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<body>
<h1 class="title toc-ignore">gateR: Flow/Mass Cytometry Gating via
Spatial Kernel Density Estimation</h1>
<h4 class="author">Ian D. Buller, Ph.D., M.A. (Github: <span class="citation">@idblr</span>)</h4>
<h4 class="date">2023-02-01</h4>
<p>The gateR package is a suite of R functions to identify significant
spatial clustering of mass and flow cytometry data used in immunological
investigations. The gateR package can be used for a panel of all surface
markers or a mixture of surface markers and functional readouts. The
gateR package performs a gating technique that estimates statistically
significant marker combination values within which one immunologically
distinctive group (i.e., disease case) is more associated than another
group (i.e., healthy control), successively, using various combinations
(i.e., “gates”) of markers to examine features of cells that may be
different between groups. For a two-group comparison, the gateR package
uses the spatial relative risk function estimated using the <a href="https://CRAN.R-project.org/package=sparr">sparr</a> package. The
gates are conducted in two-dimensional space comprised of two
markers.</p>
<p>Examples of a single condition with two groups:</p>
<ol style="list-style-type: decimal">
<li>Disease case vs. Healthy control</li>
<li>Time 2 vs. Time 1 (baseline)</li>
</ol>
<p>For a two-group comparison of two conditions, we estimate two
relative risk surfaces for one condition and then a ratio of the
relative risks. For example:</p>
<ol style="list-style-type: decimal">
<li>Estimate a relative risk surface for:
<ol style="list-style-type: decimal">
<li>Condition 2B vs. Condition 2A</li>
<li>Condition 1B vs. Condition 1A</li>
</ol></li>
<li>Estimate the relative risk surface for the ratio:</li>
</ol>
<p><span class="math display">\[\frac{(\frac{Condition2B}{Condition2A})}{(\frac{Condition1B}{Condition1A})}\]</span></p>
<p>Within areas where the relative risk exceeds an asymptotic normal
assumption, the gateR package has the functionality to examine the
features of these cells.</p>
<p>This vignette implements the gateR package using a randomly generated
data set. Please see the README.md file within the <a href="https://github.com/lance-waller-lab/gateR">gateR GitHub
repository</a> for an example using publicly available flow cytometry
data from the <a href="https://bioconductor.org/packages/release/data/experiment/html/flowWorkspaceData.html">flowWorkspaceData</a>
package available via <a href="https://bioconductor.org/">Bioconductor</a>. Here, we generate
data with two conditions, four markers, and two additional features.</p>
<p>We start with the necessary packages and seed for the vignette.</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a> loadedPackages <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">"gateR"</span>, <span class="st">"graphics"</span>, <span class="st">"stats"</span>, <span class="st">"tibble"</span>, <span class="st">"utils"</span>)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">invisible</span>(<span class="fu">lapply</span>(loadedPackages, library, <span class="at">character.only =</span> <span class="cn">TRUE</span>))</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">set.seed</span>(<span class="dv">1234</span>) <span class="co"># for reproducibility</span></span></code></pre></div>
<div id="generate-random-toy-data" class="section level3">
<h3>Generate random toy data</h3>
<p>A unique function randomly generates multivariate normal (MVN) data
around a central point. Parameters include the centroid coordinates
(<code>centre</code>), the number of observations to generate
(<code>ncell</code>), and the standard deviation of the normal
