Merge branch 'main' of https://github.com/Trance-0/NoteNextra

Dockerfile

@@ -3,6 +3,8 @@
 
 FROM node:18-alpine AS base
 
+ENV NODE_OPTIONS="--max-old-space-size=8192"
+
 # 1. Install dependencies only when needed
 FROM base AS deps
 # Check https://github.com/nodejs/docker-node/tree/b4117f9333da4138b03a546ec926ef50a31506c3#nodealpine to understand why libc6-compat might be needed.

Jenkinsfile

@@ -1,7 +1,8 @@
 pipeline {
     environment {
-        registry = "trance0/NoteNextra"
+        registry = "trance0/notenextra"
         version = "1.0"
+        NODE_OPTIONS = "--max-old-space-size=8192"
     }
     
     agent any

docker-compose.yaml

@@ -3,7 +3,7 @@ services:
     build:
       context: ./
       dockerfile: ./Dockerfile
-    image: trance0/notenextra:v1.1.5
+    image: trance0/notenextra:v1.1.7
     restart: on-failure:5
     ports:
       - 13000:3000

package.json

@@ -1,11 +1,12 @@
 {
     "scripts": {
         "dev": "next",
-        "build": "export NODE_OPTIONS=--max-old-space-size=8192 && next build",
+        "build": "next build",
         "start": "next start"
     },
     "dependencies": {
         "@cloudflare/next-on-pages": "^1.13.7",
+        "@napi-rs/simple-git": "^0.1.19",
         "@vercel/analytics": "^1.4.1",
         "@vercel/speed-insights": "^1.1.0",
         "next": "^15.0.3",

pages/CSE332S/_meta.js

@@ -16,4 +16,5 @@ export default {
     CSE332S_L11: "Object-Oriented Programming Lab (Lecture 11)",
     CSE332S_L12: "Object-Oriented Programming Lab (Lecture 12)",
     CSE332S_L13: "Object-Oriented Programming Lab (Lecture 13)",
+    CSE332S_L14: "Object-Oriented Programming Lab (Lecture 14)",
 }

pages/CSE559A/CSE559A_L14.md

@@ -0,0 +1,77 @@
+# CSE559A Lecture 14
+
+## Neural Network Training
+
+## Object Detection
+
+AP (Average Precision)
+
+### Benchmarks
+
+#### PASCAL VOC Challenge
+
+20 Challenge classes.
+
+CNN increases the accuracy of object detection.
+
+#### COCO dataset
+
+Common objects in context.
+
+Semantic segmentation. Every pixel is classified to tags.
+
+Instance segmentation. Every pixel is classified and grouped into instances.
+
+### Object detection: outline
+
+Proposal generation
+
+Object recognition
+
+#### R-CNN
+
+Proposal generation
+
+Use CNN to extract features from proposals.
+
+with SVM to classify proposals.
+
+Use selective search to generate proposals.
+
+Use AlexNet finetuned on PASCAL VOC to extract features.
+
+Pros:
+
+- Much more accurate than previous approaches
+- Andy deep architecture can immediately be "plugged in"
+
+Cons:
+
+- Not a single end-to-end trainable system
+  - Fine-tune network with softmax classifier (log loss)
+  - Train post-hoc linear SVMs (hinge loss)
+  - Train post-hoc bounding box regressors (least squares)
+- Training is slow 2000CNN passes for each image
+- Inference (detection) was slow
+
+#### Fast R-CNN
+
+Proposal generation
+
+Use CNN to extract features from proposals.
+
+##### ROI pooling and ROI alignment
+
+ROI pooling:
+
+- Pooling is applied to the feature map.
+- Pooling is applied to the proposal.
+
+ROI alignment:
+
+- Align the proposal to the feature map.
+- Align the proposal to the feature map.
+
+Use bounding box regression to refine the proposal.
+
+

pages/CSE559A/_meta.js

@@ -16,4 +16,5 @@ export default {
     CSE559A_L11: "Computer Vision (Lecture 11)",
     CSE559A_L12: "Computer Vision (Lecture 12)",
     CSE559A_L13: "Computer Vision (Lecture 13)",
+    CSE559A_L14: "Computer Vision (Lecture 14)",
 }

