Analytic spike-field and spike-spike coherence adjustment for conditions with different mean firing rates

rate_adjustment.py

def coherence_rate_adjustment(firing_rate_condition1,
                              firing_rate_condition2, spike_power_spectrum,
                              homogeneous_poisson_noise=0, dt=1):
    '''Correction for the spike-field or spike-spike coherence when the
    conditions have different firing rates.

    When comparing the coherence of two conditions, a change in firing rate
    results in a change in coherence without an increase in coupling.
    This adjustment modifies the coherence of one of the conditions, so
    that a difference in coherence between conditions indicates a change
    in coupling, not firing rate. See [1] for details.

    If using to compare spike-spike coherence, not that the coherence
    adjustment must be applied twice, once for each spike train.

    Adjusts `firing_rate_condition1` to `firing_rate_condition2`.

    Parameters
    ----------
    firing_rate_condition1, firing_rate_condition2 : float
        Average firing rates for each condition.
    spike_power_spectrum : ndarray, shape (n_frequencies,)
        Power spectrum of the spike train in condition 1.
    homogeneous_poisson_noise : float, optional
        Beta in [1].
    dt : float, optional
        Size of time step.

    Returns
    -------
    rate_adjustment_factor : ndarray, shape (n_frequencies)

    References
    ----------
    .. [1] Aoi, M.C., Lepage, K.Q., Kramer, M.A., and Eden, U.T. (2015).
           Rate-adjusted spike-LFP coherence comparisons from spike-train
           statistics. Journal of Neuroscience Methods 240, 141-153.

    '''
    # alpha in [1]
    firing_rate_ratio = firing_rate_condition2 / firing_rate_condition1
    adjusted_firing_rate = (
        (1 / firing_rate_ratio - 1) * firing_rate_condition1 +
        homogeneous_poisson_noise / firing_rate_ratio ** 2) * dt ** 2
    return 1 / np.sqrt(1 + (adjusted_firing_rate / spike_power_spectrum))