result images

This commit is contained in:
a.ott 2020-09-10 17:24:28 +02:00
parent 6ac778e84a
commit 3577b86cbb
13 changed files with 364 additions and 130 deletions

View File

@ -20,10 +20,11 @@ def main():
# data_mean_freq_step_stimulus_examples()
# data_mean_freq_step_stimulus_with_detections()
# data_fi_curve()
# p_unit_example()
# fi_point_detection()
p_unit_example()
fi_point_detection()
p_unit_heterogeneity()
# test_fi_curve_colors()
pass
@ -227,7 +228,7 @@ def fi_point_detection():
f_baseline = fi.get_f_baseline_frequencies()[-1]
f_base_idx = fi.indices_f_baseline[-1]
axes[0].plot(f_trace_times[-1][:idx], f_traces[-1][:idx])
axes[0].plot(f_trace_times[-1][:idx], f_traces[-1][:idx], color=consts.COLOR_DATA)
axes[0].plot([f_trace_times[-1][idx] for idx in f_zero_idx], (f_zero, ), ",", marker=consts.f0_marker, color=consts.COLOR_DATA_f0)
axes[0].plot([f_trace_times[-1][idx] for idx in f_inf_idx], (f_inf, f_inf), color=consts.COLOR_DATA_finf, linewidth=4)
axes[0].plot([f_trace_times[-1][idx] for idx in f_base_idx], (f_baseline, f_baseline), color="grey", linewidth=4)

