![Page 1: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/1.jpg)
Extracting Time and Space Extracting Time and Space Scales with Scales with
Feedback and NonlinearityFeedback and Nonlinearity
André Longtin
Physics +Cellular and Molecular Medicine
CENTER FOR NEURAL DYNAMICS
UNIVERSITY OF OTTAWA
Funding by NSERC, CIHR, PREA
![Page 2: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/2.jpg)
Processing of spatio-temporal signals Processing of spatio-temporal signals Global Feedback + common noise: Global Feedback + common noise:
oscillations oscillations Spatial scale for feedback and inputSpatial scale for feedback and input Envelope processing for narrowband in time Envelope processing for narrowband in time Information resonancesInformation resonances Coincidence transforms for synchronous Coincidence transforms for synchronous
firingfiring Short term Plasticity and information Short term Plasticity and information
processingprocessing
Overview
![Page 3: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/3.jpg)
Research Program: Research Program:
Stochastic neural networkStochastic neural network
driven bydriven by
Stochastic input in space and timeStochastic input in space and time
Experimental <-> TheoreticalExperimental <-> Theoretical
![Page 4: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/4.jpg)
Relevance to this group:Relevance to this group:
What nonlinearity (if any) supports What nonlinearity (if any) supports patterns or computations ? patterns or computations ?
![Page 5: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/5.jpg)
HIGHER BRAIN AREA I
HIGHER BRAIN AREA II
THALAMUS
RECEPTORS
PHYSICAL STIMULI
![Page 6: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/6.jpg)
Brain Diagram by Arab philosopher Avicenna (circa 1300)Brain Diagram by Arab philosopher Avicenna (circa 1300)Five ventriclesFive ventricles: common sense, imagination, judging, : common sense, imagination, judging,
second imagination (composing/combining images), memory.second imagination (composing/combining images), memory.((University University LibraryLibrary, Cambridge, Cambridge) )
From Da Vinci’s notes
![Page 7: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/7.jpg)
Courtesy W. Ellis (1991)
Electrosensory lateralline lobe (ELL)
Courtesy N. Berman and L. Maler, J. Exp. Biol., 1999
![Page 8: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/8.jpg)
Electrosensory Lateral Line Lobe (ELL)
Electroreceptors
Higher Brain
Electrosensory Input
Amplitude Modulation (AM)
Krahe and Gabbiani (2004) Nat. Neurosci.Rev. 5:13-23
Electric Organ Discharge (EOD)
afferents
The electric sense
![Page 9: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/9.jpg)
Temporal Characteristics: Spatial Characteristics:
Harmonic
“local”
“global”
Broadband (noise)
Chacron, et al., Nature, 2003
- Frequency tuning is highly correlated with spatial frequency
- Tuning for harmonics or broadband signals are qualitatively the same
![Page 10: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/10.jpg)
Weakly Electric Fish: Weakly Electric Fish: main negative feedback loopmain negative feedback loop
ELL Pyramidal Cells: the first stage of sensory processing
![Page 11: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/11.jpg)
Prey StimuliPrey Stimuli
Prey (bug) excites a fraction of the electroreceptors:
Local stimulation
![Page 12: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/12.jpg)
Communication StimuliCommunication Stimuli
Communication calls between fish stimulate the whole body:
Global Stimulation
![Page 13: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/13.jpg)
Oscillation MechanismOscillation Mechanism(Doiron, Chacron, Bastian, Longtin, Maler, (Doiron, Chacron, Bastian, Longtin, Maler, Nature 2003Nature 2003))
Local Stimuli :applied heterogeneously in space: No stimulus-induced correlations.
Global Stimuli :acts homogenously in space (strong spatial correlations). Correlated activity and delay cause “waves” of inhibition
![Page 14: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/14.jpg)
Electrosensory CircuitryElectrosensory Circuitry
Sodium channel blocker can open the feedback loop.
![Page 15: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/15.jpg)
Network Model – Global Network Model – Global StimuliStimuli
To mimic communication stimuli we apply the external stimulus to all neurons equally.
Autocorrelation Histogram
![Page 16: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/16.jpg)
Experimental VerificationExperimental VerificationDoiron, Chacron, Maler, Longtin and Bastian, Doiron, Chacron, Maler, Longtin and Bastian, NatureNature 42, 539 42, 539
(2003)(2003)
ISI Histogram Autocorrelation
control block recover
![Page 17: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/17.jpg)
Correlated Stimuli in Correlated Stimuli in ExperimentsExperiments
Dipole 1
Dipole 2
Dipole 3
Dipole 4
)()(1)( tctct Gii
Each dipole emits an intrinsic noise i(t), and global source, G(t). Their relative strengths is c, i.e. the covariance between dipoles.
![Page 18: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/18.jpg)
Integrate-and-fire dynamics Integrate-and-fire dynamics
y
![Page 19: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/19.jpg)
Linear ResponseLinear Response
Consider the spike train from the ith neuron in our network, . Assuming weak inputs, the Fourier transform of the spike train is
)()( iji ttty
)()()()( ibgi XAYY
A( intrinsic frequency response of the noisy neuron. Xi(w): Fourier transform of input (external + feedback) to
neuron i.
