From ec1ed7710b2e586646fe4b3aecc6b161384e19ed Mon Sep 17 00:00:00 2001 From: ago109 Date: Wed, 26 Jun 2024 21:55:42 -0400 Subject: [PATCH] sync --- docs/tutorials/neurocog/short_term_plasticity.md | 16 +++++++++------- 1 file changed, 9 insertions(+), 7 deletions(-) diff --git a/docs/tutorials/neurocog/short_term_plasticity.md b/docs/tutorials/neurocog/short_term_plasticity.md index 057eaa82a..30864f775 100755 --- a/docs/tutorials/neurocog/short_term_plasticity.md +++ b/docs/tutorials/neurocog/short_term_plasticity.md @@ -111,26 +111,28 @@ with Context("Model") as model: ``` Notice that the `STPDenseSynapse` has two important time constants to configure; -`tau_f` ($\tau_f$), the facilitation time constant, and `tau_d` ($\tau_d$, the +`tau_f` ($\tau_f$), the facilitation time constant, and `tau_d` ($\tau_d$), the depression time constant. In effect, it is these two constants that you will want to set to obtain different desired behavior from this in-built dynamic -synapse -- setting $\tau_f > \tau_d$ will result in STF-dominated behavior -whereas setting $\tauf < \tau_d$ will produce STD-dominated behavior. Note -that setting $\tau_d = 0$ will result in short-term depression being turned off -completely ($\tau_f 0$ disables STF). +synapse: +1. setting $\tau_f > \tau_d$ will result in STF-dominated behavior; whereas +2. setting $\tau_f < \tau_d$ will produce STD-dominated behavior. + +Note that setting $\tau_d = 0$ will result in short-term depression being turned off +completely ($\tau_f = 0$ disables STF). Formally, given the time constants above the dynamics of the `STPDenseSynapse` operate according to the following coupled ordinary differential equations (ODEs): $$ -\tau_f \frac{\partial u_j(t)}{\partial t} &= -u_j(t) + N_R (1 - u_j(t)) s_j(t) \\ +\tau_f \frac{\partial u_j(t)}{\partial t} &= -u_j(t) + N_R \big(1 - u_j(t)\big) s_j(t) \\ \tau_d \frac{\partial x_j}{\partial t} &= (1 - x_j(t)) - u_j(t + \Delta t) x_j(t) s_j(t) \\ $$ and the resulting (short-term) synaptic efficacy: $$ -W^{dyn}(t + \Delta t) = \Big( W^{max}_{ij} u_j(t + \Delta t) x_j(t) s_j(t) \Big) +W^{dyn}_{ij}(t + \Delta t) = \Big( W^{max}_{ij} u_j(t + \Delta t) x_j(t) s_j(t) \Big) + W^{dyn}_{ij} (1 - s_j(t)) $$