View File

@ -1,23 +1,135 @@
import numpy as np
import matplotlib.pyplot as plt
from analysis import get_fit_info, get_behaviour_values, calculate_percent_errors
import matplotlib.gridspec as gridspec
from analysis import get_fit_info, get_behaviour_values, get_parameter_values, behaviour_correlations, parameter_correlations
from ModelFit import get_best_fit
from Baseline import BaselineModel, BaselineCellData
import Figure_constants as consts
parameter_titles = {"input_scaling": r"$\alpha$", "delta_a": r"$\Delta_A$",
"mem_tau": r"$\tau_m$", "noise_strength": r"$\sqrt{2D}$",
"refractory_period": "$t_{ref}$", "tau_a": r"$\tau_A$",
"v_offset": r"$I_{Bias}$", "dend_tau": r"$\tau_{dend}$"}
behaviour_titles = {"baseline_frequency": "base rate", "Burstiness": "Burst", "coefficient_of_variation": "CV",
"serial_correlation": "SC", "vector_strength": "VS",
"f_inf_slope": r"$f_{\infty}$ Slope", "f_zero_slope": r"$f_0$ Slope",
"f_zero_middle": r"$f_0$ middle"}
def main():
dir_path = "results/final_2/"
fits_info = get_fit_info(dir_path)
# cell_behaviour, model_behaviour = get_behaviour_values(fits_info)
# behaviour_overview_pairs(cell_behaviour, model_behaviour)
# plot_cell_model_comp_baseline(cell_behaviour, model_behaviour)
# plot_cell_model_comp_adaption(cell_behaviour, model_behaviour)
# plot_cell_model_comp_burstiness(cell_behaviour, model_behaviour)
#
behaviour_correlations_plot(fits_info)
#
# labels, corr_values, corrected_p_values = parameter_correlations(fits_info)
# par_labels = [parameter_titles[l] for l in labels]
# fig, ax = plt.subplots(1, 1)
# create_correlation_plot(ax, par_labels, corr_values, corrected_p_values, "", colorbar=True)
# plt.savefig(consts.SAVE_FOLDER + "parameter_correlations.png")
# plt.close()
# create_parameter_distributions(get_parameter_values(fits_info))
# errors = calculate_percent_errors(fits_info)
# create_boxplots(errors)
example_good_hist_fits(dir_path)
# example_good_hist_fits(dir_path)
def create_parameter_distributions(par_values):
fig, axes = plt.subplots(4, 2)
if len(par_values.keys()) != 8:
print("not eight parameters")
labels = ["input_scaling", "v_offset", "mem_tau", "noise_strength",
"tau_a", "delta_a", "dend_tau", "refractory_period"]
axes_flat = axes.flatten()
for i, l in enumerate(labels):
min_v = min(par_values[l]) * 0.95
max_v = max(par_values[l]) * 1.05
step = (max_v - min_v) / 20
bins = np.arange(min_v, max_v+step, step)
axes_flat[i].hist(par_values[l], bins=bins, color=consts.COLOR_MODEL, alpha=0.75)
axes_flat[i].set_title(parameter_titles[l])
plt.tight_layout()
plt.savefig(consts.SAVE_FOLDER + "parameter_distributions.png")
plt.close()
def behaviour_correlations_plot(fits_info):
fig = plt.figure(tight_layout=True, figsize=consts.FIG_SIZE_MEDIUM_WIDE)
gs = gridspec.GridSpec(2, 2, width_ratios=(1, 1), height_ratios=(5, 1), hspace=0.025, wspace=0.05)
# fig, axes = plt.subplots(1, 2, figsize=consts.FIG_SIZE_MEDIUM_WIDE)
keys, corr_values, corrected_p_values = behaviour_correlations(fits_info, model_values=False)
labels = [behaviour_titles[k] for k in keys]
img = create_correlation_plot(fig.add_subplot(gs[0, 0]), labels, corr_values, corrected_p_values, "Data")
keys, corr_values, corrected_p_values = behaviour_correlations(fits_info, model_values=True)
labels = [behaviour_titles[k] for k in keys]
img = create_correlation_plot(fig.add_subplot(gs[0, 1]), labels, corr_values, corrected_p_values, "Model", y_label=False)
ax_col = fig.add_subplot(gs[1, :])
data = [np.arange(-1, 1.001, 0.01)] * 10
ax_col.set_xticks([0, 25, 50, 75, 100, 125, 150, 175, 200])
ax_col.set_xticklabels([-1, -0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75, 1])
ax_col.set_yticks([])
ax_col.imshow(data)
ax_col.set_xlabel("Correlation Coefficients")
plt.tight_layout()
plt.savefig(consts.SAVE_FOLDER + "behaviour_correlations.png")
plt.close()
