What is Stochastic Resonance ?
Clément Douarre
- KAIST 2015 -
1 France !
2 France !
3 France !
4 The article
What is Stochastic Resonance ? Definitions, Misconceptions, Debates, and Its Relevance to Biology
Authors : Mark D. McDonnell & Derek Abbott, Institute of Telecommunications Research, University of South Australia
5 Outline
1 Evolution of the definition of SR - First definition - Modern definition - Critics and clarifications
2 Its role in biology - Does it happen in the brain ? - A biomedical example
6 PART I : DEFINITION
7 Main idea : "Stochastic"
Physical systems in which we are uncertain about the values of parameters, measurements, expected input and disturbances are termed Stochastic Systems (Wikipedia)
8 Main idea : "Resonance"
Resonance is a phenomenon that consists of a given system being driven by another vibrating system or by external forces to oscillate with greater amplitude at some preferential frequencies (Wikipedia)
9 We consider here signal processing systems which transform an input to an output, and so where there is almost inevitably noise "Good noise"
Main idea
What is SR ? "Getting resonance from stochasticism"
10 "Good noise"
Main idea
What is SR ? "Getting resonance from stochasticism"
We consider here signal processing systems which transform an input to an output, and so where there is almost inevitably noise
10 Main idea
What is SR ? "Getting resonance from stochasticism"
We consider here signal processing systems which transform an input to an output, and so where there is almost inevitably noise "Good noise"
10 Main idea (2)
11 Since then, interest has been growing rapidly
History
First used in 1980 by Roberto Benzi, at the NATO International School of Climatology, as an explanation for the periodic ice ages of the earth.
12 History
First used in 1980 by Roberto Benzi, at the NATO International School of Climatology, as an explanation for the periodic ice ages of the earth.
Since then, interest has been growing rapidly
12 A growing interest
13 -Over enthusiasm
First reactions
When SR started to get well known, it met several problems :
-Skepticism
14 First reactions
When SR started to get well known, it met several problems :
-Skepticism
-Over enthusiasm
14 -Presence of a certain noise may help to get a better output
-Happens when noise and input are in resonance, in the physical sense of the word. Signal must be periodic.
-Input signal must be weak compared to the noise. Output must have a threshold.
First definition (1981)
-Phenomenon that occurs in non linear systems, which recieve an input and produce an output.
15 -Happens when noise and input are in resonance, in the physical sense of the word. Signal must be periodic.
-Input signal must be weak compared to the noise. Output must have a threshold.
First definition (1981)
-Phenomenon that occurs in non linear systems, which recieve an input and produce an output.
-Presence of a certain noise may help to get a better output
15 -Input signal must be weak compared to the noise. Output must have a threshold.
First definition (1981)
-Phenomenon that occurs in non linear systems, which recieve an input and produce an output.
-Presence of a certain noise may help to get a better output
-Happens when noise and input are in resonance, in the physical sense of the word. Signal must be periodic.
15 -Input signal must be weak compared to the noise. Output must have a threshold.
First definition (1981)
-Phenomenon that occurs in non linear systems, which recieve an input and produce an output.
-Presence of a certain noise may help to get a better output
-Happens when noise and input are in resonance, in the physical sense of the word. Signal must be periodic.
15 First definition (1981)
-Phenomenon that occurs in non linear systems, which recieve an input and produce an output.
-Presence of a certain noise may help to get a better output
-Happens when noise and input are in resonance, in the physical sense of the word. Signal must be periodic.
-Input signal must be weak compared to the noise. Output must have a threshold.
15 How does it work ?
"Random noise can benefit signals by boosting them in a correlated manner over a threshold"
Article : How Noise Can Enhance Detection of Weak Signals and Help Improve Biological Information Processing - Peter Hänggi 16 SSR (Suprathreshold Stochastic Resonance)
Modern definition (Early 2000)
SR occurs when the output signal from a non linear system provides a better representation of the input signal than it would in complete absence of noise
17 Modern definition (Early 2000)
SR occurs when the output signal from a non linear system provides a better representation of the input signal than it would in complete absence of noise
SSR (Suprathreshold Stochastic Resonance)
17 ... We do not really know.
