[pointprocesses] imporoved plot scripts
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@ -354,6 +354,7 @@ def common_format():
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mpl.rcParams['ytick.direction'] = 'out'
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mpl.rcParams['xtick.major.width'] = 1.25
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mpl.rcParams['ytick.major.width'] = 1.25
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mpl.rcParams['axes.facecolor'] = 'none'
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if 'axes.prop_cycle' in mpl.rcParams:
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mpl.rcParams['axes.prop_cycle'] = cycler(color=[colors['blue'], colors['red'],
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colors['orange'], colors['green'],
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@ -35,7 +35,6 @@ def plot_isi_rate(spike_times, max_t=30, dt=1e-4):
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ax1.set_xlim(0, 5)
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ax2.plot(time, rate, label="instantaneous rate, trial 1")
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ax2.set_ylabel('Firing rate', 'Hz')
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ax2.legend()
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ax3.fill_between(time, avg_rate+rate_std, avg_rate-rate_std, color="dodgerblue",
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alpha=0.5, label="standard deviation")
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@ -144,39 +143,47 @@ def plot_comparison(spike_times, bin_width, sigma, max_t=30., dt=1e-4):
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time, inst_rate = get_instantaneous_rate(times)
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time, binn_rate = get_binned_rate(times, bin_width)
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fig, (ax1, ax2, ax3, ax4) = plt.subplots(4, 1, figsize=cm_size(figure_width, 2.0*figure_height))
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fig, (ax1, ax2, ax3, ax4) = plt.subplots(4, 1, figsize=cm_size(figure_width, 1.8*figure_height))
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fig.subplots_adjust(**adjust_fs(fig, left=6.0, right=1.5, bottom=3.0, top=1.0))
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ax1.show_spines('b')
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ax1.vlines(times[times < (100000*dt)], ymin=0, ymax=1, color=colors['blue'], lw=1.5)
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ax1.set_ylabel('Spikes')
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#ax1.set_ylabel('Spikes')
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ax1.text(-0.105, 0.5, 'Spikes', transform=ax1.transAxes,
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rotation='vertical', va='center')
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ax1.set_xlim(2.5, 3.5)
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ax1.set_ylim(0, 1)
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ax1.set_yticks([0, 1])
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ax1.set_ylim(-0.2, 1)
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ax1.set_xticks([2.5, 2.75, 3.0, 3.25, 3.5])
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ax1.set_xticklabels([])
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ax2.plot(time, inst_rate, color=colors['orange'], lw=1.5, label="instantaneous rate")
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ax2.legend()
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ax2.set_ylabel('Rate', 'Hz')
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ax2.plot(time, inst_rate, color=colors['orange'], lw=2)
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ax2.text(1.0, 1.0, 'instantaneous rate', transform=ax2.transAxes, ha='right')
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#ax2.set_ylabel('Rate', 'Hz')
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ax2.text(-0.105, 0.5, axis_label('Rate', 'Hz'), transform=ax2.transAxes,
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rotation='vertical', va='center')
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ax2.set_xlim(2.5, 3.5)
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ax2.set_ylim(0, 300)
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ax2.set_yticks(np.arange(0, 400, 100))
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ax2.set_xticks([2.5, 2.75, 3.0, 3.25, 3.5])
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ax2.set_xticklabels([])
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ax3.plot(time, binn_rate, color=colors['orange'], lw=1.5, label="binned rate")
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ax3.set_ylabel('Rate', 'Hz')
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ax3.legend()
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ax3.plot(time, binn_rate, color=colors['orange'], lw=2)
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ax3.text(1.0, 1.0, 'binned rate', transform=ax3.transAxes, ha='right')
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#ax3.set_ylabel('Rate', 'Hz')
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ax3.text(-0.105, 0.5, axis_label('Rate', 'Hz'), transform=ax3.transAxes,
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rotation='vertical', va='center')
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ax3.set_xlim(2.5, 3.5)
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ax3.set_ylim(0, 300)
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ax3.set_yticks(np.arange(0, 400, 100))
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ax3.set_xticks([2.5, 2.75, 3.0, 3.25, 3.5])
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ax3.set_xticklabels([])
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ax4.plot(time, conv_rate, color=colors['orange'], lw=1.5, label="convolved rate")
