Interpretation of Inter-Spike Interval statistics through the Markov Switching Poisson Process

1. Interpretation of Inter-Spike Interval statistics through the Markov Switching Poisson Process Yutaka Sakai, Shuji Yoshizawa Saitama Univ., Japan Hiroshi Ohno Tamagawa Univ., Japan

2. Inter-Spike Interval (ISI: T) statistics(CV, SK, COR) ~ dimensionless Coefficient of Variation ~ Irregularity Skewness coefficient (asymmetry) ~ long silence Correlation coefficient of consecutive ISIs ~ serial correlation

3. Random Sequence : Poisson Process (1, 2, 0) What do the combinations mean? PS area &MT area（Funahashi, 1996）（Ohno, 1999）

4. reproduce model parameters projection What does a combination(CV,SK,COR)tell us? Simple spike event process (CV,SK,COR)

5. Markov Switching Poisson Process Switch state at each spike event Active state Random spiking at Inactive state Random spiking at

6. 1 to 1 Interval (ISI) statistics Markov Switching Poisson Process Parameters (4 time scales)

7. Dimensionless Parameters for Interpretaion Staying Time Scale Staying Time Balance

8. section COR=-0.1 section COR=0 section COR=0.1 section COR=0.2 Projection to the Markov Switching ISI statistics Model Parameters

9. Sample data PS area of awake monkey Delay response task (Funahashi 1996) MT area of anesthetized monkey Random dots flowing (Ohno 1999)

10. Sample Data (CV,SK,COR)s … for Interpretation PS typical (SK: Large) MT all PS typical (COR: Large)

11. Large COR : balance ~ inactive Large SK/CV: balance ~ active MT data Sequence Properties … trough the Markov Switching Staying Time Scale inactive active Staying Time Balance

12. Summary SK/CV large or COR large long staying time SK/CV　largestay longer in active SK/CV　smallstay longer in inactive