def create_correlation_plot(ax, labels, correlations, p_values, title, y_label=True):
cleaned_cors = np.zeros(correlations.shape)
for i in range(correlations.shape[0]):
for j in range(correlations.shape[1]):
if abs(p_values[i, j]) < 0.05:
cleaned_cors[i, j] = correlations[i, j]
im = ax.imshow(cleaned_cors, vmin=-1, vmax=1)
# We want to show all ticks...
ax.set_xticks(np.arange(len(labels)))
ax.set_xticklabels(labels)
# ... and label them with the respective list entries
if y_label:
ax.set_yticks(np.arange(len(labels)))
ax.set_yticklabels(labels)
else:
ax.set_yticklabels([])
ax.set_title(title)
# Rotate the tick labels and set their alignment.
plt.setp(ax.get_xticklabels(), rotation=45, ha="right",
rotation_mode="anchor")
# Loop over data dimensions and create text annotations.
for i in range(len(labels)):
for j in range(len(labels)):
text = ax.text(j, i, "{:.2f}".format(correlations[i, j]),
ha="center", va="center", color="w")
return im
def example_good_hist_fits(dir_path):
strong_bursty_cell = "2018-05-08-ac-invivo-1"
@ -66,98 +178,245 @@ def create_boxplots(errors):
plt.close()
def behaviour_overview_pairs(cell_behaviour, model_behaviour):
# behaviour_keys = ["Burstiness", "coefficient_of_variation", "serial_correlation",
# "vector_strength", "f_inf_slope", "f_zero_slope", "baseline_frequency"]
pairs = [("baseline_frequency", "vector_strength", "serial_correlation"),
("Burstiness", "coefficient_of_variation"),
("f_inf_slope", "f_zero_slope")]
def plot_cell_model_comp_baseline(cell_behavior, model_behaviour):
fig = plt.figure(figsize=(12, 6))
# ("baseline_frequency", "vector_strength", "serial_correlation")
# Add a gridspec with two rows and two columns and a ratio of 2 to 7 between
# the size of the marginal axes and the main axes in both directions.
# Also adjust the subplot parameters for a square plot.
gs = fig.add_gridspec(2, 3, width_ratios=[5, 5, 5], height_ratios=[3, 7],
left=0.1, right=0.9, bottom=0.1, top=0.9,
wspace=0.25, hspace=0.05)
num_of_bins = 20
# baseline freq plot:
i = 0
cell = cell_behavior["baseline_frequency"]
model = model_behaviour["baseline_frequency"]
minimum = min(min(cell), min(model))
maximum = max(max(cell), max(model))
step = (maximum - minimum) / num_of_bins
bins = np.arange(minimum, maximum + step, step)
ax = fig.add_subplot(gs[1, i])
ax_histx = fig.add_subplot(gs[0, i], sharex=ax)
scatter_hist(cell, model, ax, ax_histx, behaviour_titles["baseline_frequency"], bins)
i += 1
cell = cell_behavior["vector_strength"]
model = model_behaviour["vector_strength"]
minimum = min(min(cell), min(model))
maximum = max(max(cell), max(model))
step = (maximum - minimum) / num_of_bins
bins = np.arange(minimum, maximum + step, step)
ax = fig.add_subplot(gs[1, i])
ax_histx = fig.add_subplot(gs[0, i], sharex=ax)
scatter_hist(cell, model, ax, ax_histx, behaviour_titles["vector_strength"], bins)
i += 1
cell = cell_behavior["serial_correlation"]
model = model_behaviour["serial_correlation"]
minimum = min(min(cell), min(model))
maximum = max(max(cell), max(model))
step = (maximum - minimum) / num_of_bins
bins = np.arange(minimum, maximum + step, step)
ax = fig.add_subplot(gs[1, i])
ax_histx = fig.add_subplot(gs[0, i], sharex=ax)
scatter_hist(cell, model, ax, ax_histx, behaviour_titles["serial_correlation"], bins)
i += 1
for pair in pairs:
cell = []
model = []
for behaviour in pair:
cell.append(cell_behaviour[behaviour])
model.append(model_behaviour[behaviour])
overview_pair(cell, model, pair)
plt.tight_layout()
plt.savefig(consts.SAVE_FOLDER + "fit_baseline_comparison.png", transparent=True)
plt.close()
def overview_pair(cell, model, titles):
def plot_cell_model_comp_adaption(cell_behavior, model_behaviour):
fig = plt.figure(figsize=(8, 6))
columns = len(cell)
