Stochastic resonance
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Stochastic resonance (also known as SR) is observed when noise added to a system improves the system's performance in some fashion. More technically, SR occurs if the signal-to-noise ratio of a nonlinear system or device increases for moderate values of noise intensity. It often occurs in bistable systems or in systems with a sensory threshold and when the input signal to the system is "sub-threshold". 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 a '∩' 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] Neuroscience/Psychology & Biology
Stochastic resonance has been observed in the neural tissue of the sensory systems of several organisms [2] Computationally, neurons exhibit SR because of non-linearities in their processing. SR has yet to be fully explained in biological systems, but neural synchrony in the brain (specifically in the Gamma wave frequency[3]) has been suggested as an possible neural mechanism for SR by researchers who have investigated the perception of "subconscious" visual sensation.[4]
[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[5] 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.[6]. 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.[7]
[edit] See also
- Stochastic Resonance (book)
- Neural oscillations
- Stochastic resonance on Scholarpedia
- Stochastic
[edit] References
- Hänggi P (Mar 2002). "Stochastic resonance in biology. How noise can enhance detection of weak signals and help improve biological information processing". Chemphyschem 3 (3): 285–90. doi:. PMID 12503175. http://www.physik.uni-augsburg.de/theo1/hanggi/Papers/282.pdf.
- Moss F, Ward LM, Sannita WG (Feb 2004). "Stochastic resonance and sensory information processing: a tutorial and review of application". Clin Neurophysiol 115 (2): 267–81. doi:. PMID 14744566. http://linkinghub.elsevier.com/retrieve/pii/S1388245703003304.
- Wiesenfeld K, Moss F (Jan 1995). "Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs". Nature 373 (6509): 33–6. doi:. PMID 7800036.
- Bulsara A, Gammaitoni L (1996). "Tuning in to noise". Physics Today 49 (3): 39–45. doi:. http://nipslab.fisica.unipg.it/files/vol49no3p39-45.pdf.
- Priplata AA, Patritti BL, Niemi JB, et al (Jan 2006). "Noise-enhanced balance control in patients with diabetes and patients with stroke". Ann Neurol. 59 (1): 4–12. doi:. PMID 16287079.
[edit] External links
- Articles
- Harry JD, Niemi JB, Priplata AA, Collins JJ (Apr 2005). "Balancing Act". IEEE Spectrum 42: 36. doi:. http://www.spectrum.ieee.org/apr05/1294.
- Newsweek Being messy, both at home and in foreign policy, may have its own advantages
- Conferences
- Stochastic Resonance Conference 1998-2008 ten years of continuous growth. 17-21 Aug. 2008, Perugia (Italy)
[edit] References
- ^ Benzi R, Parisi G, Sutera A, Vulpiani A (1982). "Stochastic resonance in climatic change". Tellus 34: 10–6.
- ^ Kosko, Bart (2006). Noise. New York, N.Y: Viking. ISBN 0-670-03495-9.
- ^ Ward LM, Doesburg SM, Kitajo K, MacLean SE, Roggeveen AB (Dec 2006). "Neural synchrony in stochastic resonance, attention, and consciousness". Can J Exp Psychol 60 (4): 319–26. PMID 17285879.
- ^ Melloni L, Molina C, Pena M, Torres D, Singer W, Rodriguez E (Mar 2007). "Synchronization of neural activity across cortical areas correlates with conscious perception". J Neurosci. 27 (11): 2858–65. doi:. PMID 17360907. http://www.jneurosci.org/cgi/pmidlookup?view=long&pmid=17360907. "Final proof of role of neural coherence in consciousness?".
- ^ Gammaitoni L, Hänggi P, Jung P, Marchesoni F (1998). "Stochastic resonance". Review of Modern Physics 70 (1): 223–87. doi:. http://www.physik.uni-augsburg.de/theo1/hanggi/Papers/195.pdf.
- ^ Gammaitoni L (1995). "Stochastic resonance and the dithering effect in threshold physical systems". Phys Rev E 52: 4691–8. doi:. http://nipslab.fisica.unipg.it/files/PRE1995-SR-and-dithering-p4691_1.pdf.
- ^ Palonpon A, Amistoso J, Holdsworth J, Garcia W, Saloma C (1998). "Measurement of weak transmittances by stochastic resonance". Optics Letters 23 (18): 1480–2. doi:. http://www.opticsinfobase.org/abstract.cfm?id=36963.
