程序代写代做代考 ER Point Process Spectrum Examples

Point Process Spectrum Examples

Point Process Spectral Analysis
Examples

Example #1: Simple Poisson Process

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Time (msec)

Poisson ISI Histogram

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ISI (msec)

Sample Spectrum from Poisson Data

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0

0.05

0.1

0.15

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0.3

0.35

0.4

0.45

0.5

Frequency (kHz)

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Po
w

er
(H

z)

Example #1: Simple Poisson Process

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Time (msec)

Example #2: Hard Refractory Period

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Time (msec)

Poisson ISI Histogram

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ISI (msec)

Refractory Process ISI Histogram

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ISI (msec)

Sample Spectrum from Poisson Data

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Frequency (kHz)

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Po
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Refractory Process Sample Spectrum

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0

0.05

0.1

0.15

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Frequency (kHz)

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Po
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Example #1: Simple Poisson Process

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Time (msec)

Example #3: Duplicate each spike at
10 ms lag

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Time (msec)

10 ms Repetition ISI Histogram

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ISI (msec)

Repeated Spike Sample Spectrum

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
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Frequency (kHz)

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Example #4: Realistic Baseline
Spiking Data

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Time (msec)

Baseline Spiking ISI

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ISI (msec)

Sample Spectrum for Baseline Spiking

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
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0.05

0.1

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Frequency (kHz)

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Case 1: An Analysis of the Spiking Activity of Retinal
Neurons in Culture (Iygengar and Liu, 1997)

Retinal neurons are grown in culture under constant
light and environmental conditions. The spontaneous
spiking activity of these neurons is recorded. The
objective is to develop a statistical model which
accurately describes the stochastic structure of this
activity.

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Retinal Baseline Data Spectrum

Frequency (Hz)

Po
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(H

z)

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Retinal Baseline Data Spectrogram

Time (sec)

Fr
eq

ue
nc

y
(H

z)

Autocorrelation of interspike intervals

-10 -8 -6 -4 -2 0 2 4 6 8 10
-0.2

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1.2

Lag

C
or

re
la

tio
n

co
ef

fi
ci

en
t

Interval Spectrum

Inverse Lag

Po
w

er

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
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ISI Histogram

ISI (msec)

Pr
ob

ab
ili

ty
D

en
si

ty

Exponential
Gamma
Inverse Gaussian
Order 50 GLM

Hippocampal Place Field

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

-1

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1

Hippocampal Place Field

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Place Field Spectrogram

Time (msec)
1000 2000 3000 4000 5000 6000 7000 8000 9000

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Fr
eq

ue
nc

y
(H

z)

Place Field Spectrogram

Time (msec)
500 1000 1500 2000 2500 3000 3500 4000 4500 5000

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Fr
eq

ue
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(H

z)

Place Field Analysis from Problem Set #3

1
( | ) ( ( ), ( ))exp

=

⎧ ⎫
= ⋅⎨ ⎬

⎩ ⎭

p

S
t i

i
t H t tλ λ βxN yN spikes_hist(:,i)

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Empirical CDF

M
od

el
C

D
F

Conclusions

• Point process spectral analysis is useful for
visualizing point process data and
suggesting classes of conditional intensity
models.

• The interpretation of sample point process
spectra differs from that of continuous
valued signals.