bug fixes

jupyter/Fig1-designProcess.ipynb

@@ -70,13 +70,10 @@
     "\n",
     "Applying this objective allows us to select the smallest subset that covers the convex hull of the original dataset.\n",
     "\n",
-    "$$\n",
-    "\\min_{S \\in \\mathbb{S}} \\ \\|S\\|\n",
-    "$$\n",
-    "\n",
-    "$$\n",
-    "\\text{s.t.} \\ \\text{Hull}(S) = 0\n",
-    "$$"
+    "\\begin{align*}\n",
+    "\\min_{S \\in \\mathbb{S}} & \\quad \\|S\\| \\\\\n",
+    "\\text{s.t.} & \\quad \\text{Hull}(S) = 0\n",
+    "\\end{align*}"
    ]
   },
   {
@@ -110,12 +107,10 @@
     "\n",
     "Applying this objective allows us to select a subset of 40 points with the highest local outlier effect.\n",
     "\n",
-    "$$\n",
-    "\\max_{S \\in \\mathbb{S}} \\ \\text{LOF}(S)\n",
-    "$$\n",
-    "$$\n",
-    "\\text{s.t.} \\ \\|S\\| = 40\n",
-    "$$"
+    "\\begin{align*}\n",
+    "\\max_{S \\in \\mathbb{S}} & \\quad \\text{LOF}(S) \\\\\n",
+    "\\text{s.t.} & \\quad \\|S\\| = 40\n",
+    "\\end{align*}"
    ]
   },
   {
@@ -145,8 +140,10 @@
     "\n",
     "Applying this objective allows us to select a subset of 60 points that are distant from their nearest neighbors in 2D space.\n",
     "\n",
-    "$$\\max_{S \\in \\mathbb{S}} \\space \\text{Distinctness}(S)$$\n",
-    "$$\\text{s.t.} \\space \\|S\\| = 60$$"
+    "\\begin{align*}\n",
+    "\\max_{S \\in \\mathbb{S}} & \\quad \\text{Distinctness}(S) \\\\\n",
+    "\\text{s.t.} & \\quad \\|S\\| = 60\n",
+    "\\end{align*}"
    ]
   },
   {
@@ -218,8 +215,10 @@
     "\n",
     "For visualizations with multiple criteria, objectives can be combined together to achieve more complicated outcomes. Multiple criteria can be balanced using the weight parameters to ensure the objectives apply to the subsets at desirable levels. Here we create three different subsets that blend a distribution objective (using the earth movers distance as the metric) with the distinctness objective from the previous section. Each subset blends the two objectives differently by varying the weights.\n",
     "\n",
-    "$$\\min_{S \\in \\mathbb{S}} \\space \\lambda_0 \\text{EMD}(S) + \\lambda_1 \\text{Distinctness}(S)$$\n",
-    "$$\\text{s.t.} \\space \\|S\\| = 80$$"
+    "\\begin{align*}\n",
+    "\\min_{S \\in \\mathbb{S}} & \\quad \\lambda_0 \\text{EMD}(S) + \\lambda_1 \\text{Distinctness}(S) \\\\\n",
+    "\\text{s.t.} & \\quad \\|S\\| = 80\n",
+    "\\end{align*}"
    ]
   },
   {