diff --git a/notebooks/DIY-Figure1.ipynb b/notebooks/DIY-Figure1.ipynb
index d6735c4..feeb197 100644
--- a/notebooks/DIY-Figure1.ipynb
+++ b/notebooks/DIY-Figure1.ipynb
@@ -7,7 +7,7 @@
    "source": [
     "## DIY Figure 1\n",
     "\n",
-    "In this notebook, we shown how to use the theoretical approximation to obtain accurate estimates of the angular error for the paleopole estimation for different choices of parameters. "
+    "In this notebook, we show how to use the theoretical approximation to obtain accurate estimates of the angular error for the paleopole estimation for different choices of parameters. A full simulation will be more expensive to run, but our simulations showed that theoretical approximations and numerical simulations differ at most $1\\%$ from each other when there are no outliers in the sample. "
    ]
   },
   {
@@ -20,7 +20,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/tmp/ipykernel_4124/2909491422.py:4: DeprecationWarning: Please use `gaussian_filter` from the `scipy.ndimage` namespace, the `scipy.ndimage.filters` namespace is deprecated.\n",
+      "/tmp/ipykernel_8973/2909491422.py:4: DeprecationWarning: Please use `gaussian_filter` from the `scipy.ndimage` namespace, the `scipy.ndimage.filters` namespace is deprecated.\n",
       "  from scipy.ndimage.filters import gaussian_filter\n"
      ]
     }
@@ -51,7 +51,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 2,
    "id": "e4029aad-7ac2-48e9-989b-23e60b16a5ef",
    "metadata": {},
    "outputs": [],
@@ -65,7 +65,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 3,
    "id": "779bead0-ee1c-4a77-8278-01872fd24d38",
    "metadata": {},
    "outputs": [
@@ -145,17 +145,20 @@
        "4  5   1                87.642494                 8.676167"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
+    "# Create a template data frames with all the combinations of number of sites and samples per site\n",
     "N_flat = np.tile(np.arange(1, N_max+1, 1), (n0_max,1)).ravel()\n",
     "n0_flat = np.tile(np.arange(1, n0_max+1, 1), (N_max,1)).T.ravel()\n",
     "\n",
     "df = pd.DataFrame({'N' : N_flat, 'n0' : n0_flat})\n",
     "\n",
+    "# Compute theoretical error in paleopole estimation\n",
+    "\n",
     "df[\"error_kappa_theoretical\"] = df.apply(lambda row: smp.kappa_theoretical(smp.Params(N=row.N, \n",
     "                                                                                      n0=row.n0, \n",
     "                                                                                      kappa_within_site=kappa_within_site,\n",
@@ -181,7 +184,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 4,
    "id": "701d20fc-c043-4cb2-96b3-da632087245c",
    "metadata": {},
    "outputs": [],
@@ -194,7 +197,7 @@
     "    idx = ((np.tile(a, (len(a0),1)).T - a0)**2).argmin(axis=1)\n",
     "    return a0[idx].reshape(A.shape)\n",
     "\n",
-    "def plot_angle_error(df, df_in=None, save_plot=True):\n",
+    "def plot_angle_error(df):\n",
     "    \n",
     "    fig, axes = plt.subplots()\n",
     "    fig.set_size_inches(14, 10)\n",
@@ -248,19 +251,12 @@
     "                 cmap='viridis', \n",
     "                 cbar_title=\"RMSE for pole estimation (degrees)\",\n",
     "                 color_max=14, \n",
-    "                 ticks=[1, 4, 7, 10, 15, 20, 30, 40])\n",
-    "\n",
-    "     \n",
-    "    if save_plot:\n",
-    "        plt.savefig(\"Figure1.png\", dpi=300, format=\"png\", bbox_inches='tight')\n",
-    "        plt.savefig(\"Figure1.pdf\", format=\"pdf\", bbox_inches='tight')\n",
-    "    else: \n",
-    "        plt.show()"
+    "                 ticks=[1, 4, 7, 10, 15, 20, 30, 40])"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 5,
    "id": "0d68f2bc-00d9-4457-b923-551ed76b1644",
    "metadata": {},
    "outputs": [
@@ -276,12 +272,18 @@
     }
    ],
    "source": [
-    "df_pivot = df.pivot('N', 'n0', 'error_angle_theoretical')\n",
+    "df_pivot = df.pivot(index='N', columns='n0', values='error_angle_theoretical')\n",
     "\n",
-    "plot_angle_error(df_pivot, \n",
-    "                 df_pivot,\n",
-    "                 save_plot=True)"
+    "plot_angle_error(df_pivot)"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ccb48e2d-c60d-490f-a594-137f9fc382f5",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
@@ -300,7 +302,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.11"
+   "version": "3.10.9"
   }
  },
  "nbformat": 4,