diff --git a/figures/Schmidt2018_dyn/Fig2_bistability.py b/figures/Schmidt2018_dyn/Fig2_bistability.py
index 4fb78cd5d60cfc1f9ad9ecebee042b1d1de6e558..dcf78beb698a82df52b805a6d2874c8a0d0dc77b 100644
--- a/figures/Schmidt2018_dyn/Fig2_bistability.py
+++ b/figures/Schmidt2018_dyn/Fig2_bistability.py
@@ -84,7 +84,7 @@ pl.savefig('Fig2_bistability_mpl.eps')
 """
 Merging files
 """
-pyx.text.set(mode='latex')
+pyx.text.set(cls=pyx.text.LatexRunner)
 pyx.text.preamble(r"\usepackage{helvet}")
 
 c = pyx.canvas.canvas()
diff --git a/figures/Schmidt2018_dyn/Fig4_metastability.py b/figures/Schmidt2018_dyn/Fig4_metastability.py
index 3aa268a9570083fbce3bf95ea203ddc0f8de93ad..756f3f86eddc2c275f29a9de0b0e8f3cc6d1379c 100644
--- a/figures/Schmidt2018_dyn/Fig4_metastability.py
+++ b/figures/Schmidt2018_dyn/Fig4_metastability.py
@@ -294,7 +294,7 @@ pl.savefig('Fig4_metastability_mpl.eps')
 """
 Merge with sketch figure
 """
-pyx.text.set(mode='latex')
+pyx.text.set(cls=pyx.text.LatexRunner)
 pyx.text.preamble(r"\usepackage{helvet}")
 
 c = pyx.canvas.canvas()
diff --git a/figures/Schmidt2018_dyn/Fig7_surface_plot_lateral.eps b/figures/Schmidt2018_dyn/Fig7_surface_plot_lateral.eps
new file mode 100644
index 0000000000000000000000000000000000000000..e20e0c4654ce1a9da62f0d9f54f17ac7bc273b88
--- /dev/null
+++ b/figures/Schmidt2018_dyn/Fig7_surface_plot_lateral.eps
@@ -0,0 +1,8158 @@
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+showpage
+%%Trailer
+end
+%%EOF
diff --git a/figures/Schmidt2018_dyn/Fig7_temporal_hierarchy.py b/figures/Schmidt2018_dyn/Fig7_temporal_hierarchy.py
new file mode 100644
index 0000000000000000000000000000000000000000..2fd8ff6e798ce825871a9c288258b13a1d3d68c5
--- /dev/null
+++ b/figures/Schmidt2018_dyn/Fig7_temporal_hierarchy.py
@@ -0,0 +1,638 @@
+import copy
+import json
+import numpy as np
+import pyx
+import os
+
+from helpers import original_data_path, population_labels
+from multiarea_model import MultiAreaModel
+from multiarea_model.multiarea_helpers import vector_to_dict, create_vector_mask
+from plotcolors import myblue, myred
+from scipy.signal import find_peaks_cwt
+from scipy.optimize import minimize
+from matplotlib.colors import LogNorm
+from mpl_toolkits.axes_grid1 import make_axes_locatable
+
+import matplotlib.pyplot as pl
+from matplotlib import gridspec
+from matplotlib import rc_file
+rc_file('plotstyle.rc')
+
+cmap = pl.cm.coolwarm
+cmap = cmap.from_list('mycmap', [myblue, 'white', myred], N=256)
+
+"""
+Figure layout
+"""
+width = 7.0866
+panel_wh_ratio = 0.7 * (1. + np.sqrt(5)) / 2.  # golden ratio
+
+nrows = 3
+ncols = 3
+height = width / panel_wh_ratio * float(nrows) / ncols
+height = 6.375
+pl.rcParams['figure.figsize'] = (width, height)
+
+
+axes = {}
+
+
+gs1 = gridspec.GridSpec(3, 3)
+gs1.update(left=0.055, right=0.9425, top=0.95,
+           bottom=0.07, wspace=0.4, hspace=0.4)
+
+axes['A'] = pl.subplot(gs1[0, 0])
+axes['B'] = pl.subplot(gs1[0, 1])
+axes['C'] = pl.subplot(gs1[0, 2])
+axes['D'] = pl.subplot(gs1[1, 0])
+axes['E'] = pl.subplot(gs1[1, 1])
+axes['F'] = pl.subplot(gs1[1, 2])
+
+axes['G'] = pl.subplot(gs1[2, 0])
+pos = axes['G'].get_position()
+axes['G2'] = pl.axes([pos.x1 - 0.08 + 0.5, pos.y0,
+                      0.1,
+                      pos.y1 - pos.y0])
+
+fd = {'fontsize': 10, 'weight': 'bold', 'horizontalalignment':
+      'left', 'verticalalignment': 'bottom'}
+
+
+for label in ['C', 'D', 'E', 'F']:
+    label_pos = [-0.15, 1.04]
+    pl.text(label_pos[0], label_pos[1], r'\bfseries{}' + label,
+            fontdict=fd, transform=axes[label].transAxes)
+
+pl.text(-0.15, 1.0, r'\bfseries{}' + 'A',
+        fontdict=fd, transform=axes['A'].transAxes)
+
+pl.text(-0.05, 1.0, r'\bfseries{}' + 'G',
+        fontdict=fd, transform=axes['G'].transAxes)
+
+"""
+Load data
+"""
+LOAD_ORIGINAL_DATA = True
+
+if LOAD_ORIGINAL_DATA:
+    """
+    Create MultiAreaModel instance to have access to data structures
+    """
+    M = MultiAreaModel({})
+    label = '99c0024eacc275d13f719afd59357f7d12f02b77'
+    rate_time_series = {}
+    for area in M.area_list:
+        fn = os.path.join(original_data_path, label,
+                          'Analysis',
+                          'rate_time_series_full',
+                          'rate_time_series_full_{}.npy'.format(area))