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ax4.plot(time, conv_rate, color=colors['orange'], lw=2)
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ax4.text(1.0, 1.0, 'convolved rate', transform=ax4.transAxes, ha='right')
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ax4.set_xlabel('Time', 's')
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ax4.set_ylabel('Rate', 'Hz')
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ax4.legend()
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#ax4.set_ylabel('Rate', 'Hz')
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ax4.text(-0.105, 0.5, axis_label('Rate', 'Hz'), transform=ax4.transAxes,
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rotation='vertical', va='center')
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ax4.set_xlim(2.5, 3.5)
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ax4.set_xticks([2.5, 2.75, 3.0, 3.25, 3.5])
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ax4.set_ylim(0, 300)
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@ -1,9 +1,10 @@
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import numpy as np
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import matplotlib.pyplot as plt
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import matplotlib.gridspec as gridspec
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from plotstyle import *
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fig_size = cm_size(figure_width, 1.2*figure_height)
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fig_size = cm_size(figure_width, figure_height)
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def create_spikes(nspikes=11, duration=0.5, seed=1000):
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@ -27,11 +28,12 @@ def gaussian(sigma, dt):
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def setup_axis(spikes_ax, rate_ax):
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spikes_ax.show_spines('b')
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spikes_ax.show_spines('')
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spikes_ax.set_yticks([])
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spikes_ax.set_ylim(-0.2, 1.0)
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spikes_ax.text(-0.1, 0.5, 'Spikes', transform=spikes_ax.transAxes, rotation='vertical', va='center')
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spikes_ax.set_xlim(-1, 500)
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spikes_ax.set_xticklabels([])
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#spikes_ax.set_xticklabels(np.arange(0., 600, 100))
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spikes_ax.show_spines('lb')
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@ -56,8 +58,10 @@ def plot_bin_method():
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count, _ = np.histogram(spike_times, bins)
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fig = plt.figure(figsize=fig_size)
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spikes_ax = plt.subplot2grid((7,1), (0,0), rowspan=3, colspan=1)
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rate_ax = plt.subplot2grid((7,1), (3,0), rowspan=4, colspan=1)
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spec = gridspec.GridSpec(nrows=2, ncols=1, height_ratios=[3, 4], hspace=0.2,
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**adjust_fs(fig, left=5.5, right=1.5, top=1.5))
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spikes_ax = fig.add_subplot(spec[0, 0])
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rate_ax = fig.add_subplot(spec[1, 0])
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setup_axis(spikes_ax, rate_ax)
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for ti in spike_times:
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@ -71,7 +75,7 @@ def plot_bin_method():
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ha='center')
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rate = count / 0.05
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rate_ax.step(1000.0*bins, np.hstack((rate, rate[-1])), color=colors['orange'], where='post')
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rate_ax.step(1000.0*bins, np.hstack((rate, rate[-1])), color=colors['orange'], lw=2, where='post')
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fig.savefig("binmethod.pdf")
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plt.close()
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@ -89,8 +93,10 @@ def plot_conv_method():
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rate = np.roll(rate, -1)
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fig = plt.figure(figsize=fig_size)
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spikes_ax = plt.subplot2grid((7,1), (0,0), rowspan=3, colspan=1)
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rate_ax = plt.subplot2grid((7,1), (3,0), rowspan=4, colspan=1)
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spec = gridspec.GridSpec(nrows=2, ncols=1, height_ratios=[3, 4], hspace=0.2,
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**adjust_fs(fig, left=5.5, right=1.5, top=1.5))
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spikes_ax = fig.add_subplot(spec[0, 0])
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rate_ax = fig.add_subplot(spec[1, 0])
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setup_axis(spikes_ax, rate_ax)
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for ti in spike_times:
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@ -109,9 +115,11 @@ def plot_isi_method():
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spike_times = create_spikes()
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fig = plt.figure(figsize=fig_size)
