diff --git a/sources/1-s2.0-S009630032100881X-main.pdf b/sources/1-s2.0-S009630032100881X-main.pdf
index 9276f4d..6284330 100644
Binary files a/sources/1-s2.0-S009630032100881X-main.pdf and b/sources/1-s2.0-S009630032100881X-main.pdf differ
diff --git a/src/algo1_testing.ipynb b/src/algo1_testing.ipynb
index 0e6d9b5..1b4f0b4 100644
--- a/src/algo1_testing.ipynb
+++ b/src/algo1_testing.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -130,11 +130,12 @@
    "outputs": [],
    "source": [
     "# define v as the probability vector of size n x 1, where n is the number of nodes in the graph. The vector is filled with 1/n\n",
-    "# https://en.wikipedia.org/wiki/Probability_vector\n",
     "\n",
     "v = sp.sparse.lil_matrix((n,1))\n",
     "for i in range(n):\n",
-    "    v[i] = 1/n  "
+    "    v[i] = 1/n  \n",
+    "\n",
+    "# maybe I could have done it with a lambda more concisely? idk"
    ]
   },
   {