+        rate_time_series[area] = np.load(fn)
+
+    fn = os.path.join(original_data_path, label,
+                      'Analysis',
+                      'rate_time_series_full',
+                      'rate_time_series_full_Parameters.json')
+    with open(fn, 'r') as f:
+        rate_time_series['Parameters'] = json.load(f)
+
+    cross_correlation = {}
+    for area in M.area_list:
+        cross_correlation[area] = {}
+        for area2 in M.area_list:
+            fn = os.path.join(original_data_path, label,
+                              'Analysis',
+                              'cross_correlation',
+                              'cross_correlation_{}_{}.npy'.format(area, area2))
+            cross_correlation[area][area2] = np.load(fn)
+
+    fn = os.path.join(original_data_path, label,
+                      'Analysis',
+                      'cross_correlation',
+                      'cross_correlation_time.npy')
+    cross_correlation['time'] = np.load(fn)
+
+
+# Correlation peak
+def correlation_peak(area, area2, t_min, t_max, width=[5.], max_lag=100.):
+    t = cross_correlation['time']
+    cross = cross_correlation[area][area2]
+
+    # First look for maxima in cc
+    cc = cross[0][1]
+    indices = np.where(np.logical_and(t > -max_lag, t < max_lag))
+    maxima = find_peaks_cwt(cc[indices], np.array(width))
+    max_times = t[indices][maxima]
+    if len(maxima) > 0:
+        if area == area2:
+            selected_max = np.where(t[indices] == 0)[0]
+            selected_max_time = 0.
+        else:
+            selected_max = maxima[np.argmax(cc[indices][maxima])]
+            selected_max_time = max_times[np.argmax(cc[indices][maxima])]
+        selected_max_value = cc[indices][selected_max]
+    else:
+        selected_max = np.nan
+        selected_max_time = np.nan
+        selected_max_value = 0.
+
+    # 2nd, look for minima in cc, i.e., maxima in -cc
+    cc = -1. * cross[0][1]
+    minima = find_peaks_cwt(cc[indices], np.array(width))
+    min_times = t[indices][minima]
+    if len(minima) > 0:
+        if area == area2:
+            selected_min = np.where(t[indices] == 0)[0]
+            selected_min_time = 0.
+        else:
+            selected_min = minima[np.argmax(cc[indices][minima])]
+            selected_min_time = min_times[np.argmax(cc[indices][minima])]
+        selected_min_value = cc[indices][selected_min]
+    else:
+        selected_min = np.nan
+        selected_min_time = np.nan
+        selected_min_value = 0.
+
+    # Then select the one with the larger absolute value
+    if abs(selected_max_value) > abs(selected_min_value):
+        selected_peak = selected_max
+        selected_peak_time = selected_max_time
+    else:
+        selected_peak = selected_min
+        selected_peak_time = selected_min_time
+ 
+    # selected_peak = selected_max
+    # selected_peak_time = selected_max_time
+    cc = cross[0][1]
+    if area != 'MDP' and area2 != 'MDP':
+        return selected_peak_time, cc[indices][selected_peak]
+    else:
+        return np.nan, np.nan
+
+
+"""
+Plotting
+"""
+
+"""
+Panel A: Matrix plot of rate time series
+"""
+interval = (10750., 11250.)
+x_ticks = np.array([10800, 11200])
+
+tmin = interval[0]
+tmax = interval[1]
+
+i_min = int(tmin - rate_time_series['Parameters']['t_min'])
+i_max = int(tmax - rate_time_series['Parameters']['t_min'])
+
+areas = []
+transitions = []
+for area in M.area_list:
+    rate = rate_time_series[area][i_min:i_max]
+    indices = np.where(rate > 2. * np.mean(rate))
+    if len(indices[0]) > 0:
+        transitions.append(indices[0][0])
+    else:
+        transitions.append(rate.size - 1)
+    areas.append(area)
+areas = np.array(areas)
+areas = areas[np.argsort(transitions)]
+transitions = np.sort(transitions)
+
+
+matrix = np.array([])
+time_interval = int(tmax - tmin)
+for area in areas:
+    rate = rate_time_series[area][i_min:i_max]
+    matrix = np.append(matrix, rate / np.mean(rate))
+matrix = matrix.reshape((len(areas), time_interval))
+
+
+y_index = list(range(len(areas)))
+y_index = [(a + 0.5) for a in y_index]
+ytick_labels = areas
+pl.yticks(y_index, ytick_labels)
+
+
+ax1 = axes['A']
+ax1.yaxis.set_ticks_position("left")
+ax1.xaxis.set_ticks_position("bottom")
+ax1.tick_params(axis='y', length=0.)