Article : Suprathreshold stochastic resonance Mark D. McDonnell and Nigel Stocks (2009), Scholarpedia
How does it work ?
18 Article : Suprathreshold stochastic resonance Mark D. McDonnell and Nigel Stocks (2009), Scholarpedia
How does it work ? ... We do not really know.
18 How does it work ? ... We do not really know.
Article : Suprathreshold stochastic resonance Mark D. McDonnell and Nigel Stocks (2009), Scholarpedia 18 • SR occurs only in systems where output SNR (Signal to Noise Ratio) decreases non monotonically when noise increases.
• There is no way to detect an otherwise undetectable signal using SR.
• Using noise is rarely as efficient as trying to diminish it or as increasing output SNR. Thus, SR is a suboptimal strategy.
Critics
J. Tougaard
19 • There is no way to detect an otherwise undetectable signal using SR.
• Using noise is rarely as efficient as trying to diminish it or as increasing output SNR. Thus, SR is a suboptimal strategy.
Critics
• SR occurs only in systems where output SNR (Signal to Noise Ratio) decreases non monotonically when noise increases.
J. Tougaard
19 • Using noise is rarely as efficient as trying to diminish it or as increasing output SNR. Thus, SR is a suboptimal strategy.
Critics
• SR occurs only in systems where output SNR (Signal to Noise Ratio) decreases non monotonically when noise increases.
• There is no way to detect an otherwise undetectable signal using SR.
J. Tougaard
19 Critics
• SR occurs only in systems where output SNR (Signal to Noise Ratio) decreases non monotonically when noise increases.
• There is no way to detect an otherwise undetectable signal using SR.
• Using noise is rarely as efficient as trying to diminish it or as increasing output SNR. J. Tougaard Thus, SR is a suboptimal strategy.
19 -Has been showed partly wrong by Ward and al
-Detection techniques like SNR may not be appliable to non linear systems.
-Is SNR the real goal ?
Tougaard’s arguments (1)
SR occurs only in systems where output SNR (Signal to Noise Ratio) decreases non monotonically when noise increases.
20 -Detection techniques like SNR may not be appliable to non linear systems.
-Is SNR the real goal ?
Tougaard’s arguments (1)
SR occurs only in systems where output SNR (Signal to Noise Ratio) decreases non monotonically when noise increases.
-Has been showed partly wrong by Ward and al
20 -Is SNR the real goal ?
Tougaard’s arguments (1)
SR occurs only in systems where output SNR (Signal to Noise Ratio) decreases non monotonically when noise increases.
-Has been showed partly wrong by Ward and al
-Detection techniques like SNR may not be appliable to non linear systems.
20 Tougaard’s arguments (1)
SR occurs only in systems where output SNR (Signal to Noise Ratio) decreases non monotonically when noise increases.
-Has been showed partly wrong by Ward and al
-Detection techniques like SNR may not be appliable to non linear systems.
-Is SNR the real goal ?
20 Tougaard’s arguments (2)
There is no way to detect an otherwise undetectable signal using SR.
21 Thinking of SR as a strategy is confusing cause with effect.
Rather say "Some systems are capable of SR. It can occur when random noise level is changed to a certain value."
SR must not be seen as and end in itself, but as a way to benefit from noise we cannot get rid of.
Tougaard’s arguments (3)
Using noise is rarely as efficient as trying to diminish it or as increasing output SNR. Thus, SR is a suboptimal strategy.
22 Rather say "Some systems are capable of SR. It can occur when random noise level is changed to a certain value."
SR must not be seen as and end in itself, but as a way to benefit from noise we cannot get rid of.
Tougaard’s arguments (3)
Using noise is rarely as efficient as trying to diminish it or as increasing output SNR. Thus, SR is a suboptimal strategy.
