Stochastic resonance

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Stochastic resonance (also known as SR) occurs when the signal-to-noise ratio of a nonlinear device is maximized for a moderate value of noise intensity. It often occurs in bistable and excitable systems with subthreshold inputs. For lower noise intensities, the signal does not cause the device to cross threshold, so little signal is passed through it. For large noise intensities, the output is dominated by the noise, also leading to a low signal-to-noise ratio. For moderate intensities, the noise allows the signal to reach threshold, but the noise intensity is not so large as to swamp it. Thus, a plot of signal-to-noise ratio as a function of noise intensity shows an upside-down "U" shape.

Strictly speaking, stochastic resonance occurs in bistable systems, when a small periodic (sinusoidal) force is applied together with a large wide band stochastic force (noise). The system response is driven by the combination of the two forces that compete/cooperate to make the system switch between the two stable states. The degree of order is related to the amount of periodic function that it shows in the system response. When the periodic force is chosen small enough in order to not make the system response switch, the presence of a non-negligible noise is required for it to happen. When the noise is small very few switches occur, mainly at random with no significant periodicity in the system response. When the noise is very strong a large number of switches occur for each period of the sinusoid and the system response does not show remarkable periodicity. Quite surprisingly, between these two conditions, there exists an optimal value of the noise that cooperatively concurs with the periodic forcing in order to make almost exactly one switch per period (a maximum in the signal-to-noise ratio).

Such a favorable condition is quantitatively determined by the matching of two time scales: the period of the sinusoid (the deterministic time scale) and the Kramers rate (i.e. the inverse of the average switch rate induced by the sole noise: the stochastic time scale). Thus the term "stochastic resonance".

Stochastic resonance was discovered and proposed for the first time in 1981 to explain the periodic recurrence of ice ages.[1] Since then the same principle has been applied in a wide variety of systems. Nowadays stochastic resonance is commonly invoked when noise and nonlinearity concur to determine an increase of order in the system response.

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[edit] Biology

SR has yet to be fully explained in biological systems, but neural synchrony in the brain (specifically in the Gamma wave frequency[2]) has been argued to explain the effect stochasic resonance in regard to perception of subconscious visual sensation.[3]

[edit] Medicine

SR-based techniques has been used to create a novel class of medical devices (such as vibrating insoles) for enhancing sensory and motor function in the elderly, patients with diabetic neuropathy, and patients with stroke.

See the Review of Modern Physics[4] article below for a comprehensive overview of stochastic resonance.

[edit] Signal Analysis

A related phenomenon is dithering applied to analog signals before analog-to-digital conversion.[5]. Stochastic resonance can be used to measure transmittance amplitudes below an instrument's detection limit. If Gaussian noise is added to a subthreshold (i.e. immeasurable) signal, then it can be brought into a detectable region. After detection, the noise is removed. A fourfold improvement in the detection limit can be obtained.[6]

[edit] See also


[edit] References

  • Hänggi P. Stochastic resonance in biology: how noise can enhance detection of weak signals and help improve biological information processing. Chemphyschem 2002;3:285–290.
  • Moss F, Ward LM, Sannita WG. Stochastic resonance and sensory information processing: a tutorial and review of application. Clin Neurophys 2004;27:677– 682.
  • Wiesenfeld K, Moss F. Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs. Nature 1995;373:33–36.
  • A. Bulsara, L. Gammaitoni, Tuning in to noise, Physics Today, 03/1996, Volume 49, Issue 3, p.39-45, (1996)[7]
  • Priplata A. et al. Noise-Enhanced Balance Control in Patients with Diabetes and Patients with Stroke. Ann Neurol 2006;59:4–12. PMID 16287079.

[edit] External links

Articles
Conferences

[edit] References

  1. ^ Benzi R, Parisi G, Sutera A, and Vulpiani A, "Stochastic resonance in climatic change." Tellus 34:10-16. 1982.
  2. ^ Ward LM, Doesburg SM, Kitajo K, MacLean SE, Roggeveen AB. [1] Neural synchrony in stochastic resonance, attention, and consciousness. Can J Exp Psychol. 2006 Dec;60(4):319-26.
  3. ^ Lucia Melloni, Carlos Molina, Marcela Pena, David Torres, Wolf Singer and Eugenio Rodriguez Final proof of role of neural coherence in consciousness? The Journal of Neuroscience, March 14, 2007, 27(11):2858-2865; doi:10.1523/JNEUROSCI.4623-06.2007.
  4. ^ Review of Modern Physics, Vol. 70 (1), p.223-287 (1998)
  5. ^ [2] L. Gammaitoni, Stochastic resonance and the dithering effect in threshold physical systems Phys. Rev. E 52, 4691 - 4698 (1995)
  6. ^ [3] A. Palonpon, J. Amistoso, J. Holdsworth, W. Garcia, and C. Saloma, Measurement of weak transmittances by stochastic resonance Optics Letters 23, Issue 18, 1480-1482 (1998)
  7. ^ [4]A. Bulsara, L. Gammaitoni, Tuning in to noise, Physics Today, 03/1996, Volume 49, Issue 3, p.39-45, (1996)