Chronux Tutorial: Part I

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Chronux Tutorial Part I

• Hemant Bokil
• Cold Spring Harbor Laboratory

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People
Hemant Bokil
Catherine Loader
Partha Mitra
Peter Andrews
Contributors Dan Hill Chris
Fall Samar Mehta Hirak Parikh Andrew
Sornborger
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Outline

• Introduction to Chronux
• ? Aim
• ? Website
• ? Download
• ? Documentation
• ? Key functions
• Analysis of LIP data - Example 2 of the previous
  talk rates, spike and LFP spectra and
  coherences, coherences between cells
• Analysis protocol
• F-test for line noise

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Chronux Aim
To provide a comprehensive set of tools for the
analysis of neurobiological time series data
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Current version
Spectral analysis
Locfit local regression and likelihood based
analyses
MATLAB Toolboxes
Spike sorting

• Univariate and multivariate time series data.
• Continuous data (e.g. LFPs) and point process
  data (e.g. spikes).
• Multiple modalities Image data (examples in
  Chris Falls talk)
• Extensive online and within-Matlab help
• GUI under active development, release in a few
  months

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Website (www.chronux.org)
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Documentation
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Key routines for continuous processesDenoising
Slow variations (e.g. movements of a patient for
EEG data)
50/60 Hz line noise
locdetrend.m Loess method
rmlinesc.m rmlinesmovingwinc.m
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Spectra, Coherences etc
Fourier transforms using multiple tapers mtfftc.m
Spectrum mtspectrumc.m
Coherencymtcoherencyc.m
Spectrogram mtspecgramc.m
Coherogrammtcohgramc.m
Local regression and likelihood
Regression and likelihood locfit.m
Plotting the fit lfplot.m
Plotting local confidence bands lfband.m

Plotting global confidence bands scb.m
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Chronux data format

• Continuous/binned point process data
• matrices with dimension time x
  channels/trials
• e.g. 1000 x 10 dimensional
  matrix
• interpreted as 1000
  samples
• 10 channels/trials
• Spikes times
• struct array with dimension number of
  channels/trials
• e.g. data(1).times0.3 0.35
  0.42 0.6
• data(2).times0.2 0.22
  0.35
• 2 spike trains with 4 and 3
  spikes

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Important parameter in mulitple Chronux functions

• params structure with multiple fields
• Fs sampling frequency (slightly different
  interpretation for spike times
• tapers controls the number of tapers
• pad controls the padding
• fpass frequency range of interest
• err controls error computation
• trialave controls whether or not to average
  over trials

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Example II Spike rates, spectra and coherence
(from the previous lecture)

• Simultaneous two-cell recording from Macaque area
  LIP dataset DynNeuroLIP.mat

Reach and Saccade
Delay
Cue
Delay
Cue
Reach and Saccade Task
Pesaran et al (Unpublished)
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Example II

• 3 local field potentials (LFP) and 2 single
  units, LFP sampled at 1 kHz
• Trial 3 seconds of data for 9 trials to one of
  the
• directions
• 1 s (Baseline), 2 s (Delay post movement)
• Baseline 1 second of data for 74 trials (pooled
  
• across all directions)

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Tasks

• Compute the following for the Memory trials
• Spike rates
• LFP and spike spectra
• Spike-field coherence
• Spike-Spike coherence

Compare spike-spike coherence during the memory
period and the baseline period.
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The main script for this tutorial lip_master_scri
pt.m Calls other scripts to run through the
various analyses
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The main script for this tutorial lip_master_scri
pt.m Calls other scripts to run through the
various analyses
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Spike rate 1 trial Basic locfit usage (rate
estimate)
gtgt fitlocfit(data,'family','rate') gtgt
lfplot(fit) gtgt lfband(fit)
Density estimate replace 'rate by dens
Regression gtgt fitlocfit(x,y)
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Setting the bandwidth fixed (h), nearest
neighbor (nn)
h fixed/absolute bandwidth e.g. h1 is
interpreted as 1 s if data is in seconds
nn fixed fraction of the total number of points
e.g. nn0.3 takes the 30 closest points to a
given point Default nn0.7, h0
gtgt fitlocfit(data,'family','rate,nn,0.3) gtgt
lfplot(fit) gtgt lfband(fit)
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Multiple trials pool the spikes and
compute fit rescale fits and confidence intervals
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LFP spectrum mtspectrumc.m
gtgtS,fmtspectrumc(data) gtgt plot(f,10log10(S))
S spectrum f frequency
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Sampling frequency
Set params.Fs Default 1
gtgtparams.Fs1000 gtgtS,fmtspectrumc(data,params)
gtgt plot_vector(S,f)
plot_vector Allows plotting errors and choice
of color and scale (default log scale for
S) gtgt plot_vector(S,f,n) Uses linear
scale for S
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Restricting frequencies of interest
Set params.fpass Default 0 params.Fs/2
gtgtparams.Fs1000 gtgtparams.fpass0
100 gtgtS,fmtspectrumc(data,params) gtgt
plot_vector(S,f)
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Changing the padding
Set params.pad Default0
Allowed values -1 0 1 2
... For N500, NFFT 500 512 1024 2048
Default 0
gtgt params.pad2 gtgtS,fmtspectrumc(data,params)
gtgt plot_vector(S,f)
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Smoothing (changing the bandwidth)

