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fixed lif and noisefi projects

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This commit is contained in:
Jan Benda 2018-01-19 14:54:03 +01:00
parent eca31e3c95
commit c2e37b516e
5 changed files with 71 additions and 41 deletions
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5
projects/project_lif/lif.tex
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@ -58,7 +58,7 @@ time = [0.0:dt:tmax]; % t_i
\part Response of the passive membrane to a step input. \part Response of the passive membrane to a step input.
Set $V_0=0$. Construct a vector for the input $E(t)$ such that Set $V_0=0$. Construct a vector for the input $E(t)$ such that
$E(t)=0$ for $t\le 20$\,ms and $t\ge 70$\,ms and $E(t)=10$\,mV for $E(t)=0$ for $t\le 20$\,ms or $t\ge 70$\,ms, and $E(t)=10$\,mV for
$20$\,ms $<t<70$\,ms. Plot $E(t)$ and the resulting $V(t)$ for $20$\,ms $<t<70$\,ms. Plot $E(t)$ and the resulting $V(t)$ for
$t_{max}=120$\,ms. $t_{max}=120$\,ms.
@ -92,7 +92,7 @@ time = [0.0:dt:tmax]; % t_i
spike'' only means that we note down the time of the threshold spike'' only means that we note down the time of the threshold
crossing as a time where an action potential occurred. The crossing as a time where an action potential occurred. The
waveform of the action potential is not modeled. Here we use a waveform of the action potential is not modeled. Here we use a
voltage threshold of one. voltage threshold of 1\,mV.
Write a function that implements this leaky integrate-and-fire Write a function that implements this leaky integrate-and-fire
neuron by expanding the function for the passive neuron neuron by expanding the function for the passive neuron
@ -114,7 +114,6 @@ time = [0.0:dt:tmax]; % t_i
\label{firingrate} \label{firingrate}
r = \frac{n-1}{t_n - t_1} r = \frac{n-1}{t_n - t_1}
\end{equation} \end{equation}
What do you observe? Does the firing rate encode the frequency of What do you observe? Does the firing rate encode the frequency of
the stimulus? the stimulus?
\end{parts} \end{parts}

12
projects/project_noiseficurves/lifspikes.m
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@ -1,8 +1,8 @@
function spikes = lifspikes(trials, input, tmax, D) function spikes = lifspikes(trials, current, tmax, D)
% Generate spike times of a leaky integrate-and-fire neuron % Generate spike times of a leaky integrate-and-fire neuron
% trials: the number of trials to be generated % trials: the number of trials to be generated
% input: the stimulus either as a single value or as a vector % current: the stimulus either as a single value or as a vector
% tmax: duration of a trial % tmax: duration of a trial if input is a single number
% D: the strength of additive white noise % D: the strength of additive white noise
tau = 0.01; tau = 0.01;
@ -13,7 +13,11 @@ function spikes = lifspikes(trials, input, tmax, D)
vthresh = 10.0; vthresh = 10.0;
dt = 1e-4; dt = 1e-4;
n = length( current );
if n <= 1
n = ceil(tmax/dt); n = ceil(tmax/dt);
current = zeros( n, 1 ) + current;
end
spikes = cell(trials, 1); spikes = cell(trials, 1);
for k=1:trials for k=1:trials
times = []; times = [];
@ -21,7 +25,7 @@ function spikes = lifspikes(trials, input, tmax, D)
v = vreset + (vthresh-vreset)*rand(); v = vreset + (vthresh-vreset)*rand();
noise = sqrt(2.0*D)*randn(n, 1)/sqrt(dt); noise = sqrt(2.0*D)*randn(n, 1)/sqrt(dt);
for i=1:n for i=1:n
v = v + (- v + noise(i) + input)*dt/tau; v = v + (- v + noise(i) + current(i))*dt/tau;
if v >= vthresh if v >= vthresh
v = vreset; v = vreset;
times(j) = i*dt; times(j) = i*dt;

