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Interpretation of Inter-Spike Interval statistics through the Markov Switching Poisson Process. Yutaka Sakai , Shuji Yoshizawa Saitama Univ., Japan Hiroshi Ohno Tamagawa Univ., Japan. Inter-Spike Interval (ISI: T) statistics ( CV, SK, COR) ~ dimensionless. Coefficient of Variation. - PowerPoint PPT Presentation
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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