+
+x_index = [np.where(np.arange(tmin, tmax, 1.) == i)[0][0] for i in x_ticks]
+ax1.set_xticks(x_index)
+ax1.set_xticklabels(x_ticks)
+
+ax1.set_ylabel('Area')
+ax1.yaxis.set_label_coords(-0.18, 0.5)
+ax1.set_yticks(np.arange(32.) + 0.5)
+ax1.set_yticklabels(areas, size=4.3)
+ax1.set_xlabel('Time (ms)', labelpad=-0.05)
+im = ax1.pcolormesh(matrix, cmap=pl.get_cmap('inferno'), vmin=0., vmax=12.)
+pl.colorbar(im, ax=ax1, ticks=[0., 10., 20.])
+ax1.set_ylim((0., 32.))
+ax1.text(1.32, 0.65, r'$\nu (\mathrm{spikes/s})$',
+         rotation=90, transform=ax1.transAxes)
+
+
+# ################### PANEL B ####################
+"""
+Panel B: Cross-correlation of 3 pairs of areas
+"""
+
+ax2 = axes['B']
+ax2.spines['right'].set_color('none')
+ax2.spines['top'].set_color('none')
+ax2.yaxis.set_ticks_position("left")
+ax2.xaxis.set_ticks_position("bottom")
+pl.text(-0.1, 1.0, r'\bfseries{}' + 'B',
+        fontdict=fd, transform=ax2.transAxes)
+
+area = 'V1'
+areas2 = [area, 'V2', 'FEF']
+colors = ['0.0', '0.4', '0.6']
+
+for i, area2 in enumerate(areas2):
+    t = cross_correlation['time']
+    cross = cross_correlation[area][area2]
+    cc = cross[0][1]
+    tp, pp = correlation_peak(
+        area, area2, 500., 100500., max_lag=100.)
+
+    ax2.plot(t, cc, color=colors[i])
+    ax2.vlines(tp, -5000., pp, color=colors[i], linestyle='dashed')
+
+ax2.set_xticks([-100., -50., 0., 50., 100.])
+ax2.set_xlim((-100., 100.))
+ax2.set_yticks([0., 20000., 100000.])
+ax2.set_yticklabels([r'$0.$', r'$2\cdot10^4$', r'$10^5$'])
+ax2.set_ylim((-5000., 35000.))
+ax2.text(-130., 15000., r'$C(\tau)$', rotation=90)
+ax2.set_xlabel(r'Time lag $\tau$ ($\mathrm{ms}$)', labelpad=-0.05)
+
+
+print("Constructing CC Matrix")
+cc_matrix = []
+peak_matrix = []
+
+cc_matrix = np.zeros((32, 32))
+for i, area in enumerate(M.area_list):
+    cc_list = []
+    peak_list = []
+    for j, area2 in enumerate(M.area_list):
+        if cc_matrix[j][i] != 0.:
+            cc_matrix[i][j] = -1. * cc_matrix[j][i]
+        else:
+            tp, peak = correlation_peak(area, area2,
+                                        500., 100500., max_lag=100.)
+            cc_matrix[i][j] = tp
+            peak_list.append(peak)
+    peak_matrix.append(peak_list)
+
+peak_matrix = np.array(peak_matrix)
+d = {'matrix': cc_matrix}
+
+cc_matrix_masked = np.ma.masked_where(np.isnan(cc_matrix), cc_matrix)
+
+"""
+Panel C: Extremum matrix unsorted
+"""
+ax = axes['C']
+ax.yaxis.set_ticks_position("none")
+ax.xaxis.set_ticks_position("none")
+
+ax.set_xlabel('Area B')
+ax.xaxis.set_label_coords(0.5, -0.2)
+
+ax.set_ylabel('Area A')
+ax.set_xlim((0, 32))
+ax.set_ylim((0, 32))
+
+ax.set_aspect(1. / ax.get_data_ratio())
+vlim = np.max(np.abs(cc_matrix_masked))
+cmap.set_bad('0.5')
+im = ax.pcolormesh(cc_matrix_masked[::-1], cmap=cmap, vmin=-vlim, vmax=vlim)
+
+ax.set_xticklabels(M.area_list, rotation=90, size=4.2)
+ax.set_xticks(np.arange(32) + 0.5)
+
+ax.set_yticklabels(M.area_list[::-1], size=4.2)
+ax.set_yticks(np.arange(32) + 0.5)
+
+pl.colorbar(im, ax=ax, fraction=0.044, ticks=[-80, -40, 0, 40, 80])
+ax.text(42.8, 27., r'Extremum time ($\mathrm{ms}$)', rotation=90)
+
+
+def dev(i, j, hierarchy, cc_matrix):
+    """
+    Deviation function for the linear programming algorithm
+    determining the hierarchy.
+    """
+    return (hierarchy[i] - hierarchy[j] - cc_matrix[i][j])
+
+
+def hier_dev(hierarchy, cc_matrix):
+    deviation = 0.
