def fire_area_analysis(fireRange, numberOfNodes, numberOfIterations):
coverageList = []
for f in fireRange:
small = SmallWorldBrain(numberOfNodes=numberOfNodes,
averageDegree=5,
rewireProbability=0.15,
neuronThreshold=1,
refractoryPeriod=1,
numberOfIterations=numberOfIterations,
fractionToFire=f,
inhibitoryEdgeMultiplier=12,
fireRate=0.01,
directed=False)
small.execute(makeRandom=False)
coverageList.append(
check_coverage(brain=small, numberOfNodes=numberOfNodes))
plt.figure()
plt.plot(
np.linspace(0, numberOfIterations, len(coverageList)),
coverageList,
'.',
label='Nodes=%d, ref=%d, threshold=%d, rewire=%.2f, time=%d' %
(small.numberOfNodes, small.refractoryPeriod, small.neuronThreshold,
small.rewireProbability, small.numberOfIterations))
plt.xlabel('Fraction of Nodes Fired Selectively')
plt.ylabel('Coverage of Network')
plt.legend()
def fire_rate_analysis(drivingRates, numberOfNodes, numberOfIterations):
coverageList = []
for r in drivingRates:
small = SmallWorldBrain(numberOfNodes=numberOfNodes,
averageDegree=5,
rewireProbability=0.15,
neuronThreshold=1,
refractoryPeriod=1,
numberOfIterations=numberOfIterations,
fractionToFire=0.05,
inhibitoryEdgeMultiplier=12,
fireRate=r,
directed=False)
small.execute()
coverageList.append(
check_coverage(brain=small, numberOfNodes=numberOfNodes))
plt.figure()
plt.plot(
drivingRates,
coverageList,
'.',
label='Nodes=%d, ref=%d, threshold=%d, rewire=%.2f, time=%d' %
(small.numberOfNodes, small.refractoryPeriod, small.neuronThreshold,
small.rewireProbability, small.numberOfIterations))
plt.xlabel('Driving Rate')
plt.ylabel('Coverage of Network')
plt.legend()
def run_c_l_p_k_variation(k, seed, plot=True):
np.random.seed(seed)
random.seed(seed)
print('Running for seed=', seed)
ps = np.logspace(-3, -1, 15)
ps = np.append(ps, np.linspace(0.15, 1, 15))
#kList = [5, 7, 10, 15]
if plot:
plt.figure(figsize=(8,6))
#colors = ['black', 'yellow', 'purple', 'green']
pathlength = []
ccoeff = []
for p in ps:
print(p)
brain = SmallWorldBrain(numberOfNodes=10000, numberOfIterations=1000, rewireProbability=p, refractoryPeriod=1, fractionToFire=1/10000, neuronThreshold=1,
fireRate=0.1, inhibitoryEdgeMultiplier=0, averageDegree=k, directed=False)
pathlength.append(nx.average_shortest_path_length(brain.network))
ccoeff.append(nx.average_clustering(brain.network))
np.save('results/cpk_repeats/pathslengths_'+str(k)+'_'+str(seed), np.array(pathlength))
np.save('results/cpk_repeats/clustercoeffs_'+str(k)+'_'+str(seed), np.array(ccoeff))
if plot:
frac = np.array(ccoeff)/np.array(pathlength)
cubicspline = CubicSpline(ps, frac)
ps_smooth = np.linspace(0.0005, 1, 100)
plt.plot(ps, frac, '.', color='black')
plt.plot(ps_smooth, cubicspline(ps_smooth), '-', color='black', label='$<k>$=%d' % k)
plt.xlabel('$p_r$', size=16)
plt.legend()
plt.tick_params(labelsize=16)
plt.ylabel('$C/L$', size=16)
def calculate_omega():
ps = np.linspace(0.15, 1, 15)
ps = np.append(ps, np.logspace(-3, -1, 15))
omegas = []
for p in ps:
print('calculating omega for...', p)
brain = SmallWorldBrain(numberOfNodes=10000, inhibitoryEdgeProbability=0, numberOfIterations=1000,
rewireProbability=p, averageDegree=8, neuronThreshold=1, refractoryPeriod=1, fractionToFire=0.01, probabilityOfFiring=0.2, directed=False)
