Stochastic resonance

Stochastic resonance (SR) is a phenomenon that occurs in a threshold measurement system (e.g. a man-made instrument or device; a natural cell, organ or organism) when an appropriate measure of information transfer (signal-to-noise ratio, mutual information, coherence, d, etc.) is maximized in the presence of a specific non-zero level of stochastic input noise thereby lowering the response threshold;[1] the system resonates at a particular noise level.

Contents

Definition

Stochastic resonance is observed when noise added to a system changes the system's behaviour 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. 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.[2] 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.

Suprathreshold stochastic resonance

Suprathreshold stochastic resonance is a particular form of stochastic resonance. It is the phenomenon where random fluctuations, or noise, provide a signal processing benefit in a nonlinear system. Unlike most of the nonlinear systems where stochastic resonance occurs, suprathreshold stochastic resonance occurs not only when the strength of the fluctuations is small relative to that of an input signal, but occurs even for the smallest amount of random noise. Furthermore, it is not restricted to a subthreshold signal, hence the qualifier, suprathreshold, in suprathreshold stochastic resonance.

Neuroscience/psychology and biology

Main article: Stochastic resonance (sensory neurobiology)

Stochastic resonance has been observed in the neural tissue of the sensory systems of several organisms.[3] 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[4]) has been suggested as a possible neural mechanism for SR by researchers who have investigated the perception of "subconscious" visual sensation.[5]

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[6] article for a comprehensive overview of stochastic resonance.

Signal analysis

A related phenomenon is dithering applied to analog signals before analog-to-digital conversion.[7] 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.[8]

See also

References

  1. ^ Moss F, Ward LM, Sannita WG (February 2004). "Stochastic resonance and sensory information processing: a tutorial and review of application". Clinical Neurophysiology 115 (2): 267–81. doi:10.1016/j.clinph.2003.09.014. PMID 14744566. 
  2. ^ Benzi R, Parisi G, Sutera A, Vulpiani A (1982). "Stochastic resonance in climatic change". Tellus 34 (1): 10–6. doi:10.1111/j.2153-3490.1982.tb01787.x. 
  3. ^ Kosko, Bart (2006). Noise. New York, N.Y: Viking. ISBN 0-670-03495-9. 
  4. ^ 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. doi:10.1037/cjep2006029. PMID 17285879. 
  5. ^ 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:10.1523/JNEUROSCI.4623-06.2007. PMID 17360907. http://www.jneurosci.org/cgi/pmidlookup?view=long&pmid=17360907. "Final proof of role of neural coherence in consciousness?" 
  6. ^ Gammaitoni L, Hänggi P, Jung P, Marchesoni F (1998). "Stochastic resonance". Review of Modern Physics 70 (1): 223–87. Bibcode 1998RvMP...70..223G. doi:10.1103/RevModPhys.70.223. http://www.physik.uni-augsburg.de/theo1/hanggi/Papers/195.pdf. 
  7. ^ Gammaitoni L (1995). "Stochastic resonance and the dithering effect in threshold physical systems". Phys Rev E 52 (5): 4691–8. Bibcode 1995PhRvE..52.4691G. doi:10.1103/PhysRevE.52.4691. http://nipslab.fisica.unipg.it/files/PRE1995-SR-and-dithering-p4691_1.pdf. 
  8. ^ Palonpon A, Amistoso J, Holdsworth J, Garcia W, Saloma C (1998). "Measurement of weak transmittances by stochastic resonance". Optics Letters 23 (18): 1480–2. Bibcode 1998OptL...23.1480P. doi:10.1364/OL.23.001480. PMID 18091823. http://www.opticsinfobase.org/abstract.cfm?id=36963. 

Bibliography

Bibliography for suprathreshold stochastic resonance

External links