Update DTAT399A_backend.core.ipynb

Author: giovannivolpe

tutorials/3-advanced-topics/DTAT399A_backend.core.ipynb

@@ -239,7 +239,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### 2.5. Validation and Invalidation\n",
+    "### 2.5. Validating and Invalidating\n",
     "\n",
     "When you invalidate the parent for a particular `_ID`, the child’s value for that `_ID` will also be marked as invalid (since it depends on the parent). This ensures that downstream computations are never out of sync."
    ]
@@ -433,7 +433,7 @@
    "source": [
     "### 2.8. Evaluating, Resetting, and Recomputing Node Values\n",
     "\n",
-    "The value of a `DeepTrackNode` is evaluated and stored when the node is called with `.__call__()` (e.g., `node()`). Wehn you call a node multiple times, you will always get the same value as the node value is retrieved from memory (and not recomputed) each time.\n",
+    "The value of a `DeepTrackNode` is evaluated and stored when the node is called with `.__call__()` (e.g., `node()`). When you call a node multiple times, you will always get the same value as the node value is retrieved from memory (and not recomputed) each time.\n",
     "\n",
     "The state of the node (and its dependencies) can be reset using the `.update()` method. After this, calling the node will result in a recomputation of its value (e.g., `node.update()()`).\n",
     "\n",
@@ -765,7 +765,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 3. Lazy Evaluation and Caching\n",
+    "## 3. Performing Lazy Evaluation and Caching\n",
     "\n",
     "A powerful feature of DeepTrack2 nodes is lazy evaluation: the node’s value is only computed when it is needed, and the result is cached until the node (or its dependencies) is invalidated. This avoids redundant computations and ensures high efficiency, especially in large graphs.\n",
     "\n",
@@ -892,7 +892,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### 3.3 Invalidation Forces Recalculation\n",
+    "### 3.3 Forcing Recalculation though Invalidation\n",
     "\n",
     "If you invalidate the node, the cache is cleared and the next call will recompute the value:"
    ]
@@ -992,7 +992,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 4. Data Management with IDs\n",
+    "## 4. Managing Data with IDs\n",
     "\n",
     "The `DeepTrackDataDict` class provides an efficient, validated way to manage multiple data objects, each indexed by a unique tuple of integers.\n",
     "\n",
@@ -1124,7 +1124,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 5. Operator Overloading and Pipeline Composition\n",
+    "## 5. Overloading Operators and Composing Pipeline\n",
     "\n",
     "A unique and powerful feature of `DeepTrackNode` is its support for operator overloading. This allows you to build complex computational pipelines by composing nodes using familiar arithmetic and comparison operators, making your code both expressive and readable.\n",
     "\n",
@@ -1291,7 +1291,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### 5.3. Comparison Operators for Graphs\n",
+    "### 5.3. Using Comparison Operators for Graphs\n",
     "\n",
     "Comparison operators also work on nodes, returning new nodes that compute boolean results."
    ]