• Set params.tapers of the form TW K
• Default 3 5
• TW time-bandwidth product
• Klt2TW well concentrated
• Slepian sequences

gtgtparams.tapers5 9 gtgtS,fmtspectrumc(data,pa
rams) gtgt plot_vector(S,f,,,r)
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Averaging over trials
Set params.trialave1
gtgt params.trialave1 gtgtS,fmtspectrumc(data,par
ams) gtgt plot_vector(S,f)
Note computing the spectrum separately for each
trial and averaging will work for the spectrum,
but not for the Jackknife error bars
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Errors
params.err 1 p
params.err2 p Jackknife
Set params.err
Serr (1-p) confidence interval of S
gtgtp0.05 gtgtparams.err1 p gtgtS,f,Serrmtspect
rumc(data,params) gtgtplot_vector(S,f,,Serr) gtgt
hold on
gtgtp0.05 gtgtparams.err2 p gtgtS,f,Serrmtspect
rumc(data,params) gtgtplot(f,10log10(Serr(1,)),r
) gtgtplot(f,10log10(Serr(2,)),r)
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Spike spectrum
mtspectrumpt.m
gtgtparams.err1 p gtgtS,f,R,Serrmtspectrumpt(da
ta,params)
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Spectrogram mtspecgramc
Set duration and step size of moving
windowmovingwin
gtgt movingwin0.5 0.05 gtgt S,t,fmtspecgramc(da
ta,movingwin,params)
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Spike spectrogram mtspecgrampt.m
gtgtS,t,f,Rmtspecgrampt(data,movingwin,params)
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Coherence between LFP and spikes
coherencycpt.m
gtgtparams.err1 p gtgtC,phi,S12,S1,S2,f,zerosp,co
nfC,phistdcoherencycpt(datalfp, datasp,params)
C coherence Phi phase confC
Probability(CgtconfC)p phistd
asymptotic standard deviation of phase
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Coherence between cells
coherencypt.m
gtgt params.err2 p gtgt C,phi,S12,S1,S2,f,zerosp
,confC,phistd,Cerrcoherencypt(datasp1,
datasp2,params)
Phistd Jackknifed standard deviation of the
phase Cerr (1-p) confidence intervals for C
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Comparison of coherences and spectra

• Two experimental conditions with unequal number
  of trials
• Coherence and spectral estimates are biased and
  the bias depends on sample size
• Would like a simple hypothesis test with a
  corresponding p value

Bokil et al., J Neurosci Methods. 2006 Aug 28
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Comparison of coherences and spectra

• If ztanh-1 (C)
• E(z)tanh-1(Cpop)1/(2m-2)
• V(z)?(m)

Null hypothesis C1,popC2,pop ? zN(0,1)
Bokil et al., J Neurosci Methods. 2006 Aug 28
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Chronux code for comparing coherences
dz,vdz,Adztwo_group_test_coherence(J1c1,J2c1,J1
c2,J2c2,p,'y',f)
Fourier transforms
Bokil et al, 2006
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Electrophysiology Analysis Protocol
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Electrophysiolgy Data Conditioning
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Removing 50/60 Hz
N samples X1, X2, , XN
Model X(t)a cos(2?f0t?)?(t)
Potential Method Least squares

• ?(t) is non-white in general
• non-linear in f0 and ?

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Thomsons F testIdea Equation can be
transformed to a linear regression in frequency
Notice
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Thomsons F test

• Multiply both sides by kth Slepian sequence ukn
  and Fourier transform

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Thomsons F-test
Used in touch-tone phones to detect the key