+    for i in range(hierarchy.size):
+        for j in range(hierarchy.size):
+            deviation += (dev(i, j, hierarchy, cc_matrix)) ** 2
+    return np.sqrt(deviation)
+
+
+def create_hierarchy(cc_matrix, areas):
+    """
+    Determined the heirarchy for a given set of areas and their
+    cross-correlation peak matrix.
+    """
+    res = minimize(hier_dev, np.random.rand(
+        cc_matrix[0].size), args=(cc_matrix,))
+    hierarchy = res['x']
+    index_transformation = np.argsort(hierarchy)
+    hierarchical_areas = copy.copy(areas)
+    hierarchical_areas = np.array(hierarchical_areas)
+    hierarchical_areas = hierarchical_areas[index_transformation]
+    hierarchy = hierarchy[index_transformation]
+    # Map hierarchy onto [0,1] interval
+    hierarchy -= np.min(hierarchy)
+    hierarchy /= np.max(hierarchy)
+    return res, hierarchy, hierarchical_areas, index_transformation
+
+
+def count_violations(hierarchy, cc_matrix):
+    """
+    Count the violations of a given hierarchy based on the given
+    matrix of cross-correlation peaks.
+    """
+
+    violations = 0
+    for i in range(hierarchy.size):
+        for j in range(hierarchy.size):
+            x1 = hierarchy[i] - hierarchy[j]
+            x2 = cc_matrix[i][j]
+            if np.sign(x1) != np.sign(x2):
+                violations += 1
+
+    return violations / 2.  # Divide by two to not count each pair double
+
+
+print("Computing hierarchy")
+area_list = np.array(M.area_list)
+# We exclude area MDP because it does not receive connections from any
+# other area and thus does not participate in cortico-cortical
+# communication
+ind_without_MDP = np.isfinite(cc_matrix[0])
+cc_matrix_without_MDP = cc_matrix[ind_without_MDP][:, ind_without_MDP]
+area_list_without_MDP = area_list[ind_without_MDP]
+res, hierarchy, hierarchical_areas, index_transformation = create_hierarchy(
+    cc_matrix_without_MDP, area_list_without_MDP)
+hierarchy_to_area_list = []
+
+for area in area_list:
+    if area not in ['MDP']:
+        hierarchy_to_area_list.append(
+            np.where(hierarchical_areas == area)[0][0])
+
+# Export hierarchy to csv
+with open('Fig7_temporal_hierarchy.csv', 'w') as f:
+    for hier, area in zip(hierarchy, hierarchical_areas):
+        f.write(area + ',' + str(hier) + '\n')
+
+
+"""
+Panel D: Extremum matrix sorted
+"""
+
+ax = axes['D']
+cc_matrix_hier = cc_matrix_without_MDP[index_transformation][:,
+                                                             index_transformation]
+# Add area MDP to the matrix for plotting purposes
+cc_matrix_hier = np.insert(cc_matrix_hier, 0, cc_matrix[14][:-1], axis=0)
+cc_matrix_hier = np.insert(cc_matrix_hier, 0, cc_matrix[14], axis=1)
+
+cc_matrix_hier_masked = np.ma.masked_where(
+    np.isnan(cc_matrix_hier), cc_matrix_hier)
+ax.yaxis.set_ticks_position("none")
+ax.xaxis.set_ticks_position("none")
+ax.set_xlabel('Area B')
+ax.xaxis.set_label_coords(0.5, -0.2)
+ax.set_ylabel('Area A')
+ax.yaxis.set_label_coords(-0.17, 0.5)
+
+
+ax.set_xlim((0, 32))
+ax.set_ylim((0, 32))
+
+ax.set_aspect(1. / ax.get_data_ratio())
+im = ax.pcolormesh(
+    cc_matrix_hier_masked[:, ::-1], cmap=cmap, vmin=-vlim, vmax=vlim)
+
+ax.set_xticklabels(
+    list(hierarchical_areas[::-1]) + ['MDP'], rotation=90, size=4.2)
+ax.set_xticks(np.arange(32) + 0.5)
+
+ax.set_yticklabels(['MDP'] + list(hierarchical_areas), size=4.2)
+ax.set_yticks(np.arange(32) + 0.3)
+
+pl.colorbar(im, ax=ax, fraction=0.044, ticks=[-80, -40, 0, 40, 80])
+ax.text(42.8, 27., r'Extremum time ($\mathrm{ms}$)', rotation=90)
+
+"""
+Eigenvalue spectrum and eigenvector projection
+"""
+conn_params = {'replace_non_simulated_areas': 'het_poisson_stat',
+               'g': -11.,
+               'K_stable': '../../K_stable.npy',
+               'fac_nu_ext_TH': 1.2,
+               'fac_nu_ext_5E': 1.125,
+               'fac_nu_ext_6E': 1.41666667,
+               'cc_weights_I_factor': 2.,
+               'cc_weights_factor': 1.9,
+               'av_indegree_V1': 3950.}
+input_params = {'rate_ext': 10.}
+neuron_params = {'V0_mean': -150.,
+                 'V0_sd': 50.}
+network_params = {'connection_params': conn_params,
+                  'neuron_params': neuron_params}
+
+theory_params = {'T': 50.,
+                 'dt': 0.1,
+                 'initial_rates': 'random_uniform',
+                 'initial_rates_iter': 15}
+
+M = MultiAreaModel(network_params, theory=True, simulation=False,
+                   theory_spec=theory_params)
+pops, rates_full = M.theory.integrate_siegert()
+# Here, pick a calculation that converges to the LA state
+ana_rates = rates_full[12][:, -1]
+lambda_max, slope, slope_sigma, G, EV = M.theory.lambda_max(ana_rates, full_output=True)
+
+"""
+Panel E: Eigenvalues
+"""
+ax = axes['E']
+ax.set_frame_on(False)
+ax.set_xticks([])
+ax.set_yticks([])
+
+pos = ax.get_position()
+
+# Real part < 0
+ax0 = pl.axes([pos.x0 + 0.02,
+               pos.y0,
+               0.6 * (pos.x1 - pos.x0),
+               pos.y1 - pos.y0])
+ax0.spines['right'].set_color('none')
+ax0.spines['top'].set_color('none')
+
+ax0.plot(np.real(EV[0]),
+         np.imag(EV[0]), '.')
