Update notebook

docs/notebooks/Differentiation with Persistence Landscapes.ipynb

@@ -18,6 +18,7 @@
     "The experiment is to determine if persistent homology can distinguish between spheres of different dimensions. Here we restrict to differentiating $S^2$ from $S^3$. We will further restrict ourselves to persistent homology in degree one (but one can use all relevant homological degrees as well). A priori, we would not expect this to be an effective discriminator, since the ordinary first homology of both spheres is trivial. Note that this is a simplified version of the experiment from Bubenik and Dlotko's *A persistence landscapes toolbox for topological statistics* [1]. \n",
     "\n",
     "In detail: \n",
+    "\n",
     "- Repeat the following `num_runs = 100` times:\n",
     "  - Sample `num_pts = 100` points from the 2-sphere and the 3-sphere. We rescale the spheres so the average distance between the points on each sphere is approximately 1.\n",
     "  - Compute the VR persistent homology (using `ripser`) and compute the associated landscapes. Store each of these landscapes.\n",
@@ -356,7 +357,7 @@
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@@ -370,7 +371,7 @@
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