index.xml

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    <title>X-Lab - 技术传播文明，践行同步世界</title>
    <link>http://www.x-lab.info/</link>
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    <description>X-Lab - 技术传播文明，践行同步世界</description>
    <generator>Source Themes Academic (https://sourcethemes.com/academic/)</generator><language>en-us</language><copyright>© 2021 X-Lab</copyright><lastBuildDate>Sat, 01 Jun 2030 13:00:00 +0000</lastBuildDate>
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      <url>http://www.x-lab.info/images/logo_hu3ace0f88f5b266a672736d37108d6485_140636_300x300_fit_lanczos_2.png</url>
      <title>X-Lab - 技术传播文明，践行同步世界</title>
      <link>http://www.x-lab.info/</link>
    </image>
    
    <item>
      <title>Example Page 1</title>
      <link>http://www.x-lab.info/courses/example/example1/</link>
      <pubDate>Sun, 05 May 2019 00:00:00 +0100</pubDate>
      <guid>http://www.x-lab.info/courses/example/example1/</guid>
      <description>&lt;p&gt;In this tutorial, I&amp;rsquo;ll share my top 10 tips for getting started with Academic:&lt;/p&gt;
&lt;h2 id=&#34;tip-1&#34;&gt;Tip 1&lt;/h2&gt;
&lt;p&gt;Lorem ipsum dolor sit amet, consectetur adipiscing elit. Duis posuere tellus ac convallis placerat. Proin tincidunt magna sed ex sollicitudin condimentum. Sed ac faucibus dolor, scelerisque sollicitudin nisi. Cras purus urna, suscipit quis sapien eu, pulvinar tempor diam. Quisque risus orci, mollis id ante sit amet, gravida egestas nisl. Sed ac tempus magna. Proin in dui enim. Donec condimentum, sem id dapibus fringilla, tellus enim condimentum arcu, nec volutpat est felis vel metus. Vestibulum sit amet erat at nulla eleifend gravida.&lt;/p&gt;
&lt;p&gt;Nullam vel molestie justo. Curabitur vitae efficitur leo. In hac habitasse platea dictumst. Sed pulvinar mauris dui, eget varius purus congue ac. Nulla euismod, lorem vel elementum dapibus, nunc justo porta mi, sed tempus est est vel tellus. Nam et enim eleifend, laoreet sem sit amet, elementum sem. Morbi ut leo congue, maximus velit ut, finibus arcu. In et libero cursus, rutrum risus non, molestie leo. Nullam congue quam et volutpat malesuada. Sed risus tortor, pulvinar et dictum nec, sodales non mi. Phasellus lacinia commodo laoreet. Nam mollis, erat in feugiat consectetur, purus eros egestas tellus, in auctor urna odio at nibh. Mauris imperdiet nisi ac magna convallis, at rhoncus ligula cursus.&lt;/p&gt;
&lt;p&gt;Cras aliquam rhoncus ipsum, in hendrerit nunc mattis vitae. Duis vitae efficitur metus, ac tempus leo. Cras nec fringilla lacus. Quisque sit amet risus at ipsum pharetra commodo. Sed aliquam mauris at consequat eleifend. Praesent porta, augue sed viverra bibendum, neque ante euismod ante, in vehicula justo lorem ac eros. Suspendisse augue libero, venenatis eget tincidunt ut, malesuada at lorem. Donec vitae bibendum arcu. Aenean maximus nulla non pretium iaculis. Quisque imperdiet, nulla in pulvinar aliquet, velit quam ultrices quam, sit amet fringilla leo sem vel nunc. Mauris in lacinia lacus.&lt;/p&gt;
&lt;p&gt;Suspendisse a tincidunt lacus. Curabitur at urna sagittis, dictum ante sit amet, euismod magna. Sed rutrum massa id tortor commodo, vitae elementum turpis tempus. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean purus turpis, venenatis a ullamcorper nec, tincidunt et massa. Integer posuere quam rutrum arcu vehicula imperdiet. Mauris ullamcorper quam vitae purus congue, quis euismod magna eleifend. Vestibulum semper vel augue eget tincidunt. Fusce eget justo sodales, dapibus odio eu, ultrices lorem. Duis condimentum lorem id eros commodo, in facilisis mauris scelerisque. Morbi sed auctor leo. Nullam volutpat a lacus quis pharetra. Nulla congue rutrum magna a ornare.&lt;/p&gt;
&lt;p&gt;Aliquam in turpis accumsan, malesuada nibh ut, hendrerit justo. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Quisque sed erat nec justo posuere suscipit. Donec ut efficitur arcu, in malesuada neque. Nunc dignissim nisl massa, id vulputate nunc pretium nec. Quisque eget urna in risus suscipit ultricies. Pellentesque odio odio, tincidunt in eleifend sed, posuere a diam. Nam gravida nisl convallis semper elementum. Morbi vitae felis faucibus, vulputate orci placerat, aliquet nisi. Aliquam erat volutpat. Maecenas sagittis pulvinar purus, sed porta quam laoreet at.&lt;/p&gt;
&lt;h2 id=&#34;tip-2&#34;&gt;Tip 2&lt;/h2&gt;
&lt;p&gt;Lorem ipsum dolor sit amet, consectetur adipiscing elit. Duis posuere tellus ac convallis placerat. Proin tincidunt magna sed ex sollicitudin condimentum. Sed ac faucibus dolor, scelerisque sollicitudin nisi. Cras purus urna, suscipit quis sapien eu, pulvinar tempor diam. Quisque risus orci, mollis id ante sit amet, gravida egestas nisl. Sed ac tempus magna. Proin in dui enim. Donec condimentum, sem id dapibus fringilla, tellus enim condimentum arcu, nec volutpat est felis vel metus. Vestibulum sit amet erat at nulla eleifend gravida.&lt;/p&gt;
&lt;p&gt;Nullam vel molestie justo. Curabitur vitae efficitur leo. In hac habitasse platea dictumst. Sed pulvinar mauris dui, eget varius purus congue ac. Nulla euismod, lorem vel elementum dapibus, nunc justo porta mi, sed tempus est est vel tellus. Nam et enim eleifend, laoreet sem sit amet, elementum sem. Morbi ut leo congue, maximus velit ut, finibus arcu. In et libero cursus, rutrum risus non, molestie leo. Nullam congue quam et volutpat malesuada. Sed risus tortor, pulvinar et dictum nec, sodales non mi. Phasellus lacinia commodo laoreet. Nam mollis, erat in feugiat consectetur, purus eros egestas tellus, in auctor urna odio at nibh. Mauris imperdiet nisi ac magna convallis, at rhoncus ligula cursus.&lt;/p&gt;
&lt;p&gt;Cras aliquam rhoncus ipsum, in hendrerit nunc mattis vitae. Duis vitae efficitur metus, ac tempus leo. Cras nec fringilla lacus. Quisque sit amet risus at ipsum pharetra commodo. Sed aliquam mauris at consequat eleifend. Praesent porta, augue sed viverra bibendum, neque ante euismod ante, in vehicula justo lorem ac eros. Suspendisse augue libero, venenatis eget tincidunt ut, malesuada at lorem. Donec vitae bibendum arcu. Aenean maximus nulla non pretium iaculis. Quisque imperdiet, nulla in pulvinar aliquet, velit quam ultrices quam, sit amet fringilla leo sem vel nunc. Mauris in lacinia lacus.&lt;/p&gt;
&lt;p&gt;Suspendisse a tincidunt lacus. Curabitur at urna sagittis, dictum ante sit amet, euismod magna. Sed rutrum massa id tortor commodo, vitae elementum turpis tempus. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean purus turpis, venenatis a ullamcorper nec, tincidunt et massa. Integer posuere quam rutrum arcu vehicula imperdiet. Mauris ullamcorper quam vitae purus congue, quis euismod magna eleifend. Vestibulum semper vel augue eget tincidunt. Fusce eget justo sodales, dapibus odio eu, ultrices lorem. Duis condimentum lorem id eros commodo, in facilisis mauris scelerisque. Morbi sed auctor leo. Nullam volutpat a lacus quis pharetra. Nulla congue rutrum magna a ornare.&lt;/p&gt;
&lt;p&gt;Aliquam in turpis accumsan, malesuada nibh ut, hendrerit justo. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Quisque sed erat nec justo posuere suscipit. Donec ut efficitur arcu, in malesuada neque. Nunc dignissim nisl massa, id vulputate nunc pretium nec. Quisque eget urna in risus suscipit ultricies. Pellentesque odio odio, tincidunt in eleifend sed, posuere a diam. Nam gravida nisl convallis semper elementum. Morbi vitae felis faucibus, vulputate orci placerat, aliquet nisi. Aliquam erat volutpat. Maecenas sagittis pulvinar purus, sed porta quam laoreet at.&lt;/p&gt;
</description>
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    <item>
      <title>Example Page 2</title>
      <link>http://www.x-lab.info/courses/example/example2/</link>
      <pubDate>Sun, 05 May 2019 00:00:00 +0100</pubDate>
      <guid>http://www.x-lab.info/courses/example/example2/</guid>
      <description>&lt;p&gt;Here are some more tips for getting started with Academic:&lt;/p&gt;
&lt;h2 id=&#34;tip-3&#34;&gt;Tip 3&lt;/h2&gt;
&lt;p&gt;Lorem ipsum dolor sit amet, consectetur adipiscing elit. Duis posuere tellus ac convallis placerat. Proin tincidunt magna sed ex sollicitudin condimentum. Sed ac faucibus dolor, scelerisque sollicitudin nisi. Cras purus urna, suscipit quis sapien eu, pulvinar tempor diam. Quisque risus orci, mollis id ante sit amet, gravida egestas nisl. Sed ac tempus magna. Proin in dui enim. Donec condimentum, sem id dapibus fringilla, tellus enim condimentum arcu, nec volutpat est felis vel metus. Vestibulum sit amet erat at nulla eleifend gravida.&lt;/p&gt;
&lt;p&gt;Nullam vel molestie justo. Curabitur vitae efficitur leo. In hac habitasse platea dictumst. Sed pulvinar mauris dui, eget varius purus congue ac. Nulla euismod, lorem vel elementum dapibus, nunc justo porta mi, sed tempus est est vel tellus. Nam et enim eleifend, laoreet sem sit amet, elementum sem. Morbi ut leo congue, maximus velit ut, finibus arcu. In et libero cursus, rutrum risus non, molestie leo. Nullam congue quam et volutpat malesuada. Sed risus tortor, pulvinar et dictum nec, sodales non mi. Phasellus lacinia commodo laoreet. Nam mollis, erat in feugiat consectetur, purus eros egestas tellus, in auctor urna odio at nibh. Mauris imperdiet nisi ac magna convallis, at rhoncus ligula cursus.&lt;/p&gt;
&lt;p&gt;Cras aliquam rhoncus ipsum, in hendrerit nunc mattis vitae. Duis vitae efficitur metus, ac tempus leo. Cras nec fringilla lacus. Quisque sit amet risus at ipsum pharetra commodo. Sed aliquam mauris at consequat eleifend. Praesent porta, augue sed viverra bibendum, neque ante euismod ante, in vehicula justo lorem ac eros. Suspendisse augue libero, venenatis eget tincidunt ut, malesuada at lorem. Donec vitae bibendum arcu. Aenean maximus nulla non pretium iaculis. Quisque imperdiet, nulla in pulvinar aliquet, velit quam ultrices quam, sit amet fringilla leo sem vel nunc. Mauris in lacinia lacus.&lt;/p&gt;
&lt;p&gt;Suspendisse a tincidunt lacus. Curabitur at urna sagittis, dictum ante sit amet, euismod magna. Sed rutrum massa id tortor commodo, vitae elementum turpis tempus. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean purus turpis, venenatis a ullamcorper nec, tincidunt et massa. Integer posuere quam rutrum arcu vehicula imperdiet. Mauris ullamcorper quam vitae purus congue, quis euismod magna eleifend. Vestibulum semper vel augue eget tincidunt. Fusce eget justo sodales, dapibus odio eu, ultrices lorem. Duis condimentum lorem id eros commodo, in facilisis mauris scelerisque. Morbi sed auctor leo. Nullam volutpat a lacus quis pharetra. Nulla congue rutrum magna a ornare.&lt;/p&gt;
&lt;p&gt;Aliquam in turpis accumsan, malesuada nibh ut, hendrerit justo. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Quisque sed erat nec justo posuere suscipit. Donec ut efficitur arcu, in malesuada neque. Nunc dignissim nisl massa, id vulputate nunc pretium nec. Quisque eget urna in risus suscipit ultricies. Pellentesque odio odio, tincidunt in eleifend sed, posuere a diam. Nam gravida nisl convallis semper elementum. Morbi vitae felis faucibus, vulputate orci placerat, aliquet nisi. Aliquam erat volutpat. Maecenas sagittis pulvinar purus, sed porta quam laoreet at.&lt;/p&gt;
&lt;h2 id=&#34;tip-4&#34;&gt;Tip 4&lt;/h2&gt;
&lt;p&gt;Lorem ipsum dolor sit amet, consectetur adipiscing elit. Duis posuere tellus ac convallis placerat. Proin tincidunt magna sed ex sollicitudin condimentum. Sed ac faucibus dolor, scelerisque sollicitudin nisi. Cras purus urna, suscipit quis sapien eu, pulvinar tempor diam. Quisque risus orci, mollis id ante sit amet, gravida egestas nisl. Sed ac tempus magna. Proin in dui enim. Donec condimentum, sem id dapibus fringilla, tellus enim condimentum arcu, nec volutpat est felis vel metus. Vestibulum sit amet erat at nulla eleifend gravida.&lt;/p&gt;
&lt;p&gt;Nullam vel molestie justo. Curabitur vitae efficitur leo. In hac habitasse platea dictumst. Sed pulvinar mauris dui, eget varius purus congue ac. Nulla euismod, lorem vel elementum dapibus, nunc justo porta mi, sed tempus est est vel tellus. Nam et enim eleifend, laoreet sem sit amet, elementum sem. Morbi ut leo congue, maximus velit ut, finibus arcu. In et libero cursus, rutrum risus non, molestie leo. Nullam congue quam et volutpat malesuada. Sed risus tortor, pulvinar et dictum nec, sodales non mi. Phasellus lacinia commodo laoreet. Nam mollis, erat in feugiat consectetur, purus eros egestas tellus, in auctor urna odio at nibh. Mauris imperdiet nisi ac magna convallis, at rhoncus ligula cursus.&lt;/p&gt;
&lt;p&gt;Cras aliquam rhoncus ipsum, in hendrerit nunc mattis vitae. Duis vitae efficitur metus, ac tempus leo. Cras nec fringilla lacus. Quisque sit amet risus at ipsum pharetra commodo. Sed aliquam mauris at consequat eleifend. Praesent porta, augue sed viverra bibendum, neque ante euismod ante, in vehicula justo lorem ac eros. Suspendisse augue libero, venenatis eget tincidunt ut, malesuada at lorem. Donec vitae bibendum arcu. Aenean maximus nulla non pretium iaculis. Quisque imperdiet, nulla in pulvinar aliquet, velit quam ultrices quam, sit amet fringilla leo sem vel nunc. Mauris in lacinia lacus.&lt;/p&gt;