+
+ax0.set_xlabel(r'$\mathrm{Re}(\lambda_i)$')
+ax0.xaxis.set_label_coords(1., -0.2)
+ax0.yaxis.set_label_coords(-0.15, 0.5)
+ax0.set_ylabel(r'$\mathrm{Im}(\lambda_i)$')
+ax0.yaxis.set_label_coords(-0.17, 0.5)
+
+ax0.vlines(1., -3., 3., lw=0.9)
+ax0.set_xlim((-20., 0.1))
+kwargs = dict(transform=ax.transAxes, color='k', clip_on=False, lw=1.)
+ax0.plot([0.7, 0.72], [-0.05, 0.03], **kwargs)
+ax0.plot([0.73, 0.75], [-0.05, 0.03], **kwargs)
+
+# Real part > 0
+ax1 = pl.axes([pos.x0 + 0.18,
+               pos.y0,
+               0.35 * (pos.x1 - pos.x0),
+               pos.y1 - pos.y0])
+ax1.spines['right'].set_color('none')
+ax1.spines['left'].set_color('none')
+ax1.spines['top'].set_color('none')
+ax1.set_yticks([])
+ax1.plot(np.real(EV[0]),
+         np.imag(EV[0]), '.')
+critical_eval = EV[0][np.argsort(np.real(EV[0]))[-1]]
+ax1.plot(np.real(critical_eval),
+         np.imag(critical_eval), '.', color=myred)
+
+ax1.vlines(1., -3., 3., lw=0.7)
+ax1.set_xlim((0., 1.))
+
+"""
+Panel F: Projection of critical eigenvector onto network
+"""
+ax = axes['F']
+pos = ax.get_position()
+divider = make_axes_locatable(ax)
+ax_cb = pl.axes([pos.x1,
+                 pos.y0,
+                 0.02,
+                 pos.y1 - pos.y0])
+
+ax_cb.set_frame_on(False)
+ax_cb.set_xticks([])
+ax_cb.set_yticks([])
+
+critical_eigenvector = np.real(EV[1][:, np.argsort(np.real(EV[0]))[-1]])
+r = vector_to_dict(critical_eigenvector, area_list, M.structure)
+
+ev_matrix = np.zeros((8, 32))
+for i, area in enumerate(area_list):
+    vm = create_vector_mask(M.structure, areas=[area])
+    r = critical_eigenvector[vm]
+    if area == 'TH':
+        r = np.insert(r, 2, np.zeros(2))
+    ev_matrix[:, i] = r
+
+ind = [list(area_list).index(area) for area in hierarchical_areas[::-1]]
+
+im = ax.pcolormesh(np.abs(ev_matrix[::-1][:, ind]), cmap=pl.get_cmap('inferno'),
+                   norm=LogNorm(vmin=1e-3, vmax=1e0))
+ax.set_xticklabels(area_list[ind], rotation=90, size=4.3)
+ax.tick_params(axis='x', length=0.)
+ax.set_xticks(np.arange(32.) + 0.5)
+ax.set_yticklabels(population_labels[::-1])
+ax.set_yticks(np.arange(8.) + 0.5)
+cb = pl.colorbar(im, ax=ax_cb, fraction=1.)
+cb.set_ticks([0.001, 0.01, 0.1, 1.])
+cb.set_ticklabels([r'$0.001$', r'$0.01$', r'$0.1$', r'$1$'])
+cb.ax.tick_params(labelsize=5, length=0, rotation=0)
+ax_cb.text(1.2, 0.8, 'critical eigenvector',
+           rotation=90, transform=ax.transAxes)
+
+
+"""
+Create 100 surrogate matrices by shuffling the cross-correlation peak
+matrix and measure the violations of the temporal hierarchy to judge
+the significance of the temporal hierarchy.
