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diff --git a/index.json b/index.json
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diff --git a/posts/kbhalpha_vector/index.html b/posts/kbhalpha_vector/index.html
@@ -9,7 +9,7 @@
 At every belief \(b\), there is a policy which has the highest \(U(b)\) at that \(b\) given be the alpha vector formulation."><meta name=author content="Houjun Liu"><link rel=stylesheet href=/css/global.css><link rel=stylesheet href=/css/syntax.css></head><body><div class=center-clearfix><header><span id=header-name onclick='window.location.href="/"' style=cursor:pointer>Houjun Liu</span><div id=socialpanel><a href=https://www.jemoka.com/search/ class=header-social id=header-search><i class="ic fa-solid fa-magnifying-glass"></i></i></a>
 <a href=https://github.com/Jemoka/ class=header-social id=header-github><i class="ic fa-brands fa-github"></i></a>
 <a href=https://maly.io/@jemoka class=header-social id=header-twitter><i class="ic fa-brands fa-mastodon"></i></a>
-<a href=https://www.reddit.com/user/Jemoka/ class=header-social id=header-reddit><i class="ic fa-brands fa-reddit"></i></a></div></header><div id=title><h1>alpha vector</h1><span class=tagbox></span></div><aside id=toc><h1 id=toc-title>table of contents</h1><nav id=TableOfContents><ul><li><a href=#additional-information>Additional Information</a><ul><li><a href=#top-action>top action</a></li><li><a href=#optimal-value-function-for-pomdp--kbhconditional-plan-dot-md--with-alpha-vector--kbhalpha-vector-dot-md><a href=HAHAHUGOSHORTCODE64s9HBHB>optimal value function for POMDP</a> with <a href=HAHAHUGOSHORTCODE64s10HBHB>alpha vector</a></a></li><li><a href=#one-step-lookahead-in-pomdp>one-step lookahead in POMDP</a></li><li><a href=#alpha-vector--kbhalpha-vector-dot-md--pruning><a href=HAHAHUGOSHORTCODE64s16HBHB>alpha vector</a> pruning</a></li></ul></li></ul></nav></aside><main><article><div><p>Recall, from <a href=/posts/kbhconditional_plan/#id-6f19368f-74b5-4606-a882-ec9bc5619873-conditional-plan-evaluation>conditional plan evaluation</a>, we had that:</p><p>\begin{equation}
+<a href=https://www.reddit.com/user/Jemoka/ class=header-social id=header-reddit><i class="ic fa-brands fa-reddit"></i></a></div></header><div id=title><h1>alpha vector</h1><span class=tagbox></span></div><aside id=toc><h1 id=toc-title>table of contents</h1><nav id=TableOfContents><ul><li><a href=#additional-information>Additional Information</a><ul><li><a href=#top-action>top action</a></li><li><a href=#optimal-value-function-for-pomdp--kbhconditional-plan-dot-md--with-alpha-vector--kbhalpha-vector-dot-md><a href=HAHAHUGOSHORTCODE65s9HBHB>optimal value function for POMDP</a> with <a href=HAHAHUGOSHORTCODE65s10HBHB>alpha vector</a></a></li><li><a href=#one-step-lookahead-in-pomdp>one-step lookahead in POMDP</a></li><li><a href=#alpha-vector--kbhalpha-vector-dot-md--pruning><a href=HAHAHUGOSHORTCODE65s16HBHB>alpha vector</a> pruning</a></li></ul></li></ul></nav></aside><main><article><div><p>Recall, from <a href=/posts/kbhconditional_plan/#id-6f19368f-74b5-4606-a882-ec9bc5619873-conditional-plan-evaluation>conditional plan evaluation</a>, we had that:</p><p>\begin{equation}
 U^{\pi}(b) = \sum_{s}^{} b(s) U^{\pi}(s)
 \end{equation}</p><p>let&rsquo;s write it as:</p><p>\begin{equation}
 U^{\pi}(b) = \sum_{s}^{} b(s) U^{\pi}(s) = {\alpha_{\pi}}^{\top} b

diff --git a/posts/kbhangelman_syndrome/index.html b/posts/kbhangelman_syndrome/index.html
@@ -3,4 +3,4 @@
