spike_train_synchrony

spike_train_synchrony#

class braintools.analysis.spike.spike_train_synchrony(spike_matrix, window_size, dt=None)#

Calculate spike train synchrony using the SPIKE-synchronization measure.

This measure quantifies the degree of synchronization between multiple spike trains by counting coincident events within sliding time windows and normalizing by the total number of possible coincidences [1].

The synchrony index is the average over neuron pairs of a symmetric coincidence ratio:

\[S = \frac{1}{N_{pairs}} \sum_{i < j} \frac{C_{i \to j} + C_{j \to i}}{N_i + N_j}\]

where \(C_{i \to j}\) is the number of spikes in train \(i\) that have at least one spike of train \(j\) within half the coincidence window, and \(N_i\) is the number of spikes in train \(i\). Counting coincidences in both directions and normalizing by the total spike count guarantees \(S \in [0, 1]\). Pairs with a silent neuron are left out of the average.

Parameters:

  • spike_matrix (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Spike matrix with shape (n_time_steps, n_neurons) where non-zero values indicate spike occurrences.

  • window_size (float) – Full width of the coincidence-detection window. Two spikes are coincident when they are at most window_size / 2 apart. Must use the same time unit as dt.

  • dt (float | None) – Time step between successive samples. If None, uses the default from brainstate.environ.get_dt(). A plain float is assumed to be in milliseconds (the brainstate convention), so it must be expressed in the same unit as window_size/max_isi/tau; a brainunit.Quantity is converted automatically.

Returns:

Spike train synchrony index, a 0-d array between 0 (no synchrony) and 1 (perfect synchrony). 0 when fewer than two neurons, or no pair of active neurons, are present.

Return type:

jax.Array

Notes

The coincidences of all pairs are counted at once: a cumulative sum marks the samples within window_size / 2 of a spike of each neuron, a matrix product counts, for every ordered pair, the spikes of one neuron on the marked samples of the other, and the pair ratios are evaluated with a vmap over the N (N - 1) / 2 upper-triangle pairs. Memory is O(T N + N^2).

window_size and dt must be concrete; the spike matrix may be traced, so the function works under jax.jit and jax.vmap (e.g. over trials). It is not differentiable (it counts spikes).

Before version 0.4 this function returned a Python float; float(s) still works on the 0-d array.

Examples

>>> import jax.numpy as jnp
>>> import braintools as braintools
>>> # Create synchronized spikes
>>> spikes = jnp.zeros((100, 5))
>>> spikes = spikes.at[20:25, :].set(1)  # Synchronized burst
>>> synchrony = braintools.analysis.spike.spike_train_synchrony(spikes, window_size=10.0, dt=1.0)
>>> print(f"Synchrony: {synchrony:.3f}")
Synchrony: 1.000

References