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            <h1 id="seo-header">【迁移】使用Bootstrap法计算自举置信区间</h1>
            
              <p id="updated-time" class="note note-info" style="">
                
                  
                    Last updated on March 19, 2024 pm
                  
                
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                <p>计算药物LD50用Bliss法最严谨，而改良寇氏法计算的结果误差也不大，因此做了一次改良寇氏法计算LD50的实验。最后需要计算一下结果的可信区间，于是来试试万能的Bootstrap法</p>
<h2 id="安装包（这个例子用不上）">安装包（这个例子用不上）</h2>
<ul>
<li><a href="/shi-yong-MICE-bao-dui-shu-ju-que-shi-zhi-jin-hang-cha-bu">conda activate MICE</a></li>
<li>conda install -c conda-forge r-boot=1.3_28 -y</li>
</ul>
<h2 id="构造样本">构造样本</h2>
<table>
<thead>
<tr>
<th>组别</th>
<th>剂量 mg/kg</th>
<th>动物数</th>
<th>死亡数</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>110.8</td>
<td>10</td>
<td>0</td>
</tr>
<tr>
<td>2</td>
<td>147.7</td>
<td>10</td>
<td>0</td>
</tr>
<tr>
<td>3</td>
<td>196.9</td>
<td>10</td>
<td>5</td>
</tr>
<tr>
<td>4</td>
<td>262.5</td>
<td>10</td>
<td>8</td>
</tr>
<tr>
<td>5</td>
<td>350.0</td>
<td>10</td>
<td>10</td>
</tr>
</tbody>
</table>
<figure class="highlight r"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line">data <span class="operator">&lt;-</span> <span class="built_in">list</span><span class="punctuation">(</span></span><br><span class="line">    g1 <span class="operator">=</span> <span class="built_in">rep</span><span class="punctuation">(</span><span class="number">0</span><span class="punctuation">,</span><span class="number">10</span><span class="punctuation">)</span><span class="punctuation">,</span></span><br><span class="line">    g2 <span class="operator">=</span> <span class="built_in">rep</span><span class="punctuation">(</span><span class="number">0</span><span class="punctuation">,</span><span class="number">10</span><span class="punctuation">)</span><span class="punctuation">,</span></span><br><span class="line">    g3 <span class="operator">=</span> <span class="built_in">c</span><span class="punctuation">(</span><span class="built_in">rep</span><span class="punctuation">(</span><span class="number">0</span><span class="punctuation">,</span><span class="number">5</span><span class="punctuation">)</span><span class="punctuation">,</span><span class="built_in">rep</span><span class="punctuation">(</span><span class="number">1</span><span class="punctuation">,</span><span class="number">5</span><span class="punctuation">)</span><span class="punctuation">)</span><span class="punctuation">,</span></span><br><span class="line">    g4 <span class="operator">=</span> <span class="built_in">c</span><span class="punctuation">(</span><span class="built_in">rep</span><span class="punctuation">(</span><span class="number">0</span><span class="punctuation">,</span><span class="number">2</span><span class="punctuation">)</span><span class="punctuation">,</span><span class="built_in">rep</span><span class="punctuation">(</span><span class="number">1</span><span class="punctuation">,</span><span class="number">8</span><span class="punctuation">)</span><span class="punctuation">)</span><span class="punctuation">,</span></span><br><span class="line">    g5 <span class="operator">=</span> <span class="built_in">rep</span><span class="punctuation">(</span><span class="number">1</span><span class="punctuation">,</span><span class="number">10</span><span class="punctuation">)</span></span><br><span class="line"><span class="punctuation">)</span></span><br></pre></td></tr></table></figure>
<h2 id="计算自举置信区间">计算自举置信区间</h2>
<h3 id="定义统计量">定义统计量</h3>
<figure class="highlight r"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre></td><td class="code"><pre><span class="line">ln <span class="operator">&lt;-</span> <span class="built_in">log</span></span><br><span class="line">ld50 <span class="operator">&lt;-</span> <span class="keyword">function</span><span class="punctuation">(</span>data<span class="punctuation">)</span><span class="punctuation">&#123;</span></span><br><span class="line">    g1 <span class="operator">&lt;-</span> mean<span class="punctuation">(</span>sample<span class="punctuation">(</span>x <span class="operator">=</span> data<span class="operator">$</span>g1<span class="punctuation">,</span> size <span class="operator">=</span> <span class="number">10</span><span class="punctuation">,</span> replace <span class="operator">=</span> <span class="built_in">T</span><span class="punctuation">)</span><span class="punctuation">)</span></span><br><span class="line">    g2 <span class="operator">&lt;-</span> mean<span class="punctuation">(</span>sample<span class="punctuation">(</span>x <span class="operator">=</span> data<span class="operator">$</span>g2<span class="punctuation">,</span> size <span class="operator">=</span> <span class="number">10</span><span class="punctuation">,</span> replace <span class="operator">=</span> <span class="built_in">T</span><span class="punctuation">)</span><span class="punctuation">)</span></span><br><span class="line">    g3 <span class="operator">&lt;-</span> mean<span class="punctuation">(</span>sample<span class="punctuation">(</span>x <span class="operator">=</span> data<span class="operator">$</span>g3<span class="punctuation">,</span> size <span class="operator">=</span> <span class="number">10</span><span class="punctuation">,</span> replace <span class="operator">=</span> <span class="built_in">T</span><span