(1)
![Page 20: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/20.jpg)
POWER SPECTRUMPOWER SPECTRUM
![Page 21: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/21.jpg)
Single Neuron Power SpectrumSingle Neuron Power Spectrumvsvs
percentage of common noise (c) percentage of common noise (c)
For an infinite network: For an infinite network:
2
~2
22
)(~
1
)(~
)(~
Re2
)()()(
AKg
AKgAKg
AcSS
d
dd
bg
)(|)(| 2 inSA
(Input-output sync) (spike-spike sync.)
![Page 22: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/22.jpg)
Fokker-Planck analysis on noisy Leaky Integrate-and-fire Fokker-Planck analysis on noisy Leaky Integrate-and-fire Neurons + Delays+ Spatial InputNeurons + Delays+ Spatial Input
Doiron, Lindner, Longtin, Bastian and Maler, Doiron, Lindner, Longtin, Bastian and Maler, Phys. Rev. LettPhys. Rev. Lett. 93, 048101 (2004). 93, 048101 (2004)
Linear Fluctuation Theory: needs noise. Linear Fluctuation Theory: needs noise. 30
25
20
15
S (
spik
es2 /s
)
140120100806040200
frequency (Hz)
simulation c=1 theory c=1 simulations c=0 theory c=0
![Page 23: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/23.jpg)
Input-output coherence for Input-output coherence for delayed feedback networkdelayed feedback network
(global feedback)(global feedback)
![Page 24: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/24.jpg)
Coherence function:
CXY ( f ) SXY ( f )
2
SXX ( f ) SYY ( f )
Correlation coefficient (in the frequency domain) between two signals, X and Y
R(t) (t tii )
Response: spike trainStimulus:
S(t) - narrowband stimulus(linear)
E(t) - envelope of narrowbandstimulus (non-linear)
![Page 25: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/25.jpg)
Network of stochastic Perfect IF’s Network of stochastic Perfect IF’s with with
+ and - global delayed feedback+ and - global delayed feedback
)2()tt(N
1)t(K
)1()t(Kg)t(Kg)t(S)t(D2VN
1k
)t(M
1jkji,ei,e
iiieeekk
k
S(t) is the stimulus
Chacron, Longtin, Maler, Phys.Rev.E (2005)
![Page 26: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/26.jpg)
Network of Perfect IF’s with Network of Perfect IF’s with global feedback: Information global feedback: Information
theorytheory
0 20 40 60 80
0.0
0.2
0.4
0.6
0.8
1.0
coh
ere
nce
frequency (Hz)
ge=g
i=0
ge=0, g
i=-0.8
ge=0.8, g
i=0
Coherence = | H(f)|2 Pss/Pxx
![Page 27: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/27.jpg)
INFORMATION RESONANCEINFORMATION RESONANCE(Chacron, Longtin, Maler, PRE 2005)(Chacron, Longtin, Maler, PRE 2005)
G<0
G=0
Experimental DATA !!
![Page 28: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/28.jpg)
Introducing…Introducing…
Spatial scale for feedbackSpatial scale for feedback Spatial scale for noiseSpatial scale for noise
Two regimes with respect to Two regimes with respect to
gamma oscillationsgamma oscillations
![Page 29: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/29.jpg)
![Page 30: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/30.jpg)
In linear response, only the ratio of length scales matters(Hutt, Sutherland, Longtin, submitted)
![Page 31: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/31.jpg)
GLOBAL IN SPACEGLOBAL IN SPACE
NARROWBAND IN TIME: NARROWBAND IN TIME:
2 TIME SCALES2 TIME SCALES
![Page 32: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/32.jpg)
EOD amplitude
EOD
![Page 33: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/33.jpg)
Hey guys
EOD amplitude
EOD
![Page 34: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/34.jpg)
EODamplitude
EOD
From: E. W. Tan et al, Behav.Brain Res., 164:83-92 (2005)
Most probable populationsize 3-5 fish
Average f inblack (white) waters:
Day: 35.3 (54.1) HzNight: 54.6 (65.8) Hz
![Page 35: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/35.jpg)
![Page 36: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/36.jpg)
P-units (primary receptors)Feed forward:
- P-units respond as linear encoders
frequency (Hz)
![Page 37: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/37.jpg)
- global stimulation: linear response to narrowband signal and its low frequency envelope
- Envelope response is absent under local stimulation
PyramidalCells
S(t)
E(t)
![Page 38: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/38.jpg)
Middleton, Longtin, Benda, Maler, PNAS (2006)
![Page 39: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/39.jpg)
input
output
- Generation of envelope signal is likely due to spike threshold nonlinearity
- Output spike train is phase- locked to fast oscillation and modulated at lower frequencies
Middleton, Harvey-Girard, Maler, Longtin,
Phys. Rev. E. (2006)
MECHANISM
![Page 40: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/40.jpg)
transferfunction
input signal output signal
(rectification)
![Page 41: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/41.jpg)
signals Spectral composition
time frequency
![Page 42: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/42.jpg)
![Page 43: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/43.jpg)
![Page 44: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/44.jpg)
