teaching/scientificComputing
Archived
3
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

improved noiseficurves projects

Browse Source
This commit is contained in:
Jan Benda 2017-01-22 16:09:16 +01:00
parent 5d2beb12eb
commit 4060b1bbae
8 changed files with 168 additions and 37 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

19
projects/project_noiseficurves/lifspikes.m
View File

@ -1,9 +1,8 @@
function spikes = lifspikes( trials, input, tmaxdt, D )
function spikes = lifspikes(trials, input, tmax, D)
% Generate spike times of a leaky integrate-and-fire neuron
% trials: the number of trials to be generated
% input: the stimulus either as a single value or as a vector
% tmaxdt: in case of a single value stimulus the duration of a trial
% in case of a vector as a stimulus the time step
% tmax: duration of a trial
% D: the strength of additive white noise
tau = 0.01;
@ -14,19 +13,15 @@ function spikes = lifspikes( trials, input, tmaxdt, D )
vthresh = 10.0;
dt = 1e-4;
if length( input ) == 1
input = input * ones( ceil( tmaxdt/dt ), 1 );
else
dt = tmaxdt;
end
spikes = cell( trials, 1 );
n = ceil(tmax/dt);
spikes = cell(trials, 1);
for k=1:trials
times = [];
j = 1;
v = vreset;
noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
for i=1:length( noise )
v = v + ( - v + noise(i) + input(i))*dt/tau;
noise = sqrt(2.0*D)*randn(n, 1)/sqrt(dt);
for i=1:n
v = v + (- v + noise(i) + input)*dt/tau;
if v >= vthresh
v = vreset;
times(j) = i*dt;

69
projects/project_noiseficurves/noiseficurves.tex
View File

@ -57,8 +57,10 @@
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
as a function of the input $I$. How does this depend on the level of
the intrinsic noise of the neuron?
as a function of the input $I$?
How does the intensity-response curve of a neuron depend on the
level of the intrinsic noise of the neuron?
The neuron is implemented in the file \texttt{lifspikes.m}. Call it
with the following parameters:
@ -67,40 +69,57 @@ trials = 10;
tmax = 50.0;
input = 10.0; % the input I
Dnoise = 1.0; % noise strength
spikes = lifspikes( trials, input, tmax, Dnoise );
spikes = lifspikes(trials, input, tmax, Dnoise);
\end{lstlisting}
The returned \texttt{spikes} is a cell array with \texttt{trials} elements, each being a vector
of spike times (in seconds) computed for a duration of \texttt{tmax} seconds.
The input is set via the \texttt{input} variable, the noise strength via \texttt{Dnoise}.
Think of calling the \texttt{lifspikes()} function as a
simple way of doing an electrophysiological experiment. You are
presenting a stimulus with a constant intensity $I$ that you set. The
neuron responds to this stimulus, and you record this
response. After detecting the timepoints of the spikes in your
recordings you get what the \texttt{lifspikes()} function
returns. The advantage over real data is, that you have the
possibility to simply modify the properties of the neuron via the
\texttt{Dnoise} parameter.
The returned \texttt{spikes} is a cell array with \texttt{trials}
elements, each being a vector of spike times (in seconds) computed
for a duration of \texttt{tmax} seconds. The input is set via the
\texttt{input} variable, the noise strength via \texttt{Dnoise}.
Think of calling the \texttt{lifspikes()} function as a simple way
of doing an electrophysiological experiment. You are presenting a
stimulus with a constant intensity $I$ that you set. The neuron
responds to this stimulus, and you record this response. After
detecting the timepoints of the spikes in your recordings you get
what the \texttt{lifspikes()} function returns. In addition you
can record from different neurons with different noise properties
by setting the \texttt{Dnoise} parameter to different values.
\begin{parts}
\part First set the noise \texttt{Dnoise=0} (no noise). Compute
and plot the mean firing rate (number of spikes within the
recording time \texttt{tmax} divided by \texttt{tmax} and averaged
over trials) as a function of the input for inputs ranging from 0
to 20.
and plot neuron's $f$-$I$ curve, i.e. the mean firing rate (number
of spikes within the recording time \texttt{tmax} divided by
\texttt{tmax} and averaged over trials) as a function of the input
for inputs ranging from 0 to 20.
How are different stimulus intensities encoded by the firing rate
of this neuron?
\part Compute the $f$-$I$ curves of neurons with various noise
strengths \texttt{Dnoise}. Use $D_{noise} = 1e-3$, $1e-2$, and
$1e-1$.
\part Do the same for various noise strength \texttt{Dnoise}. Use $D_{noise} = 1e-3$,
1e-2, and 1e-1. How does the intrinsic noise influence the response curve?
How does the intrinsic noise influence the response curve?
\part Show some interspike interval histograms for some
interesting values of the input and the noise strength.
How is the encoding of stimuli influenced by increasing intrinsic
noise?
What are possible sources of this intrinsic noise?
\part Show spike raster plots and interspike interval histograms
of the responses for some interesting values of the input and the
noise strength. For example, you might want to compare the
responses of the four different neurons to the same input, or by
the same resulting mean firing rate.
\part How does the coefficient of variation $CV_{isi}$ (standard
deviation divided by mean) of the interspike intervalls depend on
the input and the noise level?
\part Based o your results, discuss how intrinsic noise might
improve and how it might deteriote the encoding of different
stimulus intensities.
\end{parts}

