Skip to content

Commit

Permalink
fix LaTeX typesetting
Browse files Browse the repository at this point in the history
  • Loading branch information
clinssen authored Jul 13, 2023
1 parent 8695329 commit a5189c1
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions doc/tutorials/stdp_windows/stdp_windows.ipynb
Original file line number Diff line number Diff line change
Expand Up @@ -69,13 +69,13 @@
"To implement the kernel, we use two extra state variables to keep track of recent spiking activity. These could correspond to calcium concentration in biology. One presynaptic trace value and another postsynaptic trace value is used, for pre- and post spiking, respectively. These maintain a history of neuron spikes, being incremented by 1 whenever a spike is generated, and decaying back to zero exponentially; in other words, a convolution between the exponentially decaying kernel and the emitted spike train:\n",
"\n",
"\\begin{equation}\n",
"\\text{tr_pre} = K \\ast \\sum_i \\delta_{pre,i}\n",
"\\text{tr\\_pre} = K \\ast \\sum_i \\delta_{pre,i}\n",
"\\end{equation}\n",
"\n",
"and\n",
"\n",
"\\begin{equation}\n",
"\\text{tr_post} = K \\ast \\sum_i \\delta_{post,i}\n",
"\\text{tr\\_post} = K \\ast \\sum_i \\delta_{post,i}\n",
"\\end{equation}\n",
"\n",
"These are implemented in the NESTML model as follows:\n",
Expand Down Expand Up @@ -111,7 +111,7 @@
"The update rule for facilitation:\n",
"\n",
"\\begin{equation}\n",
"\\Delta^+ w = \\lambda \\cdot (1 - w)^{\\mu+} \\cdot \\text{pre_trace}\n",
"\\Delta^+ w = \\lambda \\cdot (1 - w)^{\\mu+} \\cdot \\text{pre\\_trace}\n",
"\\end{equation}\n",
"\n",
"In NESTML, this rule is written in the `onReceive` event handler block. Statements in this block will be executed when the event occurs: in this case, receiving a presynaptic spike. In NESTML, additional scaling with an absolute maximum weight ``Wmax`` is added.\n",
Expand All @@ -126,7 +126,7 @@
"The update rule for depression :\n",
"\n",
"\\begin{equation}\n",
"\\Delta^- w = -\\alpha \\cdot \\lambda \\cdot w^{\\mu_-} \\cdot \\text{post_trace}\n",
"\\Delta^- w = -\\alpha \\cdot \\lambda \\cdot w^{\\mu_-} \\cdot \\text{post\\_trace}\n",
"\\end{equation}\n",
"\n",
"```\n",
Expand Down

0 comments on commit a5189c1

Please sign in to comment.