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Noise in the nervous systems: Stochastic Resonance

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Noise in the nervous systems: Stochastic Resonance Jaeseung Jeong, Ph.D Department of Bio and Brain Engineering, KAIST – PowerPoint PPT presentation

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Title: Noise in the nervous systems: Stochastic Resonance


1
Noise in the nervous systems Stochastic
Resonance
  • Jaeseung Jeong, Ph.D
  • Department of Bio and Brain Engineering,
  • KAIST

2
Several sources of Noise in the Brain
  • Thermal noise
  • Cellular noise Stochastic opening and closing of
    ion channels
  • Membrane voltage fluctuations in the axons and
    dendrites
  • Synaptic noise Spontaneous release of vesicles
    in the synapses
  • Sensory and motor noises
  • Random generation of voltage fluctuations in
    the fibers
  • Environmental (Stimulus) noises

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4
Cortical variability
5
Cortical variability cellular noise
  • a. The shift of the overall spike pattern across
    rows reflects the average propagation speed of
    the APs. The raster plot of the somatic
    measurement reflects spike-time variability from
    AP initiation. Owing to channel noise, the
    spike-time variability rapidly increases the
    further the AP propagates, and it eventually
    reaches millisecond orders.
  • b. Trial-to-trial variability of synaptic
    transmission measured in vitro by paired
    patch-clamp recordings in rat somatosensory
    cortex slices. Six consecutive postsynaptic
    responses (black traces) to an identical
    presynaptic-stimulation pattern (top trace) are
    shown, along with the ensemble mean response
    (grey trace) from over 50 trials.

6
What is Stochastic Resonance?
  • A stochastic resonance is a phenomenon in which a
    nonlinear system is subjected to a periodic
    modulated signal so weak as to be normally
    undetectable, but it becomes detectable due to
    resonance between the weak deterministic signal
    and stochastic noise.
  • The earliest definition of stochastic resonance
    was the maximum of the output signal strength as
    a function of noise (Bulsara and Gammaitoni
    1996).

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9
Ice-age cycle of Earth
10
Noise-aided hopping events
  • Surmounting the barrier requires a certain amount
    of force. Suppose the ball is subjected to a
    force which varies in time sinusoidally, but is
    too weak to push the ball over the barrier.
  • If we add a random noise component to the
    forcing, then the ball will occasionally be able
    to hop over the barrier.
  • The presence of the sinusoid can then be seen as
    a peak in the power spectrum of the time series
    of noise-aided hopping events.

11
Signal and noise
  • We can visualize the sinusoidal forcing as a
    tilting of the container. In the time series
    below, the gray background represents the
    time-varying depth of the wells with respect to
    the barrier. The red trace represents the
    position of the ball.

12
Physical picture of Stochastic Resonance
  • If the particle is excited by a small sinusoidal
    force, it will oscillate within one of the two
    wells. But if the particle is also excited by a
    random force (i.e. noise plus sine) it will hop
    from one well to the other, more or less
    according to the frequency of the sine the
    periodical force tends to be amplified.
  • It can intuitively be sensed that if the particle
    is excited by the sine plus a very small noise it
    will hop a few times. In return, if the noise is
    too powerful, the system will become completely
    randomized. Between these two extreme situations,
    there exists an optimal power of input noise for
    which the cooperative effect between the sine and
    the noise is optimal.

13
Bistability in Stochastic Resonance
14
Power spectra of hopping events
  • In this power spectra of hopping events, the gray
    bars mark integer multiples of the sinusoidal
    forcing frequency.

15
Kramers rate for Stochastic Resonance
  • Physically, the sine posses a characteristic time
    that is its period. The dynamical system has also
    a characteristic time system that is the mean
    residence time in the absence of the sine, i.e.
    the mean (in statistical sense) time spent by the
    particle inside one well.
  • This time is the inverse of the transition rate,
    known as Kramers rate, and is function of the
    noise level. (i.e. the inverse of the average
    switch rate induced by the sole noise the
    stochastic time scale).
  • For the optimal noise level, there is a
    synchronization between the Kramers rate and the
    frequency of the sine, justifying the term of
    resonance.
  • Since this resonance is tuned by the noise level,
    it was called stochastic resonance (SR).

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18
Peak SNRs correspond to maximum spatiotemporal
synchronization.
  • SNR of the middle oscillator of an array of 65 as
    a function of noise for two different coupling
    strengths, 0.1 and 10.

19
Stochastic Resonance in multi Array oscillators
  • Time evolution (up) of an array of 65
    oscillators, subject to different noise power and
    coupling strength. The temporal scale of the
    patterns decreases with increasing noise while
    the spatial scale of the patterns increases with
    increasing coupling strength.
  • For this range of noise and coupling,
    spatiotemporal synchronization (and peak SNR)
    correspond to a coupling of about 10 and a noise
    of about 35 dB, as indicated by the striped
    pattern in the third column of the second row
    from the top.

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Stochastic Resonance in the nervous system
  • Since its first discovery in cat visual neurons,
    stochastic-resonance-type effects have been
    demonstrated in a range of sensory systems.
  • These include crayfish mechanoreceptors, shark
    multimodal sensory cells, cricket cercal sensory
    neurons and human muscle spindles.
  • The behavioural impact of stochastic resonance
    has been directly demonstrated and manipulated in
    passive electrosensing paddlefish and in human
    balance control.