Thinking of SR as a strategy is confusing cause with effect.
22 SR must not be seen as and end in itself, but as a way to benefit from noise we cannot get rid of.
Tougaard’s arguments (3)
Using noise is rarely as efficient as trying to diminish it or as increasing output SNR. Thus, SR is a suboptimal strategy.
Thinking of SR as a strategy is confusing cause with effect.
Rather say "Some systems are capable of SR. It can occur when random noise level is changed to a certain value."
22 Tougaard’s arguments (3)
Using noise is rarely as efficient as trying to diminish it or as increasing output SNR. Thus, SR is a suboptimal strategy.
Thinking of SR as a strategy is confusing cause with effect.
Rather say "Some systems are capable of SR. It can occur when random noise level is changed to a certain value."
SR must not be seen as and end in itself, but as a way to benefit from noise we cannot get rid of.
22 • Over the years, the usage of this term has broadened.
• However, one must remember that SR does not do miracles. It does not improve certain measures we are used to like output SNR.
• SR must be seen as a way of making the most out of noise that is inherently present in natural systems.
Where are we ?
• SR is the concept that noise can increase a quality of the output in a non linear signal system
23 • However, one must remember that SR does not do miracles. It does not improve certain measures we are used to like output SNR.
• SR must be seen as a way of making the most out of noise that is inherently present in natural systems.
Where are we ?
• SR is the concept that noise can increase a quality of the output in a non linear signal system
• Over the years, the usage of this term has broadened.
23 • SR must be seen as a way of making the most out of noise that is inherently present in natural systems.
Where are we ?
• SR is the concept that noise can increase a quality of the output in a non linear signal system
• Over the years, the usage of this term has broadened.
• However, one must remember that SR does not do miracles. It does not improve certain measures we are used to like output SNR.
23 Where are we ?
• SR is the concept that noise can increase a quality of the output in a non linear signal system
• Over the years, the usage of this term has broadened.
• However, one must remember that SR does not do miracles. It does not improve certain measures we are used to like output SNR.
• SR must be seen as a way of making the most out of noise that is inherently present in natural systems.
23 PART II : ITS ROLE IN BIOLOGY
24 .. but mainly in neuroscience.
Fields of research
Many fields like ion channels, ecological models, cell biology..
25 Fields of research
Many fields like ion channels, ecological models, cell biology..
.. but mainly in neuroscience.
25 It can.
But does it ?... No experiment has proved that SR occurs naturally in neurons nor that they use it in any way.
Does SR happen in neurons ?
26 But does it ?... No experiment has proved that SR occurs naturally in neurons nor that they use it in any way.
Does SR happen in neurons ? It can.
26 But does it ?... No experiment has proved that SR occurs naturally in neurons nor that they use it in any way.
Does SR happen in neurons ? It can.
26 No experiment has proved that SR occurs naturally in neurons nor that they use it in any way.
Does SR happen in neurons ? It can.
But does it ?...
26 Does SR happen in neurons ? It can.
But does it ?... No experiment has proved that SR occurs naturally in neurons nor that they use it in any way. 26 The brain would not function the way it does if it was completely deterministic.
Randomness has been known to have a role in the neurons far before SR
Does SR happen in neurons ? (2)
However, it is widely believed that SR does occur in vivo.
27 Randomness has been known to have a role in the neurons far before SR
Does SR happen in neurons ? (2)
However, it is widely believed that SR does occur in vivo.
The brain would not function the way it does if it was completely deterministic.
27 Does SR happen in neurons ? (2)
However, it is widely believed that SR does occur in vivo.
The brain would not function the way it does if it was completely deterministic.
Randomness has been known to have a role in the neurons far before SR
27 River is 1.9m wide. ± 0.2m You can jump 2m. ± 0.3m
Neurons are highly dependent on random
Article : Bayesian inference with probabilistic population codes - Ma WJ, Beck JM, Latham PE, Pouget A (2006)
28 ± 0.2m ± 0.3m
Neurons are highly dependent on random
Article : Bayesian inference with probabilistic population codes - Ma WJ, Beck JM, Latham PE, Pouget A (2006)
River is 1.9m wide. You can jump 2m.