class="punctuation">)</span><span class="punctuation">)</span></span><br><span class="line">    g4 <span class="operator">&lt;-</span> mean<span class="punctuation">(</span>sample<span class="punctuation">(</span>x <span class="operator">=</span> data<span class="operator">$</span>g4<span class="punctuation">,</span> size <span class="operator">=</span> <span class="number">10</span><span class="punctuation">,</span> replace <span class="operator">=</span> <span class="built_in">T</span><span class="punctuation">)</span><span class="punctuation">)</span></span><br><span class="line">    g5 <span class="operator">&lt;-</span> mean<span class="punctuation">(</span>sample<span class="punctuation">(</span>x <span class="operator">=</span> data<span class="operator">$</span>g5<span class="punctuation">,</span> size <span class="operator">=</span> <span class="number">10</span><span class="punctuation">,</span> replace <span class="operator">=</span> <span class="built_in">T</span><span class="punctuation">)</span><span class="punctuation">)</span></span><br><span class="line">    sigma_p <span class="operator">&lt;-</span> <span class="built_in">sum</span><span class="punctuation">(</span>g1<span class="punctuation">,</span> g2<span class="punctuation">,</span> g3<span class="punctuation">,</span> g4<span class="punctuation">,</span> g5<span class="punctuation">)</span></span><br><span class="line">    <span class="built_in">exp</span><span class="punctuation">(</span>ln<span class="punctuation">(</span><span class="number">350</span><span class="punctuation">)</span> <span class="operator">-</span> ln<span class="punctuation">(</span><span class="number">4</span><span class="operator">/</span><span class="number">3</span><span class="punctuation">)</span><span class="operator">*</span><span class="punctuation">(</span>sigma_p <span class="operator">-</span> <span class="number">0.5</span><span class="punctuation">)</span><span class="punctuation">)</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br></pre></td></tr></table></figure>
<h3 id="计算-the-bootstrap-percentile-interval">计算 the bootstrap percentile interval</h3>
<figure class="highlight r"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line">set.seed<span class="punctuation">(</span><span class="number">123</span><span class="punctuation">)</span></span><br><span class="line">res <span class="operator">&lt;-</span> vector<span class="punctuation">(</span>mode <span class="operator">=</span> <span class="string">&quot;list&quot;</span><span class="punctuation">,</span> <span class="built_in">length</span> <span class="operator">=</span> <span class="number">1000</span><span class="punctuation">)</span></span><br><span class="line"><span class="keyword">for</span> <span class="punctuation">(</span>i <span class="keyword">in</span> <span class="number">1</span><span class="operator">:</span><span class="number">1000</span><span class="punctuation">)</span><span class="punctuation">&#123;</span></span><br><span class="line">    res<span class="punctuation">[[</span>i<span class="punctuation">]</span><span class="punctuation">]</span> <span class="operator">&lt;-</span> ld50<span class="punctuation">(</span>data<span class="punctuation">)</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br><span class="line">res <span class="operator">&lt;-</span> sort<span class="punctuation">(</span>unlist<span class="punctuation">(</span>res<span class="punctuation">)</span><span class="punctuation">)</span></span><br><span class="line">hist<span class="punctuation">(</span>res<span class="punctuation">)</span></span><br><span class="line">quantile<span class="punctuation">(</span>res<span class="punctuation">,</span><span class="number">0.975</span><span class="punctuation">)</span></span><br><span class="line">quantile<span class="punctuation">(</span>res<span class="punctuation">,</span><span class="number">0.025</span><span class="punctuation">)</span></span><br></pre></td></tr></table></figure>
<h3 id="计算P值">计算P值</h3>
<figure class="highlight r"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br></pre></td><td class="code"><pre><span class="line">f_Rbisect <span class="operator">&lt;-</span> <span class="keyword">function</span><span class="punctuation">(</span>lst<span class="punctuation">,</span> value<span class="punctuation">)</span><span class="punctuation">&#123;</span></span><br><span class="line">    low<span class="operator">=</span><span class="number">1</span></span><br><span class="line">    high<span class="operator">=</span><span class="built_in">length</span><span class="punctuation">(</span>lst<span class="punctuation">)</span></span><br><span class="line">    <span class="keyword">if</span><span class="punctuation">(</span>high <span class="operator">==</span> low<span class="punctuation">)</span><span class="punctuation">&#123;</span><span class="built_in">return</span><span class="punctuation">(</span><span class="number">1</span><span class="punctuation">)</span><span class="punctuation">&#125;</span></span><br><span class="line">    mid<span class="operator">=</span><span class="built_in">length</span><span class="punctuation">(</span>lst<span class="punctuation">)</span><span class="operator">%/%</span><span class="number">2</span></span><br><span class="line">    <span class="keyword">if</span><span class="punctuation">(</span>lst<span