&lt;p&gt;Suspendisse a tincidunt lacus. Curabitur at urna sagittis, dictum ante sit amet, euismod magna. Sed rutrum massa id tortor commodo, vitae elementum turpis tempus. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean purus turpis, venenatis a ullamcorper nec, tincidunt et massa. Integer posuere quam rutrum arcu vehicula imperdiet. Mauris ullamcorper quam vitae purus congue, quis euismod magna eleifend. Vestibulum semper vel augue eget tincidunt. Fusce eget justo sodales, dapibus odio eu, ultrices lorem. Duis condimentum lorem id eros commodo, in facilisis mauris scelerisque. Morbi sed auctor leo. Nullam volutpat a lacus quis pharetra. Nulla congue rutrum magna a ornare.&lt;/p&gt;
&lt;p&gt;Aliquam in turpis accumsan, malesuada nibh ut, hendrerit justo. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Quisque sed erat nec justo posuere suscipit. Donec ut efficitur arcu, in malesuada neque. Nunc dignissim nisl massa, id vulputate nunc pretium nec. Quisque eget urna in risus suscipit ultricies. Pellentesque odio odio, tincidunt in eleifend sed, posuere a diam. Nam gravida nisl convallis semper elementum. Morbi vitae felis faucibus, vulputate orci placerat, aliquet nisi. Aliquam erat volutpat. Maecenas sagittis pulvinar purus, sed porta quam laoreet at.&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>Example Talk</title>
      <link>http://www.x-lab.info/talk/example/</link>
      <pubDate>Sat, 01 Jun 2030 13:00:00 +0000</pubDate>
      <guid>http://www.x-lab.info/talk/example/</guid>
      <description>&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Click on the &lt;strong&gt;Slides&lt;/strong&gt; button above to view the built-in slides feature.
  &lt;/div&gt;
&lt;/div&gt;
&lt;p&gt;Slides can be added in a few ways:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;strong&gt;Create&lt;/strong&gt; slides using Academic&amp;rsquo;s 
&lt;a href=&#34;https://sourcethemes.com/academic/docs/managing-content/#create-slides&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;em&gt;Slides&lt;/em&gt;&lt;/a&gt; feature and link using &lt;code&gt;slides&lt;/code&gt; parameter in the front matter of the talk file&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Upload&lt;/strong&gt; an existing slide deck to &lt;code&gt;static/&lt;/code&gt; and link using &lt;code&gt;url_slides&lt;/code&gt; parameter in the front matter of the talk file&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Embed&lt;/strong&gt; your slides (e.g. Google Slides) or presentation video on this page using 
&lt;a href=&#34;https://sourcethemes.com/academic/docs/writing-markdown-latex/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;shortcodes&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;Further talk details can easily be added to this page using &lt;em&gt;Markdown&lt;/em&gt; and $\rm \LaTeX$ math code.&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>Writing Technical Content in Academic</title>
      <link>http://www.x-lab.info/post/writing-technical-content/</link>
      <pubDate>Sun, 07 Jun 2020 16:43:13 +0800</pubDate>
      <guid>http://www.x-lab.info/post/writing-technical-content/</guid>
      <description>&lt;p&gt;Academic is designed to give technical content creators a seamless experience. You can focus on the content and Academic handles the rest.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Highlight your code snippets, take notes on math classes, and draw diagrams from textual representation.&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;On this page, you&amp;rsquo;ll find some examples of the types of technical content that can be rendered with Academic.&lt;/p&gt;
&lt;h2 id=&#34;examples&#34;&gt;Examples&lt;/h2&gt;
&lt;h3 id=&#34;code&#34;&gt;Code&lt;/h3&gt;
&lt;p&gt;Academic supports a Markdown extension for highlighting code syntax. You can enable this feature by toggling the &lt;code&gt;highlight&lt;/code&gt; option in your &lt;code&gt;config/_default/params.toml&lt;/code&gt; file.&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;```python
import pandas as pd
data = pd.read_csv(&amp;quot;data.csv&amp;quot;)
data.head()
```
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-python&#34;&gt;import pandas as pd
data = pd.read_csv(&amp;quot;data.csv&amp;quot;)
data.head()
&lt;/code&gt;&lt;/pre&gt;
&lt;h3 id=&#34;math&#34;&gt;Math&lt;/h3&gt;
&lt;p&gt;Academic supports a Markdown extension for $\LaTeX$ math. You can enable this feature by toggling the &lt;code&gt;math&lt;/code&gt; option in your &lt;code&gt;config/_default/params.toml&lt;/code&gt; file.&lt;/p&gt;
&lt;p&gt;To render &lt;em&gt;inline&lt;/em&gt; or &lt;em&gt;block&lt;/em&gt; math, wrap your LaTeX math with &lt;code&gt;$...$&lt;/code&gt; or &lt;code&gt;$$...$$&lt;/code&gt;, respectively.&lt;/p&gt;
&lt;p&gt;Example &lt;strong&gt;math block&lt;/strong&gt;:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-tex&#34;&gt;$$\gamma_{n} = \frac{ 
\left | \left (\mathbf x_{n} - \mathbf x_{n-1} \right )^T 
\left [\nabla F (\mathbf x_{n}) - \nabla F (\mathbf x_{n-1}) \right ] \right |}
{\left \|\nabla F(\mathbf{x}_{n}) - \nabla F(\mathbf{x}_{n-1}) \right \|^2}$$
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;p&gt;$$\gamma_{n} = \frac{ \left | \left (\mathbf x_{n} - \mathbf x_{n-1} \right )^T \left [\nabla F (\mathbf x_{n}) - \nabla F (\mathbf x_{n-1}) \right ] \right |}{\left |\nabla F(\mathbf{x}_{n}) - \nabla F(\mathbf{x}_{n-1}) \right |^2}$$&lt;/p&gt;
&lt;p&gt;Example &lt;strong&gt;inline math&lt;/strong&gt; &lt;code&gt;$\nabla F(\mathbf{x}_{n})$&lt;/code&gt; renders as $\nabla F(\mathbf{x}_{n})$.&lt;/p&gt;
&lt;p&gt;Example &lt;strong&gt;multi-line math&lt;/strong&gt; using the &lt;code&gt;\\\\&lt;/code&gt; math linebreak:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-tex&#34;&gt;$$f(k;p_0^*) = \begin{cases} p_0^* &amp;amp; \text{if }k=1, \\\\
1-p_0^* &amp;amp; \text {if }k=0.\end{cases}$$
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;p&gt;$$f(k;p_0^*) = \begin{cases} p_0^* &amp;amp; \text{if }k=1, \\&lt;br&gt;
1-p_0^* &amp;amp; \text {if }k=0.\end{cases}$$&lt;/p&gt;
&lt;h3 id=&#34;diagrams&#34;&gt;Diagrams&lt;/h3&gt;
&lt;p&gt;Academic supports a Markdown extension for diagrams. You can enable this feature by toggling the &lt;code&gt;diagram&lt;/code&gt; option in your &lt;code&gt;config/_default/params.toml&lt;/code&gt; file or by adding &lt;code&gt;diagram: true&lt;/code&gt; to your page front matter.&lt;/p&gt;
&lt;p&gt;An example &lt;strong&gt;flowchart&lt;/strong&gt;:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;```mermaid
graph TD
A[Hard] --&amp;gt;|Text| B(Round)
B --&amp;gt; C{Decision}
C --&amp;gt;|One| D[Result 1]
C --&amp;gt;|Two| E[Result 2]
```
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-mermaid&#34;&gt;graph TD
A[Hard] --&amp;gt;|Text| B(Round)
B --&amp;gt; C{Decision}
C --&amp;gt;|One| D[Result 1]
C --&amp;gt;|Two| E[Result 2]
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;An example &lt;strong&gt;sequence diagram&lt;/strong&gt;:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;```mermaid
sequenceDiagram
Alice-&amp;gt;&amp;gt;John: Hello John, how are you?
loop Healthcheck
    John-&amp;gt;&amp;gt;John: Fight against hypochondria
end
Note right of John: Rational thoughts!
John--&amp;gt;&amp;gt;Alice: Great!
John-&amp;gt;&amp;gt;Bob: How about you?
Bob--&amp;gt;&amp;gt;John: Jolly good!
```
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-mermaid&#34;&gt;sequenceDiagram
Alice-&amp;gt;&amp;gt;John: Hello John, how are you?
loop Healthcheck
    John-&amp;gt;&amp;gt;John: Fight against hypochondria
end
Note right of John: Rational thoughts!
John--&amp;gt;&amp;gt;Alice: Great!
John-&amp;gt;&amp;gt;Bob: How about you?
Bob--&amp;gt;&amp;gt;John: Jolly good!
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;An example &lt;strong&gt;Gantt diagram&lt;/strong&gt;:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;```mermaid
gantt
section Section
Completed :done,    des1, 2014-01-06,2014-01-08
Active        :active,  des2, 2014-01-07, 3d
Parallel 1   :         des3, after des1, 1d
Parallel 2   :         des4, after des1, 1d
Parallel 3   :         des5, after des3, 1d
Parallel 4   :         des6, after des4, 1d
```
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-mermaid&#34;&gt;gantt
section Section
Completed :done,    des1, 2014-01-06,2014-01-08
Active        :active,  des2, 2014-01-07, 3d
Parallel 1   :         des3, after des1, 1d
Parallel 2   :         des4, after des1, 1d
Parallel 3   :         des5, after des3, 1d
Parallel 4   :         des6, after des4, 1d
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;An example &lt;strong&gt;class diagram&lt;/strong&gt;:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;```mermaid
classDiagram
Class01 &amp;lt;|-- AveryLongClass : Cool
&amp;lt;&amp;lt;interface&amp;gt;&amp;gt; Class01
Class09 --&amp;gt; C2 : Where am i?
Class09 --* C3
Class09 --|&amp;gt; Class07
Class07 : equals()
Class07 : Object[] elementData
Class01 : size()
Class01 : int chimp
Class01 : int gorilla
class Class10 {
  &amp;lt;&amp;lt;service&amp;gt;&amp;gt;
  int id
  size()
}
```
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-mermaid&#34;&gt;classDiagram
Class01 &amp;lt;|-- AveryLongClass : Cool
&amp;lt;&amp;lt;interface&amp;gt;&amp;gt; Class01
Class09 --&amp;gt; C2 : Where am i?
Class09 --* C3
Class09 --|&amp;gt; Class07
Class07 : equals()
Class07 : Object[] elementData
Class01 : size()
Class01 : int chimp
Class01 : int gorilla
class Class10 {
  &amp;lt;&amp;lt;service&amp;gt;&amp;gt;
  int id
  size()
}
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;An example &lt;strong&gt;state diagram&lt;/strong&gt;:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;```mermaid
stateDiagram
[*] --&amp;gt; Still
Still --&amp;gt; [*]
Still --&amp;gt; Moving
Moving --&amp;gt; Still
Moving --&amp;gt; Crash
Crash --&amp;gt; [*]
```
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-mermaid&#34;&gt;stateDiagram
[*] --&amp;gt; Still
Still --&amp;gt; [*]
Still --&amp;gt; Moving
Moving --&amp;gt; Still
Moving --&amp;gt; Crash
Crash --&amp;gt; [*]
&lt;/code&gt;&lt;/pre&gt;
&lt;h3 id=&#34;todo-lists&#34;&gt;Todo lists&lt;/h3&gt;
&lt;p&gt;You can even write your todo lists in Academic too:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-markdown&#34;&gt;- [x] Write math example
- [x] Write diagram example
- [ ] Do something else
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;input checked=&#34;&#34; disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; Write math example&lt;/li&gt;
&lt;li&gt;&lt;input checked=&#34;&#34; disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; Write diagram example&lt;/li&gt;
&lt;li&gt;&lt;input disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; Do something else&lt;/li&gt;
&lt;/ul&gt;
&lt;h3 id=&#34;tables&#34;&gt;Tables&lt;/h3&gt;
&lt;p&gt;Represent your data in tables:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-markdown&#34;&gt;| First Header  | Second Header |
| ------------- | ------------- |
| Content Cell  | Content Cell  |
| Content Cell  | Content Cell  |
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;First Header&lt;/th&gt;
&lt;th&gt;Second Header&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Content Cell&lt;/td&gt;
&lt;td&gt;Content Cell&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Content Cell&lt;/td&gt;
&lt;td&gt;Content Cell&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;h3 id=&#34;asides&#34;&gt;Asides&lt;/h3&gt;
&lt;p&gt;Academic supports a 
&lt;a href=&#34;https://sourcethemes.com/academic/docs/writing-markdown-latex/#alerts&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;shortcode for asides&lt;/a&gt;, also referred to as &lt;em&gt;notices&lt;/em&gt;, &lt;em&gt;hints&lt;/em&gt;, or &lt;em&gt;alerts&lt;/em&gt;. By wrapping a paragraph in &lt;code&gt;{{% alert note %}} ... {{% /alert %}}&lt;/code&gt;, it will render as an aside.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-markdown&#34;&gt;{{% alert note %}}
A Markdown aside is useful for displaying notices, hints, or definitions to your readers.
{{% /alert %}}
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    A Markdown aside is useful for displaying notices, hints, or definitions to your readers.
  &lt;/div&gt;
&lt;/div&gt;
&lt;h3 id=&#34;icons&#34;&gt;Icons&lt;/h3&gt;
&lt;p&gt;Academic enables you to use a wide range of 
&lt;a href=&#34;https://sourcethemes.com/academic/docs/page-builder/#icons&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;icons from &lt;em&gt;Font Awesome&lt;/em&gt; and &lt;em&gt;Academicons&lt;/em&gt;&lt;/a&gt; in addition to 
&lt;a href=&#34;https://sourcethemes.com/academic/docs/writing-markdown-latex/#emojis&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;emojis&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;Here are some examples using the &lt;code&gt;icon&lt;/code&gt; shortcode to render icons:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-markdown&#34;&gt;{{&amp;lt; icon name=&amp;quot;terminal&amp;quot; pack=&amp;quot;fas&amp;quot; &amp;gt;}} Terminal  
{{&amp;lt; icon name=&amp;quot;python&amp;quot; pack=&amp;quot;fab&amp;quot; &amp;gt;}} Python  
{{&amp;lt; icon name=&amp;quot;r-project&amp;quot; pack=&amp;quot;fab&amp;quot; &amp;gt;}} R
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;p&gt;
  &lt;i class=&#34;fas fa-terminal  pr-1 fa-fw&#34;&gt;&lt;/i&gt; Terminal&lt;br&gt;

