Sinusoidal gamma generator example

This script demonstrates the use of the sinusoidal_gamma_generator and its different parameters and modes. The source code of the model can be found in models/sinusoidal_gamma_generator.h.

The script is structured into two parts, each of which generates its own figure. In part 1A, two generators are created with different orders of the underlying gamma process and their resulting PST (Peristiumulus time) and ISI (Inter-spike interval) histograms are plotted. Part 1B illustrates the effect of the individual_spike_trains switch. In Part 2, the effects of different settings for rate, phase and frequency are demonstrated.

First, we import all necessary modules for simulation, analysis and plotting.

import nest
import matplotlib.pyplot as plt
import numpy as np

nest.ResetKernel()   # in case we run the script multiple times from iPython

We first create a figure for the plot and set the resolution of NEST.

plt.figure()
nest.SetKernelStatus({'resolution': 0.01})

Then we create two instances of the sinusoidal_gamma_generator with two different orders of the underlying gamma process using Create. Moreover, we create devices to record firing rates (multimeter) and spikes (spike_detector) and connect them to the generators using Connect.

g = nest.Create('sinusoidal_gamma_generator', n=2,
                params=[{'rate': 10000.0, 'amplitude': 5000.0,
                         'frequency': 10.0, 'phase': 0.0, 'order': 2.0},
                        {'rate': 10000.0, 'amplitude': 5000.0,
                         'frequency': 10.0, 'phase': 0.0, 'order': 10.0}])

m = nest.Create('multimeter', n=2, params={'interval': 0.1, 'withgid': False,
                                           'record_from': ['rate']})
s = nest.Create('spike_detector', n=2, params={'withgid': False})

nest.Connect(m, g, 'one_to_one')
nest.Connect(g, s, 'one_to_one')

nest.Simulate(200)

After simulating, the spikes are extracted from the spike_detector using GetStatus and plots are created with panels for the PST and ISI histograms.

colors = ['b', 'g']

for j in range(2):

    ev = nest.GetStatus([m[j]])[0]['events']
    t = ev['times']
    r = ev['rate']

    sp = nest.GetStatus([s[j]])[0]['events']['times']
    plt.subplot(221)
    h, e = np.histogram(sp, bins=np.arange(0., 201., 5.))
    plt.plot(t, r, color=colors[j])
    plt.step(e[:-1], h * 1000 / 5., color=colors[j], where='post')
    plt.title('PST histogram and firing rates')
    plt.ylabel('Spikes per second')

    plt.subplot(223)
    plt.hist(np.diff(sp), bins=np.arange(0., 0.505, 0.01),
             histtype='step', color=colors[j])
    plt.title('ISI histogram')

The kernel is reset and the number of threads set to 4.

nest.ResetKernel()
nest.SetKernelStatus({'local_num_threads': 4})

First, a sinusoidal_gamma_generator with individual_spike_trains set to True is created and connected to 20 parrot neurons whose spikes are recorded by a spike detector. After simulating, a raster plot of the spikes is created.

g = nest.Create('sinusoidal_gamma_generator',
                params={'rate': 100.0, 'amplitude': 50.0,
                        'frequency': 10.0, 'phase': 0.0, 'order': 3.,
                        'individual_spike_trains': True})
p = nest.Create('parrot_neuron', 20)
s = nest.Create('spike_detector')

nest.Connect(g, p)
nest.Connect(p, s)

nest.Simulate(200)
ev = nest.GetStatus(s)[0]['events']
plt.subplot(222)
plt.plot(ev['times'], ev['senders'] - min(ev['senders']), 'o')
plt.ylim([-0.5, 19.5])
plt.yticks([])
plt.title('Individual spike trains for each target')

The kernel is reset again and the whole procedure is repeated for a sinusoidal_gamma_generator with individual_spike_trains set to False. The plot shows that in this case, all neurons receive the same spike train from the sinusoidal_gamma_generator.

nest.ResetKernel()
nest.SetKernelStatus({'local_num_threads': 4})

g = nest.Create('sinusoidal_gamma_generator',
                params={'rate': 100.0, 'amplitude': 50.0,
                        'frequency': 10.0, 'phase': 0.0, 'order': 3.,
                        'individual_spike_trains': False})
p = nest.Create('parrot_neuron', 20)
s = nest.Create('spike_detector')

nest.Connect(g, p)
nest.Connect(p, s)

nest.Simulate(200)
ev = nest.GetStatus(s)[0]['events']
plt.subplot(224)
plt.plot(ev['times'], ev['senders'] - min(ev['senders']), 'o')
plt.ylim([-0.5, 19.5])
plt.yticks([])
plt.title('One spike train for all targets')

In part 2, multiple generators are created with different settings for rate, phase and frequency. First, we define an auxiliary function which simulates n generators for t ms. After t/2, the parameter dictionary of the generators is changed from initial to after.

def step(t, n, initial, after, seed=1, dt=0.05):

nest.ResetKernel() nest.SetStatus([0], [{"resolution": dt}]) nest.SetStatus([0], [{"grng_seed": 256 * seed + 1}]) nest.SetStatus([0], [{"rng_seeds": [256 * seed + 2]}])

g = nest.Create('sinusoidal_gamma_generator', n, params=initial) sd = nest.Create('spike_detector') nest.Connect(g, sd) nest.Simulate(t / 2) nest.SetStatus(g, after) nest.Simulate(t / 2)

return nest.GetStatus(sd, 'events')[0]

This function serves to plot a histogram of the emitted spikes.