class="punctuation">[</span>low<span class="punctuation">]</span> <span class="operator">==</span> value <span class="operator">&amp;</span> value <span class="operator">==</span> lst<span class="punctuation">[</span>low <span class="operator">+</span> <span class="number">1</span><span class="punctuation">]</span><span class="punctuation">)</span><span class="punctuation">&#123;</span></span><br><span class="line">        <span class="built_in">return</span><span class="punctuation">(</span>low <span class="operator">+</span> <span class="number">0.5</span><span class="punctuation">)</span></span><br><span class="line">    <span class="punctuation">&#125;</span></span><br><span class="line">    <span class="keyword">if</span><span class="punctuation">(</span>lst<span class="punctuation">[</span>high<span class="punctuation">]</span> <span class="operator">==</span> value <span class="operator">&amp;</span> value <span class="operator">==</span> lst<span class="punctuation">[</span>high <span class="operator">-</span> <span class="number">1</span><span class="punctuation">]</span><span class="punctuation">)</span><span class="punctuation">&#123;</span></span><br><span class="line">        <span class="built_in">return</span><span class="punctuation">(</span>high <span class="operator">-</span> <span class="number">0.5</span><span class="punctuation">)</span></span><br><span class="line">    <span class="punctuation">&#125;</span></span><br><span class="line">    <span class="keyword">if</span> <span class="punctuation">(</span>lst<span class="punctuation">[</span>low<span class="punctuation">]</span> <span class="operator">&gt;=</span> value<span class="punctuation">)</span><span class="punctuation">&#123;</span><span class="built_in">return</span><span class="punctuation">(</span>low<span class="punctuation">)</span><span class="punctuation">&#125;</span></span><br><span class="line">    <span class="keyword">if</span> <span class="punctuation">(</span>lst<span class="punctuation">[</span>high<span class="punctuation">]</span> <span class="operator">&lt;=</span> value<span class="punctuation">)</span><span class="punctuation">&#123;</span><span class="built_in">return</span><span class="punctuation">(</span>high<span class="punctuation">)</span><span class="punctuation">&#125;</span></span><br><span class="line">    <span class="keyword">while</span> <span class="punctuation">(</span>lst<span class="punctuation">[</span>mid<span class="punctuation">]</span> <span class="operator">!=</span> value<span class="punctuation">)</span> <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="keyword">if</span> <span class="punctuation">(</span>value <span class="operator">&gt;</span> lst<span class="punctuation">[</span>mid<span class="punctuation">]</span><span class="punctuation">)</span><span class="punctuation">&#123;</span></span><br><span class="line">            low  <span class="operator">&lt;-</span>  mid <span class="operator">+</span> <span class="number">1</span></span><br><span class="line">        <span class="punctuation">&#125;</span><span class="keyword">else</span><span class="punctuation">&#123;</span></span><br><span class="line">            high  <span class="operator">&lt;-</span>  mid <span class="operator">-</span> <span class="number">1</span></span><br><span class="line">        <span class="punctuation">&#125;</span></span><br><span class="line">        <span class="keyword">if</span> <span class="punctuation">(</span>high <span class="operator">&lt;=</span> low<span class="punctuation">)</span> <span class="punctuation">&#123;</span> <span class="keyword">break</span> <span class="punctuation">&#125;</span></span><br><span class="line">        mid  <span class="operator">&lt;-</span>  <span class="punctuation">(</span>low<span class="operator">+</span>high<span class="punctuation">)</span><span class="operator">%/%</span><span class="number">2</span></span><br><span class="line">    <span class="punctuation">&#125;</span></span><br><span class="line">    <span class="keyword">while</span><span class="punctuation">(</span><span class="built_in">T</span><span class="punctuation">)</span><span class="punctuation">&#123;</span></span><br><span class="line">        mid0 <span class="operator">&lt;-</span> mid <span class="operator">-</span> <span class="number">1</span></span><br><span class="line">        mid2 <span class="operator">&lt;-</span> mid <span class="operator">+</span> <span class="number">1</span></span><br><span class="line">        <span class="keyword">if</span><span class="punctuation">(</span>lst<span class="punctuation">[</span>mid0<span class="punctuation">]</span> <span class="operator">==</span> lst<span class="punctuation">[</span>mid2<span class="punctuation">]</span><span class="punctuation">)</span><span class="punctuation">&#123;</span></span><br><span class="line">            <span class="built_in">return</span><span class="punctuation">(</span>mid<span class="punctuation">)</span></span><br><span class="line">        <span class="punctuation">&#125;</span></span><br><span class="line">        <span class="keyword">if</span><span class="punctuation">(</span>lst<span class="punctuation">[</span>mid0<span class="punctuation">]</span> <span class="operator">&lt;=</span> value <span class="operator">&amp;</span> value <span class="operator">&lt;=</span>lst<span class="punctuation">[</span>mid<span class="punctuation">]</span><span