omegas.append(nx.algorithms.smallworld.omega(brain.network))
np.save('results/omega_small_world', np.array(omegas))
def plot_transmissions_k():
charge = np.linspace(-4, 5, 100)
colors = ['black', 'darkgreen', 'blue', 'red']
labels = ['$1e^{-4}$', '$1e^{-3}$', '$1e^{-2}$', '$1e^{-1}$']
ks = [1e-4, 1e-3, 1e-2, 1e-1]
#goodk = 8.6e-3
#t = 50
brain = SmallWorldBrain(numberOfNodes=100000,
numberOfIterations=100,
rewireProbability=0.1,
refractoryPeriod=1,
fractionToFire=1 / 100000,
neuronThreshold=1,
fireRate=0.1,
averageDegree=5,
directed=False)
for idx, k in enumerate(ks):
#probTransmit = 1-1/(np.exp((charge-2)/(k*t))+1)
probTransmit = brain.transmissionProb(charge, k)
if idx == 0:
plt.plot(charge,
probTransmit,
'--',
label='k=' + labels[idx],
color=colors[idx])
else:
plt.plot(charge,
probTransmit,
label='k=' + labels[idx],
color=colors[idx])
plt.xlabel('Q', size=16)
plt.tick_params(labelsize=16)
plt.ylabel('$P_{transmit}$', size=16)
plt.legend(prop={'size': 16})
def plot_multipler_vs_static_prob(multiplierRange, N):
"""
Calculates the static fraction of inhibitory edges added for a given multiplier
"""
averagei_e = []
mean_i = []
for m in multiplierRange:
print(m)
small = SmallWorldBrain(numberOfNodes=N,
averageDegree=5,
rewireProbability=0.1,
neuronThreshold=1,
refractoryPeriod=1,
numberOfIterations=1000,
fractionToFire=0.05,
inhibitoryEdgeMultiplier=m,
fireRate=0.01,
directed=False)
# Calculate the mean frac of inhibitory per node (static)
frac = []
i_list = []
for n in np.arange(N):
i = np.argwhere(small.edgeMatrix[n] == -1).shape[0]
i_list.append(i)
e = np.argwhere(small.edgeMatrix[n] == 1).shape[0]
frac.append(i / (e + i))
averagei_e.append(np.mean(np.array(frac)))
mean_i.append(np.mean(np.array(i_list)))
_, ax = plt.subplots(1, 1)
ax.plot(multiplierRange, averagei_e, '+', color='black', label='Frac')
ax.set_xlabel('Multiplier')
ax.set_ylabel('Actual mean inhibitory fraction per node')
ax2 = ax.twinx()
ax2.plot(multiplierRange, mean_i, '^', color='black', label='#')
ax2.set_ylabel('Mean number of inhibitory edges added per node')
h1, l1 = ax.get_legend_handles_labels()
h2, l2 = ax2.get_legend_handles_labels()
ax.legend(h1 + h2, l1 + l2, loc='upper left')
def run_network_size_comparison():
Ns = np.logspace(1, 3, 10)
pathLengthArray = [[]]*4
for size in Ns:
N = int(size)
print('Running size %d' % N)
print('Random Brain...')
randomBrain = RandomBrain(numberOfNodes = N, inhibitoryEdgeProbability=0, numberOfIterations=1000,
averageDegree=8, neuronThreshold=0, refractoryPeriod=2, fractionToFire=0.005, probabilityOfFiring=0.2, directed=False)
print('Small World...')
smallworld = SmallWorldBrain(numberOfNodes = N, inhibitoryEdgeProbability=0, numberOfIterations=1000,
rewireProbability=0, averageDegree=8, neuronThreshold=0, refractoryPeriod=2, fractionToFire=0.005, probabilityOfFiring=0.2, directed=False)
print('BA...')
baBrain = BarabasiAlbertBrain(numberOfNodes = N, inhibitoryEdgeProbability=0, numberOfIterations=1000,
rewireProbability=0, averageDegree=8, neuronThreshold=0, refractoryPeriod=2, fractionToFire=0.005, probabilityOfFiring=0.2, directed=False)
print('Growing Brain...')