  &lt;i class=&#34;fab fa-python  pr-1 fa-fw&#34;&gt;&lt;/i&gt; Python&lt;br&gt;

  &lt;i class=&#34;fab fa-r-project  pr-1 fa-fw&#34;&gt;&lt;/i&gt; R&lt;/p&gt;
&lt;h3 id=&#34;did-you-find-this-page-helpful-consider-sharing-it-&#34;&gt;Did you find this page helpful? Consider sharing it 🙌&lt;/h3&gt;
</description>
    </item>
    
    <item>
      <title>Display Jupyter Notebooks with Academic</title>
      <link>http://www.x-lab.info/post/jupyter/</link>
      <pubDate>Sun, 07 Jun 2020 16:33:21 +0800</pubDate>
      <guid>http://www.x-lab.info/post/jupyter/</guid>
      <description>&lt;pre&gt;&lt;code class=&#34;language-python&#34;&gt;from IPython.core.display import Image
Image(&#39;https://www.python.org/static/community_logos/python-logo-master-v3-TM-flattened.png&#39;)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;./index_1_0.png&#34; alt=&#34;png&#34;&gt;&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-python&#34;&gt;print(&amp;quot;Welcome to Academic!&amp;quot;)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;Welcome to Academic!
&lt;/code&gt;&lt;/pre&gt;
&lt;h2 id=&#34;install-python-and-jupyterlab&#34;&gt;Install Python and JupyterLab&lt;/h2&gt;
&lt;p&gt;
&lt;a href=&#34;https://www.anaconda.com/distribution/#download-section&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Install Anaconda&lt;/a&gt; which includes Python 3 and JupyterLab.&lt;/p&gt;
&lt;p&gt;Alternatively, install JupyterLab with &lt;code&gt;pip3 install jupyterlab&lt;/code&gt;.&lt;/p&gt;
&lt;h2 id=&#34;create-or-upload-a-jupyter-notebook&#34;&gt;Create or upload a Jupyter notebook&lt;/h2&gt;
&lt;p&gt;Run the following commands in your Terminal, substituting &lt;code&gt;&amp;lt;MY-WEBSITE-FOLDER&amp;gt;&lt;/code&gt; and &lt;code&gt;&amp;lt;SHORT-POST-TITLE&amp;gt;&lt;/code&gt; with the file path to your Academic website folder and a short title for your blog post (use hyphens instead of spaces), respectively:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-bash&#34;&gt;mkdir -p &amp;lt;MY-WEBSITE-FOLDER&amp;gt;/content/post/&amp;lt;SHORT-POST-TITLE&amp;gt;/
cd &amp;lt;MY-WEBSITE-FOLDER&amp;gt;/content/post/&amp;lt;SHORT-POST-TITLE&amp;gt;/
jupyter lab index.ipynb
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;The &lt;code&gt;jupyter&lt;/code&gt; command above will launch the JupyterLab editor, allowing us to add Academic metadata and write the content.&lt;/p&gt;
&lt;h2 id=&#34;edit-your-post-metadata&#34;&gt;Edit your post metadata&lt;/h2&gt;
&lt;p&gt;The first cell of your Jupter notebook will contain your post metadata (
&lt;a href=&#34;https://sourcethemes.com/academic/docs/front-matter/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;front matter&lt;/a&gt;).&lt;/p&gt;
&lt;p&gt;In Jupter, choose &lt;em&gt;Markdown&lt;/em&gt; as the type of the first cell and wrap your Academic metadata in three dashes, indicating that it is YAML front matter:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;---
title: My post&#39;s title
date: 2019-09-01

# Put any other Academic metadata here...
---
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;Edit the metadata of your post, using the 
&lt;a href=&#34;https://sourcethemes.com/academic/docs/managing-content&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;documentation&lt;/a&gt; as a guide to the available options.&lt;/p&gt;
&lt;p&gt;To set a 
&lt;a href=&#34;https://sourcethemes.com/academic/docs/managing-content/#featured-image&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;featured image&lt;/a&gt;, place an image named &lt;code&gt;featured&lt;/code&gt; into your post&amp;rsquo;s folder.&lt;/p&gt;
&lt;p&gt;For other tips, such as using math, see the guide on 
&lt;a href=&#34;https://sourcethemes.com/academic/docs/writing-markdown-latex/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;writing content with Academic&lt;/a&gt;.&lt;/p&gt;
&lt;h2 id=&#34;convert-notebook-to-markdown&#34;&gt;Convert notebook to Markdown&lt;/h2&gt;
&lt;pre&gt;&lt;code class=&#34;language-bash&#34;&gt;jupyter nbconvert index.ipynb --to markdown --NbConvertApp.output_files_dir=.
&lt;/code&gt;&lt;/pre&gt;
&lt;h2 id=&#34;example&#34;&gt;Example&lt;/h2&gt;
&lt;p&gt;This post was created with Jupyter. The orginal files can be found at &lt;a href=&#34;https://github.com/gcushen/hugo-academic/tree/master/exampleSite/content/post/jupyter&#34;&gt;https://github.com/gcushen/hugo-academic/tree/master/exampleSite/content/post/jupyter&lt;/a&gt;&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>GitCourse</title>
      <link>http://www.x-lab.info/project/gitcourse/</link>
      <pubDate>Sat, 06 Jun 2020 14:41:40 +0800</pubDate>
      <guid>http://www.x-lab.info/project/gitcourse/</guid>
      <description></description>
    </item>
    
    <item>
      <title>Hypertrons</title>
      <link>http://www.x-lab.info/project/hypertrons/</link>
      <pubDate>Fri, 05 Jun 2020 14:02:35 +0800</pubDate>
      <guid>http://www.x-lab.info/project/hypertrons/</guid>
      <description></description>
    </item>
    
    <item>
      <title>Internal Project</title>
      <link>http://www.x-lab.info/project/internal-project/</link>
      <pubDate>Mon, 01 Jun 2020 17:05:58 +0800</pubDate>
      <guid>http://www.x-lab.info/project/internal-project/</guid>
      <description>&lt;p&gt;Lorem ipsum dolor sit amet, consectetur adipiscing elit. Duis posuere tellus ac convallis placerat. Proin tincidunt magna sed ex sollicitudin condimentum. Sed ac faucibus dolor, scelerisque sollicitudin nisi. Cras purus urna, suscipit quis sapien eu, pulvinar tempor diam. Quisque risus orci, mollis id ante sit amet, gravida egestas nisl. Sed ac tempus magna. Proin in dui enim. Donec condimentum, sem id dapibus fringilla, tellus enim condimentum arcu, nec volutpat est felis vel metus. Vestibulum sit amet erat at nulla eleifend gravida.&lt;/p&gt;
&lt;p&gt;Nullam vel molestie justo. Curabitur vitae efficitur leo. In hac habitasse platea dictumst. Sed pulvinar mauris dui, eget varius purus congue ac. Nulla euismod, lorem vel elementum dapibus, nunc justo porta mi, sed tempus est est vel tellus. Nam et enim eleifend, laoreet sem sit amet, elementum sem. Morbi ut leo congue, maximus velit ut, finibus arcu. In et libero cursus, rutrum risus non, molestie leo. Nullam congue quam et volutpat malesuada. Sed risus tortor, pulvinar et dictum nec, sodales non mi. Phasellus lacinia commodo laoreet. Nam mollis, erat in feugiat consectetur, purus eros egestas tellus, in auctor urna odio at nibh. Mauris imperdiet nisi ac magna convallis, at rhoncus ligula cursus.&lt;/p&gt;
&lt;p&gt;Cras aliquam rhoncus ipsum, in hendrerit nunc mattis vitae. Duis vitae efficitur metus, ac tempus leo. Cras nec fringilla lacus. Quisque sit amet risus at ipsum pharetra commodo. Sed aliquam mauris at consequat eleifend. Praesent porta, augue sed viverra bibendum, neque ante euismod ante, in vehicula justo lorem ac eros. Suspendisse augue libero, venenatis eget tincidunt ut, malesuada at lorem. Donec vitae bibendum arcu. Aenean maximus nulla non pretium iaculis. Quisque imperdiet, nulla in pulvinar aliquet, velit quam ultrices quam, sit amet fringilla leo sem vel nunc. Mauris in lacinia lacus.&lt;/p&gt;
&lt;p&gt;Suspendisse a tincidunt lacus. Curabitur at urna sagittis, dictum ante sit amet, euismod magna. Sed rutrum massa id tortor commodo, vitae elementum turpis tempus. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean purus turpis, venenatis a ullamcorper nec, tincidunt et massa. Integer posuere quam rutrum arcu vehicula imperdiet. Mauris ullamcorper quam vitae purus congue, quis euismod magna eleifend. Vestibulum semper vel augue eget tincidunt. Fusce eget justo sodales, dapibus odio eu, ultrices lorem. Duis condimentum lorem id eros commodo, in facilisis mauris scelerisque. Morbi sed auctor leo. Nullam volutpat a lacus quis pharetra. Nulla congue rutrum magna a ornare.&lt;/p&gt;
&lt;p&gt;Aliquam in turpis accumsan, malesuada nibh ut, hendrerit justo. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Quisque sed erat nec justo posuere suscipit. Donec ut efficitur arcu, in malesuada neque. Nunc dignissim nisl massa, id vulputate nunc pretium nec. Quisque eget urna in risus suscipit ultricies. Pellentesque odio odio, tincidunt in eleifend sed, posuere a diam. Nam gravida nisl convallis semper elementum. Morbi vitae felis faucibus, vulputate orci placerat, aliquet nisi. Aliquam erat volutpat. Maecenas sagittis pulvinar purus, sed porta quam laoreet at.&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>External Project</title>
      <link>http://www.x-lab.info/project/external-project/</link>
      <pubDate>Sat, 30 May 2020 17:14:49 +0800</pubDate>
      <guid>http://www.x-lab.info/project/external-project/</guid>
      <description></description>
    </item>
    