# ("f_inf_slope", "f_zero_slope")
# Add a gridspec with two rows and two columns and a ratio of 2 to 7 between
# the size of the marginal axes and the main axes in both directions.
# Also adjust the subplot parameters for a square plot.
gs = fig.add_gridspec(2, columns, width_ratios=[5] * columns, height_ratios=[3, 7],
gs = fig.add_gridspec(2, 2, width_ratios=[5, 5], height_ratios=[3, 7],
left=0.1, right=0.9, bottom=0.1, top=0.9,
wspace=0.2, hspace=0.05)
for i in range(len(cell)):
if titles[i] == "f_zero_slope":
length_before = len(cell[i])
idx = np.array(cell[i]) < 30000
cell[i] = np.array(cell[i])[idx]
model[i] = np.array(model[i])[idx]
idx = np.array(model[i]) < 30000
cell[i] = np.array(cell[i])[idx]
model[i] = np.array(model[i])[idx]
print("removed {} values from f_zero_slope plot.".format(length_before - len(cell[i])))
wspace=0.25, hspace=0.05)
num_of_bins = 20
# baseline freq plot:
i = 0
cell = cell_behavior["f_inf_slope"]
model = model_behaviour["f_inf_slope"]
minimum = min(min(cell), min(model))
maximum = max(max(cell), max(model))
step = (maximum - minimum) / num_of_bins
bins = np.arange(minimum, maximum + step, step)
ax = fig.add_subplot(gs[1, i])
ax_histx = fig.add_subplot(gs[0, i], sharex=ax)
scatter_hist(cell[i], model[i], ax, ax_histx, titles[i])
scatter_hist(cell, model, ax, ax_histx, behaviour_titles["f_inf_slope"], bins)
i += 1
cell = cell_behavior["f_zero_slope"]
model = model_behaviour["f_zero_slope"]
length_before = len(cell)
idx = np.array(cell) < 25000
cell = np.array(cell)[idx]
model = np.array(model)[idx]
idx = np.array(model) < 25000
cell = np.array(cell)[idx]
model = np.array(model)[idx]
print("removed {} values from f_zero_slope plot.".format(length_before - len(cell)))
minimum = min(min(cell), min(model))
maximum = max(max(cell), max(model))
step = (maximum - minimum) / num_of_bins
bins = np.arange(minimum, maximum + step, step)
# plt.tight_layout()
plt.show()
ax = fig.add_subplot(gs[1, i])
ax_histx = fig.add_subplot(gs[0, i], sharex=ax)
scatter_hist(cell, model, ax, ax_histx, behaviour_titles["f_zero_slope"], bins)
plt.tight_layout()
plt.savefig(consts.SAVE_FOLDER + "fit_adaption_comparison.png", transparent=True)
plt.close()
def grouped_error_overview_behaviour_dist(cell_behaviours, model_behaviours):
# start with a square Figure
fig = plt.figure(figsize=(12, 12))
rows = 4
columns = 2
def plot_cell_model_comp_burstiness(cell_behavior, model_behaviour):
fig = plt.figure(figsize=(8, 6))
# ("Burstiness", "coefficient_of_variation")
# Add a gridspec with two rows and two columns and a ratio of 2 to 7 between
# the size of the marginal axes and the main axes in both directions.
# Also adjust the subplot parameters for a square plot.
gs = fig.add_gridspec(rows*2, columns, width_ratios=[5]*columns, height_ratios=[3, 7] * rows,
gs = fig.add_gridspec(2, 2, width_ratios=[5, 5], height_ratios=[3, 7],
left=0.1, right=0.9, bottom=0.1, top=0.9,
wspace=0.2, hspace=0.5)
wspace=0.25, hspace=0.05)
num_of_bins = 20
# baseline freq plot:
i = 0
cell = cell_behavior["Burstiness"]
model = model_behaviour["Burstiness"]
minimum = min(min(cell), min(model))
maximum = max(max(cell), max(model))
step = (maximum - minimum) / num_of_bins
bins = np.arange(minimum, maximum + step, step)
ax = fig.add_subplot(gs[1, i])
ax_histx = fig.add_subplot(gs[0, i], sharex=ax)
scatter_hist(cell, model, ax, ax_histx, behaviour_titles["Burstiness"], bins)
i += 1
for i, behaviour in enumerate(sorted(cell_behaviours.keys())):
col = int(np.floor(i / rows))
row = i - rows*col
ax = fig.add_subplot(gs[row*2 + 1, col])
ax_histx = fig.add_subplot(gs[row*2, col])
cell = cell_behavior["coefficient_of_variation"]
model = model_behaviour["coefficient_of_variation"]
# use the previously defined function
scatter_hist(cell_behaviours[behaviour], model_behaviours[behaviour], ax, ax_histx, behaviour)
minimum = min(min(cell), min(model))
maximum = max(max(cell), max(model))
step = (maximum - minimum) / num_of_bins
bins = np.arange(minimum, maximum + step, step)
