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Spectral analysis II: Applications Bijan Pesaran Center for Neural Science New York University

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Outline Example I: LFP spectrograms Example II: Spike rates, spectra and coherence Example III: Spike-LFP coherence Example IV: Decoding and single trial analysis Example V: Combining SVD and spectra

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Spiking and LFP activity Extracellular potential Spikes LFP Current summation determines the amplitude of LFP –Spatial and temporal

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How do we analyze spike trains and field potentials together? Use spectral methods for a hybrid point- continuous process LFP Voltage Spike times Continuous process Point process

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Spectral intuition = LFP Voltage + Spectrum power 1/T Spike times = T frequency power Low High Spikes Field Coherency

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Example I: LFP spectrograms LFP recording from Macaque area LIP Memory Saccade Task MemoryCueSaccade Pesaran et al (2002)

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Example I: LFP spectrograms Example recording Cue Saccade

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Example I: LFP spectrograms Estimation issues –Bias Narrow band Broad band –Variance

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Example I: LFP spectrograms Confidence intervals –Chi2 Assume Gaussian process –Jackknife Does not assume Gaussian process

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Example I: LFP spectrograms Periodogram – Single Trial Multitaper estimate - Single Trial, [5,9]

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Periodogram – Single Trial Multitaper estimate - Single Trial Example I: LFP spectrograms

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Multitaper estimate - Single Trial [5,9] Multitaper estimate - Nine Trials [5,9]

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Example I: LFP spectrograms Multitaper estimate - Single Trial Multitaper estimate - Nine Trials

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Example I: LFP spectrograms Multitaper estimate - 95% Chi2 Multitaper estimate - 95% Jackknife Leave-one-out

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Example I: LFP spectrograms Multitaper estimate - T = 0.5s, W = 10Hz Multitaper estimate - T = 0.2s, W = 25Hz

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Example II: Spike rates, spectra and coherence Simultaneous two-cell recording from Macaque area LIP Reach and Saccade Task DelayCueReach and Saccade Pesaran et al (Unpublished)

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Example II: Spike rates, spectra and coherence Binning estimate T = 50ms Locfit estimate nn = 0.1

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Example II: Spike rates, spectra and coherence Auto-correlation fn Multitaper spectrum [8,15]

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Example II: Spike rates, spectra and coherence Inter-spike intervals

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Example II: Spike rates, spectra and coherence Inter-spike intervals Spike spectrum properties –High frequency limit –Low freq suppression –Spectral peaks

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Example II: Spike rates, spectra and coherence Cross-correlation fn Multitaper coherence 9 trials, [8,15]

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Example II: Spike rates, spectra and coherence Multitaper coherence 9 trials, [12,23] Multitaper coherence 9 trials, [8,15]

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Example III: Spike-field coherence Experimental paradigm Womelsdorf et al (2006)

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Example III: Spike-field coherence Hypothesis testing Womelsdorf et al (2006)

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Example III: Spike-field coherence Womelsdorf et al (2006) Single trial analysis

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Example IV: Decoding and single trial analysis Decoding LFP spectra Pesaran et al (2002)

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Example V: SVD and spectra SVD –Time-channel decomposition –Reduced dimensionality data set –Estimate spectra of modes

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Example V: SVD and spectra Fall et al (Unpublished)

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Summary Presented examples of neuronal time series Compared methods for their analysis Demonstrated advantages of spectral analysis

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