pages/Math4121/Math4121_L21.md

@@ -1 +1,74 @@
-# Lecture 21
+# Math4121 Lecture 21
+
+## Rolling from last lecture
+
+### Convergence of integrals
+
+#### Arzela-Osgood Theorem
+
+Let $\{f_n\}$ be a sequence of function, $f(x)=\lim_{n\to\infty}f_n(x)$ for every $x\in [0,1]$, if $f\in \mathscr{R}[0,1]$, and $\exists B>0$ such that $|f_n(x)|\leq B \forall x\in [0,1]$. (uniformly bounded and integrable)
+
+$$
+\lim_{n\to\infty}\int_0^1 f_n(x) dx = \int_0^1 f(x) dx
+$$
+
+If we let $\Gamma_{\alpha}$ be the set of intervals where $f_n$ is not continuous,
+
+$$
+\Gamma_{\alpha} = \{x\in [0,1] : \textup{ for any }m\in \mathbb{N}, \delta > 0, \exists n\geq m, y\in (x-\delta, x+\delta) \text{ s.t. } |f_n(y)-f(y)|>\alpha\}
+$$
+
+Fact: $\Gamma_{\alpha}$ is closed and nowhere dense.
+
+Proof:
+
+Without loss of generality, we can assume $f=0$. Given any $\alpha > 0$, $\exists N$ such that
+
+$$
+\left|\int_0^1 f_n(x) dx \right| < \alpha
+$$
+
+for all $n\geq N$.
+
+Consider the set $\Gamma_{\alpha/2} = \bigcup_{n=1}^{\infty} E_n$, for each $g\in \Gamma_{\alpha/2}$, we still have $\lim_{n\to\infty}f_n(g) = 0$.
+
+So we define
+
+$$
+G_i=\{g\in \Gamma_{\alpha/2} :|f_n(g)|<\frac{\alpha}{2} \text{ for all }n\geq i\}
+$$
+
+So $G_1\subset G_2\subset \cdots$ and $\Gamma_{\alpha/2} = \bigcup_{i=1}^{\infty} G_i$.
+
+By Osgood Lemma, since $\Gamma_{\alpha/2}$ is closed, $\exists K$ such that $c_e(G_K)>c_e(\Gamma_{\alpha/2})-\frac{\alpha}{4B}$.
+
+By definition of $c_e$, we cna find open $I_1,\ldots,I_N$ which cover $\Gamma_{\alpha/2}$ and
+
+$$
+\sum_{i=1}^N \ell(I_i) < c_e(\Gamma_{\alpha/2})+\frac{\alpha}{4B}
+$$
+
+Let $\mathcal{U}=\bigcup_{i=1}^N I_i$, and $\mathcal{C}=[0,1]\setminus \mathcal{U}$.
+
+Part 1: Control the integral on $\mathcal{C}$
+
+for each $x\in \mathcal{C}$, $x\notin \Gamma_{\alpha/2}$, so $\exists$ and open interval $I(x)$ and an integer $m(x)$ such that $|f_{m(x)}(x)|<\frac{\alpha}{2}$ and $\forall n\geq m(x), y\in I(x)$
+
+So $\mathcal{C}\subset \bigcup_{x\in \mathcal{C}} I(x)$, and $\mathcal{C}$ is closed and bounded, $\exists x_1,\ldots,x_J$ such that $\mathcal{C}\subset \bigcup_{j=1}^J I(x_j)$. So if $n\geq \max_{j=1,\ldots,J} m(x_j)$, and $x\in \mathcal{C}$, then $|f_n(x)|<\frac{\alpha}{2}$.
+
+So $\int_\mathcal{C} |f_n(x)| dx < \frac{\alpha}{2} c_e(\mathcal{C})$.
+
+Part 2: Control the integral on $\mathcal{U}$
+
+If $[x_i,x_{i+1}]\cap G_k\neq \emptyset$, then $\inf_{x\in [x_i,x_{i+1}]} |f_n(x)| < \frac{\alpha}{2}$ for all $n\geq K$. Denote such set as $P_1$.
+
+Otherwise, we denote such set as $P_2$.
+
+So $\ell(\mathcal{U})=\ell(P_1)+\ell(P_2)\geq c_e(G_K)+\ell(P_2)$.
+
+This implies $\ell(P_2)\leq \frac{\alpha}{4B}$.
+
+Continue on Friday.
+
+QED
+

