in Biological Information Processing 2001 177 187 Wiley Chichester

Cited by

Sorted by citations

Authors
Faisal, A. A., Selen, L. P. J., & Wolpert, D. M.
Affiliations
University of Cambridge (GB)
Corresponding author
Faisal, A. Aldo
Venue
Nature Reviews Neuroscience
Published
2008-04
Volume
9
Issue
4
Pages
292-303
ISSN
  • 1471-003X (ISSN-L)
  • 1471-0048
OpenAlex
W2131215403
Cited by
2,883
References
11
Citations by year
2026: 184 · 2025: 228 · 2024: 217 · 2023: 188 · 2022: 195 · 2021: 189 · 2020: 196 · 2019: 178 · 2018: 171 · 2017: 161 · 2016: 149 · 2015: 157 · 2014: 130 · 2013: 141 · 2012: 114
FWCI
4.43
Type
journal article
Language
en
Open access
Locations
  • Nature reviews. Neuroscience (publishedVersion)
  • PubMed (publishedVersion)
  • PubMed Central (acceptedVersion)
  • Cambridge University Engineering Department Publications Database (submittedVersion)
Funders
Wellcome Trust (077730)
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
  • Life Sciences › Neuroscience › Cellular and Molecular Neuroscience › Neuroscience and Neuropharmacology Research
Keywords
neural noise, trial-to-trial variability, behavioral variability, noise sources, neuronal networks, noise countermeasures, information processing, molecular noise
MeSH terms
Animals, Humans, Information Theory, Models, Neurological, Nerve Net, Nervous System, Nervous System Physiological Phenomena, Neural Pathways, Noise, Neural Networks, Computer

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