Yutaka SakaiYutaka Sakai, Shuji Yoshizawa, Shuji Yoshizawa

Saitama Univ., JapanSaitama Univ., Japan

Hiroshi OhnoHiroshi Ohno

Tamagawa Univ., JapanTamagawa Univ., Japan

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

Inter-Spike Interval (ISI: T) statisticsInter-Spike Interval (ISI: T) statistics ((CV, SK, COR) CV, SK, COR) ~ ~ dimensionlessdimensionless

2

1

32

3

2

)(

))((

)(

)(

)(

TT

TTTT

TT

TT

T

TT

nn

COR

SK

CV

Coefficient of Variation

Skewness coefficient (asymmetry)

Correlation coefficientof consecutive ISIs

~ Irregularity

~ long silence

~ serial correlation

PS area & MT area （ Funahashi, 1996 ） （ Ohno, 1999 ）

0

2

4

6

8

-0.5 0 0.5

COR

SK

0

2

4

6

8

0 1 2 3

CV

SK

Random Sequence : Poisson Process(1, 2, 0)

What do the combinations mean?

What does a combination (CV,SK,COR) tell us?

Simple spike event process

(CV,SK,COR)

reproduce

model parameters

projection

Active stateRandom spiking at

Markov Switching Poisson Process

0w

0

0w 01 w

01 w

Switch state at each spike event

Inactive stateRandom spiking at 01

Markov Switching Poisson Process

Active stateActive state Inactive stateInactive state

Mean Interval (ISI)Mean Interval (ISI)

Staying time scaleStaying time scale 01s

Parameters (4 time scales)

Interval (ISI) statistics

COR) SK, CV, ,T(

1 to 1

0s)/( 011 w )/( 100 w )/( 1 1 )/( 0 1

Dimensionless Parameters for Interpretaion

T

ssS 10

10

1

ss

s

Staying Time Scale

Staying Time Balance

section COR=-0.1section COR=0

Projection to the Markov SwitchingProjection to the Markov Switching

section COR=0.1section COR=0.2

S

Model ParametersISI statistics

Sample data

PS area of awake monkey

Delay response taskDelay response task

(Funahashi 1996)(Funahashi 1996)

MT area of anesthetized monkey

Random dots flowingRandom dots flowing

(Ohno 1999)(Ohno 1999)

Sample Data (CV,SK,COR)s … for Interpretation

0

2

4

6

8

- 0.3 0 0.3

COR

SK

0

2

4

6

8

0 1 2 3

CV

SK

PS typical (SK: Large) PS typical (COR: Large)

MT all

0

10

20

30

40

50

Sequence Properties … trough the Markov Switching

S

StayingTime Scale

inactive active

Staying Time Balance

Large COR : balance ~ inactiveLarge SK/CV: balance ~ activeMT data

Summary

SK/CV large or COR largeSK/CV large or COR large

long staying timelong staying time

SK/CVSK/CV largelarge stay longer in activestay longer in active

SK/CVSK/CV smallsmall stay longer in stay longer in inactiveinactive