ax = fig.add_subplot(gs[1, i])
ax_histx = fig.add_subplot(gs[0, i], sharex=ax)
scatter_hist(cell, model, ax, ax_histx, behaviour_titles["coefficient_of_variation"], bins)
plt.tight_layout()
plt.show()
plt.savefig(consts.SAVE_FOLDER + "fit_burstiness_comparison.png", transparent=True)
plt.close()
# def behaviour_overview_pairs(cell_behaviour, model_behaviour):
# # behaviour_keys = ["Burstiness", "coefficient_of_variation", "serial_correlation",
# # "vector_strength", "f_inf_slope", "f_zero_slope", "baseline_frequency"]
#
# pairs = [("baseline_frequency", "vector_strength", "serial_correlation"),
# ("Burstiness", "coefficient_of_variation"),
# ("f_inf_slope", "f_zero_slope")]
#
# for pair in pairs:
# cell = []
# model = []
# for behaviour in pair:
# cell.append(cell_behaviour[behaviour])
# model.append(model_behaviour[behaviour])
# overview_pair(cell, model, pair)
#
#
# def overview_pair(cell, model, titles):
# fig = plt.figure(figsize=(8, 6))
#
# columns = len(cell)
#
# # Add a gridspec with two rows and two columns and a ratio of 2 to 7 between
# # the size of the marginal axes and the main axes in both directions.
# # Also adjust the subplot parameters for a square plot.
# gs = fig.add_gridspec(2, columns, width_ratios=[5] * columns, height_ratios=[3, 7],
# left=0.1, right=0.9, bottom=0.1, top=0.9,
# wspace=0.2, hspace=0.05)
#
# for i in range(len(cell)):
# if titles[i] == "f_zero_slope":
# length_before = len(cell[i])
# idx = np.array(cell[i]) < 30000
# cell[i] = np.array(cell[i])[idx]
# model[i] = np.array(model[i])[idx]
#
# idx = np.array(model[i]) < 30000
# cell[i] = np.array(cell[i])[idx]
# model[i] = np.array(model[i])[idx]
# print("removed {} values from f_zero_slope plot.".format(length_before - len(cell[i])))
# ax = fig.add_subplot(gs[1, i])
# ax_histx = fig.add_subplot(gs[0, i], sharex=ax)
# scatter_hist(cell[i], model[i], ax, ax_histx, titles[i])
#
# # plt.tight_layout()
# plt.show()
#
#
# def grouped_error_overview_behaviour_dist(cell_behaviours, model_behaviours):
# # start with a square Figure
# fig = plt.figure(figsize=(12, 12))
#
# rows = 4
# columns = 2
# # Add a gridspec with two rows and two columns and a ratio of 2 to 7 between
# # the size of the marginal axes and the main axes in both directions.
# # Also adjust the subplot parameters for a square plot.
# gs = fig.add_gridspec(rows*2, columns, width_ratios=[5]*columns, height_ratios=[3, 7] * rows,
# left=0.1, right=0.9, bottom=0.1, top=0.9,
# wspace=0.2, hspace=0.5)
#
# for i, behaviour in enumerate(sorted(cell_behaviours.keys())):
# col = int(np.floor(i / rows))
# row = i - rows*col
# ax = fig.add_subplot(gs[row*2 + 1, col])
# ax_histx = fig.add_subplot(gs[row*2, col])
#
# # use the previously defined function
# scatter_hist(cell_behaviours[behaviour], model_behaviours[behaviour], ax, ax_histx, behaviour)
#
# plt.tight_layout()
# plt.show()
#
def scatter_hist(cell_values, model_values, ax, ax_histx, behaviour, ax_histy=None):
def scatter_hist(cell_values, model_values, ax, ax_histx, behaviour, bins, ax_histy=None):
# copied from matplotlib
# no labels
ax_histx.tick_params(axis="cell", labelbottom=False)
# ax_histy.tick_params(axis="model_values", labelleft=False)
# the scatter plot:
ax.scatter(cell_values, model_values)
minimum = min(min(cell_values), min(model_values))
maximum = max(max(cell_values), max(model_values))
ax.plot((minimum, maximum), (minimum, maximum), color="grey")
ax.scatter(cell_values, model_values, color="black")
ax.set_xlabel("cell")
ax.set_ylabel("model")
ax_histx.hist(cell_values, color="blue", alpha=0.5)
ax_histx.hist(model_values, color="orange", alpha=0.5)
ax_histx.hist(cell_values, bins=bins, color=consts.COLOR_DATA, alpha=0.75)
ax_histx.hist(model_values, bins=bins, color=consts.COLOR_MODEL, alpha=0.75)
ax_labels = ax.get_xticklabels()
ax_histx.set_xticklabels([])
ax.set_xticklabels(ax_labels)