distribution (<code>scalar</code>).</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a> rand_mvn <span class="ot"><-</span> <span class="cf">function</span>(centre, ncell, scalar) {</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a> x0 <span class="ot"><-</span> centre[<span class="dv">1</span>] </span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a> y0 <span class="ot"><-</span> centre[<span class="dv">2</span>]</span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a> x1 <span class="ot"><-</span> <span class="fu">rep</span>(x0, ncell)</span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a> y1 <span class="ot"><-</span> <span class="fu">rep</span>(y0, ncell)</span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a> x2 <span class="ot"><-</span> x1 <span class="sc">+</span> stats<span class="sc">::</span><span class="fu">rnorm</span>(ncell, <span class="dv">0</span>, scalar) </span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a> y2 <span class="ot"><-</span> y1 <span class="sc">+</span> stats<span class="sc">::</span><span class="fu">rnorm</span>(ncell, <span class="dv">0</span>, scalar) </span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a> x <span class="ot"><-</span> <span class="fu">cbind</span>(x2, y2)</span>
<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a> }</span></code></pre></div>
<div id="gate-1-marker-1-and-marker-2" class="section level4">
<h4>Gate 1: Marker 1 and Marker 2</h4>
<p>At Condition 1, we generate 100,000 cases and 100,000 controls
(<code>ncell = 100000</code>) randomly MVN with a case centroid at
(<code>0.55, 0.55</code>) and a control centroid at
(<code>0.40, 0.40</code>) within a unit square window
<code>(0, 1)</code>, and cases have a more focal cluster
(<code>scalar = 0.05</code>) than controls
(<code>scalar = 0.15</code>).</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Initial parameters</span></span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a> ncell <span class="ot"><-</span> <span class="dv">100000</span> <span class="co"># number of observations per group per condition</span></span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a> c1_cas_center <span class="ot"><-</span> <span class="fu">c</span>(<span class="fl">0.55</span>, <span class="fl">0.55</span>)</span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a> c1_con_center <span class="ot"><-</span> <span class="fu">c</span>(<span class="fl">0.40</span>, <span class="fl">0.40</span>)</span>
<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a><span class="co"># V1 and V2 at Condition 1</span></span>
<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a> c1_cas <span class="ot"><-</span> <span class="fu">rand_mvn</span>(<span class="at">centre =</span> c1_cas_center, <span class="at">ncell =</span> ncell, <span class="at">scalar =</span> <span class="fl">0.05</span>)</span>
<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a> c1_con <span class="ot"><-</span> <span class="fu">rand_mvn</span>(<span class="at">centre =</span> c1_con_center, <span class="at">ncell =</span> ncell, <span class="at">scalar =</span> <span class="fl">0.15</span>)</span>
<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">par</span>(<span class="at">pty =</span> <span class="st">"s"</span>)</span>
<span id="cb3-9"><a href="#cb3-9" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(c1_con,</span>
<span id="cb3-10"><a href="#cb3-10" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"blue"</span>,</span>
<span id="cb3-11"><a href="#cb3-11" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">1</span>),</span>
<span id="cb3-12"><a href="#cb3-12" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">1</span>),</span>
<span id="cb3-13"><a href="#cb3-13" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Gate 1, Condition 1"</span>,</span>
<span id="cb3-14"><a href="#cb3-14" aria-hidden="true" tabindex="-1"></a> <span class="at">xlab =</span> <span class="st">"V1"</span>,</span>
<span id="cb3-15"><a href="#cb3-15" aria-hidden="true" tabindex="-1"></a> <span class="at">ylab =</span> <span class="st">"V2"</span>)</span>