51
projects/project_noiseficurves/noiseficurves.tex
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@ -9,9 +9,6 @@
\input{../instructions.tex} \input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section{REPLACE BY SUBTHRESHOLD RESONANCE PROJECT!}
\begin{questions} \begin{questions}
\question You are recording the activity of a neuron in response to \question You are recording the activity of a neuron in response to
constant stimuli of intensity $I$ (think of that, for example, constant stimuli of intensity $I$ (think of that, for example,
@ -19,24 +16,32 @@
Measure the tuning curve (also called the intensity-response curve) of the Measure the tuning curve (also called the intensity-response curve) of the
neuron. That is, what is the mean firing rate of the neuron's response neuron. That is, what is the mean firing rate of the neuron's response
as a function of the input $I$? as a function of the constant input current $I$?
How does the intensity-response curve of a neuron depend on the How does the intensity-response curve of a neuron depend on the
level of the intrinsic noise of the neuron? level of the intrinsic noise of the neuron?
How can intrinsic noise be usefull for encoding stimuli?
The neuron is implemented in the file \texttt{lifspikes.m}. Call it The neuron is implemented in the file \texttt{lifspikes.m}. Call it
with the following parameters: with the following parameters:\\[-7ex]
\begin{lstlisting} \begin{lstlisting}
trials = 10; trials = 10;
tmax = 50.0; tmax = 50.0;
input = 10.0; % the input I current = 10.0; % the constant input current I
Dnoise = 1.0; % noise strength Dnoise = 1.0; % noise strength
spikes = lifspikes(trials, input, tmax, Dnoise); spikes = lifspikes(trials, current, tmax, Dnoise);
\end{lstlisting} \end{lstlisting}
The returned \texttt{spikes} is a cell array with \texttt{trials} The returned \texttt{spikes} is a cell array with \texttt{trials}
elements, each being a vector of spike times (in seconds) computed elements, each being a vector of spike times (in seconds) computed
for a duration of \texttt{tmax} seconds. The input is set via the for a duration of \texttt{tmax} seconds. The input current is set
\texttt{input} variable, the noise strength via \texttt{Dnoise}. via the \texttt{current} variable, the strength of the intrinsic
noise via \texttt{Dnoise}. If \texttt{current} is a single number,
then an input current of that intensity is simulated for
\texttt{tmax} seconds. Alternatively, \texttt{current} can be a
vector containing an input current that changes in time. In this
case, \texttt{tmax} is ignored, and you have to provide a value
for the input current for every 0.0001\,seconds.
Think of calling the \texttt{lifspikes()} function as a simple way Think of calling the \texttt{lifspikes()} function as a simple way
of doing an electrophysiological experiment. You are presenting a of doing an electrophysiological experiment. You are presenting a
@ -52,20 +57,17 @@ spikes = lifspikes(trials, input, tmax, Dnoise);
and plot neuron's $f$-$I$ curve, i.e. the mean firing rate (number and plot neuron's $f$-$I$ curve, i.e. the mean firing rate (number
of spikes within the recording time \texttt{tmax} divided by of spikes within the recording time \texttt{tmax} divided by
\texttt{tmax} and averaged over trials) as a function of the input \texttt{tmax} and averaged over trials) as a function of the input
for inputs ranging from 0 to 20. current for inputs ranging from 0 to 20.
How are different stimulus intensities encoded by the firing rate How are different stimulus intensities encoded by the firing rate
of this neuron? of this neuron?
\part Compute the $f$-$I$ curves of neurons with various noise \part Compute the $f$-$I$ curves of neurons with various noise
strengths \texttt{Dnoise}. Use $D_{noise} = 1e-3$, $1e-2$, and strengths \texttt{Dnoise}. Use for example $D_{noise} = 1e-3$,
$1e-1$. $1e-2$, and $1e-1$.
How does the intrinsic noise influence the response curve? How does the intrinsic noise influence the response curve?
How is the encoding of stimuli influenced by increasing intrinsic
noise?
What are possible sources of this intrinsic noise? What are possible sources of this intrinsic noise?
\part Show spike raster plots and interspike interval histograms \part Show spike raster plots and interspike interval histograms
@ -74,14 +76,21 @@ spikes = lifspikes(trials, input, tmax, Dnoise);
responses of the four different neurons to the same input, or by responses of the four different neurons to the same input, or by
the same resulting mean firing rate. the same resulting mean firing rate.
\part How does the coefficient of variation $CV_{isi}$ (standard \part Let's now use as an input to the neuron a 1\,s long sine
deviation divided by mean) of the interspike intervalls depend on wave $I(t) = I_0 + A \sin(2\pi f t)$ with offset current $I_0$,
the input and the noise level? amplitude $A$, and frequency $f$. Set $I_0=5$, $A=4$, and
$f=5$\,Hz.
Do you get a response of the noiseless ($D_{noise}=0$) neuron?
What happens if you increase the noise strength?
What happens at really large noise strengths?
\part Based o your results, discuss how intrinsic noise might Generate some example plots that illustrate your findings.
improve and how it might deteriote the encoding of different
stimulus intensities.
Explain the encoding of the sine wave based on your findings
regarding the $f$-$I$ curves.
\end{parts} \end{parts}