    <item>
      <title>十大经典排序算法整理汇总</title>
      <link>http://www.x-lab.info/post/sort-algorithm/</link>
      <pubDate>Fri, 29 May 2020 20:46:57 +0800</pubDate>
      <guid>http://www.x-lab.info/post/sort-algorithm/</guid>
      <description>&lt;h2 id=&#34;前言&#34;&gt;前言&lt;/h2&gt;
&lt;p&gt;本文整理并总结了十大经典的排序算法（冒泡排序、选择排序、插入排序、快速排序、归并排序、希尔排序、计数排序、基数排序、桶排序、堆排序）的时间复杂度、空间复杂度等性质。&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;本文并不会详细讲解每种排序算法的原理&lt;/strong&gt;，网上有很多很好的教程，大家可以自己去搜了看。&lt;/p&gt;
&lt;p&gt;最后我还亲自手写了十种排序算法的 c++ 代码，大家可以用来通过 
&lt;a href=&#34;https://leetcode-cn.com/problems/sort-an-array/&#34; title=&#34;LeetCode 912. 排序数组&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;LeetCode 912. 排序数组&lt;/a&gt; 这道题。&lt;/p&gt;
&lt;h2 id=&#34;性质汇总&#34;&gt;性质汇总&lt;/h2&gt;
&lt;blockquote&gt;
&lt;p&gt;如果发现表中有错误，请留言告知。&lt;/p&gt;
&lt;/blockquote&gt;
&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;算法&lt;/th&gt;
&lt;th&gt;最好&lt;/th&gt;
&lt;th&gt;最坏&lt;/th&gt;
&lt;th&gt;平均&lt;/th&gt;
&lt;th&gt;空间&lt;/th&gt;
&lt;th align=&#34;center&#34;&gt;稳定性&lt;/th&gt;
&lt;th align=&#34;center&#34;&gt;是否基于比较&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;冒泡排序&lt;/td&gt;
&lt;td&gt;$O(n)$&lt;/td&gt;
&lt;td&gt;$O(n^2)$&lt;/td&gt;
&lt;td&gt;$O(n^2)$&lt;/td&gt;
&lt;td&gt;$O(1)$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\checkmark$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\checkmark$&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;选择排序&lt;/td&gt;
&lt;td&gt;$O(n^2)$&lt;/td&gt;
&lt;td&gt;$O(n^2)$&lt;/td&gt;
&lt;td&gt;$O(n^2)$&lt;/td&gt;
&lt;td&gt;$O(1)$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\times$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\checkmark$&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;插入排序&lt;/td&gt;
&lt;td&gt;$O(n)$&lt;/td&gt;
&lt;td&gt;$O(n^2)$&lt;/td&gt;
&lt;td&gt;$O(n^2)$&lt;/td&gt;
&lt;td&gt;$O(1)$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\checkmark$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\checkmark$&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;快速排序&lt;/td&gt;
&lt;td&gt;$O(n\log n)$&lt;/td&gt;
&lt;td&gt;$O(n^2)$&lt;/td&gt;
&lt;td&gt;$O(n\log n)$&lt;/td&gt;
&lt;td&gt;$O(\log n)$~$O(n)$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\times$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\checkmark$&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;归并排序&lt;/td&gt;
&lt;td&gt;$O(n\log n)$&lt;/td&gt;
&lt;td&gt;$O(n\log n)$&lt;/td&gt;
&lt;td&gt;$O(n\log n)$&lt;/td&gt;
&lt;td&gt;$O(n)$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\checkmark$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\checkmark$&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;希尔排序&lt;/td&gt;
&lt;td&gt;$O(n^{1.3})$&lt;/td&gt;
&lt;td&gt;$O(n^2)$&lt;/td&gt;
&lt;td&gt;$O(n\log n)$~$O(n^2)$&lt;/td&gt;
&lt;td&gt;$O(1)$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\times$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\checkmark$&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;计数排序&lt;/td&gt;
&lt;td&gt;$O(n+k)$&lt;/td&gt;
&lt;td&gt;$O(n+k)$&lt;/td&gt;
&lt;td&gt;$O(n+k)$&lt;/td&gt;
&lt;td&gt;$O(n+k)$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\checkmark$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\times$&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;基数排序&lt;/td&gt;
&lt;td&gt;$O(nk)$&lt;/td&gt;
&lt;td&gt;$O(nk)$&lt;/td&gt;
&lt;td&gt;$O(nk)$&lt;/td&gt;
&lt;td&gt;$O(n+k)$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\checkmark$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\times$&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;桶排序&lt;/td&gt;
&lt;td&gt;$O(n)$&lt;/td&gt;
&lt;td&gt;$O(n)$&lt;/td&gt;
&lt;td&gt;$O(n)$&lt;/td&gt;
&lt;td&gt;$O(n+m)$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\checkmark$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\times$&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;堆排序&lt;/td&gt;
&lt;td&gt;$O(n\log n)$&lt;/td&gt;
&lt;td&gt;$O(n\log n)$&lt;/td&gt;
&lt;td&gt;$O(n\log n)$&lt;/td&gt;
&lt;td&gt;$O(1)$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\times$&lt;/td&gt;
&lt;td align=&#34;center&#34;&gt;$\checkmark$&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;h3 id=&#34;维基百科&#34;&gt;维基百科&lt;/h3&gt;
&lt;p&gt;我觉得还是英文维基百科讲的比较详细、严谨。如果大家看的比较累的话，可以自己百度搜索相应的教程。&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;冒泡排序&lt;/strong&gt;  : 
&lt;a href=&#34;https://en.wikipedia.org/wiki/Bubble_sort&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Bubble_sort&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;选择排序&lt;/strong&gt;  : 
&lt;a href=&#34;https://en.wikipedia.org/wiki/Selection_sort&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Selection_sort&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;插入排序&lt;/strong&gt;  : 
&lt;a href=&#34;https://en.wikipedia.org/wiki/Insertion_sort&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Insertion_sort&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;快速排序&lt;/strong&gt;  : 
&lt;a href=&#34;https://en.wikipedia.org/wiki/Quicksort&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Quicksort&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;归并排序&lt;/strong&gt;  : 
&lt;a href=&#34;https://en.wikipedia.org/wiki/Merge_sort&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Merge_sort&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;希尔排序&lt;/strong&gt;  : 
&lt;a href=&#34;https://en.wikipedia.org/wiki/Shellsort&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Shellsort&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;计数排序&lt;/strong&gt;  : 
&lt;a href=&#34;https://en.wikipedia.org/wiki/Counting_sort&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Counting_sort&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;基数排序&lt;/strong&gt;  : 
&lt;a href=&#34;https://en.wikipedia.org/wiki/Radix_sort&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Radix_sort&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;桶排序&lt;/strong&gt;  : 
&lt;a href=&#34;https://en.wikipedia.org/wiki/Bucket_sort&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Bucket_sort&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;堆排序&lt;/strong&gt;  : 
&lt;a href=&#34;https://en.wikipedia.org/wiki/Heapsort&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Heapsort&lt;/a&gt;&lt;/p&gt;
&lt;h2 id=&#34;代码实现&#34;&gt;代码实现&lt;/h2&gt;
&lt;p&gt;所有的排序算法接口都是相同的，也就是 &lt;code&gt;vector&amp;lt;int&amp;gt; xxxSort(vector&amp;lt;int&amp;gt;&amp;amp; nums)&lt;/code&gt; 。只需要你传入一个 &lt;code&gt;vector&amp;lt;int&amp;gt;&lt;/code&gt; 类型的数组，就能返回排序后的结果。&lt;/p&gt;
&lt;p&gt;运行下来可以发现，桶排序速度是比较快的。而冒泡排序、选择排序和插入排序因为时间复杂度太高无法通过本题，基数排序因为无法处理负数也不能通过本题。&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-cpp&#34;&gt;class Solution {
public:
    vector&amp;lt;int&amp;gt; sortArray(vector&amp;lt;int&amp;gt;&amp;amp; nums) {
        return quickSort(nums);
    }

    // 冒泡排序（超时）
    vector&amp;lt;int&amp;gt; bubbleSort(vector&amp;lt;int&amp;gt;&amp;amp; nums) {
        int n = nums.size();
        for (int i = 0; i &amp;lt; n; ++i) {
            for (int j = n-2; j &amp;gt;= i; --j) {
                if (nums[j] &amp;gt; nums[j+1]) {
                    swap(nums[j], nums[j+1]);
                }
            }
        }
        return nums;
    }

    // 选择排序（超时）
    vector&amp;lt;int&amp;gt; selectSort(vector&amp;lt;int&amp;gt;&amp;amp; nums) {
        int n = nums.size();
        for (int i = 0; i &amp;lt; n; ++i) {
            int idx = i;
            for (int j = i; j &amp;lt; n; ++j) {
                if (nums[j] &amp;lt; nums[idx]) {
                    idx = j;
                }
            }
            swap(nums[i], nums[idx]);
        }
        return nums;
    }

    // 插入排序（超时）
    vector&amp;lt;int&amp;gt; insertSort(vector&amp;lt;int&amp;gt;&amp;amp; nums) {
        int n = nums.size();
        for (int i = 0; i &amp;lt; n; ++i) {
            for (int j = i; j &amp;gt; 0 &amp;amp;&amp;amp; nums[j] &amp;lt; nums[j-1]; --j) {
                swap(nums[j], nums[j-1]);
            }
        }
        return nums;
    }

    // 快速排序（24 ms）
    void qSort(vector&amp;lt;int&amp;gt;&amp;amp; nums, int l, int r) {
        if (l &amp;gt;= r) return;
        int m = l;
        for (int i = l; i &amp;lt; r; ++i) {
            if (nums[i] &amp;lt; nums[r]) {
                swap(nums[m++], nums[i]);
            }
        }
        swap(nums[m], nums[r]);
        qSort(nums, l, m-1);
        qSort(nums, m+1, r);
    }

    vector&amp;lt;int&amp;gt; quickSort(vector&amp;lt;int&amp;gt;&amp;amp; nums) {
        int n = nums.size();
        qSort(nums, 0, n-1);
        return nums;
    }

    // 归并排序（192 ms）
    vector&amp;lt;int&amp;gt; mSort(vector&amp;lt;int&amp;gt;&amp;amp; nums, int l, int r) {
        if (l &amp;gt;= r) return {nums[l]};
        int m = l+(r-l)/2;
        vector&amp;lt;int&amp;gt; lnums = mSort(nums, l, m);
        vector&amp;lt;int&amp;gt; rnums = mSort(nums, m+1, r);
        vector&amp;lt;int&amp;gt; res;
        int i = 0, j = 0;
        while (i &amp;lt;= m-l &amp;amp;&amp;amp; j &amp;lt;= r-m-1) {
            if (lnums[i] &amp;lt; rnums[j]) {
                res.push_back(lnums[i++]);
            } else {
                res.push_back(rnums[j++]);
            }
        }
        while (i &amp;lt;= m-l) {
            res.push_back(lnums[i++]);
        }
        while (j &amp;lt;= r-m-1) {
            res.push_back(rnums[j++]);
        }
        return res;
    }

    vector&amp;lt;int&amp;gt; mergeSort(vector&amp;lt;int&amp;gt;&amp;amp; nums) {
        int n = nums.size();
        nums = mSort(nums, 0, n-1);
        return nums;
    }

