def test1_self_connections_yield_bistable_systems_given_correct_parameters(self):
# define network drive
drives = 10*[np.array([0, 0])] + 20*[4*np.array([1, 1])] + \
60*[np.array([0, 0])] + 20*[-4*np.array([1, 1])] + 60*[np.array([0, 0])]
# define network parameters
taus = [10, 10]
v_rests = [0, 0]
v_ths = [4, 4]
gs = [2.5, 2.5]
w_selfs = [7.5, 5.5]
nodes = [{'tau': t, 'v_rest': v_rest, 'threshold': th, 'steepness': g}
for t, v_rest, th, g in zip(taus, v_rests, v_ths, gs)]
weights = np.diag(w_selfs)
# make network
ntwk = RateBasedModel(nodes, weights)
ntwk.store_voltages = True
# initialize and run network
ntwk.vs = np.array(v_rests)
for drive in drives:
ntwk.step(drive)
# make plots
fig, axs = plt.subplots(3, 1, figsize=(14, 8), sharex=True)
axs[0].plot(ntwk.vs_history, lw=2)
axs[1].plot(ntwk.rs_history, lw=2)
axs[2].plot(drives, lw=2, c='k')
axs[1].set_ylim(-.1, 1.1)
axs[2].set_ylim(-5, 5)
axs[0].set_ylabel('voltage')
axs[1].set_ylabel('firing rate')
axs[2].set_ylabel('drive')
axs[2].set_xlabel('t')
axs[0].set_title('Self-Connected Populations')
for ax in axs:
axis_tools.set_fontsize(ax, 20)
def test0_unconnected_populations_with_different_timescales_respond_to_delta_pulse_with_exponential_decay(self):
# define network drive
drives = 10*[np.array([0, 0, 0, 0])] + 10*[2*np.array([3, 4, 6, 10])] + 60*[np.array([0, 0, 0, 0])]
# define network parameters
taus = [3, 5, 10, 20]
v_rests = [-20, -10, 0, 10]
v_ths = [-10, -1, 8, 17]
gs = [.5, .5, .5, .5]
# dake new network
nodes = [{'tau': t, 'v_rest': v_rest, 'threshold': th, 'steepness': g}
for t, v_rest, th, g in zip(taus, v_rests, v_ths, gs)]
weights = np.zeros((len(taus), len(taus)))
ntwk = RateBasedModel(nodes, weights)
ntwk.store_voltages = True
# initialize and run network
ntwk.vs = np.array(v_rests)
for drive in drives:
ntwk.step(drive)
# make plots
fig, axs = plt.subplots(3, 1, figsize=(14, 8), sharex=True)
axs[0].plot(ntwk.vs_history, lw=2)
axs[1].plot(ntwk.rs_history, lw=2)
axs[2].plot(drives, lw=2)
axs[1].set_ylim(-.1, 1.1)
axs[2].set_ylim(0, 45)
axs[0].set_ylabel('voltage')
axs[1].set_ylabel('firing rate')
axs[2].set_ylabel('drive')
axs[2].set_xlabel('t')
axs[0].set_title('Uncoupled Populations')
for ax in axs:
axis_tools.set_fontsize(ax, 20)
def test3_input_populations_coupled_to_bistable_population(self):
# define network drive
drive_1 = 10*[0] + 20*[10] + 200*[0]
drive_2 = 15*[0] + 20*[10] + 195*[0]
drive_12 = len(drive_1) * [0]
drives = np.transpose([drive_1, drive_2, drive_12])
# define network parameters
taus = [10, 10, 10]
v_rests = [0, 0, 0]
v_ths = [4, 4, 4]
gs = [2.5, 2.5, 2.5]
noise_level = 2
nodes = [{'tau': t, 'v_rest': v_rest, 'threshold': th, 'steepness': g}
for t, v_rest, th, g in zip(taus, v_rests, v_ths, gs)]
weights = np.array([
[0, 0, 0],
[0, 0, 0],
[2, 2, 5.5]
])
# make network
ntwk = RateBasedModel(nodes, weights)
ntwk.store_voltages = True
ntwk.noise_level = noise_level
# initialize and run network
np.random.seed(1)
ntwk.vs = np.array(v_rests)
for drive in drives:
ntwk.step(drive)
fig, axs = plt.subplots(3, 1, figsize=(14, 8), sharex=True)
axs[0].plot(ntwk.vs_history, lw=2)
axs[1].plot(ntwk.rs_history, lw=2)
axs[2].plot(drives, lw=2)
axs[1].set_ylim(-.1, 1.1)
axs[2].set_ylim(-1, 11)
axs[0].set_ylabel('voltage')
axs[1].set_ylabel('firing rate')
axs[2].set_ylabel('drive')
axs[2].set_xlabel('t')
axs[0].set_title('Input populations coupled to bistable population')
for ax in axs:
axis_tools.set_fontsize(ax, 20)
def test2_upstate_timecourse_with_self_connections_depends_on_noise(self):
# define network drive
drives = 10*[np.array([0, 0, 0])] + 40*[4*np.array([1, 1, 1])] + \
140*[np.array([0, 0, 0])]
# define network parameters
taus = [10, 10, 10]
v_rests = [0, 0, 0]
v_ths = [4, 4, 4]
gs = [2.5, 2.5, 2.5]
w_selfs = [5.3, 5.3, 5.3]
noise_level = np.array([1, 2, 3])
nodes = [{'tau': t, 'v_rest': v_rest, 'threshold': th, 'steepness': g}
for t, v_rest, th, g in zip(taus, v_rests, v_ths, gs)]
weights = np.diag(w_selfs)
# make network
ntwk = RateBasedModel(nodes, weights)
ntwk.store_voltages = True
ntwk.noise_level = noise_level
# initialize and run network
np.random.seed(seed=4)
ntwk.vs = np.array(v_rests)
for drive in drives:
ntwk.step(drive)
# make plots
fig, axs = plt.subplots(3, 1, figsize=(14, 8), sharex=True)
axs[0].plot(ntwk.vs_history, lw=2)
axs[1].plot(ntwk.rs_history, lw=2)
axs[2].plot(drives, lw=2, c='k')
axs[1].set_ylim(-.1, 1.1)
axs[2].set_ylim(-1, 5)
axs[0].set_ylabel('voltage')
axs[1].set_ylabel('firing rate')
axs[2].set_ylabel('drive')
axs[2].set_xlabel('t')
axs[0].set_title('Self-Connected Populations With Noise')
for ax in axs:
axis_tools.set_fontsize(ax, 20)