<span id="cb3-16"><a href="#cb3-16" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">points</span>(c1_cas, <span class="at">col =</span> <span class="st">"orangered4"</span>)</span></code></pre></div>
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" /><!-- --></p>
<p>At Condition 2, we generate 100,000 cases and 100,000 controls
(<code>ncell = 100000</code>) randomly MVN with a case centroid at
(<code>0.45, 0.45</code>) and a control centroid at
(<code>0.40, 0.40</code>) within a unit square window
<code>(0, 1)</code>, and cases have a more focal cluster
(<code>scalar = 0.05</code>) than controls
(<code>scalar = 0.10</code>).</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Initial parameters</span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a> c2_cas_center <span class="ot"><-</span> <span class="fu">c</span>(<span class="fl">0.45</span>, <span class="fl">0.45</span>)</span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a> c2_con_center <span class="ot"><-</span> <span class="fu">c</span>(<span class="fl">0.40</span>, <span class="fl">0.40</span>)</span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a><span class="co"># V1 and V2 at Condition 2</span></span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a> c2_cas <span class="ot"><-</span> <span class="fu">rand_mvn</span>(<span class="at">centre =</span> c2_cas_center, <span class="at">ncell =</span> ncell, <span class="at">scalar =</span> <span class="fl">0.05</span>)</span>
<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a> c2_con <span class="ot"><-</span> <span class="fu">rand_mvn</span>(<span class="at">centre =</span> c2_con_center, <span class="at">ncell =</span> ncell, <span class="at">scalar =</span> <span class="fl">0.10</span>)</span>
<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">par</span>(<span class="at">pty =</span> <span class="st">"s"</span>)</span>
<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(c2_con,</span>
<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"cornflowerblue"</span>,</span>
<span id="cb4-10"><a href="#cb4-10" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">1</span>),</span>
<span id="cb4-11"><a href="#cb4-11" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">1</span>),</span>
<span id="cb4-12"><a href="#cb4-12" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Gate 1, Condition 2"</span>,</span>
<span id="cb4-13"><a href="#cb4-13" aria-hidden="true" tabindex="-1"></a> <span class="at">xlab =</span> <span class="st">"V1"</span>,</span>
<span id="cb4-14"><a href="#cb4-14" aria-hidden="true" tabindex="-1"></a> <span class="at">ylab =</span> <span class="st">"V2"</span>)</span>
<span id="cb4-15"><a href="#cb4-15" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">points</span>(c2_cas, <span class="at">col =</span> <span class="st">"orangered1"</span>)</span></code></pre></div>
<p><img 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" /><!-- --></p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="co"># compile data</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a> df_full <span class="ot"><-</span> tibble<span class="sc">::</span><span class="fu">tibble</span>(<span class="st">"id"</span> <span class="ot">=</span> <span class="fu">seq</span>(<span class="dv">1</span>, ncell <span class="sc">*</span> <span class="dv">2</span> <span class="sc">*</span> <span class="dv">2</span>, <span class="dv">1</span>),</span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a> <span class="st">"group"</span> <span class="ot">=</span> <span class="fu">factor</span>(<span class="fu">c</span>(<span class="fu">rep</span>(<span class="st">"case"</span>, ncell <span class="sc">*</span> <span class="dv">2</span>),</span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">rep</span>(<span class="st">"control"</span>, ncell <span class="sc">*</span> <span class="dv">2</span>))),</span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a> <span class="st">"condition"</span> <span class="ot">=</span> <span class="fu">factor</span>(<span class="fu">c</span>(<span class="fu">rep</span>(<span class="st">"2"</span>, ncell), <span class="fu">rep</span>(<span class="st">"1"</span>, ncell),</span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">rep</span>(<span class="st">"2"</span>, ncell), <span class="fu">rep</span>(<span class="st">"1"</span>, ncell))),</span>
