Spatially-structured networks

Spatially-structured networks#

When neurons sit at positions in space and the probability (or weight) of a connection depends on the source→target distance, build the layout and the distance-dependent rule with the brainpy.state.spatial toolkit. It mirrors NEST’s spatial / topology vocabulary and rides the ordinary Simulator.connect() call — the same call any non-spatial rule uses.

Placing neurons in space#

Create a population on a layout by passing positions= to Simulator.create():

import brainunit as u
from brainpy import state as bp

sim = bp.Simulator(dt=0.1 * u.ms)
pos = bp.spatial.grid([4, 3], extent=[2.0, 1.5])     # 4 columns × 3 rows
pop = sim.create(bp.iaf_psc_alpha, positions=pos)

coords = sim.get_position(pop)                        # (12, 2) node coordinates

bp.spatial.grid([nx, ny], extent=[Lx, Ly]) lays neurons on a regular grid exactly as NEST does (column is the slow axis, row the fast axis; x increases left→right and y decreases top→bottom). Simulator.get_position() (NEST’s GetPosition) reads the node coordinates back.

Distance-dependent connectivity#

A spatial connection rule combines a probability law (a function of distance) with an optional mask (a spatial cutoff), and is passed as rule= to connect:

sim.connect(
    a, b,
    rule=bp.spatial.spatial_pairwise_bernoulli(
        p=bp.spatial.gaussian(bp.spatial.distance, std=0.5),
        mask=bp.spatial.circular(3.0)),
    weight=1.0 * u.pA, delay=1.0 * u.ms, seed=0)

The building blocks:

  • bp.spatial.distance — the source→target distance, the argument to a kernel.

  • bp.spatial.gaussian(distance, std=...) — a Gaussian connection-probability kernel \(p(d) = \exp(-d^2 / (2\,\mathrm{std}^2))\) (other kernels follow the same shape).

  • bp.spatial.circular(radius) — a circular mask clipping connections beyond radius.

  • bp.spatial.spatial_pairwise_bernoulli(p=, mask=) — draw each source→target edge with probability p inside mask.

Because the per-distance probability is a fixed law (only the PRNG draw diverges between NEST and JAX), spatial connectivity is validated distributionally: the empirical \(p(d)\) curve matches NEST within a band even though individual draws differ. See Validation status.

Querying the realized footprint#

After wiring, read back which targets a source actually connected to:

ctr = bp.spatial.center_element(pos)                  # the central node
targets = bp.spatial.target_positions(sim, a[ctr], b)[0]

bp.spatial.target_positions (NEST’s GetTargetPositions) returns the coordinates of a source’s realized targets; bp.spatial.center_element picks the node nearest the layout centre — handy for plotting a single neuron’s connection footprint.

See also#