braintools.input.DoubleExponential

class braintools.input.DoubleExponential(amplitude, tau_rise, tau_decay, duration, t_start=None, t_end=None)

Generate double exponential (alpha function) input.

Creates an input with distinct rise and decay phases, commonly used to model synaptic currents. The shape is characterized by a rapid rise followed by a slower decay, creating an asymmetric pulse.

Parameters:

• amplitude (float) – Peak amplitude of the pulse. Can include units.

• tau_rise (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Rise time constant. Smaller values give faster rise.

• tau_decay (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Decay time constant. Should be larger than tau_rise.

• duration (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Total duration of the input signal.

• t_start (Array | ndarray | bool | number | bool | int | float | complex | Quantity | None) – Start time of the pulse. Default is 0.

• t_end (Array | ndarray | bool | number | bool | int | float | complex | Quantity | None) – End time of the pulse. Default is duration.

amplitude

The peak amplitude.

Type:

float

tau_rise

The rise time constant.

Type:

Quantity or float

tau_decay

The decay time constant.

Type:

Quantity or float

duration

The total duration.

Type:

Quantity or float

t_start

The pulse start time.

Type:

Quantity or float or None

t_end

The pulse end time.

Type:

Quantity or float or None

See also

ExponentialDecay

For single exponential dynamics.

GaussianPulse

For symmetric pulse shapes.

Notes

The alpha function follows: amplitude * (exp(-t/tau_decay) - exp(-t/tau_rise)) for t >= 0

The function is normalized so the peak equals the specified amplitude. Time to peak: t_peak = (tau_rise * tau_decay)/(tau_decay - tau_rise) * ln(tau_decay/tau_rise) This class uses the functional double_exponential API internally.

Examples

AMPA-like synaptic current:

>>> ampa = DoubleExponential(
...     amplitude=1.0 * u.nA,
...     tau_rise=0.5 * u.ms,
...     tau_decay=5 * u.ms,
...     duration=50 * u.ms
... )
>>> array = ampa()

NMDA-like synaptic current (slower dynamics):

>>> nmda = DoubleExponential(
...     amplitude=0.5 * u.nA,
...     tau_rise=2 * u.ms,
...     tau_decay=50 * u.ms,
...     duration=200 * u.ms
... )

Synaptic current with noise:

>>> from braintools.input import WienerProcess
>>> alpha = DoubleExponential(1.0, 5 * u.ms, 20 * u.ms, 200 * u.ms)
>>> noise = WienerProcess(200 * u.ms, sigma=0.05)
>>> synaptic = alpha + noise

Train of synaptic inputs:

>>> # Multiple EPSPs at different times
>>> times = [10, 30, 55, 80] * u.ms
>>> epsps = []
>>> for t in times:
...     epsps.append(DoubleExponential(
...         1.0, 1 * u.ms, 10 * u.ms, 150 * u.ms, t_start=t
...     ))
>>> epsp_train = sum(epsps[1:], epsps[0])

Paired-pulse facilitation:

>>> # Second pulse larger than first
>>> pulse1 = DoubleExponential(1.0, 2 * u.ms, 15 * u.ms, 100 * u.ms, t_start=20 * u.ms)
>>> pulse2 = DoubleExponential(1.5, 2 * u.ms, 15 * u.ms, 100 * u.ms, t_start=40 * u.ms)
>>> ppf = pulse1 + pulse2

Combined fast and slow components:

>>> fast = DoubleExponential(0.7, 0.5 * u.ms, 5 * u.ms, 100 * u.ms)
>>> slow = DoubleExponential(0.3, 5 * u.ms, 50 * u.ms, 100 * u.ms)
>>> mixed = fast + slow

Inhibitory synaptic current:

>>> ipsc = DoubleExponential(
...     amplitude=-0.8 * u.nA,  # Negative for inhibition
...     tau_rise=1 * u.ms,
...     tau_decay=20 * u.ms,
...     duration=100 * u.ms
... )

__init__(amplitude, tau_rise, tau_decay, duration, t_start=None, t_end=None)

Initialize double exponential.

Parameters:

• amplitude (float) – Peak amplitude.

• tau_rise (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Rise time constant.

• tau_decay (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Decay time constant.

• duration (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Total duration of the input.

• t_start (Array | ndarray | bool | number | bool | int | float | complex | Quantity | None) – Start time of the pulse. Default is 0.

• t_end (Array | ndarray | bool | number | bool | int | float | complex | Quantity | None) – End time of the pulse. Default is duration.

Methods

__init__(amplitude, tau_rise, tau_decay, ...)	Initialize double exponential.
apply(func)	Apply a custom function to the input.
clip([min_val, max_val])	Clip the input values to a range.
generate()	Generate the double exponential array using functional API.
repeat(n_times)	Repeat the input pattern n times.
scale(factor)	Scale the input by a factor.
shift(time_shift)	Shift the input in time.
smooth(tau)	Apply exponential smoothing to the input.

Attributes

dt	Get the time step from global environment.
n_steps	Get the number of time steps.
shape	Get the shape of the input array.