ranking the projects, todos and fixes
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@ -1,70 +1,95 @@
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project_adaptation_fit
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OK
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OK, medium
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Add plotting of cost function
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project_eod
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Needs to be checked!
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OK, medium - difficult
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project_eyetracker
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OK
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OK, difficult
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no statistics, but kmeans
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project_fano_slope
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OK
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OK, difficult
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Add t-test
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project_fano_test
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OK
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OK -
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project_fano_time
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OK
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OK, difficult
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Add t-test
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project_ficurves
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OK
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OK, medium
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Maybe add correlation test or fit statistics
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project_input_resistance
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What is the problem with this project?
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medium
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What is the problem with this project? --> No difference between segments
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Improve questions
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project_isicorrelations
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medium-difficult
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Add statistical test for dependence on adapttau!
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Need to program a solution!
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project_isipdffit
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Too technical
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project_lif
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OK
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OK, difficult
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no statistics
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project_mutualinfo
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OK
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OK, medium
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project_noiseficurves
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OK
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OK, simple-medium
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no statistics
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project_numbers
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simple
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We might add some more involved statistical analysis
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project_pca_natural_images
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Needs PCA...
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medium
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Make a solution (->Lukas)
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project_photoreceptor
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OK - text needs to be improved
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Maybe also add how responses are influenced by unstable resting potential
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Maybe more cells...
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OK, simple
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project_populationvector
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difficult
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OK
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project_qvalues
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-
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Interesting! But needs solution.
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project_random_walk
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simple-medium
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Improve it! Provide code exmaples for plotting world and making movies
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project_serialcorrelation
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OK
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OK, simple-medium
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project_spectra
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-
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Needs improvements and a solution
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project_stimulus_reconstruction
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OK Fix equation?
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OK, difficult
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Add specific hints for statistics
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project_vector_strength
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OK Maybe add something for explainiong the vector strength (average unit vector).
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OK, medium-difficult
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Maybe add something for explaining the vector strength (average unit vector).
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Check text (d)
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Add statisitcs for (e)
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Peter power:
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medium
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Marius monkey data:
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medium-difficult
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@ -37,8 +37,18 @@ multiples of the fundamental frequency).
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the beginning choose $n=3$.
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\part Try different choices of $n$ and see how the fit
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changes. Plot the fits and the section of the original curve that
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you used for fitting for different choices of $n$. Also plot the
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fitting error as a function of $n$.
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you used for fitting for different choices of $n$.
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\part \label{fiterror} Plot the fitting error as a function of $n$.
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What do you observe?
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\part Another way to quantify the quality of the fit is to compute
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the correlation coefficient between the fit and the
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data. Illustrate this correlation for a few values of $n$. Plot
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the correlation coefficient as a function of $n$. What is the
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minimum $n$ needed for a good fit? How does this compare to the
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results from (\ref{fiterror})?
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\part Plot the amplitudes $\alpha_j$ and phases $\varphi_j$ as a
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function of the frequencies $\omega_j$ --- the amplitude and phase
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spectra, also called ``Bode plot''.
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\part Why does the fitting fail when you try to fit the entire recording?
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\part (optional) If you want you can also play the different fits
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and the original as sound (check the help).
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@ -33,7 +33,7 @@ shifts. The eye movements during training and test are recorded.
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speed and/or accelerations.
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\part Detect and correct the eye traces for instances in which the
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eye was not correctly detected. Interpolate linearily in these sections.
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\part Create a 'heatmap' plot that shows the eye trajectories
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\part Create a 'heatmap' plot of the eye-positions
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for one or two (nice) trials.
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\part Use the \verb+kmeans+ clustering function to
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identify fixation points. Manually select a good number of cluster
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@ -10,29 +10,29 @@
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\input{../instructions.tex}
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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
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\section*{Reverse reconstruction of the stimulus evoking neuronal responses.}
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\section*{Reverse reconstruction of the stimulus that evoked a neuronal response.}
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To analyse encoding properties of a neuron one often calculates the
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Spike-Triggered-Average (STA).
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\[ STA(\tau) = \frac{1}{\langle n \rangle} \left\langle
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\displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \right\rangle \]
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The STA is the average stimulus that led to a spike in the neuron and
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is calculated by cutting out snippets form the stimulus centered on
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the respective spike time. The Spike-Triggered-Average can be used to
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reconstruct the stimulus a neuron has been stimulated with.
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Spike-Triggered-Average (STA). The STA is the average stimulus that
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led to a spike in the neuron and is calculated by cutting out snippets
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form the stimulus centered on the respective spike time:
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\[ STA(\tau) = \frac{1}{n} \displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \],
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where $n$ is the number of trials and $t_i$ is the time of the
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$i_{th}$ spike. The Spike-Triggered-Average can be used to reconstruct
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the stimulus from the neuronal response. The reconstructed stimulus
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can then be compared to the original stimulus.
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\begin{questions}
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\question In the accompanying files you find the spike responses of
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P-units and pyramidal neurons of the weakly electric fish
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a p-type electroreceptor afferent (P-unit) and a pyramidal neurons
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recorded in the hindbrain of the weakly electric fish
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\textit{Apteronotus leptorhynchus}. The respective stimuli are
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stored in separate files. The data is sampled with 20\,kHz temporal
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resolution and spike times are given in seconds. Start with the
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P-unit and, in the end, apply the same functions to the pyramidal
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data.
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P-unit and, in the end, apply the same analyzes/functions to the
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pyramidal data.
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\begin{parts}
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\part Estimate the STA and plot it.
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\part Implement a function that does the reconstruction of the
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stimulus using the STA.
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\part Implement a function that does the reverse reconstruction and uses the STA to recopnstruct the stimulus.
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\part Implement a function that estimates the reconstruction
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error using the mean-square-error and express it relative to the
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variance of the original stimulus.
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@ -44,8 +44,8 @@ reconstruct the stimulus a neuron has been stimulated with.
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\part Analyze the robustness of the reconstruction: Estimate
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the STA with less and less data and estimate the reconstruction
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error.
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\part Plot the reconstruction error as a function of the data
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amount used to estimate the STA.
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\part Plot the reconstruction error as a function of the amount of data
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used to estimate the STA.
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\part Repeat the above steps for the pyramidal neuron, what do you
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observe?
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\end{parts}
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