class="punctuation">)</span><span class="punctuation">&#123;</span></span><br><span class="line">            <span class="keyword">if</span><span class="punctuation">(</span>lst<span class="punctuation">[</span>mid0<span class="punctuation">]</span> <span class="operator">==</span> lst<span class="punctuation">[</span>mid<span class="punctuation">]</span><span class="punctuation">)</span><span class="punctuation">&#123;</span></span><br><span class="line">                <span class="built_in">return</span><span class="punctuation">(</span>mid <span class="operator">-</span> <span class="number">0.5</span><span class="punctuation">)</span></span><br><span class="line">            <span class="punctuation">&#125;</span></span><br><span class="line">            t <span class="operator">=</span> <span class="punctuation">(</span>value <span class="operator">-</span> lst<span class="punctuation">[</span>mid0<span class="punctuation">]</span><span class="punctuation">)</span><span class="operator">/</span><span class="punctuation">(</span>lst<span class="punctuation">[</span>mid<span class="punctuation">]</span> <span class="operator">-</span> lst<span class="punctuation">[</span>mid0<span class="punctuation">]</span><span class="punctuation">)</span></span><br><span class="line">            <span class="built_in">return</span><span class="punctuation">(</span>mid0 <span class="operator">+</span> t<span class="punctuation">)</span></span><br><span class="line">        <span class="punctuation">&#125;</span></span><br><span class="line">        <span class="keyword">if</span><span class="punctuation">(</span>lst<span class="punctuation">[</span>mid<span class="punctuation">]</span> <span class="operator">&lt;=</span> value <span class="operator">&amp;</span> value <span class="operator">&lt;=</span> lst<span class="punctuation">[</span>mid2<span class="punctuation">]</span><span class="punctuation">)</span><span class="punctuation">&#123;</span></span><br><span class="line">            <span class="keyword">if</span><span class="punctuation">(</span>lst<span class="punctuation">[</span>mid<span class="punctuation">]</span> <span class="operator">==</span> lst<span class="punctuation">[</span>mid2<span class="punctuation">]</span><span class="punctuation">)</span><span class="punctuation">&#123;</span></span><br><span class="line">                <span class="built_in">return</span><span class="punctuation">(</span>mid <span class="operator">+</span> <span class="number">0.5</span><span class="punctuation">)</span></span><br><span class="line">            <span class="punctuation">&#125;</span></span><br><span class="line">            t <span class="operator">=</span> <span class="punctuation">(</span>value <span class="operator">-</span> lst<span class="punctuation">[</span>mid<span class="punctuation">]</span><span class="punctuation">)</span><span class="operator">/</span><span class="punctuation">(</span>lst<span class="punctuation">[</span>mid2<span class="punctuation">]</span> <span class="operator">-</span> lst<span class="punctuation">[</span>mid<span class="punctuation">]</span><span class="punctuation">)</span></span><br><span class="line">            <span class="built_in">return</span><span class="punctuation">(</span>mid <span class="operator">+</span> t<span class="punctuation">)</span></span><br><span class="line">        <span class="punctuation">&#125;</span></span><br><span class="line">        <span class="keyword">if</span><span class="punctuation">(</span>value <span class="operator">&lt;</span> lst<span class="punctuation">[</span>mid0<span class="punctuation">]</span><span class="punctuation">)</span><span class="punctuation">&#123;</span></span><br><span class="line">            mid  <span class="operator">&lt;-</span> mid0</span><br><span class="line">        <span class="punctuation">&#125;</span><span class="keyword">else</span><span class="punctuation">&#123;</span></span><br><span class="line">            mid  <span class="operator">&lt;-</span> mid2</span><br><span class="line">        <span class="punctuation">&#125;</span></span><br><span class="line">    <span class="punctuation">&#125;</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br></pre></td></tr></table></figure>
<figure class="highlight r"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">f_Rbisect<span class="punctuation">(</span>res<span class="punctuation">,</span> <span class="built_in">exp</span><span class="punctuation">(</span>ln<span class="punctuation">(</span><span class="number">350</span><span class="punctuation">)</span> <span class="operator">-</span> ln<span class="punctuation">(</span><span class="number">4</span><span class="operator">/</span><span class="number">3</span><span class="punctuation">)</span><span class="operator">*</span><span class="punctuation">(</span><span class="number">0</span><span class="operator">+</span><span class="number">0</span><span class="operator">+</span><span class="number">0.5</span><span class="operator">+</span><span class="number">0.8</span><span class="operator">+</span><span class="number">1</span> <span class="operator">-</span> <span class="number">0.5</span><span class="punctuation">)</span><span class="punctuation">)</span><span class="punctuation">)</span><span class="operator">/</span><span class="number">1000</span></span><br></pre></td></tr></table></figure>
                