    // 归并排序 + 非递归（80 ms）
    vector&amp;lt;int&amp;gt; mergeSortNR(vector&amp;lt;int&amp;gt;&amp;amp; nums) {
        int n = nums.size();
        for (int len = 1; len &amp;lt; n; len &amp;lt;&amp;lt;= 1) {
            for (int l = 0; l &amp;lt; n-len; l += 2*len) {
                int m = l+len-1;
                int r = min(n-1, l+2*len-1);
                vector&amp;lt;int&amp;gt; res;
                int i = l, j = m+1;
                while (i &amp;lt;= m &amp;amp;&amp;amp; j &amp;lt;= r) {
                    if (nums[i] &amp;lt; nums[j]) {
                        res.push_back(nums[i++]);
                    } else {
                        res.push_back(nums[j++]);
                    }
                }
                while (i &amp;lt;= m) {
                    res.push_back(nums[i++]);
                }
                while (j &amp;lt;= r) {
                    res.push_back(nums[j++]);
                }
                for (int i = l; i &amp;lt;= r; ++i) {
                    nums[i] = res[i-l];
                }
            }
        }
        return nums;
    }

    // 希尔排序（40 ms）
    vector&amp;lt;int&amp;gt; shellSort(vector&amp;lt;int&amp;gt;&amp;amp; nums) {
        int n = nums.size();
        for (int gap = n/2; gap &amp;gt; 0; gap /= 2) {
            for (int i = gap; i &amp;lt; n; ++i) {
                for (int j = i; j-gap &amp;gt;= 0 &amp;amp;&amp;amp; nums[j-gap] &amp;gt; nums[j]; j -= gap) {
                    swap(nums[j-gap], nums[j]);
                }
            }
        }
        return nums;
    }

    // 计数排序（32 ms）
    vector&amp;lt;int&amp;gt; countSort(vector&amp;lt;int&amp;gt;&amp;amp; nums) {
        int n = nums.size();
        if (!n) return {};
        int minv = *min_element(nums.begin(), nums.end());
        int maxv = *max_element(nums.begin(), nums.end());
        int m = maxv-minv+1;
        vector&amp;lt;int&amp;gt; count(m, 0);
        for (int i = 0; i &amp;lt; n; ++i) {
            count[nums[i]-minv]++;
        }
        vector&amp;lt;int&amp;gt; res;
        for (int i = 0; i &amp;lt; m; ++i) {
            for (int j = 0; j &amp;lt; count[i]; ++j) {
                res.push_back(i+minv);
            }
        }
        return res;
    }

    // 基数排序（不适用于负数）
    vector&amp;lt;int&amp;gt; radixSort(vector&amp;lt;int&amp;gt;&amp;amp; nums) {
        int n = nums.size();
        int maxv = *max_element(nums.begin(), nums.end());
        int maxd = 0;
        while (maxv &amp;gt; 0) {
            maxv /= 10;
            maxd++;
        }
        vector&amp;lt;int&amp;gt; count(10, 0), rank(n, 0);
        int base = 1;
        while (maxd &amp;gt; 0) {
            count.assign(10, 0);
            for (int i = 0; i &amp;lt; n; ++i) {
                count[(nums[i]/base)%10]++;
            }
            for (int i = 1; i &amp;lt; 10; ++i) {
                count[i] += count[i-1];
            }
            for (int i = n-1; i &amp;gt;= 0; --i) {
                rank[--count[(nums[i]/base)%10]] = nums[i];
            }
            for (int i = 0; i &amp;lt; n; ++i) {
                nums[i] = rank[i];
            }
            maxd--;
            base *= 10;
        }
        return nums;
    }

    // 桶排序 (20 ms)
    vector&amp;lt;int&amp;gt; bucketSort(vector&amp;lt;int&amp;gt;&amp;amp; nums) {
        int n = nums.size();
        int maxv = *max_element(nums.begin(), nums.end());
        int minv = *min_element(nums.begin(), nums.end());
        int bs = 1000;
        int m = (maxv-minv)/bs+1;
        vector&amp;lt;vector&amp;lt;int&amp;gt; &amp;gt; bucket(m);
        for (int i = 0; i &amp;lt; n; ++i) {
            bucket[(nums[i]-minv)/bs].push_back(nums[i]);
        }
        int idx = 0;
        for (int i = 0; i &amp;lt; m; ++i) {
            int sz = bucket[i].size();
            bucket[i] = quickSort(bucket[i]);
            for (int j = 0; j &amp;lt; sz; ++j) {
                nums[idx++] = bucket[i][j];
            }
        }
        return nums;
    }

    // 堆排序（32 ms）
    void adjust(vector&amp;lt;int&amp;gt;&amp;amp; nums, int p, int s) {
        while (2*p+1 &amp;lt; s) {
            int c1 = 2*p+1;
            int c2 = 2*p+2;
            int c = (c2&amp;lt;s &amp;amp;&amp;amp; nums[c2]&amp;gt;nums[c1]) ? c2 : c1;
            if (nums[c] &amp;gt; nums[p]) swap(nums[c], nums[p]);
            else break;
            p = c;
        }
    }

    vector&amp;lt;int&amp;gt; heapSort(vector&amp;lt;int&amp;gt;&amp;amp; nums) {
        int n = nums.size();
        for (int i = n/2-1; i &amp;gt;= 0; --i) {
            adjust(nums, i, n);
        }
        for (int i = n-1; i &amp;gt; 0; --i) {
            swap(nums[0], nums[i]);
            adjust(nums, 0, i);
        }
        return nums;
    }
};
&lt;/code&gt;&lt;/pre&gt;
</description>
    </item>
    
    <item>
      <title>Harmalysis: A Language for the Annotation of Roman Numerals in Symbolic Music Representations</title>
      <link>http://www.x-lab.info/paperdemo/harmalysis/</link>
      <pubDate>Thu, 28 May 2020 00:00:00 +0000</pubDate>
      <guid>http://www.x-lab.info/paperdemo/harmalysis/</guid>
      <description></description>
    </item>
    
    <item>
      <title>Do-Re-Myth: An Ear Training Game</title>
      <link>http://www.x-lab.info/paperdemo/doremyth/</link>
      <pubDate>Mon, 04 May 2020 00:00:00 +0000</pubDate>
      <guid>http://www.x-lab.info/paperdemo/doremyth/</guid>
      <description></description>
    </item>
    
    <item>
      <title>Key-Finding Based on a Hidden Markov Model and Key Profiles</title>
      <link>http://www.x-lab.info/paperdemo/keydetection19/</link>
      <pubDate>Sat, 09 Nov 2019 00:00:00 +0000</pubDate>
      <guid>http://www.x-lab.info/paperdemo/keydetection19/</guid>
      <description></description>
    </item>
    
    <item>
      <title>The Effects of Translation Between Symbolic Music Formats: A Case Study with Humdrum, Lilypond, MEI, and MusicXML</title>
      <link>http://www.x-lab.info/paperdemo/effects_of_translation/</link>
      <pubDate>Thu, 30 May 2019 00:00:00 +0000</pubDate>
      <guid>http://www.x-lab.info/paperdemo/effects_of_translation/</guid>
      <description></description>
    </item>
    
    <item>
      <title>Musical Tic-Tac-Toe</title>
      <link>http://www.x-lab.info/paperdemo/musical_tictactoe/</link>
      <pubDate>Sun, 14 Apr 2019 00:00:00 +0000</pubDate>
      <guid>http://www.x-lab.info/paperdemo/musical_tictactoe/</guid>
      <description></description>
    </item>
    
    <item>
      <title>Dandelot - Reading Music as a Game</title>
      <link>http://www.x-lab.info/paperdemo/dandelot/</link>
      <pubDate>Sat, 13 Apr 2019 00:00:00 +0000</pubDate>
      <guid>http://www.x-lab.info/paperdemo/dandelot/</guid>
      <description>&lt;h2 id=&#34;the-video-looks-promising-where-is-the-code&#34;&gt;The video looks promising, where is the code?&lt;/h2&gt;
&lt;p&gt;Although the intention of &lt;em&gt;dandelot&lt;/em&gt; is to be available for free for anyone to play, some of the assets used for developing the game are proprietary. For the time being, the code is not available online.&lt;/p&gt;
&lt;p&gt;If you &lt;strong&gt;really&lt;/strong&gt; want to play it, drop an email and I will send you a compiled version of the game. If you want the code to extend it or fork it into your own, we can talk about that.&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>Slides</title>
      <link>http://www.x-lab.info/slides/example/</link>
      <pubDate>Tue, 05 Feb 2019 00:00:00 +0000</pubDate>
      <guid>http://www.x-lab.info/slides/example/</guid>
      <description>&lt;h1 id=&#34;create-slides-in-markdown-with-academic&#34;&gt;Create slides in Markdown with Academic&lt;/h1&gt;
&lt;p&gt;
&lt;a href=&#34;https://sourcethemes.com/academic/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Academic&lt;/a&gt; | 
&lt;a href=&#34;https://sourcethemes.com/academic/docs/managing-content/#create-slides&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Documentation&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h2 id=&#34;features&#34;&gt;Features&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;Efficiently write slides in Markdown&lt;/li&gt;
&lt;li&gt;3-in-1: Create, Present, and Publish your slides&lt;/li&gt;
&lt;li&gt;Supports speaker notes&lt;/li&gt;
&lt;li&gt;Mobile friendly slides&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;h2 id=&#34;controls&#34;&gt;Controls&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;Next: &lt;code&gt;Right Arrow&lt;/code&gt; or &lt;code&gt;Space&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Previous: &lt;code&gt;Left Arrow&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Start: &lt;code&gt;Home&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Finish: &lt;code&gt;End&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Overview: &lt;code&gt;Esc&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Speaker notes: &lt;code&gt;S&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Fullscreen: &lt;code&gt;F&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Zoom: &lt;code&gt;Alt + Click&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;
&lt;a href=&#34;https://github.com/hakimel/reveal.js#pdf-export&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;PDF Export&lt;/a&gt;: &lt;code&gt;E&lt;/code&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;h2 id=&#34;code-highlighting&#34;&gt;Code Highlighting&lt;/h2&gt;
&lt;p&gt;Inline code: &lt;code&gt;variable&lt;/code&gt;&lt;/p&gt;
&lt;p&gt;Code block:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-python&#34;&gt;porridge = &amp;quot;blueberry&amp;quot;
if porridge == &amp;quot;blueberry&amp;quot;:
    print(&amp;quot;Eating...&amp;quot;)
&lt;/code&gt;&lt;/pre&gt;
&lt;hr&gt;
&lt;h2 id=&#34;math&#34;&gt;Math&lt;/h2&gt;
&lt;p&gt;In-line math: $x + y = z$&lt;/p&gt;
&lt;p&gt;Block math:&lt;/p&gt;
&lt;p&gt;$$
f\left( x \right) = ;\frac{{2\left( {x + 4} \right)\left( {x - 4} \right)}}{{\left( {x + 4} \right)\left( {x + 1} \right)}}
$$&lt;/p&gt;
&lt;hr&gt;
&lt;h2 id=&#34;fragments&#34;&gt;Fragments&lt;/h2&gt;
&lt;p&gt;Make content appear incrementally&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;{{% fragment %}} One {{% /fragment %}}
{{% fragment %}} **Two** {{% /fragment %}}
{{% fragment %}} Three {{% /fragment %}}
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;Press &lt;code&gt;Space&lt;/code&gt; to play!&lt;/p&gt;
&lt;p&gt;&lt;span class=&#34;fragment &#34; &gt;
One
&lt;/span&gt;
&lt;span class=&#34;fragment &#34; &gt;
&lt;strong&gt;Two&lt;/strong&gt;
&lt;/span&gt;
&lt;span class=&#34;fragment &#34; &gt;
Three
&lt;/span&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;p&gt;A fragment can accept two optional parameters:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;code&gt;class&lt;/code&gt;: use a custom style (requires definition in custom CSS)&lt;/li&gt;
&lt;li&gt;&lt;code&gt;weight&lt;/code&gt;: sets the order in which a fragment appears&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;h2 id=&#34;speaker-notes&#34;&gt;Speaker Notes&lt;/h2&gt;
&lt;p&gt;Add speaker notes to your presentation&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-markdown&#34;&gt;{{% speaker_note %}}
- Only the speaker can read these notes
- Press `S` key to view
{{% /speaker_note %}}
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;Press the &lt;code&gt;S&lt;/code&gt; key to view the speaker notes!&lt;/p&gt;
&lt;aside class=&#34;notes&#34;&gt;
  &lt;ul&gt;
&lt;li&gt;Only the speaker can read these notes&lt;/li&gt;
&lt;li&gt;Press &lt;code&gt;S&lt;/code&gt; key to view&lt;/li&gt;
&lt;/ul&gt;