<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a> <span class="st">"V1"</span> <span class="ot">=</span> <span class="fu">c</span>(c2_cas[ , <span class="dv">1</span>], c1_cas[ , <span class="dv">1</span>], c2_con[ , <span class="dv">1</span>], c1_con[ , <span class="dv">1</span>]),</span>
<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a> <span class="st">"V2"</span> <span class="ot">=</span> <span class="fu">c</span>(c2_cas[ , <span class="dv">2</span>], c1_cas[ , <span class="dv">2</span>], c2_con[ , <span class="dv">2</span>], c1_con[ , <span class="dv">2</span>]))</span>
<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-10"><a href="#cb5-10" aria-hidden="true" tabindex="-1"></a> <span class="fu">rm</span>(c2_cas, c1_cas, c2_con, c1_con) <span class="co"># conserve memory</span></span></code></pre></div>
</div>
<div id="gate-2-marker-3-and-marker-4" class="section level4">
<h4>Gate 2: Marker 3 and Marker 4</h4>
<p>At Condition 1, we generate 100,000 cases and 100,000 controls
(<code>ncell = 100000</code>) randomly MVN with a case centroid at
(<code>0.55, 0.55</code>) and a control centroid at
(<code>0.50, 0.50</code>) within a unit square window
<code>(0, 05)</code>, but both have the same amount of spread
(<code>scalar = 0.10</code>).</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Initial parameters</span></span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a> c1_cas_center <span class="ot"><-</span> <span class="fu">c</span>(<span class="fl">0.55</span>, <span class="fl">0.55</span>)</span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a> c1_con_center <span class="ot"><-</span> <span class="fu">c</span>(<span class="fl">0.50</span>, <span class="fl">0.50</span>)</span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="co"># V3 and V4 at Condition 1</span></span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a> c1_cas <span class="ot"><-</span> <span class="fu">rand_mvn</span>(<span class="at">centre =</span> c1_cas_center, <span class="at">ncell =</span> ncell, <span class="at">scalar =</span> <span class="fl">0.05</span>)</span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a> c1_con <span class="ot"><-</span> <span class="fu">rand_mvn</span>(<span class="at">centre =</span> c1_con_center, <span class="at">ncell =</span> ncell, <span class="at">scalar =</span> <span class="fl">0.10</span>)</span>
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">par</span>(<span class="at">pty =</span> <span class="st">"s"</span>)</span>
<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(c1_con,</span>
<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"blue"</span>,</span>
<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">1</span>),</span>
<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">1</span>),</span>
<span id="cb6-12"><a href="#cb6-12" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Gate 2, Condition 1"</span>,</span>
<span id="cb6-13"><a href="#cb6-13" aria-hidden="true" tabindex="-1"></a> <span class="at">xlab =</span> <span class="st">"V3"</span>,</span>
<span id="cb6-14"><a href="#cb6-14" aria-hidden="true" tabindex="-1"></a> <span class="at">ylab =</span> <span class="st">"V4"</span>)</span>
<span id="cb6-15"><a href="#cb6-15" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">points</span>(c1_cas, <span class="at">col =</span> <span class="st">"orangered4"</span>)</span></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>At Condition 2, we generate 100,000 cases and 100,000 controls