View File

@ -42,7 +42,7 @@ def main():
# labels, corr_values, corrected_p_values = parameter_correlations(fits_info)
# create_correlation_plot(labels, corr_values, corrected_p_values)
# create_parameter_distributions(get_parameter_values(fits_info))
create_parameter_distributions(get_parameter_values(fits_info))
cell_b, model_b = get_behaviour_values(fits_info)
create_behaviour_distributions(cell_b, model_b)
pass
@ -115,7 +115,8 @@ def behaviour_correlations(fits_info, model_values=True):
else:
behaviour_values = bv_cell
labels = sorted(behaviour_values.keys())
labels = ["baseline_frequency", "serial_correlation", "vector_strength", "coefficient_of_variation", "Burstiness",
"f_inf_slope", "f_zero_slope"]
corr_values = np.zeros((len(labels), len(labels)))
p_values = np.ones((len(labels), len(labels)))
@ -133,7 +134,8 @@ def behaviour_correlations(fits_info, model_values=True):
def parameter_correlations(fits_info):
parameter_values = get_parameter_values(fits_info)
labels = sorted(parameter_values.keys())
labels = ["input_scaling", "v_offset", "mem_tau", "noise_strength",
"tau_a", "delta_a", "dend_tau", "refractory_period"]
corr_values = np.zeros((len(labels), len(labels)))
p_values = np.ones((len(labels), len(labels)))
@ -148,64 +150,6 @@ def parameter_correlations(fits_info):
return labels, corr_values, corrected_p_values
def create_correlation_plot(labels, correlations, p_values):
cleaned_cors = np.zeros(correlations.shape)
for i in range(correlations.shape[0]):
for j in range(correlations.shape[1]):
if abs(p_values[i, j]) < 0.05:
cleaned_cors[i, j] = correlations[i, j]
fig, ax = plt.subplots()
im = ax.imshow(cleaned_cors, vmin=-1, vmax=1)
cbar = ax.figure.colorbar(im, ax=ax)
cbar.ax.set_ylabel("Correlation coefficient", rotation=-90, va="bottom")
# We want to show all ticks...
ax.set_xticks(np.arange(len(labels)))
ax.set_yticks(np.arange(len(labels)))
# ... and label them with the respective list entries
ax.set_xticklabels(labels)
ax.set_yticklabels(labels)
# Rotate the tick labels and set their alignment.
plt.setp(ax.get_xticklabels(), rotation=45, ha="right",
rotation_mode="anchor")
# Loop over data dimensions and create text annotations.
for i in range(len(labels)):
for j in range(len(labels)):
text = ax.text(j, i, "{:.2f}".format(correlations[i, j]),
ha="center", va="center", color="w")
fig.tight_layout()
plt.show()
def create_parameter_distributions(par_values):
fig, axes = plt.subplots(4, 2)
if len(par_values.keys()) != 8:
print("not eight parameters")
labels = sorted(par_values.keys())
axes_flat = axes.flatten()
for i, l in enumerate(labels):
min_v = min(par_values[l]) * 0.95
max_v = max(par_values[l]) * 1.05
step = (max_v - min_v) / 15
bins = np.arange(min_v, max_v+step, step)
axes_flat[i].hist(par_values[l], bins=bins)
axes_flat[i].set_title(l)
plt.tight_layout()
plt.show()
plt.close()
def create_behaviour_distributions(cell_b_values, model_b_values):
fig, axes = plt.subplots(4, 2)

Binary file not shown.

