def plot_meansine():
dt = 0.001 # integration time step in seconds
tmax = 4.0 # stimulus duration in seconds
cutoff = 40.0 # cutoff frequency of stimulus in Hertz
rng = np.random.RandomState(583)
stimulus = 0.5 * mv.whitenoise(0.0, cutoff, dt, tmax, rng)
time = np.arange(len(stimulus)) * dt
mean = 3.0 * (1.0 - np.cos(2.0 * np.pi * time / time[-1]))
stimulus += mean
# response:
rate0, adapt0 = mv.adaptation(time, stimulus, alpha=0.0, taua=0.3)
rate, adapt = mv.adaptation(time, stimulus, alpha=0.2, taua=0.3)
# plot stimulus and threshold:
fig, axs = plt.subplots(2, 1, figsize=(figwidth, 0.6 * figwidth))
ax = axs[0]
ax.plot(time, stimulus, color=colors['green'], label='stimulus')
ax.fill_between(time, adapt, -1.5, fc=colors['gray'], alpha=0.75)
ax.plot(time, adapt, color=colors['red'], label='threshold')
ax.set_ylim(-1.5, 7.5)
ax.set_ylabel('Stimulus')
ax.xaxis.set_major_locator(ticker.MultipleLocator(1.0))
ax.xaxis.set_major_formatter(ticker.NullFormatter())
ax.legend(loc='upper left')
# plot rate:
ax = axs[1]
ax.plot(time, rate0, color=colors['cyan'], label='non adapting')
ax.plot(time, rate, color=colors['blue'], label='adapting')
ax.set_ylim(0.0, 200.0)
ax.set_xlabel('Time [s]')
ax.set_ylabel('Spike frequency [Hz]')
ax.xaxis.set_major_locator(ticker.MultipleLocator(1.0))
ax.legend(loc='upper left')
fig.savefig('meanvariance-meansine')
def plot_meanvaradapt():
dt = 0.001 # integration time step in seconds
tmax = 4.0 # stimulus duration in seconds
cutoff = 60.0 # cutoff frequency of stimulus in Hertz
T = 1.0 # duration of segements with constant mean in seconds
means = [1.0, 3.0, 6.0, 2.0] # mean stimulus values for each segment
stdevs = [1.0, 3.0, 1.5, 0.5] # standard deviations for each segment
rng = np.random.RandomState(583)
stimulus = 0.5 * mv.whitenoise(0.0, cutoff, dt, tmax, rng)
time = np.arange(len(stimulus)) * dt
mean = np.zeros(len(stimulus))
for k, m in enumerate(means):
mean[(time > k * T) & (time <= (k + 1) * T)] += m
std = np.zeros(len(stimulus))
for k, s in enumerate(stdevs):
std[(time > k * T) & (time <= (k + 1) * T)] += s
stimulus *= std
stimulus += mean
# adaptation:
rate1, adapt1 = mv.adaptation(time, stimulus, alpha=0.2, taua=0.5)
rate1[rate1 < 0.0] = 0.0 # thresholding
rate2, adapt2 = mv.divisive_adaptation(time, rate1, taua=0.3, slope=0.1)
# plot:
fig, axs = plt.subplots(2, 1, figsize=(figwidth, 0.6 * figwidth))
ax = axs[0]
ax.plot(time, stimulus, color=colors['green'], label='stimulus')
ax.set_ylabel('Stimulus')
ax.xaxis.set_major_locator(ticker.MultipleLocator(1.0))
ax = axs[1]
ax.plot(time, rate2, color=colors['blue'], label='adapting')
ax.set_xlabel('Time [s]')
ax.set_ylabel('Spike frequency [Hz]')
ax.xaxis.set_major_locator(ticker.MultipleLocator(1.0))
fig.savefig('meanvariance-meanvaradapt')
def plot_divisiveadapt():
dt = 0.001 # integration time step in seconds
tmax = 4.0 # stimulus duration in seconds
cutoff = 60.0 # cutoff frequency of stimulus in Hertz
T = 1.0 # duration of segements with constant mean in seconds
stdevs = [0.5, 1.5, 3.0, 0.5] # standard deviations for each segment
rng = np.random.RandomState(583)
stimulus = 0.5 * mv.whitenoise(0.0, cutoff, dt, tmax, rng)
time = np.arange(len(stimulus)) * dt
std = np.zeros(len(stimulus))
for k, s in enumerate(stdevs):
std[(time > k * T) & (time <= (k + 1) * T)] += s
stimulus *= std
stimulus[stimulus < 0.0] = 0.0
rate, adapt = mv.divisive_adaptation(time, stimulus, taua=0.3, slope=0.1)
# plot:
fig, axs = plt.subplots(2, 1, figsize=(figwidth, 0.6 * figwidth))
ax = axs[0]
ax.plot(time, stimulus, color=colors['green'], label='stimulus')
ax.plot(time, adapt, color=colors['red'], label='adaptation')
ax.xaxis.set_major_locator(ticker.MultipleLocator(1.0))
ax.set_ylabel('Adaptation')
ax.legend(loc='upper left')
ax = axs[1]
ax.plot(time, rate, color=colors['blue'], label='adapting')
ax.set_xlabel('Time [s]')
ax.set_ylabel('Spike frequency [Hz]')