&lt;/aside&gt;
&lt;hr&gt;
&lt;h2 id=&#34;themes&#34;&gt;Themes&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;black: Black background, white text, blue links (default)&lt;/li&gt;
&lt;li&gt;white: White background, black text, blue links&lt;/li&gt;
&lt;li&gt;league: Gray background, white text, blue links&lt;/li&gt;
&lt;li&gt;beige: Beige background, dark text, brown links&lt;/li&gt;
&lt;li&gt;sky: Blue background, thin dark text, blue links&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;ul&gt;
&lt;li&gt;night: Black background, thick white text, orange links&lt;/li&gt;
&lt;li&gt;serif: Cappuccino background, gray text, brown links&lt;/li&gt;
&lt;li&gt;simple: White background, black text, blue links&lt;/li&gt;
&lt;li&gt;solarized: Cream-colored background, dark green text, blue links&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;

&lt;section data-noprocess data-shortcode-slide
  
      
      data-background-image=&#34;/img/boards.jpg&#34;
  &gt;

&lt;h2 id=&#34;custom-slide&#34;&gt;Custom Slide&lt;/h2&gt;
&lt;p&gt;Customize the slide style and background&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-markdown&#34;&gt;{{&amp;lt; slide background-image=&amp;quot;/img/boards.jpg&amp;quot; &amp;gt;}}
{{&amp;lt; slide background-color=&amp;quot;#0000FF&amp;quot; &amp;gt;}}
{{&amp;lt; slide class=&amp;quot;my-style&amp;quot; &amp;gt;}}
&lt;/code&gt;&lt;/pre&gt;
&lt;hr&gt;
&lt;h2 id=&#34;custom-css-example&#34;&gt;Custom CSS Example&lt;/h2&gt;
&lt;p&gt;Let&amp;rsquo;s make headers navy colored.&lt;/p&gt;
&lt;p&gt;Create &lt;code&gt;assets/css/reveal_custom.css&lt;/code&gt; with:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-css&#34;&gt;.reveal section h1,
.reveal section h2,
.reveal section h3 {
  color: navy;
}
&lt;/code&gt;&lt;/pre&gt;
&lt;hr&gt;
&lt;h1 id=&#34;questions&#34;&gt;Questions?&lt;/h1&gt;
&lt;p&gt;
&lt;a href=&#34;https://spectrum.chat/academic&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Ask&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;
&lt;a href=&#34;https://sourcethemes.com/academic/docs/managing-content/#create-slides&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Documentation&lt;/a&gt;&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>Implementing a digital model of the Boss DS-1 distortion pedal</title>
      <link>http://www.x-lab.info/docs/mumt618/</link>
      <pubDate>Sun, 09 Dec 2018 00:00:00 +0000</pubDate>
      <guid>http://www.x-lab.info/docs/mumt618/</guid>
      <description>&lt;p&gt;This is a report for my final project of the 
&lt;a href=&#34;https://www.music.mcgill.ca/~gary/618/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;MUMT 618: Computational Modeling of Musical Acoustic Systems&lt;/a&gt; class at McGill University.&lt;/p&gt;
&lt;p&gt;I will describe my experience implementing a digital model of distortion that has been presented in the paper titled &lt;em&gt;&amp;ldquo;Simplified, physically-informed models of distortion and overdrive guitar effects pedals&amp;rdquo;&lt;/em&gt;, presented in 2007 by David Yeh, Jonathan Abel, and Julius Smith at the DAFx&#39;07 Conference.&lt;/p&gt;
&lt;p&gt;Although this paper describes two models:&lt;/p&gt;
&lt;ol&gt;
&lt;li&gt;&lt;strong&gt;Boss DS-1&lt;/strong&gt;, a distortion pedal&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Ibanez TS-9&lt;/strong&gt;, an overdrive pedal&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;I have only implemented the model of the &lt;strong&gt;Boss DS-1&lt;/strong&gt; distortion pedal. The implementation provided has been done in &lt;code&gt;MATLAB&lt;/code&gt; and does not opertate in real-time, however, a real-time implementation should not be difficult to derivate from the given code. I also provide a few audio examples of the audio effect. As of my knowledge, there are no existing audio examples or code for this model previous to this write-up, therefore, I consider it is a valuable contribution for anyone following the ideas of this paper for reproducing or improving the model.&lt;/p&gt;
&lt;h2 id=&#34;overview&#34;&gt;Overview&lt;/h2&gt;
&lt;p&gt;A high-level overview can be seen in the following diagram from the paper&lt;/p&gt;





  











&lt;figure id=&#34;figure-overview-of-the-boss-ds-1-model-obtained-from-yeh-et-al-2007&#34;&gt;


  &lt;a data-fancybox=&#34;&#34; href=&#34;http://www.x-lab.info/img/mumt618/overview.png&#34; data-caption=&#34;Overview of the Boss DS-1 model, obtained from Yeh et al. (2007)&#34;&gt;


  &lt;img src=&#34;http://www.x-lab.info/img/mumt618/overview.png&#34; alt=&#34;&#34;  &gt;
&lt;/a&gt;


  
  
  &lt;figcaption data-pre=&#34;Figure &#34; data-post=&#34;:&#34; class=&#34;numbered&#34;&gt;
    Overview of the Boss DS-1 model, obtained from Yeh et al. (2007)
  &lt;/figcaption&gt;


&lt;/figure&gt;

&lt;p&gt;It is possible that all of these stages may have an audible effect in the output produced by the physical pedal, however, the model only provides a continuous-time transfer function for the &lt;code&gt;Gain + filter&lt;/code&gt; and the &lt;code&gt;Saturating nonlin&lt;/code&gt; stages, therefore, this implementation concentrates in these two stages only.&lt;/p&gt;
&lt;p&gt;The diagrams presented in the paper are excerpts of the circuit, which are sometimes difficult to follow, therefore, as an additional resource, it was very helpful to consult this article from 
&lt;a href=&#34;https://www.electrosmash.com/boss-ds1-analysis&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;ElectroSmash&lt;/a&gt;. In this document, a full view of the schematic is displayed with the different stages labeled.&lt;/p&gt;





  











&lt;figure id=&#34;figure-schematic-of-the-boss-ds-1-obtained-from-electrosmashcom&#34;&gt;


  &lt;a data-fancybox=&#34;&#34; href=&#34;http://www.x-lab.info/img/mumt618/schematic.jpg&#34; data-caption=&#34;Schematic of the Boss DS-1, obtained from ElectroSmash.com&#34;&gt;


  &lt;img src=&#34;http://www.x-lab.info/img/mumt618/schematic.jpg&#34; alt=&#34;&#34;  &gt;
&lt;/a&gt;


  
  
  &lt;figcaption data-pre=&#34;Figure &#34; data-post=&#34;:&#34; class=&#34;numbered&#34;&gt;
    Schematic of the Boss DS-1, obtained from ElectroSmash.com
  &lt;/figcaption&gt;


&lt;/figure&gt;

&lt;p&gt;The &lt;code&gt;Gain + filter&lt;/code&gt; stage in the paper&amp;rsquo;s diagram corresponds to the &lt;code&gt;Transistor Booster&lt;/code&gt; stage of the schematic, its main component is a bipolar junction transistor. The &lt;code&gt;Saturating nonlin&lt;/code&gt; stage of the paper&amp;rsquo;s diagram corresponds roughly to the &lt;code&gt;Op-Amp Gain Stage&lt;/code&gt;. From now on, I will refer to the names of the schematic as I find them more intuitive.&lt;/p&gt;
&lt;h2 id=&#34;transistor-booster-stage&#34;&gt;Transistor Booster Stage&lt;/h2&gt;
&lt;p&gt;This stage corresponds to a single bipolar junction transistor, the continuous-time transfer function provided in the paper is the following:&lt;/p&gt;
&lt;p&gt;$$
H(s) = \frac{s^{2}}{(s + \omega_1) (s + \omega_2)}
$$&lt;/p&gt;
&lt;p&gt;where $ \omega_1 = 2\pi3 $ and $ \omega_2 = 2\pi600 $&lt;/p&gt;
&lt;h2 id=&#34;op-amp-gain-stage&#34;&gt;Op-Amp Gain Stage&lt;/h2&gt;
&lt;p&gt;This stage corresponds to the main nonlinearity of the circuit, according to the paper. One parameter is provided in this stage to control the amount of distortion that the audio effect will output. The continuous-time transfer function is defined as following:&lt;/p&gt;
&lt;p&gt;$$
H(s) = \frac{(s + \frac{1}{R_t C_c}) (s + \frac{1}{R_b C_z}) + \frac{s}{R_b C_c}}{(s + \frac{1}{R_t C_c})(s + \frac{1}{R_b C_z})}
$$&lt;/p&gt;
&lt;p&gt;where
$$R_t = 100 000 D $$
$$R_b = (1-D)100 000 + 4700$$
$$C_z = 0.000 001$$
$$C_c = 0.000 000 000 250$$
and $D$ is the &lt;strong&gt;distortion&lt;/strong&gt; knob that controls the depth of the effect and ranges from $[0, 1]$.&lt;/p&gt;
&lt;p&gt;As one may guess, these continuous-time transfer functions require discretization in order to be implemented in a digital system. In order to discretize them, Yeh et al. propose the use of the &lt;em&gt;bilinear transform&lt;/em&gt;. In the paper&amp;mdash;as well as in David Yeh&amp;rsquo;s PhD dissertation&amp;mdash;a list of (very useful) templates has been included, which helps in the process of discretizing the two continuous-time transfer functions used in this model. The relevant templates for this implementation are the templates corresponding to second-order filters.&lt;/p&gt;
&lt;h2 id=&#34;bilinear-transform&#34;&gt;Bilinear Transform&lt;/h2&gt;
&lt;p&gt;In order to discretize a continuous-time transfer function, first, we should put the continuous-time transfer function in the following form
$$
H(s) = \frac{b_2 s^2 + b_1 s + b_0}{a_2 s^2 + a_1 s + a_0}
$$&lt;/p&gt;
&lt;p&gt;Once we compute the corresponding coefficients, they can be placed in a discrete-time transfer function of the form&lt;/p&gt;
&lt;p&gt;$$
H(z) = \frac{B_0 + B_1 z^{-1} + B_2 z^{-2}}{A_0 + A_1 z^{-1} + A_2 z^{-2}}
$$&lt;/p&gt;
&lt;p&gt;The discrete-time coefficients of this transfer function can be obtained from the following equations
$$
B_0 = b_0 + b_1 c = b_2 c^2
$$
$$
B_1 = 2b_0 - 2b_2 c^2
$$
$$
B_2 = b_0 - b_1 c = b_2 c^2
$$
$$
A_0 = a_0 + a_1 c = a_2 c^2
$$
$$
A_1 = 2a_0 - 2a_2 c^2
$$
$$
A_2 = a_0 - a_1 c = a_2 c^2
$$&lt;/p&gt;
&lt;p&gt;After plugging the coefficients into the discrete-time transfer function, we should be able to implement the resulting transfer function as a digital filter.&lt;/p&gt;
&lt;h2 id=&#34;implementation-of-the-transistor-booster-stage&#34;&gt;Implementation of the Transistor Booster Stage&lt;/h2&gt;
&lt;p&gt;Using the steps described above, I now describe the implementation of the &lt;code&gt;Transistor Booster Stage&lt;/code&gt; part of the model.&lt;/p&gt;
&lt;p&gt;The first step would be to put the given continuous-time transfer function in the form of the bilinear transform template
$$
H(s) = \frac{s^2}{s^2 + (\omega_1 + \omega_2)s + \omega_1 \omega_2}
$$
From here, the continuous-time coefficients can be easily extracted
$$
b_2 = 1
$$
$$
b_1 = 0
$$
$$
b_0 = 0
$$
$$
a_2 = 1
$$
$$
a_1 = \omega_1 + \omega_2 = 2\pi 3 + 2\pi 600 = 1206\pi
$$
$$
a_0 = \omega_1 \omega_2 = (2\pi 3)(2 \pi 600) = 7200\pi^2
$$&lt;/p&gt;
&lt;p&gt;Working the templates for the discrete-time coefficients results in the following
$$
B_0 = 4fs^2
$$
$$
B_1 = -8fs^2
$$
$$
B_2 = 4fs^2
$$
$$
A_0 = 7200\pi^2 + 2412\pi fs + 4fs^2
$$
$$
A_1 = 14400\pi^2 - 8fs^2
$$
$$
A_2 = 7200\pi^2 - 2412\pi fs + 4fs^2
$$&lt;/p&gt;
&lt;p&gt;Showing once again the template of the second-order discrete-time transfer function
$$
H(z) = \frac{B_0 + B_1 z^{-1} + B_2 z^{-2}}{A_0 + A_1 z^{-1} + A_2 z^{-2}}
$$&lt;/p&gt;
&lt;p&gt;Plugging the values of the coefficients recently found, gives the following equation
$$
{\scriptsize H(z) = \frac{4fs^2 - 8fs^2 z^{-1} + 4fs^2 z^{-2}}{(7200\pi^2 + 2412\pi fs + 4fs^2) +(14400\pi^2 - 8fs^2) z^{-1} + (7200\pi^2 - 2412\pi fs + 4fs^2) z^{-2}}}
$$&lt;/p&gt;
&lt;p&gt;After dividing by $4$, factorizing $fs$, and doing some algebra to simplify the equation, this can be expressed as:
$$
{\small H(z) = \frac{1 -2 z^{-1} + z^{-2}}{(1800 \Omega^2 + 603 \Omega + 1) + (3600 \Omega^2 - 2) z^{-1} + (1800\Omega^2 - 603\Omega + 1) z^{-2}} }
$$&lt;/p&gt;
&lt;p&gt;with $\Omega = \frac{\pi}{fs}$&lt;/p&gt;
&lt;p&gt;The implementation of this discrete-time transfer function results in a filter with the following magnitude response:&lt;/p&gt;





