class brainpy.initialize.DOGDecay(sigmas, max_ws, min_w=None, encoding_values=None, periodic_boundary=False, normalize=True, include_self=True)[source]#

Builds a Difference-Of-Gaussian (dog) connectivity pattern within a population of neurons.

Mathematically, for the given pair of neurons \((i, j)\), the weight between them is computed as

\[w(i, j) = w_{max}^+ \cdot \exp(-\frac{\sum_{k=1}^n |v_k^i - v_k^j|^2}{2\sigma_+^2}) - w_{max}^- \cdot \exp(-\frac{\sum_{k=1}^n |v_k^i - v_k^j|^2}{2\sigma_-^2})\]

where weights smaller than \(0.005 * max(w_{max}, w_{min})\) are not created and self-connections are avoided by default (parameter allow_self_connections).

  • sigmas (tuple) – Widths of the positive and negative Gaussian functions.

  • max_ws (tuple) – The weight amplitudes of the positive and negative Gaussian functions.

  • min_w (float, None) – The minimum weight value below which synapses are not created (default: \(0.005 * min(max\_ws)\)).

  • include_self (bool) – Whether create the connections at the same position (self-connections).

  • normalize (bool) – Whether normalize the connection probability .

  • encoding_values (optional, list, tuple, int, float) –

    The value ranges to encode for neurons at each axis.

    • If values is not provided, the neuron only encodes each positional information, i.e., \((i, j, k, ...)\), where \(i, j, k\) is the index in the high-dimensional space.

    • If values is a single tuple/list of int/float, neurons at each dimension will encode the same range of values. For example, values=(0, np.pi), neurons at each dimension will encode a continuous value space [0, np.pi].

    • If values is a tuple/list of list/tuple, it means the value space will be different for each dimension. For example, values=((-np.pi, np.pi), (10, 20), (0, 2 * np.pi)).

  • periodic_boundary (bool) – Whether the neuron encode the value space with the periodic boundary.