In response to Issue #22

bibook/protein/matrix.ipynb

@@ -207,15 +207,15 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Estimating Probabilities $ p_i $ and $ p_{ij} $ from Alignments\n",
+    "### Estimating Probabilities $ q_i $ and $ p_{ij} $ from Alignments\n",
     "\n",
-    "#### Background Frequencies ($ p_i $)\n",
+    "#### Background Frequencies ($ q_i $)\n",
     "\n",
-    "The probability $ p_i $ represents the background frequency of amino acid $ i $ across a set of alignments or within a single alignment, depending on the context. It is calculated by counting the occurrence of each amino acid $ i $ in all alignments and then dividing by the total number of amino acid occurrences.\n",
+    "The probability $ q_i $ represents the background frequency of amino acid $ i $ across a set of alignments or within a single alignment, depending on the context. It is calculated by counting the occurrence of each amino acid $ i $ in all alignments and then dividing by the total number of amino acid occurrences.\n",
     "\n",
-    "##### Calculation of $ p_i $:\n",
+    "##### Calculation of $ q_i $:\n",
     "\n",
-    "$ p_i = \\frac{n_i}{N} $\n",
+    "$ q_i = \\frac{n_i}{N} $\n",
     "\n",
     "where $ n_i $ is the number of times amino acid $ i $ appears in the alignments, and $ N $ is the total number of amino acid residues in all alignments.\n",
     "\n",
@@ -269,12 +269,12 @@
     "     \"LAMVPDPWIDD\")\n",
     "]\n",
     "\n",
-    "# Flatten all characters into a single list for p_i calculation\n",
+    "# Flatten all characters into a single list for q_i calculation\n",
     "all_characters = [char for seq in alignments for string in seq for char in string]\n",
     "\n",
-    "# Calculate p_i\n",
+    "# Calculate q_i\n",
     "unique, counts = np.unique(all_characters, return_counts=True)\n",
-    "p_i = dict(zip(unique, counts / counts.sum()))\n",
+    "q_i = dict(zip(unique, counts / counts.sum()))\n",
     "\n",
     "# Calculate p_ij\n",
     "pair_counts = {}\n",
@@ -298,7 +298,7 @@
     "\n",
     "p_ij = {pair: count / sum(pair_counts.values()) for pair, count in pair_counts.items()}\n",
     "\n",
-    "print(\"Background Frequencies (p_i):\", p_i)\n",
+    "print(\"Background Frequencies (q_i):\", q_i)\n",
     "print(\"Joint Probabilities (p_ij):\", p_ij)\n"
    ]
   },