prefattach = GrowPrefAttachmentBrain(numberOfNodes = N, mu=0.5, inhibitoryEdgeProbability=0, numberOfIterations=1000,
rewireProbability=0, m=8, vertexNumber = 8, neuronThreshold=0, refractoryPeriod=2, fractionToFire=0.005, probabilityOfFiring=0.2, directed=False)
pathLengthArray[0] = np.append(nx.average_shortest_path_length(randomBrain.network), pathLengthArray[0])
pathLengthArray[1] = np.append(nx.average_shortest_path_length(smallworld.network), pathLengthArray[1])
pathLengthArray[2] = np.append(nx.average_shortest_path_length(baBrain.network), pathLengthArray[2])
pathLengthArray[3] = np.append(nx.average_shortest_path_length(prefattach.network), pathLengthArray[3])
#np.save('results/path_lengths', np.array(clusterArray))
plt.figure()
for data, name in zip(pathLengthArray, ['Erdos-Renyi', 'Small World', 'Barabasi-Albert', 'Clustering Model']):
plt.scatter(Ns, data, label=name)
plt.legend()
plt.ylabel('Average Shortest Path Length')
plt.xlabel('$N$')
def plot_topology_EEGs(N, t, save=False, load=False, filepath=None):
if load:
res = np.load(filepath)
elif not load:
small = SmallWorldBrain(numberOfNodes=N, averageDegree=5, rewireProbability=0, neuronThreshold=1, refractoryPeriod=1,
numberOfIterations=t, fractionToFire=0.05, inhibitoryEdgeMultiplier=0, fireRate=0.01, directed=False)
small.execute()
lattice = small.get_number_of_excited_neurons()
small = SmallWorldBrain(numberOfNodes=N, averageDegree=5, rewireProbability=0.1, neuronThreshold=1, refractoryPeriod=1,
numberOfIterations=t, fractionToFire=0.05, inhibitoryEdgeMultiplier=0, fireRate=0.01, directed=False)
small.execute()
smallworld = small.get_number_of_excited_neurons()
small = SmallWorldBrain(numberOfNodes=N, averageDegree=5, rewireProbability=0.8, neuronThreshold=1, refractoryPeriod=1,
numberOfIterations=t, fractionToFire=0.05, inhibitoryEdgeMultiplier=0, fireRate=0.01, directed=False)
small.execute()
random = small.get_number_of_excited_neurons()
if save:
np.save(filepath, np.array([lattice, smallworld, random]))
res = np.array([lattice, smallworld, random])
lattice = []
for _, ye in zip(np.arange(t), [list(i) for i in res[0]]):
lattice.append(len(ye))
small = []
for _, ye in zip(np.arange(t), [list(i) for i in res[1]]):
small.append(len(ye))
rand = []
for _, ye in zip(np.arange(t), [list(i) for i in res[2]]):
rand.append(len(ye))
plt.figure()
plt.plot(np.arange(t), np.array(lattice)/10000, label='Lattice', color='black')
plt.plot(np.arange(t), np.array(small)/10000, label='Small-World', color='blue')
plt.plot(np.arange(t), np.array(rand)/10000, label='Random', color='green')
plt.xlabel('Timestep', size=16)
plt.tick_params(labelsize=16)
plt.ylabel('$N_{excited}/N_{total}$', size=16)
plt.legend(prop={'size': 16}, loc='best')
def plot_coverage_variation(N, t, multiplierRegimes=[0, 35, 60]):
small1 = SmallWorldBrain(numberOfNodes=N,
averageDegree=5,
rewireProbability=0.1,
neuronThreshold=1,
refractoryPeriod=1,
numberOfIterations=t,
fractionToFire=0.05,
inhibitoryEdgeMultiplier=multiplierRegimes[0],
fireRate=0.01,
directed=False)
small1.execute(movie=False)
small1Array = [
len(
np.unique(
np.concatenate(small1.get_number_of_excited_neurons()[:i],
axis=0))) / 1000 for i in np.arange(1, t)
]
small2 = SmallWorldBrain(numberOfNodes=N,
averageDegree=5,
rewireProbability=0.1,
neuronThreshold=1,
refractoryPeriod=1,
numberOfIterations=t,
fractionToFire=0.05,
inhibitoryEdgeMultiplier=multiplierRegimes[1],
fireRate=0.01,
directed=False)
small2.execute(movie=False)
small2Array = [
len(
np.unique(
np.concatenate(small2.get_number_of_excited_neurons()[:i],