(<code>ncell = 100000</code>) randomly with a case centroid at
(<code>0.65, 0.65</code>) and control a centroid at
(<code>0.50, 0.50</code>) within a unit square window
<code>(0, 1)</code>, and cases have a more focal cluster
(<code>scalar = 0.05</code>) than controls
(<code>scalar = 0.10</code>).</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Initial parameters</span></span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a> c2_cas_center <span class="ot"><-</span> <span class="fu">c</span>(<span class="fl">0.65</span>, <span class="fl">0.65</span>)</span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a> c2_con_center <span class="ot"><-</span> <span class="fu">c</span>(<span class="fl">0.50</span>, <span class="fl">0.50</span>)</span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a><span class="co"># V3 and V4 at Condition 2</span></span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a> c2_cas <span class="ot"><-</span> <span class="fu">rand_mvn</span>(<span class="at">centre =</span> c2_cas_center, <span class="at">ncell =</span> ncell, <span class="at">scalar =</span> <span class="fl">0.05</span>)</span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a> c2_con <span class="ot"><-</span> <span class="fu">rand_mvn</span>(<span class="at">centre =</span> c2_con_center, <span class="at">ncell =</span> ncell, <span class="at">scalar =</span> <span class="fl">0.10</span>)</span>
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">par</span>(<span class="at">pty =</span> <span class="st">"s"</span>)</span>
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(c2_con,</span>
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"cornflowerblue"</span>,</span>
<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">1</span>),</span>
<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">1</span>),</span>
<span id="cb7-12"><a href="#cb7-12" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Gate 2, Condition 2"</span>,</span>
<span id="cb7-13"><a href="#cb7-13" aria-hidden="true" tabindex="-1"></a> <span class="at">xlab =</span> <span class="st">"V3"</span>,</span>
<span id="cb7-14"><a href="#cb7-14" aria-hidden="true" tabindex="-1"></a> <span class="at">ylab =</span> <span class="st">"V4"</span>)</span>
<span id="cb7-15"><a href="#cb7-15" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">points</span>(c2_cas, <span class="at">col =</span> <span class="st">"orangered1"</span>)</span></code></pre></div>
<p><img 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" /><!-- --></p>
<p>Compile the toy data into a data frame</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a> df_full<span class="sc">$</span>V3 <span class="ot"><-</span> <span class="fu">c</span>(c2_cas[ , <span class="dv">1</span>], c1_cas[ , <span class="dv">1</span>], c2_con[ , <span class="dv">1</span>], c1_con[ , <span class="dv">1</span>])</span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a> df_full<span class="sc">$</span>V4 <span class="ot"><-</span> <span class="fu">c</span>(c2_cas[ , <span class="dv">2</span>], c1_cas[ , <span class="dv">2</span>], c2_con[ , <span class="dv">2</span>], c1_con[ , <span class="dv">2</span>])</span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">rm</span>(c2_cas, c1_cas, c2_con, c1_con) <span class="co"># conserve memory</span></span></code></pre></div>
<p>Generate random values for two example cytokines and append to the
data frame.</p>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Two Cytokines</span></span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a> Z1 <span class="ot"><-</span> stats<span class="sc">::</span><span class="fu">rchisq</span>(ncell <span class="sc">*</span> <span class="dv">4</span>, <span class="at">df =</span> <span class="dv">5</span>) <span class="co"># Random Chi-square distribution</span></span>
