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[projects] imrpoved population vector

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Jan Benda 2020-01-27 16:28:04 +01:00
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projects/project_populationvector/populationvector.tex
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@ -47,19 +47,19 @@
200\,ms. The resulting curves are the tuning curves $r(\varphi)$ 200\,ms. The resulting curves are the tuning curves $r(\varphi)$
of the neurons. of the neurons.
\part Fit the function \[ r(\varphi) = \part Fit the function \[ r(\varphi) = g \cdot
g(1+\cos(2(\varphi-\varphi_0)))/2 \] to the measured tuning curves in (1+\cos(2(\varphi-\varphi_0)))/2 + a \] to the measured tuning
order to estimated the orientation angle at which the neurons curves in order to estimated the orientation angle at which the
respond strongest. In this function $\varphi_0$ is the position of neurons respond strongest. In this function $\varphi_0$ is the
the peak and $g$ is a gain factor that sets the maximum firing position of the peak, $g$ is a gain factor that sets the
rate. modulation depth of the firing rate, and $a$ is an offset.
\part How can the orientation angle of the presented bar be read \part How can the orientation angle of the presented bar be read
out from one trial of the population activity of the 6 neurons? out from one trial of the population activity of the 6 neurons?
One is the so called ``population vector'' where unit vectors One possible method is the so called ``population vector'' where
pointing into the direction of the maximum response of each neuron unit vectors pointing into the direction of the maximum response
are weighted by their firing rate. The stimulus orientation is of each neuron are weighted by their firing rate. The stimulus
then the direction of the averaged vectors. orientation is then the direction of the averaged vectors.
%Think of another (simpler) method how the orientation of the bar %Think of another (simpler) method how the orientation of the bar
%may be approximately read out from the population. %may be approximately read out from the population.