View File

@ -161,13 +161,13 @@ When the fish's EOD is unperturbed P units fire every few EOD periods but they h
\begin{figure}[H]
{\caption{\label{fig:heterogeneity_isi_hist} \textbf{A--C} 100\,ms of cell membrane voltage and \textbf{D--F} interspike interval histograms, each for three different cells. Showing the variability between cells of spiking behavior of P units in baseline conditions. \textbf{A} and \textbf{D}: A non bursting cell with a baseline firing rate of 133\,Hz (EODf: 806\,Hz), \textbf{B} and \textbf{E}: A cell with some bursts and a baseline firing rate of 235\,Hz (EODf: 682\,Hz) and \textbf{C} and \textbf{F}: A strongly bursting cell with longer breaks between bursts. Baseline rate of 153\,Hz and EODf of 670\,Hz }}
{\includegraphics[width=1\textwidth]{figures/isi_hist_heterogeneity.png}}
{\caption{\label{fig:heterogeneity_isi_hist} Variability in spiking behavior between P units under baseline conditions. \textbf{A--C} 100\,ms of cell membrane voltage and \textbf{D--F} interspike interval histograms, each for three different cells. \textbf{A} and \textbf{D}: A non bursting cell with a baseline firing rate of 133\,Hz (EODf: 806\,Hz), \textbf{B} and \textbf{E}: A cell with some bursts and a baseline firing rate of 235\,Hz (EODf: 682\,Hz) and \textbf{C} and \textbf{F}: A strongly bursting cell with longer breaks between bursts. Baseline rate of 153\,Hz and EODf of 670\,Hz }}
{\includegraphics[width=\textwidth]{figures/isi_hist_heterogeneity.png}}
\end{figure}
\todo{heterogeneity more}
Furthermore show P units a pronounced heterogeneity in their spiking behavior (fig.~\ref{fig:heterogeneity_isi_hist}, \cite{gussin2007limits}). This is an important aspect one needs to consider when trying to understand what and how information is encoded in the spike trains of the neuron. A single neuron might be an independent unit from all other neurons but through different tuning curves a full picture of the stimulus can be encoded in the population while a single neuron only encodes a small feature space. This type of encoding is ubiquitous in the nervous system and is used in (EXAMPLE) for (EXAMPLE feature) PLUS MORE... \todo{refs}. Even though P units were already modelled based on a simple leaky integrate-and-fire neuron \citep{chacron2001simple} and conductance based \citep{kashimori1996model} and well studied (\todo{refS}), but up to this point there no model that tries to cover the full breadth of heterogeneity of the P unit population. Having such a model could help shed light into the population code used in the electric sense, allow researchers gain a better picture how higher brain areas might process the information and get one step closer to the full path between sensory input and behavioural output.
Furthermore show P units a pronounced heterogeneity in their spiking behavior (fig.~\ref{fig:heterogeneity_isi_hist}, \cite{gussin2007limits}). This is an important aspect one needs to consider when trying to understand what and how information is encoded in the spike trains of the neuron. A single neuron might be an independent unit from all other neurons but through different tuning curves a full picture of the stimulus can be encoded in the population while a single neuron only encodes a small feature space. This type of encoding is ubiquitous in the nervous system and is used in the visual sense for color vision, PLUS MORE... \todo{refs}. Even though P units were already modelled based on a simple leaky integrate-and-fire neuron \citep{chacron2001simple} and conductance based \citep{kashimori1996model} and well studied (\todo{refS}), but up to this point there no model that tries to cover the full breadth of heterogeneity of the P unit population. Having such a model could help shed light into the population code used in the electric sense, allow researchers gain a better picture how higher brain areas might process the information and get one step closer to the full path between sensory input and behavioural output.
@ -371,7 +371,7 @@ Together this results in the dynamics seen in equations \ref{eq:full_model_dynam
parameter & explanation & unit \\
\hline
$\alpha$ & stimulus scaling factor & [cm] \\
$tau_m$ & membrane time constant & [ms]\\
$\tau_m$ & membrane time constant & [ms]\\
$I_{Bias}$ & bias current & [mV] \\
$\sqrt{2D}$ & noise strength & [mV$\sqrt{\text{s}}$]\\
$\tau_A$ & adaption time constant & [ms] \\
@ -447,13 +447,43 @@ All errors were then summed up for the full error. The fits were done with the N
\section{Results}
\begin{figure}[H]
\includegraphics[scale=0.5]{figures/fit_baseline_comparison.png}
\caption{\label{fig:comp_baseline} }
\end{figure}
\begin{figure}[H]
\includegraphics[scale=0.5]{figures/fit_adaption_comparison.png}
\caption{\label{fig:comp_adaption} Excluded 8 value pairs from Onset Slope as they had slopes higher than 30000}
\end{figure}
\section{Discussion}
\begin{figure}[H]
\includegraphics[scale=0.5]{figures/fit_burstiness_comparison.png}
\caption{\label{fig:comp_burstiness} }
\end{figure}
\begin{figure}[H]
\includegraphics[scale=0.6]{figures/behaviour_correlations.png}
\caption{\label{fig:behavior_correlations} Additional $f_{\infty}$ correlation hängt vermutlich mit der bursty-baseline freq correlation zusammen. Je höher die feuerrate umso höher chance zu bursten und bursts haben eine stärker negative SC.}
\end{figure}
\begin{figure}[H]
\includegraphics[scale=0.6]{figures/parameter_distributions.png}
\caption{\label{fig:parameter_distributions} }
\end{figure}
\begin{figure}[H]
\includegraphics[scale=0.6]{figures/parameter_correlations.png}
\caption{\label{fig:parameter_correlations} }
\end{figure}
\section{Discussion}
\newpage
\bibliography{citations}
\bibliographystyle{apalike}

Binary file not shown.

Binary file not shown.

After

Width:  |  Height:  |  Size: 62 KiB

Binary file not shown.

Before

Width:  |  Height:  |  Size: 28 KiB

After

Width:  |  Height:  |  Size: 28 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 34 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 46 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 30 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 59 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 22 KiB