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a> Z2 <span class="ot"><-</span> stats<span class="sc">::</span><span class="fu">rnorm</span>(ncell <span class="sc">*</span> <span class="dv">4</span>, <span class="dv">0</span>, <span class="dv">1</span>) <span class="co"># Random Gaussian distribution</span></span>
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a><span class="co"># Append to data.frame</span></span>
<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a> df_full<span class="sc">$</span>Z1 <span class="ot"><-</span> Z1</span>
<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a> df_full<span class="sc">$</span>Z2 <span class="ot"><-</span> Z2</span>
<span id="cb9-7"><a href="#cb9-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">rm</span>(Z1, Z2) <span class="co"># conserve memory</span></span>
<span id="cb9-8"><a href="#cb9-8" aria-hidden="true" tabindex="-1"></a><span class="co"># Visualize histograms by the two group conditions</span></span>
<span id="cb9-9"><a href="#cb9-9" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">2</span>, <span class="dv">2</span>), <span class="at">pty =</span> <span class="st">"s"</span>)</span>
<span id="cb9-10"><a href="#cb9-10" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(df_full<span class="sc">$</span>Z1[df_full<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span> </span>
<span id="cb9-11"><a href="#cb9-11" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> df_full<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"1"</span>]),</span>
<span id="cb9-12"><a href="#cb9-12" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 1 of Cases at Condition 1"</span>)</span>
<span id="cb9-13"><a href="#cb9-13" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(df_full<span class="sc">$</span>Z1[df_full<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span> </span>
<span id="cb9-14"><a href="#cb9-14" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> df_full<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"2"</span>]),</span>
<span id="cb9-15"><a href="#cb9-15" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 1 of Cases at Condition 2"</span>)</span>
<span id="cb9-16"><a href="#cb9-16" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(df_full<span class="sc">$</span>Z1[df_full<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"control"</span></span>
<span id="cb9-17"><a href="#cb9-17" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> df_full<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"1"</span>]),</span>
<span id="cb9-18"><a href="#cb9-18" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 1 of Controls at Condition 1"</span>)</span>
<span id="cb9-19"><a href="#cb9-19" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(df_full<span class="sc">$</span>Z1[df_full<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"control"</span></span>
<span id="cb9-20"><a href="#cb9-20" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> df_full<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"2"</span>]),</span>
<span id="cb9-21"><a href="#cb9-21" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 1 of Controls at Condition 2"</span>)</span>
<span id="cb9-22"><a href="#cb9-22" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(df_full<span class="sc">$</span>Z2[df_full<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span></span>
<span id="cb9-23"><a href="#cb9-23" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> df_full<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"1"</span>]),</span>
<span id="cb9-24"><a href="#cb9-24" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 2 of Cases at Condition 1"</span>)</span>
<span id="cb9-25"><a href="#cb9-25" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(df_full<span class="sc">$</span>Z2[df_full<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span> </span>
<span id="cb9-26"><a href="#cb9-26" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> df_full<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"2"</span>]),</span>
