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

2. 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

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

4. 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

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

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

7. Example I: LFP spectrograms Example recording Cue Saccade

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

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

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

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

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

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

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

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

16. 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Simultaneous two-cell recording from Macaque area LIP Reach and Saccade Task DelayCueReach and Saccade Pesaran et al (Unpublished)

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

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

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

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

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

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

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

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

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

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

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

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

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