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@@ -231,3 +231,69 @@ The following example computes and plots the ISI- and SPIKE-distance matrix as w
plt.title("SPIKE-Sync")
plt.show()
+
+
+Quantifying Leaders and Followers: Spike Train Order
+---------------------------------------
+
+PySpike provides functionality to quantify how much a set of spike trains
+resembles a synfire pattern (ie perfect leader-follower pattern). For details
+on the algorithms please see
+`our article in NJP <http://iopscience.iop.org/article/10.1088/1367-2630/aa68c3>`_.
+
+The following example computes the Spike Order profile and Synfire Indicator
+of two Poissonian spike trains.
+
+.. code:: python
+ import numpy as np
+ from matplotlib import pyplot as plt
+ import pyspike as spk
+
+
+ st1 = spk.generate_poisson_spikes(1.0, [0, 20])
+ st2 = spk.generate_poisson_spikes(1.0, [0, 20])
+
+ d = spk.spike_directionality(st1, st2)
+
+ print "Spike Directionality of two Poissonian spike trains:", d
+
+ E = spk.spike_train_order_profile(st1, st2)
+
+ plt.figure()
+ x, y = E.get_plottable_data()
+ plt.plot(x, y, '-ob')
+ plt.ylim(-1.1, 1.1)
+ plt.xlabel("t")
+ plt.ylabel("E")
+ plt.title("Spike Train Order Profile")
+
+ plt.show()
+
+Additionally, PySpike can also compute the optimal ordering of the spike trains,
+ie the ordering that most resembles a synfire pattern. The following example
+computes the optimal order of a set of 20 Poissonian spike trains:
+
+.. code:: python
+
+ M = 20
+ spike_trains = [spk.generate_poisson_spikes(1.0, [0, 100]) for m in xrange(M)]
+
+ F_init = spk.spike_train_order(spike_trains)
+ print "Initial Synfire Indicator for 20 Poissonian spike trains:", F_init
+
+ D_init = spk.spike_directionality_matrix(spike_trains)
+ phi, _ = spk.optimal_spike_train_sorting(spike_trains)
+ F_opt = spk.spike_train_order(spike_trains, indices=phi)
+ print "Synfire Indicator of optimized spike train sorting:", F_opt
+
+ D_opt = spk.permutate_matrix(D_init, phi)
+
+ plt.figure()
+ plt.imshow(D_init)
+ plt.title("Initial Directionality Matrix")
+
+ plt.figure()
+ plt.imshow(D_opt)
+ plt.title("Optimized Directionality Matrix")
+
+ plt.show()