 cause of Angelman Syndrome Angelman Syndrome is primarily caused by the UBE3A and the ubiquitin proteasome system. Poly-ubiquitin chain asks to discard cells."><meta name=author content="Houjun Liu"><link rel=stylesheet href=/css/global.css><link rel=stylesheet href=/css/syntax.css></head><body><div class=center-clearfix><header><span id=header-name onclick='window.location.href="/"' style=cursor:pointer>Houjun Liu</span><div id=socialpanel><a href=https://www.jemoka.com/search/ class=header-social id=header-search><i class="ic fa-solid fa-magnifying-glass"></i></i></a>
 <a href=https://github.com/Jemoka/ class=header-social id=header-github><i class="ic fa-brands fa-github"></i></a>
 <a href=https://maly.io/@jemoka class=header-social id=header-twitter><i class="ic fa-brands fa-mastodon"></i></a>
-<a href=https://www.reddit.com/user/Jemoka/ class=header-social id=header-reddit><i class="ic fa-brands fa-reddit"></i></a></div></header><div id=title><h1>Angelman Syndrome</h1><span class=tagbox></span></div><aside id=toc><h1 id=toc-title>table of contents</h1><nav id=TableOfContents><ul><li><a href=#cause-of-angelman-syndrome--kbhangelman-syndrome-dot-md>cause of <a href=HAHAHUGOSHORTCODE75s1HBHB>Angelman Syndrome</a></a></li></ul></nav></aside><main><article><div><p><a href=/posts/kbhangelman_syndrome/>Angelman Syndrome</a> is a syndrome is ~1 in 15000, clinically recognizable, developmental delay syndrome.</p><h2 id=cause-of-angelman-syndrome--kbhangelman-syndrome-dot-md>cause of <a href=/posts/kbhangelman_syndrome/>Angelman Syndrome</a></h2><p><a href=/posts/kbhangelman_syndrome/>Angelman Syndrome</a> is primarily caused by the <a href>UBE3A</a> and the <a href>ubiquitin proteasome system.</a> Poly-<a href>ubiquitin</a> chain asks to discard cells.</p></div></article></main><footer><p id=footer>&copy; 2019-2024 Houjun Liu. Licensed CC BY-NC-SA 4.0.</p></footer></div></body></html>
+<a href=https://www.reddit.com/user/Jemoka/ class=header-social id=header-reddit><i class="ic fa-brands fa-reddit"></i></a></div></header><div id=title><h1>Angelman Syndrome</h1><span class=tagbox></span></div><aside id=toc><h1 id=toc-title>table of contents</h1><nav id=TableOfContents><ul><li><a href=#cause-of-angelman-syndrome--kbhangelman-syndrome-dot-md>cause of <a href=HAHAHUGOSHORTCODE77s1HBHB>Angelman Syndrome</a></a></li></ul></nav></aside><main><article><div><p><a href=/posts/kbhangelman_syndrome/>Angelman Syndrome</a> is a syndrome is ~1 in 15000, clinically recognizable, developmental delay syndrome.</p><h2 id=cause-of-angelman-syndrome--kbhangelman-syndrome-dot-md>cause of <a href=/posts/kbhangelman_syndrome/>Angelman Syndrome</a></h2><p><a href=/posts/kbhangelman_syndrome/>Angelman Syndrome</a> is primarily caused by the <a href>UBE3A</a> and the <a href>ubiquitin proteasome system.</a> Poly-<a href>ubiquitin</a> chain asks to discard cells.</p></div></article></main><footer><p id=footer>&copy; 2019-2024 Houjun Liu. Licensed CC BY-NC-SA 4.0.</p></footer></div></body></html>
diff --git a/posts/kbhautism/index.html b/posts/kbhautism/index.html
@@ -4,4 +4,4 @@
 autism gene signature The gene signature of autism can be measured in clean and quantitative assays."><meta name=author content="Houjun Liu"><link rel=stylesheet href=/css/global.css><link rel=stylesheet href=/css/syntax.css></head><body><div class=center-clearfix><header><span id=header-name onclick='window.location.href="/"' style=cursor:pointer>Houjun Liu</span><div id=socialpanel><a href=https://www.jemoka.com/search/ class=header-social id=header-search><i class="ic fa-solid fa-magnifying-glass"></i></i></a>
 <a href=https://github.com/Jemoka/ class=header-social id=header-github><i class="ic fa-brands fa-github"></i></a>
 <a href=https://maly.io/@jemoka class=header-social id=header-twitter><i class="ic fa-brands fa-mastodon"></i></a>