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spikes_ax = plt.subplot2grid((7,1), (0,0), rowspan=3, colspan=1)
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rate = plt.subplot2grid((7,1), (3,0), rowspan=4, colspan=1)
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setup_axis(spikes_ax, rate)
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spec = gridspec.GridSpec(nrows=2, ncols=1, height_ratios=[3, 4], hspace=0.2,
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**adjust_fs(fig, left=5.5, right=1.5, top=1.5))
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spikes_ax = fig.add_subplot(spec[0, 0])
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rate_ax = fig.add_subplot(spec[1, 0])
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setup_axis(spikes_ax, rate_ax)
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spike_times = np.hstack((0.005, spike_times))
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for i in range(1, len(spike_times)):
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@ -119,13 +127,13 @@ def plot_isi_method():
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t = 1000*spike_times[i]
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spikes_ax.plot([t_start, t_start], [0., 1.], color=colors['blue'], lw=2)
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spikes_ax.annotate(s='', xy=(t_start, 0.5), xytext=(t,0.5), arrowprops=dict(arrowstyle='<->'), color=colors['red'])
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spikes_ax.text(0.5*(t_start+t), 0.75,
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spikes_ax.text(0.5*(t_start+t), 1.05,
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"{0:.0f}".format((t - t_start)),
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color=colors['red'], ha='center')
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#spike_times = np.hstack((0, spike_times))
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i_rate = 1./np.diff(spike_times)
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rate.step(1000*spike_times, np.hstack((i_rate, i_rate[-1])),color=colors['orange'], lw=2, where="post")
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rate_ax.step(1000*spike_times, np.hstack((i_rate, i_rate[-1])),color=colors['orange'], lw=2, where="post")
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fig.savefig("isimethod.pdf")
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@ -2,6 +2,8 @@
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\input{../../header}
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\renewcommand{\exercisesolutions}{here} % 0: here, 1: chapter, 2: end
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\lstset{inputpath=../code}
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\graphicspath{{figures/}}
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@ -175,7 +175,7 @@ with itself and is always 1.
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Implement a function \varcode{isiserialcorr()} that takes a vector of
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interspike intervals as input argument and calculates the serial
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correlation. The function should further plot the serial
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correlation. \pagebreak[4]
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correlation.
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\end{exercise}
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@ -223,7 +223,7 @@ that is given in Hertz
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window. The function should take two input arguments: (i) a
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cell-array of vectors containing the spike times in seconds observed
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in a number of trials, and (ii) the duration of the time window that
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is used to evaluate the counts.\pagebreak[4]
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is used to evaluate the counts.
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\end{exercise}
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@ -340,13 +340,11 @@ closely.
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\begin{figure}[tp]
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\includegraphics[width=\columnwidth]{firingrates}
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\titlecaption{Estimating the time-dependent firing
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rate.}{\textbf{A)} Rasterplot showing the spiking activity of a
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neuron. \textbf{B)} Firing rate calculated from the
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\emph{instantaneous rate}. \textbf{C)} classical PSTH with the
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\emph{binning} method. \textbf{D)} Firing rate estimated by
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\emph{convolution} of the activity with a Gaussian
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kernel.}\label{psthfig}
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\titlecaption{Estimating time-dependent firing rates.}{Rasterplot
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showing one trial of spiking activity of a neuron (top).
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\emph{Instantaneous rate}, classical PSTH estimatd with the
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\emph{binning} method and by \emph{convolution} of the spike train
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with a Gaussian kernel (bottom).}\label{psthfig}
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\end{figure}
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@ -354,11 +352,11 @@ closely.