+"""
+print("Surrogate matrices")
+surrogate_matrix = copy.deepcopy(cc_matrix_without_MDP)
+violation_list = []
+np.random.seed(123)
+for i in range(100):
+    for j in range(len(area_list_without_MDP)):
+        ind = np.extract(np.arange(len(area_list_without_MDP)) != i,
+                         np.arange(len(area_list_without_MDP)))
+        ind = np.arange(j, len(area_list_without_MDP))
+        surr = surrogate_matrix[j][ind][np.random.shuffle(ind)]
+        surrogate_matrix[j][ind] = surr
+        surrogate_matrix[:, j][ind] = -1.*surr
+    (surrogate_res, surrogate_hierarchy,
+     surrogate_hierarchical_areas,
+     sit) = create_hierarchy(surrogate_matrix, area_list_without_MDP)
+    violation_list.append(count_violations(hierarchy, surrogate_matrix[sit][:, sit]))
+
+print("Mean violations of surrogates: ", np.mean(violation_list), " +- ", np.std(violation_list))
+
+print(("Violations of hierarchy: ", count_violations(
+    hierarchy, cc_matrix[index_transformation][:, index_transformation])))
+
+
+for label in ['E', 'G', 'G2']:
+    axes[label].spines['right'].set_color('none')
+    axes[label].spines['left'].set_color('none')
+    axes[label].spines['top'].set_color('none')
+    axes[label].spines['bottom'].set_color('none')
+    axes[label].yaxis.set_ticks_position("none")
+    axes[label].xaxis.set_ticks_position("none")
+    axes[label].set_xticks([])
+    axes[label].set_yticks([])
+
+
+"""
+Plot the colorbar for the surface plots.
+"""
+ax = axes['G2']
+
+sm = pl.cm.ScalarMappable(cmap=pl.get_cmap('inferno_r'), norm=pl.Normalize(
+    vmax=np.min(hierarchy), vmin=np.max(hierarchy)))
+sm.set_array([])
+cbticks = []
+cbar = pl.colorbar(sm, ax=ax, ticks=cbticks, shrink=0.9)
+ax.annotate('', xy=(1.3, .8), xycoords='axes fraction',
+            xytext=(1.3, .1), arrowprops=dict(arrowstyle="->", color='k'))
+ax.text(1.45, 23., 'Temporal hierarchy', rotation=90)
+
+
+"""
+Save figure
+"""
+pl.savefig('Fig7_temporal_hierarchy_mpl.eps')
+
+
+"""
+Merge eps files
+"""
+pyx.text.set(cls=pyx.text.LatexRunner)
+pyx.text.preamble(r"\usepackage{helvet}")
+
+c = pyx.canvas.canvas()
+
+c.insert(pyx.epsfile.epsfile(
+    0., 0., "Fig7_temporal_hierarchy_mpl.eps", width=18.))
+c.insert(pyx.epsfile.epsfile(
+    2., 1.5, "Fig7_surface_plot_lateral.eps", width=5.5))
+c.insert(pyx.epsfile.epsfile(
+    8., 1.5, "Fig7_surface_plot_medial.eps", width=5.5))
+
+c.writeEPSfile("Fig7_temporal_hierarchy.eps")
diff --git a/figures/Schmidt2018_dyn/Snakefile b/figures/Schmidt2018_dyn/Snakefile
index f9d950b0e0cef664b63daa1676d1cde91d472067..94a3513285cbad8f246b7c22bb99217c0c623082 100644
--- a/figures/Schmidt2018_dyn/Snakefile
+++ b/figures/Schmidt2018_dyn/Snakefile
@@ -37,7 +37,8 @@ ORIGINAL_SIMULATIONS = {'all': ['533d73357fbe99f6178029e6054b571b485f40f6',
                         'Fig6': ['33fb5955558ba8bb15a3fdce49dfd914682ef3ea',
                                  '5bdd72887b191ec22a5abcc04ca4a488ea216e32',
                                  '99c0024eacc275d13f719afd59357f7d12f02b77',
-                                 '3afaec94d650c637ef8419611c3f80b3cb3ff539']}
+                                 '3afaec94d650c637ef8419611c3f80b3cb3ff539'],
+                        'Fig7': ['99c0024eacc275d13f719afd59357f7d12f02b77']}
 
 
 if LOAD_ORIGINAL_DATA:
@@ -51,7 +52,8 @@ rule all:
         'Fig3_ground_state_chi1.eps',
         'Fig4_metastability.eps',
         'Fig5_ground_state.eps',
-        'Fig6_comparison_exp_spiking_data.eps'
+        'Fig6_comparison_exp_spiking_data.eps',
+        'Fig7_temporal_hierarchy.eps'
 
 include: './Snakefile_preprocessing'
 
@@ -137,3 +139,14 @@ rule Fig6_comparison_exp_spiking_data:
         'Fig6_comparison_exp_spiking_data.eps'
     shell:
         'python3 Fig6_comparison_exp_spiking_data.py'
+
+rule Fig7_temporal_hierarchy:
+    input:
+        expand(os.path.join(DATA_DIR, '{simulation}', 'Analysis', 'rate_time_series_full', 'rate_time_series_full_{area}.npy'),
+               simulation=SIMULATIONS['Fig7'], area=area_list),
+        expand(os.path.join(DATA_DIR, '{simulation}', 'Analysis', 'cross_correlation', 'cross_correlation_{area1}_{area2}.npy'),
+               simulation=SIMULATIONS['Fig7'], area1=area_list, area2=area_list),
+    output:
+        'Fig7_temporal_hierarchy.eps'
+    shell:
+        'python3 Fig7_temporal_hierarchy.py'
diff --git a/figures/Schmidt2018_dyn/Snakefile_preprocessing b/figures/Schmidt2018_dyn/Snakefile_preprocessing
index 048694445abc0cfb81c02e7bd89deb4dc44d03c2..9bbfda2f9510250b7f23a94d0ed439f59b5ac4d1 100644
--- a/figures/Schmidt2018_dyn/Snakefile_preprocessing
+++ b/figures/Schmidt2018_dyn/Snakefile_preprocessing
@@ -68,3 +68,15 @@ rule process_chu2014_data:
         os.path.join(chu2014_path, 'Analysis', 'rate_histogram_full.npy')
     shell:
         'python3 process_chu2014_data.py {} {}'.format(DATA_DIR, SIMULATIONS['Fig6'][-1])
+
+rule cross_correlation:
+    input:
+        os.path.join(DATA_DIR, '{simulation}', 'Analysis',
+                     'rate_time_series_full', 'rate_time_series_full_{area1}.npy'),
+        os.path.join(DATA_DIR, '{simulation}', 'Analysis',
+                     'rate_time_series_full', 'rate_time_series_full_{area2}.npy')
+    output:
+        os.path.join(DATA_DIR, '{simulation}', 'Analysis', 'cross_correlation',
+                     'cross_correlation_{area1}_{area2}.npy')
+    shell:
+        'python3 compute_cross_correlation.py {} {{wildcards.simulation}} {{wildcards.area1}} {{wildcards.area2}}'.format(DATA_DIR)
diff --git a/figures/Schmidt2018_dyn/compute_cross_correlation.py b/figures/Schmidt2018_dyn/compute_cross_correlation.py
new file mode 100644
index 0000000000000000000000000000000000000000..fe607f781acb6cbb1b3d5d7dc79db703576f0807
--- /dev/null
+++ b/figures/Schmidt2018_dyn/compute_cross_correlation.py
@@ -0,0 +1,66 @@
+import correlation_toolbox.helper as ch
+import correlation_toolbox.correlation_analysis as corr
+import json
+import numpy as np
+import os
+import sys
+
+data_path = sys.argv[1]
+label = sys.argv[2]
+area1 = sys.argv[3]
+area2 = sys.argv[4]
+
+
+load_path = os.path.join(data_path,
+                         label,
+                         'Analysis',
+                         'rate_time_series_full')
+save_path = os.path.join(data_path,
+                         label,
+                         'Analysis',
+                         'cross_correlation')
+
+with open(os.path.join(data_path, label, 'custom_params_{}'.format(label)), 'r') as f:
+    sim_params = json.load(f)
+T = sim_params['T']
+
+fn1 = os.path.join(load_path,
+                   'rate_time_series_full_{}.npy'.format(area1))
+rate_time_series1 = np.load(fn1)
+
+
+fn2 = os.path.join(load_path,
+                   'rate_time_series_full_{}.npy'.format(area2))
+rate_time_series2 = np.load(fn2)
+
+fn = os.path.join(load_path,
+                  'rate_time_series_full_Parameters.json')
+with open(fn, 'r') as f:
+    params = json.load(f)
+
+i_min = int(500. - params['t_min'])
+i_max = int(T - params['t_min'])
+
+rates = [rate_time_series1[i_min:i_max],
+         rate_time_series2[i_min:i_max]]
+
+dat = [ch.centralize(rates[0], units=True),
+       ch.centralize(rates[1], units=True)]
+freq, crossspec = corr.crossspec(dat, 1.)
+t, cross = corr.crosscorrfunc(freq, crossspec)
+
+sigma = 2.
+time_range = np.arange(-5., 5.)