axis=0))) / 1000 for i in np.arange(1, t)
]
small3 = SmallWorldBrain(numberOfNodes=N,
averageDegree=5,
rewireProbability=0.1,
neuronThreshold=1,
refractoryPeriod=1,
numberOfIterations=t,
fractionToFire=0.05,
inhibitoryEdgeMultiplier=multiplierRegimes[2],
fireRate=0.01,
directed=False)
small3.execute(movie=False)
small3Array = [
len(
np.unique(
np.concatenate(small3.get_number_of_excited_neurons()[:i],
axis=0))) / 1000 for i in np.arange(1, t)
]
plt.figure()
plt.plot(np.arange(1, t),
np.array(small1Array),
label='Supercritical',
color='blue')
plt.plot(np.arange(1, t),
np.array(small2Array),
label='Critical',
color='red')
plt.plot(np.arange(1, t),
np.array(small3Array),
label='Subcritical',
color='black')
#plt.title('Nodes: %d, <k>:%d, Refractory: %d, Threshold: %d' % (small1.numberOfNodes, small1.averageDegree, small1.refractoryPeriod, small1.neuronThreshold))
plt.xlabel('Timestep', size=16)
plt.tick_params(labelsize=16)
plt.ylabel('Coverage', size=16)
plt.xlim([0, t])
plt.legend()
def plot_critical_regimes(N, t, multiplerRegimes=[0, 35, 60]):
small1 = SmallWorldBrain(numberOfNodes=N,
averageDegree=5,
rewireProbability=0.1,
neuronThreshold=1,
refractoryPeriod=1,
numberOfIterations=t,
fractionToFire=0.05,
inhibitoryEdgeMultiplier=multiplerRegimes[0],
fireRate=0.01,
directed=False)
small1.execute(movie=False)
small1Array = []
for _, ye in zip(np.arange(small1.numberOfIterations),
[list(i) for i in small1.numberOfExcitedNeurons]):
small1Array.append(len(ye))
ex, inhib, q1 = small1.get_effective_charge()
#np.save('results/meanQ/subcritical', [ex, inhib, q1])
print('m=%d, <Q>=%.3f:' %
(multiplerRegimes[0], np.mean(np.array(ex) - np.array(inhib))))
small2 = SmallWorldBrain(numberOfNodes=N,
averageDegree=5,
rewireProbability=0.1,
neuronThreshold=1,
refractoryPeriod=1,
numberOfIterations=t,
fractionToFire=0.05,
inhibitoryEdgeMultiplier=multiplerRegimes[1],
fireRate=0.01,
directed=False)
small2.execute(movie=False)
small2Array = []
for _, ye in zip(np.arange(small2.numberOfIterations),
[list(i) for i in small2.numberOfExcitedNeurons]):
small2Array.append(len(ye))
ex2, inhib2, q2 = small2.get_effective_charge()
#np.save('results/meanQ/critical', [ex2, inhib2, q2])
print('m=%d, <Q>=%.3f:' %
(multiplerRegimes[1], np.mean(np.array(ex2) - np.array(inhib2))))
small3 = SmallWorldBrain(numberOfNodes=N,
averageDegree=5,
rewireProbability=0.1,
neuronThreshold=1,
refractoryPeriod=1,
numberOfIterations=t,
fractionToFire=0.05,
inhibitoryEdgeMultiplier=multiplerRegimes[2],
fireRate=0.01,
directed=False)
small3.execute(movie=False)
small3Array = []
for _, ye in zip(np.arange(small3.numberOfIterations),
[list(i) for i in small3.numberOfExcitedNeurons]):
small3Array.append(len(ye))
ex3, inhib3, q3 = small3.get_effective_charge()
#np.save('results/meanQ/supercritical', [ex3, inhib3, q3])
print('m=%d, <Q>=%.3f:' %
(multiplerRegimes[2], np.mean(np.array(ex3) - np.array(inhib3))))
plt.figure()
plt.plot(np.arange(t),
np.array(small1Array) / small1.numberOfNodes,
label='Supercritical',
color='blue')
plt.plot(np.arange(t),
np.array(small2Array) / small1.numberOfNodes,
label='Critical',
color='red')
plt.plot(np.arange(t),
np.array(small3Array) / small1.numberOfNodes,
label='Subcritical',
color='black')
#plt.title('Nodes: %d, <k>:%d, Refractory: %d, Threshold: %d' % (small1.numberOfNodes, small1.averageDegree, small1.refractoryPeriod, small1.neuronThreshold))
plt.xlabel('Timestep', size=16)
plt.tick_params(labelsize=16)
plt.ylabel('$N_{excited}/N_{total}$', size=16)
plt.legend(prop={'size': 16})