-<a href=https://www.reddit.com/user/Jemoka/ class=header-social id=header-reddit><i class="ic fa-brands fa-reddit"></i></a></div></header><div id=title><h1>autism</h1><span class=tagbox></span></div><aside id=toc><h1 id=toc-title>table of contents</h1><nav id=TableOfContents><ul><li><a href=#autism--kbhautism-dot-md--gene-signature><a href=HAHAHUGOSHORTCODE117s2HBHB>autism</a> gene signature</a></li></ul></nav></aside><main><article><div><p>autism is a spectrum disorder that are caused by both environmental and genetic factors.</p><p>Key Question: how can different <a href=/posts/kbhchromatin/>chromatin</a> regulators lead to the same set of symptoms named &ldquo;<a href=/posts/kbhautism/>autism</a>&rdquo;.</p><h2 id=autism--kbhautism-dot-md--gene-signature><a href=/posts/kbhautism/>autism</a> gene signature</h2><p>The gene signature of autism can be measured in clean and quantitative assays.</p></div></article></main><footer><p id=footer>&copy; 2019-2024 Houjun Liu. Licensed CC BY-NC-SA 4.0.</p></footer></div></body></html>
+<a href=https://www.reddit.com/user/Jemoka/ class=header-social id=header-reddit><i class="ic fa-brands fa-reddit"></i></a></div></header><div id=title><h1>autism</h1><span class=tagbox></span></div><aside id=toc><h1 id=toc-title>table of contents</h1><nav id=TableOfContents><ul><li><a href=#autism--kbhautism-dot-md--gene-signature><a href=HAHAHUGOSHORTCODE112s2HBHB>autism</a> gene signature</a></li></ul></nav></aside><main><article><div><p>autism is a spectrum disorder that are caused by both environmental and genetic factors.</p><p>Key Question: how can different <a href=/posts/kbhchromatin/>chromatin</a> regulators lead to the same set of symptoms named &ldquo;<a href=/posts/kbhautism/>autism</a>&rdquo;.</p><h2 id=autism--kbhautism-dot-md--gene-signature><a href=/posts/kbhautism/>autism</a> gene signature</h2><p>The gene signature of autism can be measured in clean and quantitative assays.</p></div></article></main><footer><p id=footer>&copy; 2019-2024 Houjun Liu. Licensed CC BY-NC-SA 4.0.</p></footer></div></body></html>
diff --git a/posts/kbhbinomial_distribution/index.html b/posts/kbhbinomial_distribution/index.html
@@ -8,7 +8,7 @@
 \begin{equation} P(X=k) = {n \choose k} p^{k}(1-p)^{n-k} \end{equation}"><meta name=author content="Houjun Liu"><link rel=stylesheet href=/css/global.css><link rel=stylesheet href=/css/syntax.css></head><body><div class=center-clearfix><header><span id=header-name onclick='window.location.href="/"' style=cursor:pointer>Houjun Liu</span><div id=socialpanel><a href=https://www.jemoka.com/search/ class=header-social id=header-search><i class="ic fa-solid fa-magnifying-glass"></i></i></a>
 <a href=https://github.com/Jemoka/ class=header-social id=header-github><i class="ic fa-brands fa-github"></i></a>
 <a href=https://maly.io/@jemoka class=header-social id=header-twitter><i class="ic fa-brands fa-mastodon"></i></a>
-<a href=https://www.reddit.com/user/Jemoka/ class=header-social id=header-reddit><i class="ic fa-brands fa-reddit"></i></a></div></header><div id=title><h1>binomial distribution</h1><span class=tagbox></span></div><aside id=toc><h1 id=toc-title>table of contents</h1><nav id=TableOfContents><ul><li><a href=#constituents>constituents</a></li><li><a href=#requirements>requirements</a></li><li><a href=#additional-information>additional information</a><ul><li><a href=#properties-of-binomial-distribution--kbhbinomial-distribution-dot-md>properties of <a href=HAHAHUGOSHORTCODE156s3HBHB>binomial distribution</a></a></li><li><a href=#deriving-the-expectation--kbhexpectation-dot-md>deriving the <a href=HAHAHUGOSHORTCODE156s6HBHB>expectation</a></a></li><li><a href=#approximating-binomial>approximating binomial</a></li><li><a href=#adding-binomial-distribution--kbhbinomial-distribution-dot-md>adding <a href=HAHAHUGOSHORTCODE156s13HBHB>binomial distribution</a></a></li></ul></li></ul></nav></aside><main><article><div><p>A <a href=/posts/kbhbinomial_distribution/>binomial distribution</a> is a typo of distribution whose contents are:</p><ul><li>Binary</li><li>Independent</li><li>Fixed number</li><li><strong>Same probability</strong>: &ldquo;That means: WITH REPLACEMENT&rdquo;</li></ul><p>Think: &ldquo;what&rsquo;s the <a href=/posts/kbhprobability/>probability</a> of \(n\) coin flips getting \(k\) heads given the head&rsquo;s probability is \(p\)&rdquo;.