  











&lt;figure id=&#34;figure-magnitude-response-of-the-implemented-transistor-booster-stage-uncorrected&#34;&gt;


  &lt;a data-fancybox=&#34;&#34; href=&#34;http://www.x-lab.info/img/mumt618/original_plot_bjt.png&#34; data-caption=&#34;Magnitude response of the implemented Transistor Booster Stage (uncorrected)&#34;&gt;


  &lt;img src=&#34;http://www.x-lab.info/img/mumt618/original_plot_bjt.png&#34; alt=&#34;&#34;  &gt;
&lt;/a&gt;


  
  
  &lt;figcaption data-pre=&#34;Figure &#34; data-post=&#34;:&#34; class=&#34;numbered&#34;&gt;
    Magnitude response of the implemented Transistor Booster Stage (uncorrected)
  &lt;/figcaption&gt;


&lt;/figure&gt;

&lt;p&gt;By inspecting the original magnitude response shown in the paper, it can be concluded that the implemented filter should output above $30dB$ of gain in its bandpass.&lt;/p&gt;





  











&lt;figure id=&#34;figure-magnitude-response-of-the-transistor-booster-stage-shown-at-yeh-et-al-2007&#34;&gt;


  &lt;a data-fancybox=&#34;&#34; href=&#34;http://www.x-lab.info/img/mumt618/corrected_plot_bjt.png&#34; data-caption=&#34;Magnitude response of the Transistor Booster Stage shown at Yeh et al. (2007)&#34;&gt;


  &lt;img src=&#34;http://www.x-lab.info/img/mumt618/corrected_plot_bjt.png&#34; alt=&#34;&#34;  &gt;
&lt;/a&gt;


  
  
  &lt;figcaption data-pre=&#34;Figure &#34; data-post=&#34;:&#34; class=&#34;numbered&#34;&gt;
    Magnitude response of the Transistor Booster Stage shown at Yeh et al. (2007)
  &lt;/figcaption&gt;


&lt;/figure&gt;

&lt;p&gt;Luckily, in the corresponding section of this stage, the paper mentions that the expected gain in the bandpass is, in fact, $36dB$. Using this information, an additional gain, $g$, is included in the discrete-time transfer function:&lt;/p&gt;
&lt;p&gt;$$
{\small H(z) = \frac{g(1 -2 z^{-1} + z^{-2})}{(1800 \Omega^2 + 603 \Omega + 1) + (3600 \Omega^2 - 2) z^{-1} + (1800\Omega^2 - 603\Omega + 1) z^{-2}} }
$$&lt;/p&gt;
&lt;p&gt;where the equation, $36dB = \log_{10}(g) * 20$, can be used to obtain the value of $g$&lt;/p&gt;
&lt;p&gt;$$
g = 10^{\frac{36}{20}} = 63.0957
$$&lt;/p&gt;
&lt;p&gt;The resulting magnitude response resembles much more the magnitude response shown in the paper&lt;/p&gt;





  











&lt;figure id=&#34;figure-magnitude-response-of-the-implemented-transistor-booster-stage-corrected&#34;&gt;


  &lt;a data-fancybox=&#34;&#34; href=&#34;http://www.x-lab.info/img/mumt618/corrected_plot_bjt.png&#34; data-caption=&#34;Magnitude response of the implemented Transistor Booster Stage (corrected)&#34;&gt;


  &lt;img src=&#34;http://www.x-lab.info/img/mumt618/corrected_plot_bjt.png&#34; alt=&#34;&#34;  &gt;
&lt;/a&gt;


  
  
  &lt;figcaption data-pre=&#34;Figure &#34; data-post=&#34;:&#34; class=&#34;numbered&#34;&gt;
    Magnitude response of the implemented Transistor Booster Stage (corrected)
  &lt;/figcaption&gt;


&lt;/figure&gt;

&lt;p&gt;This filter&amp;mdash;including its correction&amp;mdash;can be implemented with the following &lt;code&gt;MATLAB&lt;/code&gt; function:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-matlab&#34;&gt;% Transistor Booster Stage
% Implementation by Nestor Napoles Lopez
% based on the paper by Yeh et al. (2007)

function y = bjtfilt(x, fs)

% After working the math, I put all the discrete-time
% coefficients in terms of this variable coeff
coeff = pi/fs;

B0 = 1;
B1 = -2;
B2 = 1;

A0 = 1800.*coeff.^2 + 603.*coeff + 1;
A1 = 3600.*coeff.^2 - 2;
A2 = 1800.*coeff.^2 - 603.*coeff + 1;

% We obtain the gain from
% 36dB = log10(x) * 20
amp = 10.^(36/20);
B = amp .* [B0, B1, B2];
A = [A0, A1, A2];

y = filter(B, A, x);

end
&lt;/code&gt;&lt;/pre&gt;
&lt;h2 id=&#34;implementation-of-the-op-amp-gain-stage&#34;&gt;Implementation of the Op-Amp Gain Stage&lt;/h2&gt;
&lt;p&gt;Just as done during the &lt;code&gt;Transistor Booster Stage&lt;/code&gt;, the implementation of the &lt;code&gt;Op-Amp Gain Stage&lt;/code&gt; starts from a given continuous-time transfer function
$$
H(s) = \frac{(s + \frac{1}{R_t C_c}) (s + \frac{1}{R_b C_z}) + \frac{s}{R_b C_c}}{(s + \frac{1}{R_t C_c})(s + \frac{1}{R_b C_z})}
$$&lt;/p&gt;
&lt;p&gt;Putting this transfer function in the form of the bilinear transform template
$$
H(s) = \frac{s^2 + (\frac{1}{R_b C_z} + \frac{1}{R_t C_c} + \frac{1}{R_b C_c})s + \frac{1}{R_t C_c R_b C_z}}{s^2 + (\frac{1}{R_b C_z} + \frac{1}{R_t C_c})s + \frac{1}{R_t C_c R_b C_z}}
$$&lt;/p&gt;
&lt;p&gt;The continous-time coefficients can be obtained
$$
b_2 = 1
$$
$$
b_1 = \frac{1}{R_b C_z} + \frac{1}{R_t C_c} + \frac{1}{R_b C_c}
$$
$$
b_0 = \frac{1}{R_t C_c R_b C_z}
$$
$$
a_2 = 1
$$
$$
a_1 = \frac{1}{R_b C_z} + \frac{1}{R_t C_c}
$$
$$
a_0 = \frac{1}{R_t C_c R_b C_z}
$$&lt;/p&gt;
&lt;p&gt;Some of these coefficients are equivalent (e.g., $a_0 = b_0$), therefore, they can be summarized in the following coefficients:
$$
ab_2 = 1
$$
$$
a_1 = \frac{1}{R_b C_z} + \frac{1}{R_t C_c}
$$
$$
b_1 = a_1 + \frac{1}{R_b C_c}
$$
$$
ab_0 = \frac{1}{R_t C_c R_b C_z}
$$&lt;/p&gt;
&lt;p&gt;The next step is to obtain the discrete-time coefficients, these can be expressed in terms of the simplified list of continuous-time coefficients presented above:
$$
B_0 = ab_0 + b_1 c + c^2
$$
$$
B_1 = 2ab_0 - 2c^2
$$
$$
B_2 = ab_0 - b_1 c + c^2
$$
$$
A_0 = ab_0 + a_1 c + c^2
$$
$$
A_1 = 2ab_0 - 2c^2
$$
$$
A_2 = ab_0 - a_1 c + c^2
$$&lt;/p&gt;
&lt;p&gt;In this case, the resulting magnitude response&lt;/p&gt;





  











&lt;figure id=&#34;figure-magnitude-response-of-the-implemented-op-amp-gain-stage&#34;&gt;


  &lt;a data-fancybox=&#34;&#34; href=&#34;http://www.x-lab.info/img/mumt618/opamp_original.png&#34; data-caption=&#34;Magnitude response of the implemented Op-Amp Gain Stage&#34;&gt;


  &lt;img src=&#34;http://www.x-lab.info/img/mumt618/opamp_original.png&#34; alt=&#34;&#34;  &gt;
&lt;/a&gt;


  
  
  &lt;figcaption data-pre=&#34;Figure &#34; data-post=&#34;:&#34; class=&#34;numbered&#34;&gt;
    Magnitude response of the implemented Op-Amp Gain Stage
  &lt;/figcaption&gt;


&lt;/figure&gt;

&lt;p&gt;is quite similar to the magnitude response shown in the paper&lt;/p&gt;





  











&lt;figure id=&#34;figure-magnitude-response-of-the-op-amp-gain-stage-shown-at-yeh-et-al-2007&#34;&gt;


  &lt;a data-fancybox=&#34;&#34; href=&#34;http://www.x-lab.info/img/mumt618/opamp_paper.png&#34; data-caption=&#34;Magnitude response of the Op-Amp Gain Stage shown at Yeh et al. (2007)&#34;&gt;


  &lt;img src=&#34;http://www.x-lab.info/img/mumt618/opamp_paper.png&#34; alt=&#34;&#34;  &gt;
&lt;/a&gt;


  
  
  &lt;figcaption data-pre=&#34;Figure &#34; data-post=&#34;:&#34; class=&#34;numbered&#34;&gt;
    Magnitude response of the Op-Amp Gain Stage shown at Yeh et al. (2007)
  &lt;/figcaption&gt;


&lt;/figure&gt;

&lt;p&gt;The different colors of the first plot represent the magnitude response with values of $D$ going from $0.1$ to $1.0$. This is the  &lt;code&gt;MATLAB&lt;/code&gt; function that implements this filter:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-matlab&#34;&gt;% Op-Amp Gain Stage
% Implementation by Nestor Napoles Lopez
% based on the paper by Yeh et al. (2007)

function y = opampfilt(x, fs, DIST)

% Resistors and capacitors from the model
Rt = 100000 * DIST;
Rb = 100000*(1-DIST) + 4700;
Cz = 0.000001;
Cc = 0.000000000250;

% Constant for the bilinear transform
c = 2*fs;

% Continuous-time coefficients (reduced)
ab0 = 1 / (Rt*Cc*Rb*Cz);
a1 = 1/(Rb*Cz) + 1/(Rt*Cc);
b1 = a1 + 1/(Rb*Cc);

% Discrete-time coefficients
B0 = ab0 + b1*c + c.^2;
B1 = 2*ab0 - 2*c.^2;
B2 = ab0 - b1*c + c.^2;

A0 = ab0 + a1*c + c.^2;
A1 = B1;
A2 = ab0 - a1*c + c.^2;

B = [B0, B1, B2];
A = [A0, A1, A2];

y = filter(B, A, x);

end
&lt;/code&gt;&lt;/pre&gt;
&lt;h3 id=&#34;diode-clipper&#34;&gt;Diode-Clipper&lt;/h3&gt;
&lt;p&gt;At the end of the &lt;code&gt;Op-Amp Gain Stage&lt;/code&gt;, there is an additional step that simulates the diode that clips the samples exceeding a gain threshold, in the case of the digital implementation, that threshold consists of $abs(x[n]) \geq 1.0$. The diode-clipper has been implemented using one of the proposed methods in the paper:&lt;/p&gt;
&lt;p&gt;$$
\text{clipper}(x) = \frac{x}{(1 + |x|^n)^{1/n}}
$$&lt;/p&gt;
&lt;p&gt;with $n = 2.5$&lt;/p&gt;
&lt;p&gt;The &lt;code&gt;MATLAB&lt;/code&gt; code for the clipping function is the following:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-matlab&#34;&gt;% Diode clipper
% Implementation by Nestor Napoles Lopez, December 2018
% based on the paper by Yeh et al. (2007)

function x = diodeclip(x)

n = 2.5;

for i=1:length(x)
    x(i) = x(i) / (1 + abs(x(i)).^n).^(1/n);
end

end
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;As a final step, I provide a script that cascades the two stages of the models to process an input audio example:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-matlab&#34;&gt;% DS-1, main script
% Implementation by Nestor Napoles Lopez, December 2018
% based on the paper by Yeh et al. (2007)

% Sample audio
[x, fs] = audioread(&#39;guitar_clean.wav&#39;);