+kernel = 1 / (np.sqrt(2.0 * np.pi) * sigma) * np.exp(-(time_range ** 2 / (2 * sigma ** 2)))
+cross_conv = np.zeros_like(cross)
+cross_conv[0][0] = np.convolve(kernel, cross[0][0], mode='same')
+cross_conv[0][1] = np.convolve(kernel, cross[0][1], mode='same')
+cross_conv[1][0] = np.convolve(kernel, cross[1][0], mode='same')
+cross_conv[1][1] = np.convolve(kernel, cross[1][1], mode='same')
+cross = cross_conv
+
+fp = '_'.join(('cross_correlation',
+               area1,
+               area2))
+np.save('{}/{}.npy'.format(save_path, fp), cross)
+np.save('{}/{}.npy'.format(save_path, 'cross_correlation_time'), t)
diff --git a/figures/Schmidt2018_dyn/compute_rate_time_series.py b/figures/Schmidt2018_dyn/compute_rate_time_series.py
index 3408f6f0e3312110b225710bba87b2246e5d8728..ec3a776fb0041cf6382211b30088490cf6e9ca1e 100644
--- a/figures/Schmidt2018_dyn/compute_rate_time_series.py
+++ b/figures/Schmidt2018_dyn/compute_rate_time_series.py
@@ -25,16 +25,16 @@ assert(method in ['subsample', 'full', 'auto_kernel'])
 #               (see Method parts of the paper)
 
 load_path = os.path.join(data_path,
-                       label,
-                       'recordings')
+                         label,
+                         'recordings')
 save_path = os.path.join(data_path,
                          label,
                          'Analysis',
                          'rate_time_series_{}'.format(method))
 
 with open(os.path.join(data_path, label, 'custom_params_{}'.format(label)), 'r') as f:
-    par = json.load(f)
-T = par['T']
+    sim_params = json.load(f)
+T = sim_params['T']
 
 """
 Create MultiAreaModel instance to have access to data structures
diff --git a/multiarea_model/theory.py b/multiarea_model/theory.py
index 00e1519060e4f5fd5d72052524a3949445c94bd7..f4e93620365ef6558c6bbbaae51cccd6ba6f37bc 100644
--- a/multiarea_model/theory.py
+++ b/multiarea_model/theory.py
@@ -305,7 +305,36 @@ class Theory():
 
         return mu, sigma
 
-    def stability_matrix(self, rates, matrix_filter=None,
+    def d_nu(self, mu, sigma):
+        """
+        Compute the derivative of the Siegert function by mu and sigma
+        for given mu and sigma.
+
+        Parameters
+        ----------
+        mu : numpy.ndarray
+            Mean input to the populations
+        sigma : numpy.ndarray
+            Variance of input to the populations
+        """
+        d_nu_d_mu = np.array([d_nu_d_mu_fb_numeric(1.e-3*self.NP['tau_m'],
+                                                   1.e-3*self.NP['tau_syn'],
+                                                   1.e-3*self.NP['t_ref'],
+                                                   self.NP['theta'],
+                                                   self.NP['V_reset'],
+                                                   mu[ii], sigma[ii]) for ii in range(len(mu))])
+        # Unit: 1/(mV)**2
+        d_nu_d_sigma = np.array([d_nu_d_sigma_fb_numeric(1.e-3*self.NP['tau_m'],
+                                                         1.e-3*self.NP['tau_syn'],
+                                                         1.e-3*self.NP['t_ref'],
+                                                         self.NP['theta'],
+                                                         self.NP['V_reset'],
+                                                         mu[ii], sigma[ii])*1/(
+                                                             2. * sigma[ii])
+                                 for ii in range(len(mu))])
+        return d_nu_d_mu, d_nu_d_sigma
+
+    def gain_matrix(self, rates, matrix_filter=None,
                          vector_filter=None, full_output=False):
         """
         Computes stability matrix on the population level.
@@ -349,24 +378,10 @@ class Theory():
         if np.any(vector_filter is not None):
             mu = mu[vector_filter]
             sigma = sigma[vector_filter]
-        slope = np.array([d_nu_d_mu_fb_numeric(1.e-3*self.NP['tau_m'],
-                                               1.e-3*self.NP['tau_syn'],
-                                               1.e-3*self.NP['t_ref'],
-                                               self.NP['V_th'],
-                                               self.NP['V_reset'],
-                                               mu[ii], sigma[ii]) for ii in range(N.size)])
 
-        # Unit: 1/(mV)**2
-        slope_sigma = np.array([d_nu_d_sigma_fb_numeric(1.e-3*self.NP['tau_m'],
-                                                        1.e-3*self.NP['tau_syn'],
-                                                        1.e-3*self.NP['t_ref'],
-                                                        self.NP['V_th'],
-                                                        self.NP['V_reset'],
-                                                        mu[ii], sigma[ii])*1/(
-                                                            2. * sigma[ii])
-                                for ii in range(N.size)])
-
-        slope_matrix = np.zeros_like(J)
+        d_nu_d_mu, d_nu_d_sigma = self.d_nu(mu, sigma)
+
+        slope_mu_matrix = np.zeros_like(J)
         slope_sigma_matrix = np.zeros_like(J)
         for ii in range(N.size):
             slope_mu_matrix[:, ii] = d_nu_d_mu
@@ -398,18 +413,17 @@ class Theory():
             contributing. Defaults to False.
         """
         if full_output:
-            (M, slope, slope_sigma,
-             M, EV, C, V, G_N) = self.stability_matrix(rates,
+            (G, slope, slope_sigma) = self.gain_matrix(rates,
                                                        matrix_filter=matrix_filter,
                                                        vector_filter=vector_filter,
                                                        full_output=full_output)
         else:
-            M = self.stability_matrix(rates, matrix_filter=matrix_filter,
-                                      vector_filter=vector_filter,
-                                      full_output=full_output)
-        EV = np.linalg.eig(M)
+            G = self.gain_matrix(rates, matrix_filter=matrix_filter,
+                                 vector_filter=vector_filter,
+                                 full_output=full_output)
+        EV = np.linalg.eig(G)
         lambda_max = np.sqrt(np.max(np.real(EV[0])))
         if full_output:
-            return lambda_max, slope, slope_sigma, M, EV, C, V
+            return lambda_max, slope, slope_sigma, G, EV
         else:
             return lambda_max