![Page 45: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/45.jpg)
![Page 46: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/46.jpg)
Network instead of single cellNetwork instead of single cell
![Page 47: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/47.jpg)
![Page 48: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/48.jpg)
![Page 49: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/49.jpg)
Stochastic Envelope GatingStochastic Envelope Gating(and not SR! See Middleton et al., PRE 2006)(and not SR! See Middleton et al., PRE 2006)
![Page 50: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/50.jpg)
Leaky Integrate-and-Fire (LIF) neuron:
dv
dt
v
2D
(t) S(t)
r() dzez2
erfc(z) vR 2 D
vR 2 D
1
(t) o a S(t)
Mean firing rate:
where
![Page 51: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/51.jpg)
![Page 52: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/52.jpg)
GLOBAL SPATIAL SIGNALSGLOBAL SPATIAL SIGNALS
EXTRACTING EXTRACTING
HIGH FREQUENCY CHIRPS HIGH FREQUENCY CHIRPS
FROM FROM
LOWER FREQUENCY BEATSLOWER FREQUENCY BEATS
““SYNC-DESYNC CODE”SYNC-DESYNC CODE”
![Page 53: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/53.jpg)
Context: Context: electrocommunicationelectrocommunication
Male-male or female-female call Male-male or female-female call causes synchronization of receptorscauses synchronization of receptors
Male-female or female-male call Male-female or female-male call causes desynchronization of causes desynchronization of receptorsreceptors
(Benda, Longtin, Maler, Neuron 2006)(Benda, Longtin, Maler, Neuron 2006)
![Page 54: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/54.jpg)
Encoding a modulatory Encoding a modulatory signalsignal
![Page 55: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/55.jpg)
![Page 56: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/56.jpg)
Coincidence transforms…Coincidence transforms…
Middleton, Longtin, Benda, Maler (submitted)
![Page 57: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/57.jpg)
Short-term Plasticity Short-term Plasticity
![Page 58: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/58.jpg)
![Page 59: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/59.jpg)
![Page 60: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/60.jpg)
![Page 61: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/61.jpg)
![Page 62: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/62.jpg)
![Page 63: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/63.jpg)
![Page 64: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/64.jpg)
Broadband Coding
Depression
dominates
Facilitation
dominates
![Page 65: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/65.jpg)
-Gamma rhythms for global correlated inputs
- Gamma strength proportional to correlation
- Spatial feedback can assess spatial correlation of input
- Information resonances with delayed feedback
- Envelope generation due to spike threshold nonlinearity
- Envelope generation is dependent on mean bias and noise
![Page 66: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/66.jpg)
Intrinsic noise can gate a signal competing with envelope
Plasticity: paradoxical effects on coding
Importance of spatiotemporal statistics of input
![Page 67: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/67.jpg)
![Page 68: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/68.jpg)
Brent Doiron
Maurice Chacron
Jason Middleton Carlo Laing Eric Harvey-Girard John Lewis
Jan Benda
Benjamin Lindner
Len Maler & André Longtin
Joe Bastian
Connie Sutherland
Axel Hutt
![Page 69: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/69.jpg)
![Page 70: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/70.jpg)
COHERENCE AND STOCHASTIC RESONANCE COHERENCE AND STOCHASTIC RESONANCE WITH DELAYED FEEDBACKWITH DELAYED FEEDBACK
Morse and Longtin, Phys. Lett. A (2006)Morse and Longtin, Phys. Lett. A (2006)
![Page 71: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/71.jpg)
MULTIPLE RESONANCESMULTIPLE RESONANCES(fixed driving frequency)(fixed driving frequency)
![Page 72: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/72.jpg)
The analytic signal:• The Hilbert transform: 90o phaseshift•Mapping of a time varying signal onto a 2D phase plane•Allows for the definition of phase and amplitude variables
A(t) x(t)2 xH (t)2 (t) arctanxH (t)
x(t)
H[x](t)
A(t)
(t)
z(t) x(t) ixH (t)
xH (t) H[x](t) 1
P
x( )
t
d
![Page 73: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/73.jpg)
- Ovoid Cells are high-pass
- Ovoid spike trains are coherent with narrowband signals (blue) and their envelopes (red)
- Subthreshold voltage shows no coherence with signal envelope
![Page 74: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/74.jpg)
Courtesy R. Krahe and F. Gabbiani,
Nat. Neurosci. Rev. (2004)
Electric Fields
Courtesy G. Hupe and J. Lewis (2005)
Apteronotus Leptorhynchus
![Page 75: Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular and Molecular Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY](https://reader036.vdocuments.us/reader036/viewer/2022062516/56649e425503460f94b34232/html5/thumbnails/75.jpg)