% Bipolar Junction Transistor Stage
y = bjtfilt(x, fs);

% Op-amp Gain Stage
D = 1; % D lies between [0, 1]
y = opampfilt(y, fs, D);

% Diode clipper
y = diodeclip(y);

s = audioplayer(y, fs);
play(s);
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;Here is an example of the model applied to an audio sample of a clean electric guitar&lt;sup id=&#34;fnref:1&#34;&gt;&lt;a href=&#34;#fn:1&#34; class=&#34;footnote-ref&#34; role=&#34;doc-noteref&#34;&gt;1&lt;/a&gt;&lt;/sup&gt;:&lt;/p&gt;
&lt;p&gt;&lt;a href=&#34;http://www.x-lab.info/audio/mumt618/guitar_clean.wav&#34;&gt;Original audio&lt;/a&gt; $ $&lt;/p&gt;
&lt;p&gt;&lt;a href=&#34;http://www.x-lab.info/audio/mumt618/bjt.wav&#34;&gt;Transistor Booster Stage only&lt;/a&gt; $ $&lt;/p&gt;
&lt;p&gt;&lt;a href=&#34;http://www.x-lab.info/audio/mumt618/opamp.wav&#34;&gt;Op-Amp Gain Stage only&lt;/a&gt; $ $&lt;/p&gt;
&lt;p&gt;&lt;a href=&#34;http://www.x-lab.info/audio/mumt618/bjt_opamp.wav&#34;&gt;Transistor Booster Stage and Op-Amp Gain Stage&lt;/a&gt; $ $&lt;/p&gt;
&lt;section class=&#34;footnotes&#34; role=&#34;doc-endnotes&#34;&gt;
&lt;hr&gt;
&lt;ol&gt;
&lt;li id=&#34;fn:1&#34; role=&#34;doc-endnote&#34;&gt;
&lt;p&gt;This audio sample has been obtained from 
&lt;a href=&#34;https://freesound.org/people/LG/sounds/16054/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;FreeSound&lt;/a&gt;. &lt;a href=&#34;#fnref:1&#34; class=&#34;footnote-backref&#34; role=&#34;doc-backlink&#34;&gt;&amp;#x21a9;&amp;#xfe0e;&lt;/a&gt;&lt;/p&gt;
&lt;/li&gt;
&lt;/ol&gt;
&lt;/section&gt;
</description>
    </item>
    
    <item>
      <title>Encoding Matters</title>
      <link>http://www.x-lab.info/paperdemo/encoding_matters/</link>
      <pubDate>Fri, 28 Sep 2018 00:00:00 +0000</pubDate>
      <guid>http://www.x-lab.info/paperdemo/encoding_matters/</guid>
      <description></description>
    </item>
    
    <item>
      <title></title>
      <link>http://www.x-lab.info/docs/backup/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
      <guid>http://www.x-lab.info/docs/backup/</guid>
      <description>&lt;h2 id=&#34;representative-journal-papers&#34;&gt;Representative Journal Papers&lt;/h2&gt;
&lt;ol&gt;
&lt;li&gt;Partitioning big graph with respect to arbitrary proportions in a streaming manner, Future Generation Computer Systems, 2018, 80(3): 1-11.&lt;/li&gt;
&lt;li&gt;A Reliability Analysis for Successful Execution of Parallel DAG Tasks, Journal of Information Science and Engineering, 2017, 33(1): 81-99.&lt;/li&gt;
&lt;li&gt;Schedulability Analysis and Symbolic Verification Method for Heterogeneous Multicore Real-time Systems, International Journal of Performability Engineering, 2017, 13(6): 785-795.&lt;/li&gt;
&lt;li&gt;Energy Consumption Analysis Satisfying Time-Energy-Probability Constraints for Modern DVFS Microprocessor, IETE Technical Review, 2015, 32(4): 260-272.&lt;/li&gt;
&lt;li&gt;Security-aware Intermediate Data Placement Strategy in Scientific Cloud Workflows, Knowledge and Information Systems, 2014, 41(2): 423-447.&lt;/li&gt;
&lt;li&gt;Using Priced Timed Automaton to Analyze the Energy Consumption in Cloud Computing Environment, Cluster Computing, 2014, 17(4): 1295-1307.&lt;/li&gt;
&lt;li&gt;A Novel Scalability Metric About Iso-area of Performance for Parallel Computing, The Journal of Supercomputing, 2014, 68(2): 652-671.&lt;/li&gt;
&lt;li&gt;Adaptive Energy-efficient Scheduling Algorithm for Parallel Tasks on Homogeneous Clusters, Journal of Network and Computer Applications, 2014, 41: 101–113.&lt;/li&gt;
&lt;li&gt;Time-Efficient Protocols for Neighbor Discovery in Wireless Ad Hoc Networks, IEEE Transactions on Vehicular Technology, 2013, 62(6): 2780-2791.&lt;/li&gt;
&lt;li&gt;A Bayesian Network Based Knowledge Engineering Framework for IT Service Management, IEEE Transactions on Services Computing, 2013, 6(1): 76-88.&lt;/li&gt;
&lt;li&gt;Cloud-DLS: Dynamic Trusted Scheduling for Cloud Computing, Expert System with Applications, 2012, 39(3): 2321-2329.&lt;/li&gt;
&lt;li&gt;Towards Reliable Self-Clustering Mobile Ad Hoc Networks, Computers and Electrical Engineering, 2012, 38(3): 551-562.&lt;/li&gt;
&lt;li&gt;Bayesian Intelligent Semantic Mashup for Tourism, Concurrency and Computation: Practice and Experience, 2011, 17(23): 850–862.&lt;/li&gt;
&lt;li&gt;Adaptive Bare Bones Particle Swarm Inspired by Cloud Model, IEICE Transactions on Information and Systems, 2011, E94.D(8): 1527-1538.&lt;/li&gt;
&lt;li&gt;Using Evidence Based Content Trust Model for Spam Detection, Expert System with Applications, 2010, 37 (8): 5599-5606.&lt;/li&gt;
&lt;li&gt;Bayesian Cognitive Trust Model Based Self-Clustering Algorithm for MANETs, Science in China: Series F Information Sciences, 2010, 53(3): 494-505.&lt;/li&gt;
&lt;li&gt;An Evidence Based Iterative Content Trust Algorithm for the Credibility of Online News, Concurrency and Computation: Practice and Experience, 2009, 15(21), 1857-1881.&lt;/li&gt;
&lt;li&gt;Trusted Dynamic Level Scheduling Based on Bayes Trust Model. Science in China: Series F Information Sciences, 2007, 50(3): 456-469.&lt;/li&gt;
&lt;li&gt;Reg：一种最大化内存共享与最小化运行时环境的超轻量级容器, 计算机研究与发展, 2019.&lt;/li&gt;
&lt;li&gt;一种面向云构软件的云操作系统, 计算机科学, 2017, 44(11): 33-40.&lt;/li&gt;
&lt;li&gt;高效可证明安全的基于属性的在线/离线加密机制, 通信学报, 2014, 35(7): 104-112.&lt;/li&gt;
&lt;li&gt;绿色评价模型的互模拟等价及逻辑保持, 计算机学报, 2013, 36(5): 967-976.&lt;/li&gt;
&lt;li&gt;同构DVS集群中基于自适应阈值的并行任务节能调度算法, 计算机学报, 2013, 36(2): 393-407.&lt;/li&gt;
&lt;li&gt;基于内存操作的动态软件水印算法, 通信学报, 2013, 34(2): 128-137.&lt;/li&gt;
&lt;li&gt;一种基于线程关系的软件水印算法, 电子学报, 2012, 40(5): 891-896.&lt;/li&gt;
&lt;li&gt;基于软件水印的软件服务保护安全协议, 通信学报, 2012, 33(z2): 176-181.&lt;/li&gt;
&lt;li&gt;随机任务在云计算平台中能耗的优化管理方法, 软件学报, 2012, 23(2): 266-278.&lt;/li&gt;
&lt;li&gt;基于模型检测的时间空间性能验证方法, 计算机学报, 2010, 33(9): 1621-1633.&lt;/li&gt;
&lt;li&gt;基于Bayes认知信任模型的MANETs自聚集算法, 中国科学E辑, 2010, 40(2): 228-239.&lt;/li&gt;
&lt;li&gt;P2P网络中防止欺骗行为的一种信任度计算方法, 通信学报, 2008, 29(10): 215-222.&lt;/li&gt;
&lt;li&gt;一种基于Bayes信任模型的可信动态级调度算法, 中国科学E辑, 2007, 37(2): 285-296.&lt;/li&gt;
&lt;li&gt;构造基于信任机制的自组织资源拓扑, 计算机研究与发展, 2007, 44(11): 1849-1856.&lt;/li&gt;
&lt;li&gt;一种基于信任机制的协作系统形成与演化机制, 通信学报, 2007, 27(11): 31-35.&lt;/li&gt;
&lt;/ol&gt;
&lt;h2 id=&#34;representative-conference-papers&#34;&gt;Representative Conference Papers&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;Topic Crawler for OpenStack QA Knowledge Base, International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC), IEEE Computer Society, 2017.&lt;/li&gt;
&lt;li&gt;Towards an Emerging Cloudware Paradigm for Transparent Computing, In Proceedings of the 9th IEEE/ACM International Conference on Utility and Cloud Computing, Shanghai, China, IEEE Computer Society, 2016.&lt;/li&gt;
&lt;li&gt;Cloudware: An Emerging Software Paradigm for Cloud Computing, In Proceedings of the Internetware 2016, Beijing, China, September 18, 2016, pp1-10.&lt;/li&gt;
&lt;li&gt;Towards Cloudware Paradigm for Cloud Computing, The 9th IEEE International Conference on Cloud Computing, 2016, San Francisco, USA, June 27 - July 2, 2016, pp164-171.&lt;/li&gt;
&lt;li&gt;Reachability Analysis of Cost-Reward Timed Automata for Energy Efficiency Scheduling, The 2014 International Workshop on Programming Models and Applications for Multicores and Manycores (PMAN 2014), in conjunction with PPoPP 2014, Orlando, Florida,
USA, February 15-19, 2014.&lt;/li&gt;
&lt;li&gt;Parallel Time-space Processing Model based Fast  N-body Simulation on GPUs,In: Proceedings of the 2013 International Workshop on Programming Models and Applications for Multicores and Manycores (PMAN 2013), in conjunction with PPoPP 2013, Shenzhen, China, February 23, 2013.&lt;/li&gt;
&lt;li&gt;Large-Scale Multimedia Data Mining Using MapReduce Framework, In: Proceedings of the 4th IEEE International Conference on Cloud Computing Technology and Science (CloudCom 2012), Taipei, Taiwan, December 3-6, 2012.&lt;/li&gt;
&lt;li&gt;Towards Unified Heterogeneous Event Processing for the Internet of Things, In: Proceedings of the 3rd International Conference on the Internet of Things (IoT2012), Wuxi, China, October 24-26, 2012.&lt;/li&gt;
&lt;li&gt;A Software Watermarking Algorithm Based on Stack-State Transition Graph, In: Proceeding of the 4th International Conference on Network and System Security, Melbourne, Australia, September 1-3, 2010.&lt;/li&gt;
&lt;li&gt;An Intelligent Ontology and Bayesian Network based Semantic Mashup for Tourism, In: Proceedings of the 2008 IEEE Congress on Services(SERVICES 2008), Beijing, China, September 23-26, 2008.&lt;/li&gt;
&lt;li&gt;A Bayesian Knowledge Engineering Framework for Service Management, In: Proceedings of the IEEE/IFIP Network Operations and Management Symposium (NOMS 2008), Salvador, Bahia, Brazil, April 7-11, 2008.&lt;/li&gt;
&lt;li&gt;A Semantic Reputation Mechanism in P2P Semantic Web, In: Proceedings of the 1st Asian Semantic Web Conference (ASWC 2006), Beijing, China, September 3-7, 2006, Lecture Notes in Computer Science (LNCS), 4185, 682-688.&lt;/li&gt;
&lt;/ul&gt;
</description>
    </item>
    
    <item>
      <title>苗晓变</title>
      <link>http://www.x-lab.info/author/%E8%8B%97%E6%99%93%E5%8F%98/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
      <guid>http://www.x-lab.info/author/%E8%8B%97%E6%99%93%E5%8F%98/</guid>
      <description>&lt;h2 id=&#34;a-new-member-in-x-lab&#34;&gt;A new member in X-Lab.&lt;/h2&gt;
</description>
    </item>
    
    <item>
      <title>邹韬</title>
      <link>http://www.x-lab.info/author/%E9%82%B9%E9%9F%AC/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
      <guid>http://www.x-lab.info/author/%E9%82%B9%E9%9F%AC/</guid>
      <description>&lt;h2 id=&#34;k&#34;&gt;K.&lt;/h2&gt;
</description>
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