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    var boardTop = boardCtn.offset().top;

    window.tocbot.init(Object.assign({
      tocSelector     : '#toc-body',
      contentSelector : '.markdown-body',
      linkClass       : 'tocbot-link',
      activeLinkClass : 'tocbot-active-link',
      listClass       : 'tocbot-list',
      isCollapsedClass: 'tocbot-is-collapsed',
      collapsibleClass: 'tocbot-is-collapsible',
      scrollSmooth    : true,
      includeTitleTags: true,
      headingsOffset  : -boardTop,
    }, CONFIG.toc));
    if (toc.find('.toc-list-item').length > 0) {
      toc.css('visibility', 'visible');
    }

    Fluid.events.registerRefreshCallback(function() {
      if ('tocbot' in window) {
        tocbot.refresh();
        var toc = jQuery('#toc');
        if (toc.length === 0 || !tocbot) {
          return;
        }
        if (toc.find('.toc-list-item').length > 0) {
          toc.css('visibility', 'visible');
        }
      }
    });
  });
</script>


  <script src=https://lib.baomitu.com/clipboard.js/2.0.11/clipboard.min.js></script>

  <script>Fluid.plugins.codeWidget();</script>


<script>
  Fluid.utils.createScript('https://jscdn.limour.top/npm/anchor-js@4.3.1/anchor.min.js', function() {
    window.anchors.options = {
      placement: CONFIG.anchorjs.placement,
      visible  : CONFIG.anchorjs.visible
    };
    if (CONFIG.anchorjs.icon) {
      window.anchors.options.icon = CONFIG.anchorjs.icon;
    }
    var el = (CONFIG.anchorjs.element || 'h1,h2,h3,h4,h5,h6').split(',');
    var res = [];
    for (var item of el) {
      res.push('.markdown-body > ' + item.trim());
    }
    if (CONFIG.anchorjs.placement === 'left') {
      window.anchors.options.class = 'anchorjs-link-left';
    }
    window.anchors.add(res.join(', '));

    Fluid.events.registerRefreshCallback(function() {
      if ('anchors' in window) {
        anchors.removeAll();
        var el = (CONFIG.anchorjs.element || 'h1,h2,h3,h4,h5,h6').split(',');
        var res = [];
        for (var item of el) {
          res.push('.markdown-body > ' + item.trim());
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        if (CONFIG.anchorjs.placement === 'left') {
          anchors.options.class = 'anchorjs-link-left';
        }
        anchors.add(res.join(', '));
      }
    });
  });
</script>


  <script>Fluid.plugins.imageCaption();</script>

  <script  src="/js/local-search.js" ></script>


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<script  src="/js/boot.js" ></script>


  <noscript>
    <div class="noscript-warning">Blog works best with JavaScript enabled</div>
  </noscript>
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</html>