def plot_hist(spikes): plt.hist(spikes['times'], bins=np.arange(0., max(spikes['times']) + 1.5, 1.), histtype='step')

t = 1000 n = 1000 dt = 1.0 steps = t / dt offset = t / 1000. * 2 * np.pi

We create a figure with a 2x3 grid.

grid = (2, 3) fig = plt.figure(figsize=(15, 10))

Simulate a `sinusoidal_gamma_generator` with default parameter
values, i.e. ac=0 and the DC value being changed from 20 to 50 after
``t/2`` and plot the number of spikes per second over time.

plt.subplot(grid[0], grid[1], 1) spikes = step(t, n, {'rate': 20.0}, {'rate': 50.0, }, seed=123, dt=dt) plot_hist(spikes) exp = np.ones(steps) exp[:int(steps / 2)] = 20 exp[int(steps / 2):] = 50 plt.plot(exp, 'r') plt.title('DC rate: 20 -> 50') plt.ylabel('Spikes per second')

Simulate a `sinusoidal_gamma_generator` with the DC value being
changed from 80 to 40 after ``t/2`` and plot the number of spikes per
second over time.

plt.subplot(grid[0], grid[1], 2) spikes = step(t, n, {'order': 6.0, 'rate': 80.0, 'amplitude': 0., 'frequency': 0., 'phase': 0.}, {'order': 6.0, 'rate': 40.0, 'amplitude': 0., 'frequency': 0., 'phase': 0.}, seed=123, dt=dt) plot_hist(spikes) exp = np.ones(steps) exp[:int(steps / 2)] = 80 exp[int(steps / 2):] = 40 plt.plot(exp, 'r') plt.title('DC rate: 80 -> 40')

Simulate a `sinusoidal_gamma_generator` with the AC value being
changed from 40 to 20 after ``t/2`` and plot the number of spikes per
second over time.

plt.subplot(grid[0], grid[1], 3) spikes = step(t, n, {'order': 3.0, 'rate': 40.0, 'amplitude': 40., 'frequency': 10., 'phase': 0.}, {'order': 3.0, 'rate': 40.0, 'amplitude': 20., 'frequency': 10., 'phase': 0.}, seed=123, dt=dt) plot_hist(spikes) exp = np.zeros(int(steps)) exp[:int(steps / 2)] = (40. + 40. * np.sin(np.arange(0, t / 1000. * np.pi * 10, t / 1000. * np.pi * 10. / (steps / 2)))) exp[int(steps / 2):] = (40. + 20. * np.sin(np.arange(0, t / 1000. * np.pi * 10, t / 1000. * np.pi * 10. / (steps / 2)) + offset)) plt.plot(exp, 'r') plt.title('Rate Modulation: 40 -> 20')

Simulate a `sinusoidal_gamma_generator` with a non-zero AC value
and the DC value being changed from 80 to 40 after ``t/2`` and plot
the number of spikes per second over time.

plt.subplot(grid[0], grid[1], 4) spikes = step(t, n, {'order': 6.0, 'rate': 20.0, 'amplitude': 20., 'frequency': 10., 'phase': 0.}, {'order': 6.0, 'rate': 50.0, 'amplitude': 50., 'frequency': 10., 'phase': 0.}, seed=123, dt=dt) plot_hist(spikes) exp = np.zeros(int(steps)) exp[:int(steps / 2)] = (20. + 20. * np.sin(np.arange(0, t / 1000. * np.pi * 10, t / 1000. * np.pi * 10. / (steps / 2)))) exp[int(steps / 2):] = (50. + 50. * np.sin(np.arange(0, t / 1000. * np.pi * 10, t / 1000. * np.pi * 10. / (steps / 2)) + offset)) plt.plot(exp, 'r') plt.title('DC Rate and Rate Modulation: 20 -> 50') plt.ylabel('Spikes per second') plt.xlabel('Time [ms]')

Simulate a `sinusoidal_gamma_generator` with the AC value being
changed from 0 to 40 after ``t/2`` and plot the number of spikes per
second over time.

plt.subplot(grid[0], grid[1], 5) spikes = step(t, n, {'rate': 40.0, }, {'amplitude': 40.0, 'frequency': 20.}, seed=123, dt=1.) plot_hist(spikes) exp = np.zeros(int(steps)) exp[:int(steps / 2)] = 40. * np.ones(steps / 2) exp[int(steps / 2):] = (40. + 40. * np.sin(np.arange(0, t / 1000. * np.pi * 20, t / 1000. * np.pi * 20. / (steps / 2)))) plt.plot(exp, 'r') plt.title('Rate Modulation: 0 -> 40') plt.xlabel('Time [ms]')

Simulate a `sinusoidal_gamma_generator` with a phase shift at
``t/2`` and plot the number of spikes per second over time.

plt.subplot(grid[0], grid[1], 6) spikes = step(t, n, {'order': 6.0, 'rate': 60.0, 'amplitude': 60., 'frequency': 10., 'phase': 0.}, {'order': 6.0, 'rate': 60.0, 'amplitude': 60., 'frequency': 10., 'phase': 180.}, seed=123, dt=1.) plot_hist(spikes) exp = np.zeros(int(steps))

exp[:int(steps / 2)] = (60. + 60. * np.sin(np.arange(0, t / 1000. * np.pi * 10, t / 1000. * np.pi * 10. / (steps / 2)))) exp[int(steps / 2):] = (60. + 60. * np.sin(np.arange(0, t / 1000. * np.pi * 10, t / 1000. * np.pi * 10. / (steps / 2)) + offset + np.pi)) plt.plot(exp, 'r') plt.title('Modulation Phase: 0 -> Pi') plt.xlabel('Time [ms]')