28 Neurons are highly dependent on random
Article : Bayesian inference with probabilistic population codes - Ma WJ, Beck JM, Latham PE, Pouget A (2006)
River is 1.9m wide. ± 0.2m You can jump 2m. ± 0.3m
28 -They are non linear systems in which SR can occur.
-Noise plays an important role in other neuronal features.
So does SR happen in neurons ? (3)
Even it has not been shown, it is very probable because :
29 -Noise plays an important role in other neuronal features.
So does SR happen in neurons ? (3)
Even it has not been shown, it is very probable because :
-They are non linear systems in which SR can occur.
29 So does SR happen in neurons ? (3)
Even it has not been shown, it is very probable because :
-They are non linear systems in which SR can occur.
-Noise plays an important role in other neuronal features.
29 Colchear implant
A colchear implant is a group of 20 electrodes, each one stimulating nerves
A biomedical application of SR
Deaf people often have damaged or missing hair cells in the colchea
30 A colchear implant is a group of 20 electrodes, each one stimulating nerves
A biomedical application of SR
Deaf people often have damaged or missing hair cells in the colchea
Colchear implant
30 A biomedical application of SR
Deaf people often have damaged or missing hair cells in the colchea
Colchear implant
A colchear implant is a group of 20 electrodes, each one stimulating nerves
30 These has been found to be not very efficient..
Observation "The healthy mammalian cochlea has a significant amount of spontaneous activity (neural firing) ‘in quiet’ that is largely not observed if the hair cells and presynaptic connections are damaged or absent"
A biomedical application of SR (2)
Since every electrode is the same, the global output message is just the sum of every electrode’s output message
31 Observation "The healthy mammalian cochlea has a significant amount of spontaneous activity (neural firing) ‘in quiet’ that is largely not observed if the hair cells and presynaptic connections are damaged or absent"
A biomedical application of SR (2)
Since every electrode is the same, the global output message is just the sum of every electrode’s output message
These has been found to be not very efficient..
31 A biomedical application of SR (2)
Since every electrode is the same, the global output message is just the sum of every electrode’s output message
These has been found to be not very efficient..
Observation "The healthy mammalian cochlea has a significant amount of spontaneous activity (neural firing) ‘in quiet’ that is largely not observed if the hair cells and presynaptic connections are damaged or absent"
31 A biomedical application of SR (3)
Article : The application of suprathreshold stochastic resonance to cochlear implant coding - N.G. Stocks and D. Allingham
32 • It is strongly believed to occur in the brain, along with other usages of noise.
• Even if your neurons are on it, I would recommend avoiding rivers with piranhas as much as possible.
So what have we learned, class ?
• Stochastic resonance is a process that occurs in some non linear signal systems, by which random noise somehow increases some quality of the output.
33 • Even if your neurons are on it, I would recommend avoiding rivers with piranhas as much as possible.
So what have we learned, class ?
• Stochastic resonance is a process that occurs in some non linear signal systems, by which random noise somehow increases some quality of the output.
• It is strongly believed to occur in the brain, along with other usages of noise.
33 So what have we learned, class ?
• Stochastic resonance is a process that occurs in some non linear signal systems, by which random noise somehow increases some quality of the output.
• It is strongly believed to occur in the brain, along with other usages of noise.
• Even if your neurons are on it, I would recommend avoiding rivers with piranhas as much as possible.
33 Image sources
Definition : Picture by me Dice : http ://www.zontikgames.com Resonant bridge : science.howstuffworks.com Stochastic peak : the article Scrat from Ice Age : 7-themes.com Nb of articles about SR : the article J. Tougaard : http ://scholar.google.com Confused neuron : imgkid.com & my Paint skills Jungle : inetgrafx.deviantart.com Ear : www.easyeartraining.com
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