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23
Noise produces nonlinearity
  • in spike-generating neurons, sub-threshold
    signals have no effect on the output of the
    system. Noise can transform such threshold
    nonlinearities by making sub-threshold inputs
    more likely to cross the threshold, and this
    becomes more likely the closer the inputs are to
    the threshold.
  • Thus, when outputs are averaged over time, this
    noise produces an effectively smoothed
    nonlinearity.
  • This facilitates spike initiation and can improve
    neural-network behaviour, as was shown in studies
    of contrast invariance of orientation tuning in
    the primary visual cortex.
  • Neuronal networks in the presence of noise will
    be more robust and explore more states,
    facilitating learning/adaptation to the changing
    demands of a dynamic environment.

24
SR-based techniques
  • 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.

25
Balancing act using vibrating insoles
  • Using a phenomenon called stochastic resonance,
    the human body can make use of random vibrations
    to help maintain its balance.
  • In experiments on people in their 20s and people
    in their 70s, actuators embedded in gel insoles
    generated noisy vibrations with such a small
    amount of force that a person standing on the
    insoles could not feel them. A reflective marker
    was fixed to the research subject's shoulder, and
    a video camera recorded its position.

26
  • People always sway a small amount even when they
    are trying to stand still. The amount of sway
    increases with age. But under the influence of a
    small amount of vibration, which improves the
    mechanical senses in the feet, both old and young
    sway much less.
  • Remarkably, noise made people in their 70s sway
    about as much as people in their 20s swayed
    without noise.

27
Noise reduction mechanisms in the Brain
  • Thresholding systems in the neurons
  • Low Reliability (Bursts) between neurons
  • Rate coding hypothesis
  • Averaging (Neuronal Population coding)
  • Using prior knowledge about the noise
    characteristics

28
Accuracy in the Information processing of the
Brain vs. Noise
29
How can neural networks maintain stable activity
in the presence of noise?
Part a shows convergence of signals onto a single
neuron. If the incoming signals have independent
noise, then noise levels in the postsynaptic
neuron will scale in proportion to the square
root of the number of signals (N), whereas the
signal scales in proportion to N. cf. If the
noise in the signals is perfectly correlated,
then the noise in the neuron will also scale in
proportion to N.
30
Homeostatic plasticity mechanisms
  • Experimental evidence suggests that average
    neuronal activity levels are maintained by
    homeostatic plasticity mechanisms that
    dynamically set synaptic strengths, ion-channel
    expression or the release of neuromodulators.
  • This in turn suggests that networks of neurons
    can dynamically adjust to attenuate noise
    effects. Moreover, these networks might be wired
    so that large variations in the response
    properties of individual neurons have little
    effect on network behaviour.

31
Principles of how the CNS manages noise
  • The principle of averaging can be applied
    whenever redundant information is present across
    the sensory inputs to the CNS or is generated by
    the CNS.
  • Averaging can counter noise if several units
    (such as receptor molecules, neurons or muscles)
    carry the same signal and each unit is affected
    by independent sources of noise.
  • Averaging is seen at the very first stage of
    sensory processing.

32
Divergence
  • Counterintuitively, divergence (one neuron
    synapsing onto many) can also support averaging.
  • When signals are sent over long distances through
    noisy axons, rather than using a single axon it
    can be beneficial to send the same signal
    redundantly over multiple axons and then combine
    these signals at the destination.
  • Crucially, for such a mechanism to reduce noise
    the initial divergence of one signal into many
    must be highly reliable.
  • Such divergence is seen in auditory inner hair
    cells, which provide a divergent input to 1030
    ganglion cells through a specialized 'ribbon
    synapse'.

33
  • Averaging is used in many neural systems in which
    information is encoded as patterns of activity
    across a population of neurons that all subserve
    a similar function these are termed neural
    population codes.

34
Prior knowledge about noises
  • Prior knowledge can also be used to counter
    noise. If the structure of the signal and/or
    noise is known it can be used to distinguish the
    signal from the noise. This principle is
    especially helpful in dealing with sensory
    signals that, in the natural world, are highly
    structured and redundant.
  • Signal-detection theory shows that the optimal
    signal detector, subject to additive noise, is
    obtained by matching all parameters of the
    detector to those of the signal to be detected
    in neuroscience this is termed the matched-filter
    principle.
  • Thus, the structures of receptive fields embody
    prior knowledge about the expected inputs and
    thereby allow neurons to attenuate the impact of
    noise.

35
Bayesian inference combining averaging and
prior knowledge
  • The principles of averaging and prior knowledge
    can be placed into a larger mathematical
    framework of optimal statistical estimation and
    decision theory, known as Bayesian inference.
  • Bayesian inference assigns probabilities to
    propositions about the world (beliefs). These
    beliefs are calculated by combining prior
    knowledge (for example, that an animal is a
    predator) and noisy observations (for example,
    the heading of animal) to infer the probability
    of propositions (for example, animal attacks).
  • Psychophysical experiments have confirmed that
    humans use these Bayesian inferences to allow
    them to cope with noise (and, more generally,
    with uncertainty) in both perception and action.
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