diff --git a/src/vonFoersterHazards.ipynb b/src/vonFoersterHazards.ipynb
index c82e736..837c4bd 100644
--- a/src/vonFoersterHazards.ipynb
+++ b/src/vonFoersterHazards.ipynb
@@ -50,7 +50,13 @@
     "\n",
     "## Methods\n",
     "\n",
-    "In general when we are unable to observe or model every transition, such as when the integral of the hazard rate is taken over a duration larger than the smallest [characteristic dwelling time](https://en.wikipedia.org/wiki/Relaxation_%28physics%29) of the states, the probability density matrix requires calculation of the [adjoint derivative](https://en.wikipedia.org/wiki/Derivative_of_the_exponential_map) of the cumulative probability matrix, where the dot is the [currying](https://en.wikipedia.org/wiki/Currying) application of $\\operatorname{ad}_X Y=XY-YX$, the [adjoint operator](https://en.wikipedia.org/wiki/Adjoint_representation), to the parenthesized hazard rate $H$:\n",
+    "In general when we are unable to observe or model every transition, such as when the integral of the hazard rate is taken over a duration larger than the smallest [characteristic dwelling time](https://en.wikipedia.org/wiki/Relaxation_%28physics%29) of the states, the probability density matrix requires calculation of the [adjoint derivative](https://en.wikipedia.org/wiki/Derivative_of_the_exponential_map) of the cumulative probability matrix, where the dot is the [currying](https://en.wikipedia.org/wiki/Currying) application of the [adjoint operator](https://en.wikipedia.org/wiki/Adjoint_representation):\n",
+    "\n",
+    "$$\n",
+    "\\operatorname{ad}_X Y=XY-YX\n",
+    "$$\n",
+    "\n",
+    "to the parenthesized hazard rate $H$:\n",
     "\n",
     "$$\n",
     "\\operatorname{\\mathbb{P}}\\left[ T_{i \\rightarrow j} = t \\right] = \\operatorname{\\left[ \\frac{e^{-\\operatorname{ad}_{\\int_0^t H ds} \\cdot} - 1}{\\operatorname{ad}_{\\int_0^t H ds} \\cdot} \\right]} \\left(H\\right)  e^{- \\int_0^t H ds}\n",
@@ -109,7 +115,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [],
    "source": [