</p><h2 id=constituents>constituents</h2><p>We write:</p><p>\begin{equation}
+<a href=https://www.reddit.com/user/Jemoka/ class=header-social id=header-reddit><i class="ic fa-brands fa-reddit"></i></a></div></header><div id=title><h1>binomial distribution</h1><span class=tagbox></span></div><aside id=toc><h1 id=toc-title>table of contents</h1><nav id=TableOfContents><ul><li><a href=#constituents>constituents</a></li><li><a href=#requirements>requirements</a></li><li><a href=#additional-information>additional information</a><ul><li><a href=#properties-of-binomial-distribution--kbhbinomial-distribution-dot-md>properties of <a href=HAHAHUGOSHORTCODE158s3HBHB>binomial distribution</a></a></li><li><a href=#deriving-the-expectation--kbhexpectation-dot-md>deriving the <a href=HAHAHUGOSHORTCODE158s6HBHB>expectation</a></a></li><li><a href=#approximating-binomial>approximating binomial</a></li><li><a href=#adding-binomial-distribution--kbhbinomial-distribution-dot-md>adding <a href=HAHAHUGOSHORTCODE158s13HBHB>binomial distribution</a></a></li></ul></li></ul></nav></aside><main><article><div><p>A <a href=/posts/kbhbinomial_distribution/>binomial distribution</a> is a typo of distribution whose contents are:</p><ul><li>Binary</li><li>Independent</li><li>Fixed number</li><li><strong>Same probability</strong>: &ldquo;That means: WITH REPLACEMENT&rdquo;</li></ul><p>Think: &ldquo;what&rsquo;s the <a href=/posts/kbhprobability/>probability</a> of \(n\) coin flips getting \(k\) heads given the head&rsquo;s probability is \(p\)&rdquo;.</p><h2 id=constituents>constituents</h2><p>We write:</p><p>\begin{equation}
 X \sim Bin(n,p)
 \end{equation}</p><p>where, \(n\) is the number of trials, \(p\) is the probability of success on each trial.</p><h2 id=requirements>requirements</h2><p>Here is the <a href=/posts/kbhprobability_mass_function/>probability mass function</a>:</p><p>\begin{equation}
 P(X=k) = {n \choose k} p^{k}(1-p)^{n-k}

diff --git a/posts/kbhbuffer_overflow/index.html b/posts/kbhbuffer_overflow/index.html
@@ -4,4 +4,4 @@
 strcpy: which keeps copying strcat: gets: it keeps taking input forever and forever https://www."><meta name=author content="Houjun Liu"><link rel=stylesheet href=/css/global.css><link rel=stylesheet href=/css/syntax.css></head><body><div class=center-clearfix><header><span id=header-name onclick='window.location.href="/"' style=cursor:pointer>Houjun Liu</span><div id=socialpanel><a href=https://www.jemoka.com/search/ class=header-social id=header-search><i class="ic fa-solid fa-magnifying-glass"></i></i></a>
 <a href=https://github.com/Jemoka/ class=header-social id=header-github><i class="ic fa-brands fa-github"></i></a>
 <a href=https://maly.io/@jemoka class=header-social id=header-twitter><i class="ic fa-brands fa-mastodon"></i></a>
