From ae3fcc178d859615390e2b775233d2e700204d03 Mon Sep 17 00:00:00 2001 From: ago109 Date: Wed, 26 Jun 2024 22:03:22 -0400 Subject: [PATCH] sync --- docs/tutorials/neurocog/short_term_plasticity.md | 15 ++++++++++----- 1 file changed, 10 insertions(+), 5 deletions(-) diff --git a/docs/tutorials/neurocog/short_term_plasticity.md b/docs/tutorials/neurocog/short_term_plasticity.md index 30864f775..278ec8c44 100755 --- a/docs/tutorials/neurocog/short_term_plasticity.md +++ b/docs/tutorials/neurocog/short_term_plasticity.md @@ -119,14 +119,14 @@ synapse: 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). +completely (and $\tau_f = 0$ disables STF). Formally, given the time constants above the dynamics of the `STPDenseSynapse` operate according to the following coupled ordinary differential equations (ODEs): $$ \tau_f \frac{\partial u_j(t)}{\partial t} &= -u_j(t) + N_R \big(1 - u_j(t)\big) s_j(t) \\ -\tau_d \frac{\partial x_j}{\partial t} &= (1 - x_j(t)) - u_j(t + \Delta t) x_j(t) s_j(t) \\ +\tau_d \frac{\partial x_j}{\partial t} &= \big(1 - x_j(t)\big) - u_j(t + \Delta t) x_j(t) s_j(t) \\ $$ and the resulting (short-term) synaptic efficacy: @@ -136,13 +136,18 @@ W^{dyn}_{ij}(t + \Delta t) = \Big( W^{max}_{ij} u_j(t + \Delta t) x_j(t) s_j(t) + W^{dyn}_{ij} (1 - s_j(t)) $$ -where $N_R$ represents an increment produced by a pre-synaptic spike (and -in essence, the neurotransmitter resources available to yield facilitation), +where $N_R$ represents an increment produced by a pre-synaptic spike $\mathbf{s}_j(t)$ +(and in essence, the neurotransmitter resources available to yield facilitation), $W^{max}_{ij}$ denotes the absolute synaptic efficacy (or maximum response amplitude of this synapse in the case of a complete release of all neurotransmitters; $x_j(t) = u_j(t) = 1$) of the connection between pre-synaptic neuron $j$ and post-synaptic neuron $i$, and $W^{dyn}_{ij}(t)$ is the value -of the dynamic synapse's efficacy at time `t`. +of the dynamic synapse's efficacy at time `t`. +$\mathbf{x}_j$ is a variable (which lies in the range of $[0,1]$) that indicates +the fraction of (neurotransmitter) resources available after a depletion of the +neurotransmitter resource pool. $\mathbf{u}_j$, on the hand, +represents the neurotransmitter "release probability", or the fraction of available +resources ready for the dynamic synapse's use. ### Simulating and Visualizing STF