12
projects/project_noiseficurves/solution/lifspikes.m
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@ -1,8 +1,8 @@
function spikes = lifspikes(trials, input, tmax, D) function spikes = lifspikes(trials, current, tmax, D)
% Generate spike times of a leaky integrate-and-fire neuron % Generate spike times of a leaky integrate-and-fire neuron
% trials: the number of trials to be generated % trials: the number of trials to be generated
% input: the stimulus either as a single value or as a vector % current: the stimulus either as a single value or as a vector
% tmax: duration of a trial % tmax: duration of a trial if input is a single number
% D: the strength of additive white noise % D: the strength of additive white noise
tau = 0.01; tau = 0.01;
@ -13,7 +13,11 @@ function spikes = lifspikes(trials, input, tmax, D)
vthresh = 10.0; vthresh = 10.0;
dt = 1e-4; dt = 1e-4;
n = length( current );
if n <= 1
n = ceil(tmax/dt); n = ceil(tmax/dt);
current = zeros( n, 1 ) + current;
end
spikes = cell(trials, 1); spikes = cell(trials, 1);
for k=1:trials for k=1:trials
times = []; times = [];
@ -21,7 +25,7 @@ function spikes = lifspikes(trials, input, tmax, D)
v = vreset + (vthresh-vreset)*rand(); v = vreset + (vthresh-vreset)*rand();
noise = sqrt(2.0*D)*randn(n, 1)/sqrt(dt); noise = sqrt(2.0*D)*randn(n, 1)/sqrt(dt);
for i=1:n for i=1:n
v = v + (- v + noise(i) + input)*dt/tau; v = v + (- v + noise(i) + current(i))*dt/tau;
if v >= vthresh if v >= vthresh
v = vreset; v = vreset;
times(j) = i*dt; times(j) = i*dt;

24
projects/project_noiseficurves/solution/noiseficurves.m
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@ -7,20 +7,34 @@ figure()
Ds = [0, 0.001, 0.01, 0.1]; Ds = [0, 0.001, 0.01, 0.1];
for j = 1:length(Ds) for j = 1:length(Ds)
D = Ds(j); D = Ds(j);
inputs = 0.0:0.5:20.0; currents = 0.0:0.5:20.0;
rates = ficurve(trials, inputs, tmax, D); rates = ficurve(trials, currents, tmax, D);
plot(inputs, rates); plot(currents, rates);
hold on; hold on;
end end
hold off; hold off;
%% spike raster and CVs %% spike raster and CVs
input = 12.0; figure()
current = 12.0;
for j = 1:length(Ds) for j = 1:length(Ds)
D = Ds(j); D = Ds(j);
spikes = lifspikes(trials, input, tmax, D); spikes = lifspikes(trials, current, tmax, D);
subplot(4, 2, 2*j-1); subplot(4, 2, 2*j-1);
spikeraster(spikes, 0.0, 1.0); spikeraster(spikes, 0.0, 1.0);
subplot(4, 2, 2*j); subplot(4, 2, 2*j);
isih(spikes, [0:0.001:0.04]); isih(spikes, [0:0.001:0.04]);
end end
%% subthreshold resonance:
time = [0.0:0.0001:1.0];
current = 5.0 + 4.0*sin(2.0*pi*5.0*time);
D = 0.1;
spikes = lifspikes(trials, current, tmax, D);
subplot(2, 1, 1);
spikeraster(spikes, 0.0, 1.0);
subplot(2, 1, 2);
plot(time, current);