-<a href=https://www.reddit.com/user/Jemoka/ class=header-social id=header-reddit><i class="ic fa-brands fa-reddit"></i></a></div></header><div id=title><h1>buffer overflow</h1><span class=tagbox></span></div><aside id=toc><h1 id=toc-title>table of contents</h1><nav id=TableOfContents><ul><li><a href=#buffer-overflow--kbhbuffer-overflow-dot-md--horror-stories><a href=HAHAHUGOSHORTCODE186s2HBHB>buffer overflow</a> horror stories</a></li><li><a href=#identifying-buffer-overflow--kbhbuffer-overflow-dot-md--s>identifying <a href=HAHAHUGOSHORTCODE186s3HBHB>buffer overflow</a>s</a><ul><li><a href=#valgrind>valgrind</a></li></ul></li></ul></nav></aside><main><article><div><p><a href=/posts/kbhbuffer_overflow/>buffer overflow</a> happens when operations like <code>stcpy</code> runs beyond the edge of the allocated buffer. We need to find and fix <a href=/posts/kbhbuffer_overflow/>buffer overflow</a>s, which causes people who use o</p><h2 id=buffer-overflow--kbhbuffer-overflow-dot-md--horror-stories><a href=/posts/kbhbuffer_overflow/>buffer overflow</a> horror stories</h2><ul><li>AOL messanger</li><li></li></ul><h2 id=identifying-buffer-overflow--kbhbuffer-overflow-dot-md--s>identifying <a href=/posts/kbhbuffer_overflow/>buffer overflow</a>s</h2><p>Think about whether or not what you are going to do will cause <a href=/posts/kbhbuffer_overflow/>buffer overflow</a>s. There are stuff which you shouldn&rsquo;t do:</p><ul><li><a href=/posts/kbhstring/#strcpy>strcpy</a>: which keeps copying</li><li><a href=/posts/kbhstring/#strcat>strcat</a>:</li><li>gets: it keeps taking input forever and forever</li></ul><p><a href=https://www.acm.org/code-of-ethics>https://www.acm.org/code-of-ethics</a> &ldquo;Design and implement systems that are robustly and usably secure.&rdquo;</p><h3 id=valgrind>valgrind</h3><p><a href=#valgrind>valgrind</a> is a good tool to check whether or not something will buffer overflow.</p></div></article></main><footer><p id=footer>&copy; 2019-2024 Houjun Liu. Licensed CC BY-NC-SA 4.0.</p></footer></div></body></html>
+<a href=https://www.reddit.com/user/Jemoka/ class=header-social id=header-reddit><i class="ic fa-brands fa-reddit"></i></a></div></header><div id=title><h1>buffer overflow</h1><span class=tagbox></span></div><aside id=toc><h1 id=toc-title>table of contents</h1><nav id=TableOfContents><ul><li><a href=#buffer-overflow--kbhbuffer-overflow-dot-md--horror-stories><a href=HAHAHUGOSHORTCODE179s2HBHB>buffer overflow</a> horror stories</a></li><li><a href=#identifying-buffer-overflow--kbhbuffer-overflow-dot-md--s>identifying <a href=HAHAHUGOSHORTCODE179s3HBHB>buffer overflow</a>s</a><ul><li><a href=#valgrind>valgrind</a></li></ul></li></ul></nav></aside><main><article><div><p><a href=/posts/kbhbuffer_overflow/>buffer overflow</a> happens when operations like <code>stcpy</code> runs beyond the edge of the allocated buffer. We need to find and fix <a href=/posts/kbhbuffer_overflow/>buffer overflow</a>s, which causes people who use o</p><h2 id=buffer-overflow--kbhbuffer-overflow-dot-md--horror-stories><a href=/posts/kbhbuffer_overflow/>buffer overflow</a> horror stories</h2><ul><li>AOL messanger</li><li></li></ul><h2 id=identifying-buffer-overflow--kbhbuffer-overflow-dot-md--s>identifying <a href=/posts/kbhbuffer_overflow/>buffer overflow</a>s</h2><p>Think about whether or not what you are going to do will cause <a href=/posts/kbhbuffer_overflow/>buffer overflow</a>s. There are stuff which you shouldn&rsquo;t do:</p><ul><li><a href=/posts/kbhstring/#strcpy>strcpy</a>: which keeps copying</li><li><a href=/posts/kbhstring/#strcat>strcat</a>:</li><li>gets: it keeps taking input forever and forever</li></ul><p><a href=https://www.acm.org/code-of-ethics>https://www.acm.org/code-of-ethics</a> &ldquo;Design and implement systems that are robustly and usably secure.&rdquo;</p><h3 id=valgrind>valgrind</h3><p><a href=#valgrind>valgrind</a> is a good tool to check whether or not something will buffer overflow.</p></div></article></main><footer><p id=footer>&copy; 2019-2024 Houjun Liu. Licensed CC BY-NC-SA 4.0.</p></footer></div></body></html>