ax.xaxis.set_major_locator(ticker.MultipleLocator(1.0))
fig.savefig('meanvariance-divisiveadapt')
def plot_meanstimulus():
dt = 0.001 # integration time step in seconds
tmax = 4.0 # stimulus duration in seconds
cutoff = 20.0 # cutoff frequency of stimulus in Hertz
T = 1.0 # duration of segements with constant mean in seconds
means = [0.0, 3.0, 6.0, 1.5] # mean stimulus values for each segment
rng = np.random.RandomState(583)
stimulus = 0.5 * mv.whitenoise(0.0, cutoff, dt, tmax, rng)
time = np.arange(len(stimulus)) * dt
mean = np.zeros(len(stimulus))
for k, m in enumerate(means):
mean[(time > k * T) & (time <= (k + 1) * T)] += m
stimulus += mean
# plot stimulus:
fig, ax = plt.subplots(figsize=(figwidth, 0.4 * figwidth))
ax.plot(time, stimulus, color=colors['green'])
ax.plot(time, mean, '--', color=colors['lightgreen'])
ax.set_ylim(-1.5, 7.5)
ax.set_xlabel('Time [s]')
ax.set_ylabel('Stimulus')
ax.xaxis.set_major_locator(ticker.MultipleLocator(1.0))
fig.savefig('meanvariance-meanstimulus')
# response:
rate0, adapt0 = mv.adaptation(time, stimulus, alpha=0.0, taua=0.5)
rate, adapt = mv.adaptation(time, stimulus, alpha=0.2, taua=0.5)
# plot rate:
fig, ax = plt.subplots(figsize=(figwidth, 0.4 * figwidth))
ax.plot(time, rate0, color=colors['cyan'], label='non adapting')
ax.plot(time, rate, color=colors['blue'], label='adapting')
ax.set_ylim(0.0, 200.0)
ax.set_xlabel('Time [s]')
ax.set_ylabel('Spike frequency [Hz]')
ax.xaxis.set_major_locator(ticker.MultipleLocator(1.0))
ax.legend(loc='upper left')
fig.savefig('meanvariance-meanresponse')
# plot adaptation:
fig, ax = plt.subplots(figsize=(figwidth, 0.4 * figwidth))
ax.plot(time, adapt, color=colors['red'], label='adapting')
ax.set_ylim(0.0, 8.0)
ax.set_xlabel('Time [s]')
ax.set_ylabel('Adaptation')
ax.xaxis.set_major_locator(ticker.MultipleLocator(1.0))
fig.savefig('meanvariance-meanadapt')
# plot stimulus and threshold:
fig, ax = plt.subplots(figsize=(figwidth, 0.4 * figwidth))
ax.plot(time, stimulus, color=colors['green'], label='stimulus')
ax.fill_between(time, adapt, -1.5, fc=colors['gray'], alpha=0.75)
ax.plot(time, adapt, color=colors['red'], label='threshold')
ax.set_ylim(-1.5, 7.5)
ax.set_xlabel('Time [s]')
ax.set_ylabel('Stimulus')
ax.xaxis.set_major_locator(ticker.MultipleLocator(1.0))
ax.legend(loc='upper left')
fig.savefig('meanvariance-meanthreshold')
def plot_variancestimulus():
dt = 0.001 # integration time step in seconds
tmax = 4.0 # stimulus duration in seconds
cutoff = 60.0 # cutoff frequency of stimulus in Hertz
T = 1.0 # duration of segements with constant mean in seconds
stdevs = [0.5, 1.5, 3.0, 0.5] # standard deviations for each segment
rng = np.random.RandomState(583)
stimulus = 0.5 * mv.whitenoise(0.0, cutoff, dt, tmax, rng)
time = np.arange(len(stimulus)) * dt
std = np.zeros(len(stimulus))
for k, s in enumerate(stdevs):
std[(time > k * T) & (time <= (k + 1) * T)] += s
stimulus *= std
stimulus += 2.0
# response:
rate0, adapt0 = mv.adaptation(time, stimulus, alpha=0.0, taua=0.3)
rate, adapt = mv.adaptation(time, stimulus, alpha=0.2, taua=0.3)
# plot stimulus and threshold:
fig, axs = plt.subplots(2, 1, figsize=(figwidth, 0.6 * figwidth))
ax = axs[0]
ax.plot(time, stimulus, color=colors['green'], label='stimulus')
ax.fill_between(time, adapt, -1.5, fc=colors['gray'], alpha=0.75)
ax.plot(time, adapt, color=colors['red'], label='threshold')
ax.set_ylim(-1.5, 7.5)
ax.set_ylabel('Stimulus')
ax.xaxis.set_major_locator(ticker.MultipleLocator(1.0))
ax.xaxis.set_major_formatter(ticker.NullFormatter())
ax.legend(loc='upper left')
# plot rate:
ax = axs[1]
ax.plot(time, rate0, color=colors['cyan'], label='non adapting')
ax.plot(time, rate, color=colors['blue'], label='adapting')
ax.set_ylim(0.0, 200.0)
ax.set_xlabel('Time [s]')
ax.set_ylabel('Spike frequency [Hz]')
ax.xaxis.set_major_locator(ticker.MultipleLocator(1.0))
ax.legend(loc='upper left')
fig.savefig('meanvariance-variancethreshold')