8
projects/project_noiseficurves/solution/ficurve.m Normal file
View File

@ -0,0 +1,8 @@
function rates = ficurve(trials, inputs, tmax, D)
% compute f-I curve.
rates = zeros(length(inputs), 1);
for k=1:length(inputs)
spikes = lifspikes(trials, inputs(k), tmax, D);
rates(k) = firingrate(spikes, 0.0, tmax);
end
end

9
projects/project_noiseficurves/solution/firingrate.m Normal file
View File

@ -0,0 +1,9 @@
function rate = firingrate(spikes, tmin, tmax)
% mean firing rate between tmin and tmax.
rates = zeros(length(spikes), 1);
for i = 1:length(spikes)
times= spikes{i};
rates(i) = length(times((times>=tmin)&(times<=tmax)))/(tmax-tmin);
end
rate = mean(rates);
end

11
projects/project_noiseficurves/solution/isih.m Normal file
View File

@ -0,0 +1,11 @@
function isih(spikes, bins)
isis = [];
for i = 1:length(spikes)
times= spikes{i};
isis = [isis; diff(times(:))];
end
[h, b] = hist(isis, bins);
h = h / sum(h) / (bins(2)-bins(1));
bar(1000.0*b, h);
xlim([0 1000.0*b(end)])
end

33
projects/project_noiseficurves/solution/lifspikes.m Normal file
View File

@ -0,0 +1,33 @@
function spikes = lifspikes(trials, input, tmax, D)
% Generate spike times of a leaky integrate-and-fire neuron
% trials: the number of trials to be generated
% input: the stimulus either as a single value or as a vector
% tmax: duration of a trial
% D: the strength of additive white noise
tau = 0.01;
if nargin < 4
D = 1e0;
end
vreset = 0.0;
vthresh = 10.0;
dt = 1e-4;
n = ceil(tmax/dt);
spikes = cell(trials, 1);
for k=1:trials
times = [];
j = 1;
v = vreset;
noise = sqrt(2.0*D)*randn(n, 1)/sqrt(dt);
for i=1:n
v = v + (- v + noise(i) + input)*dt/tau;
if v >= vthresh
v = vreset;
times(j) = i*dt;
j = j + 1;
end
end
spikes{k} = times;
end
end

26
projects/project_noiseficurves/solution/noiseficurves.m Normal file
View File

@ -0,0 +1,26 @@
%% general settings for the model neuron:
trials = 10;
tmax = 50.0;
%% f-I curves:
figure()
Ds = [0, 0.001, 0.01, 0.1];
for j = 1:length(Ds)
D = Ds(j);
inputs = 0.0:0.5:20.0;
rates = ficurve(trials, inputs, tmax, D);
plot(inputs, rates);
hold on;
end
hold off;
%% spike raster and CVs
input = 12.0;
for j = 1:length(Ds)
D = Ds(j);
spikes = lifspikes(trials, input, tmax, D);
subplot(4, 2, 2*j-1);
spikeraster(spikes, 0.0, 1.0);
subplot(4, 2, 2*j);
isih(spikes, [0:0.001:0.04]);
end

30
projects/project_noiseficurves/solution/spikeraster.m Normal file
View File

@ -0,0 +1,30 @@
function spikeraster(spikes, tmin, tmax)
% Display a spike raster of the spike times given in spikes.
%
% spikeraster(spikes, tmax)
% spikes: a cell array of vectors of spike times in seconds
% tmin: plot spike raster starting at tmin seconds
% tmax: plot spike raster upto tmax seconds
ntrials = length(spikes);
for k = 1:ntrials
times = spikes{k};
times = times((times>=tmin) & (times<=tmax));
if tmax < 1.5
times = 1000.0*times; % conversion to ms
end
for i = 1:length( times )
line([times(i) times(i)],[k-0.4 k+0.4], 'Color', 'k');
end
end
if (tmax-tmin) < 1.5
xlabel('Time [ms]');
xlim([1000.0*tmin 1000.0*tmax]);
else
xlabel('Time [s]');
xlim([tmin tmax]);
end
ylabel('Trials');
ylim([0.3 ntrials+0.7 ]);
end