<span id="cb9-27"><a href="#cb9-27" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 2 of Cases at Condition 2"</span>)</span>
<span id="cb9-28"><a href="#cb9-28" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(df_full<span class="sc">$</span>Z2[df_full<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"control"</span> </span>
<span id="cb9-29"><a href="#cb9-29" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> df_full<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"1"</span>]),</span>
<span id="cb9-30"><a href="#cb9-30" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 2 of Controls at Condition 1"</span>)</span>
<span id="cb9-31"><a href="#cb9-31" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(df_full<span class="sc">$</span>Z2[df_full<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"control"</span> </span>
<span id="cb9-32"><a href="#cb9-32" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> df_full<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"2"</span>]),</span>
<span id="cb9-33"><a href="#cb9-33" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 2 of Controls at Condition 2"</span>)</span></code></pre></div>
<p><img 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" 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" /></p>
<p>The toy data frame has nine columns (id, groups, markers, and
cytokines).</p>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a> utils<span class="sc">::</span><span class="fu">head</span>(df_full)</span></code></pre></div>
<pre><code>## # A tibble: 6 × 9
## id group condition V1 V2 V3 V4 Z1 Z2
## <dbl> <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 case 2 0.491 0.402 0.677 0.586 4.35 -0.488
## 2 2 case 2 0.407 0.493 0.714 0.698 8.61 0.279
## 3 3 case 2 0.508 0.409 0.547 0.644 6.79 -0.786
## 4 4 case 2 0.423 0.480 0.657 0.656 1.04 -0.552
## 5 5 case 2 0.367 0.420 0.635 0.637 4.10 0.239
## 6 6 case 2 0.499 0.405 0.547 0.656 6.99 0.0472</code></pre>
</div>
</div>
<div id="for-two-conditions" class="section level3">
<h3>For two conditions</h3>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Initial parameters</span></span>
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a> alpha <span class="ot"><-</span> <span class="fl">0.05</span></span>
<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a> vars <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">"V1"</span>, <span class="st">"V2"</span>, <span class="st">"V3"</span>, <span class="st">"V4"</span>)</span>
<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a> p_correct <span class="ot"><-</span> <span class="st">"correlated Bonferroni"</span></span>
<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">set.seed</span>(<span class="dv">1234</span>) <span class="co"># for reproducibility</span></span>
<span id="cb12-6"><a href="#cb12-6" aria-hidden="true" tabindex="-1"></a> df_full <span class="ot"><-</span> <span class="fu">as.data.frame</span>(df_full)</span>
<span id="cb12-7"><a href="#cb12-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb12-8"><a href="#cb12-8" aria-hidden="true" tabindex="-1"></a><span class="co"># Gates 1 and 2</span></span>
<span id="cb12-9"><a href="#cb12-9" aria-hidden="true" tabindex="-1"></a> start_time <span class="ot"><-</span> <span class="fu">Sys.time</span>() <span class="co"># record start time</span></span>
<span id="cb12-10"><a href="#cb12-10" aria-hidden="true" tabindex="-1"></a> out_gate <span class="ot"><-</span> gateR<span class="sc">::</span><span class="fu">gating</span>(<span class="at">dat =</span> df_full,</span>
<span id="cb12-11"><a href="#cb12-11" aria-hidden="true" tabindex="-1"></a> <span class="at">vars =</span> vars,</span>
<span id="cb12-12"><a href="#cb12-12" aria-hidden="true" tabindex="-1"></a> <span class="at">n_condition =</span> <span class="dv">2</span>,</span>
<span id="cb12-13"><a href="#cb12-13" aria-hidden="true" tabindex="-1"></a> <span class="at">plot_gate =</span> <span class="cn">TRUE</span>,</span>