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\begin{figure}[tp]
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\includegraphics[width=\columnwidth]{isimethod}
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\titlecaption{Instantaneous firing rate.}{Sketch of the recorded
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spiketrain (top). Arrows illustrate the interspike intervals and
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number give the intervals in milliseconds. The inverse of the
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interspike interval is the \emph{instantaneous firing
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rate}.}\label{instratefig}
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\titlecaption{Instantaneous firing rate.}{The recorded spiketrain
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(top). Arrows illustrate the interspike intervals and numbers
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give the intervals in milliseconds. The inverse of the interspike
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intervals is the \emph{instantaneous firing rate}
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(bottom).}\label{instratefig}
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\end{figure}
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A very simple method for estimating the time-dependent firing rate is
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@ -415,11 +413,11 @@ methods make an assumption about the relevant observation time-scale
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\begin{figure}[tp]
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\includegraphics[width=\columnwidth]{binmethod}
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\titlecaption{Estimating the PSTH using the binning method.}{The
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same spiketrain as shown in \figref{instratefig} is used
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here. Vertical gray lines indicate the borders between adjacent
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bins in which the number of action potentials is counted (red
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numbers). The firing rate is then the histogram normalized to the
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binwidth.}\label{binpsthfig}
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same spiketrain as shown in \figref{instratefig} (top). Vertical
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gray lines indicate the borders between adjacent bins in which the
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number of action potentials is counted (red numbers). The firing
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rate is then the histogram normalized to the binwidth
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(bottom).}\label{binpsthfig}
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\end{figure}
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The \entermde[firing rate!binning
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@ -440,7 +438,6 @@ estimation Changes that happen within a bin cannot be resolved. Thus
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chosing a bin width implies an assumption about the relevant
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time-scale.
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\pagebreak[4]
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\begin{exercise}{binnedRate.m}{}
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Implement a function that estimates the firing rate using the
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binning method. The method should take the spike-times as an
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@ -452,12 +449,12 @@ time-scale.
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\begin{figure}[tp]
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\includegraphics[width=\columnwidth]{convmethod}
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\titlecaption{Estimating the firing rate using the convolution
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method.}{The same spiketrain as in \figref{instratefig}. The
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convolution of the spiketrain with a convolution kernel basically
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replaces each spike event with the kernel (top). A Gaussian kernel
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is used here, but other kernels are also possible. If the kernel
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is properly normalized the firing rate results directly form the
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superposition of the kernels.}\label{convratefig}
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method.}{The same spiketrain as in \figref{instratefig} (top). The
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convolution of the spiketrain with a kernel replaces each spike
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event with the kernel (red). A Gaussian kernel is used here, but
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other kernels are also possible. If the kernel is properly
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normalized the firing rate results directly form the superposition
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of the kernels (bottom).}\label{convratefig}
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\end{figure}
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With the \entermde[firing rate!convolution
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@ -484,7 +481,6 @@ width defines, similar to the bin width of the binning method, the
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temporal resolution of the method and thus makes assumptions about the
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relevate time-scale.
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\pagebreak[4]
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\begin{exercise}{convolutionRate.m}{}
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Implement the function that estimates the firing rate using the
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convolution method. The method takes the spiketrain, the temporal
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@ -512,16 +508,15 @@ snippets are then averaged (\figref{stafig}).
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\begin{figure}[t]
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\includegraphics[width=\columnwidth]{sta}
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\titlecaption{Spike-triggered average of a P-type electroreceptors
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\titlecaption{Spike-triggered average of a P-type electroreceptor
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and the stimulus reconstruction.}{The neuron was driven by a
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\enterm{white-noise} stimulus (blue curve, right panel). The STA
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(left) is the average stimulus that surrounds the times of the
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recorded action potentials (40\,ms before and 20\,ms after the
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spike). Using the STA as a convolution kernel for convolving the
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spiketrain we can reconstruct the stimulus from the neuronal
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response. In this way we can get an impression of the stimulus
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features that are encoded in the neuronal response (right
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panel).}\label{stafig}
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\enterm{white-noise} stimulus (blue, right). The STA (left) is the
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average stimulus that surrounds the times of the recorded action
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potentials (40\,ms before and 20\,ms after the spike). Using the
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STA as a kernel for convolving the spiketrain we can reconstruct
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the stimulus from the neuronal response. In this way we can get an
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impression of the stimulus features that are linearly encoded in
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the neuronal response (orange, right).}\label{stafig}
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\end{figure}
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From the STA we can extract several pieces of information about the
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