pages/Math4121/Math4121_L22.md

@@ -1 +1,123 @@
-# Lecture 22
+# Math 4121 Lecture 22
+
+## Continue on Arzela-Osgood Theorem
+
+
+
+Proof:
+
+Part 2: Control the integral on $\mathcal{U}$
+
+If $[x_i,x_{i+1}]\cap G_k\neq \emptyset$, then $\inf_{x\in [x_i,x_{i+1}]} |f_n(x)| < \frac{\alpha}{2}$ for all $n\geq K$. Denote such set as $P_1$.
+
+Otherwise, we denote such set as $P_2$.
+
+So $\ell(\mathcal{U})=\ell(P_1)+\ell(P_2)\geq c_e(G_K)+\ell(P_2)$.
+
+This implies $\ell(P_2)\leq \frac{\alpha}{4B}$ since $c_e(G_K)\leq c_e(\mathcal{U})+\frac{\alpha}{2B}$.
+
+Thus, for $n\geq K$,
+
+$$
+L(P,f_n)\leq \ell(P_1)\frac{\alpha}{2}+\ell(P_2)B
+$$
+
+So
+
+$$
+\int_\mathcal{U} |f_n(x)| dx \leq c_e(\mathcal{U})\frac{\alpha}{2}+\frac{\alpha}{2}
+$$
+
+All in all,
+
+$$
+\begin{aligned}
+\left\vert \int_\mathcal{U} f_n(x) dx\right\vert &\leq \frac{\alpha}{2}+\frac{\alpha}{2}\\
+&= \int_0^1 |f_n(x)| dx\\
+&\leq \int_\mathcal{U} |f_n(x)| dx + \int_\mathcal{C} |f_n(x)|dx\\
+&\leq c_e(\mathcal{U})\frac{\alpha}{2}+\frac{\alpha}{2}+c_e(\mathcal{C})\frac{\alpha}{2}\\
+&= \alpha
+\end{aligned}
+$$
+
+$\forall N\geq K$.
+
+QED
+
+### Baire Category Theorem
+
+Nowhere dense sets can be large, but they canot cover an open (or closed) interval.
+
+#### Theorem 4.7 (Baire Category Theorem)
+
+An open interval cannot be covered by a countable union of nowhere dense sets.
+
+Proof:
+
+Suppose $(0,1)\subset \bigcup_{n=1}^\infty S_n$ where each $S_n$ is nowhere dense. In particular, $\exists I_1$ closed interval such that $I_1\subset (0,1)$ and $I_1\cap S_1=\emptyset$.
+
+Now for each $k\geq 2$, $S_k$ is not dense in $I_{k-1}$ so $\exists I_k\subsetneq I_{k-1}$ such that $I_k\cap S_k=\emptyset$ for all $j\leq k$.
+
+By nested interval property, $\exists x\in \bigcap_{n=1}^\infty I_n$.
+
+Then $x\in (0,1)$ and $x\notin \bigcup_{n=1}^\infty S_n$.
+
+Contradiction with the assumption that $(0,1)\subset \bigcup_{n=1}^\infty S_n$.
+
+QED
+
+#### Definition First Category
+
+A countable union of nowhere dense sets is called a set of **first category**.
+
+#### Corollary 4.8
+
+Complement of a set of first category in $\mathbb{R}$ is dense in $\mathbb{R}$.
+
+Proof:
+
+We need to show that for every interval $I$, $\exists x\in I\cap S^c$. ($\exists x\in I$ and $x\notin S$)
+
+This is equivalent to the Baire Category Theorem.
+
+QED
+
+Recall a function is pointwise discontinuous if $\mathcal{C}=\{c\in [a,b]: f\text{ is continuous at } c\}$ is dense in $[a,b]$.
+
+$\mathcal{D}=[a,b]\setminus \mathcal{C}$ is called the set of points of discontinuity of $f$.
+
+#### Corollary 4.9
+
+$f$ is pointwise discontinuous if and only if $\mathcal{D}$ is of first category.
+
+Proof:
+
+Part 1: If $\mathcal{D}$ is of first category, then $f$ is pointwise discontinuous.
+
+Immediate from Corollary 4.8.
+
+Part 2: If $f$ is pointwise discontinuous, then $\mathcal{D}$ is of first category.
+
+Let $P_k=\{x\in [a,b]: w(f;x)\geq \frac{1}{k}\}$, $\mathcal{D}=\bigcup_{k=1}^\infty P_k$.
+
+Need to show that each $P_k$ is nowhere dense. (under the assumption that $\mathcal{C)$ is dense).
+
+Let $I\subseteq [a,b]$ so $\exists c\in \mathcal{C}\cap I$. So by definition of $w(f;c)$, $\exists J\subseteq I$ and $c\in J$ such that $w(f;J)\leq \frac{1}{k}$ so for all $x\in J$, $w(f;x)\leq \frac{1}{k}$. so $J\subseteq P_k=\emptyset$.
+
+Thus, $P_k$ is nowhere dense.
+
+QED
+
+#### Corollary 4.10
+
+Let $\{f_n\}$ be a sequence of pointwise discontinuous functions. The set of points at which all $f_n$ are simultaneously continuous is dense (it's also uncountable).
+
+Proof:
+
+$$
+\bigcap_{n=1}^\infty \mathcal{C}_n=\left(\bigcup_{n=1}^\infty \mathcal{D}_n\right)^c
+$$
+
+The complement of a set of first category is dense.
+
+QED

pages/Math4121/_meta.js

@@ -22,15 +22,9 @@ export default {
     Math4121_L17: "Introduction to Lebesgue Integration (Lecture 17)",
     Math4121_L18: "Introduction to Lebesgue Integration (Lecture 18)",
     Math4121_L19: "Introduction to Lebesgue Integration (Lecture 19)",
-    Math4121_L20: {
-        display: 'hidden'
-    },
-    Math4121_L21: {
-        display: 'hidden'
-    },
-    Math4121_L22: {
-        display: 'hidden'
-    },
+    Math4121_L20: "Introduction to Lebesgue Integration (Lecture 20)",
+    Math4121_L21: "Introduction to Lebesgue Integration (Lecture 21)",
+    Math4121_L22: "Introduction to Lebesgue Integration (Lecture 22)",
     Math4121_L23: {
         display: 'hidden'
     },