Add cleaner titels

tutorials/01_methods_create_synthetic_data.ipynb

@@ -109,7 +109,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Ring $\\mathcal{S}^1$ in Neural State Space $\\mathbb{R}^3$\n",
+    "## Ring $\\mathcal{S}^1$ in Neural State Space $\\mathbb{R}^3$\n",
     "\n",
     "We use $N=3$ encoding vectors to represent the recording of $N=3$ neurons.\n",
     "\n",
@@ -19488,7 +19488,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Cylinder ($\\mathcal{S}^1 \\times [0,1]$) in Neural State Space $\\mathbb{R}^3$"
+    "## Cylinder ($\\mathcal{S}^1 \\times [0,1]$) in Neural State Space $\\mathbb{R}^3$"
    ]
   },
   {
@@ -23424,7 +23424,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Flat torus $\\mathcal{T}^2$ in Neural State Space $\\mathbb{R}^3$"
+    "## Flat torus $\\mathcal{T}^2$ in Neural State Space $\\mathbb{R}^3$"
    ]
   },
   {
@@ -27381,7 +27381,16 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Extrinsic dimension of curved low-dim manifold"
+    "## Estimate Extrinsic Dimension of Neural Manifold"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Here, we use `skdim` to estimate the extrinsic dimension of a ring (circle) manifold embedded in neural state space $\\mathbb{R}^N$ where the number of neurons $N$ can vary.\n",
+    "\n",
+    "We observe whether the estimated extrinsic dimension varies with $N$."
    ]
   },
   {
@@ -43367,7 +43376,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Synthetic neural activity encoding Van der Pol Oscillator"
+    "## Synthetic Neural Activity Encoding: Van der Pol Oscillator"
    ]
   },
   {