<span id="cb12-14"><a href="#cb12-14" aria-hidden="true" tabindex="-1"></a> <span class="at">alpha =</span> alpha,</span>
<span id="cb12-15"><a href="#cb12-15" aria-hidden="true" tabindex="-1"></a> <span class="at">p_correct =</span> p_correct,</span>
<span id="cb12-16"><a href="#cb12-16" aria-hidden="true" tabindex="-1"></a> <span class="at">c1n =</span> <span class="st">"case"</span>, <span class="co"># level "case" as the numerator of first condition</span></span>
<span id="cb12-17"><a href="#cb12-17" aria-hidden="true" tabindex="-1"></a> <span class="at">c2n =</span> <span class="st">"2"</span>) <span class="co"># level "2" as the numerator of second condition</span></span>
<span id="cb12-18"><a href="#cb12-18" aria-hidden="true" tabindex="-1"></a> end_time <span class="ot"><-</span> <span class="fu">Sys.time</span>() <span class="co"># record end time</span></span>
<span id="cb12-19"><a href="#cb12-19" aria-hidden="true" tabindex="-1"></a> total_time <span class="ot"><-</span> end_time <span class="sc">-</span> start_time <span class="co"># calculate duration of gating() example</span></span></code></pre></div>
<p><img src="data:image/png;base64,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" 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XkSIVYkeWK/33AXRfdFZuO+G5yDfm0W30jd9zLvqwQO8Bel191bkCe5x34luZrVuKiSSK+kn3cfuWcga68uDXhqBauLEj737FDfEPyeDRZdrbIwub4DfEFbhdGDBUnCh7mw/c+ITIBhh4TpHeCHS7ab9llSP2yUP6SXbHAO+rWZhr5259jqChXmCO/hAE8ImVWKRr2DnY2V7KNYQYKDghxG6gku+/Sm9sk8oxc9IpYdN0v5rFPp4NY75UX/rUuybJRu4M9pRT8U936m7dumzz5UMLXW/QzAND0CbfCEkBnF+1OqCMjd1YUbLmpS2N/fXl/oaz7fvrGgihTub98o2GV/fWHhxna6zfqCshaf87gD451Jb75jqbReQm5rnfrBuZI6F6C+GwDYXTXqfLG/v31jYamHgbxvm8tbe3t71toeZe3yvZhtOMATQmYTHyKZ1jb1VWW68xZ7d85eOH3qjUVFTqRJ1uSNjGfnxY47ELuPOC/Uff8Usl/8FCLdKc8qIa6nfTcAdlelPFY2f/N+efTMAG3mdvHOtelDgfN4HdmFm3I4wBNCZpN8bOX82p611tqtNRzu7m6uLuVCKspY2dlangeAeR8mko+bXHlwzW2TCXYZ/rh+8yIKc1ocPo3FRaS2g4MkH0WvlFMXwT1RLG48sOxSQaw9JEN8zxQYQx1i1SeMzIYLAWAAqoMDPCFkJilONXG+jNHpJABKI1oLYiLVMHTRTNU9mXf5F/aSpxA33I5L6vZPjJ1U5T1XCOGhKqC9uPFA/4s/o3CAJ4QQYRQZo4tTI430uMUh7cMNlb6T42FcibEByNVKR/eDi+XhrDeNSXeAEEKqgcpb7EeN80wnD52FckTHHRnz91wHikdoOae+GyzcuwjsAys7vVzihjuocLi55KcCOLr3hQqeEEIAXCRjdMbenm9mbMcdjMPN1aWlpay69253hZ1089xq/r4r4KDfBv3zNy9vdXsO9D0otN2do/tAjCrejhBCporSFIsumNy7oqltyuLgkfOiz8dm6wj17KH7H/eCqANIDpkkPr3kvJL3K/0S3ZRt4M9wsfu6lGehGbjNXo30zPM1c3CA74H8VNxPabK/mwscfaA8WkXtH+ysbORSTowkR1Qm/UXPZHrDbV+QtqSXKXOs+a4KL1jmkg7WAP9OjY/yzCp5+g/wxTsU7KP362q2VzOjOdeSO6AoseZFU9UOlxi7f5u90vvkskYzmZ21lolueuBiLHVBttnhcHd1aeHG9lPjaHpzKZP+IqnZcrHtD3dXl7zjTSUZ9pK6yoD9q+6R8+KLL6YO1/NreyV5i/vUClzZUQmPF1c2dg4GNT1f7LhDHaEr2fJOzynurh3y59R3g+WtgvzNvWfVe7XpHRV642b1Z/PPdgGTfsKoLN1ZjadWwZ+n/fzhRqXgh01hPcj2XTk+e/cxlQGX+02e4xtkYu2xc2G5xwnhasF7JgsVfAm771zfR/GDoKpXmC9neLi7uapCWJaWVrUAU4UjVVXE7DZ9j+ECSJXDTBJSmipbv2p1t7BYZZ/2vRTevlFQfrFHz/sWxkxyh7mUH/NrD/QUKv23P9xc8jk+F8tn8NIOugwiixtlEiu9crl1yWkN8D1mLkXZJT3c7Cp9mfkqnMAcXWYQ0s2y/JyYFaUuiLsi9XvCpJ8wKkreOjeIsa1ko952re5tetqaVnZsXnYUuJ4oYTGYdU21nzuJlZ1BjYR9dX65lbx4l/7b+0f2HuX1cs31fMAv0mRlperyFFezG+aS9jouGTkXdHWggq8UGbcpQgVfQj5JtSJJKO0zUt5I9NjgCaUT31L3V15t4yYPtFtudiTw4SROdqgczt2rCvvfr/3lra4/W1mpW5pPewCGTTc90PbXF1d2DnyKrp5H95mrCzJbnpce36Oi6JL6ryHJ1e1/Tup6MrH22HFZY0dl6iYTxN3gI7y9px4O8IX0yMO0uPHQWknS6SESSq886HNGOj+fdBsfn6qTW2czV/t95LAZ35PsquLxvW/7PSnPp430ClxifOr82tYggzvSB5tsZsuL0eN77EPy7HLzkYPDQwDzPjC44OJxCnmMyHUfyieue+dz705Gifvzw+8ihQN8Eb2yTGTyQuTyHg+YULqgImL3sTODs1NyyT7a+9c9jKysrPhVPcf3QdrvQe982lUmebAZ4fN9j++xH+kTwfaNhYUiEzzAxNqEkAvAAX5IemWWGkki64GSOLvRZP/hRw/duLXy1gfuXXSr8nWVh22/hiTje9FTTx96WArOz/zaQ1nbyP7+9vqNBbO0ycliQsgo4AA/JD3kqkoobfe21taW58+jFAfTbIlx9p2PSNjnvQve5/qpd7pCjcWepBPVhD1kbuHjyLDbl3OR8X1czC9v7Vl7sLOhg4Wxv87Id0LIKOAAPyzlSadHk1C6sBKVH55S/Ai/vZ2Ehbg9t7d7je+Dtj8mBkk3fZHtyxhifC94AhrrrMf88pqr5emD/KfE5kEIqTgc4IvoWe5x+8aqWEoPd1dv6GHDjwzODfpwd7Pcya4H3h5ecJyizQD40U6vKo8EHaT988r8vnHw3vK8//A7dw8BHG56X3I38na10Hf7Aft1jict/1BxuOud7y9E9yX14fZLid398OCpXC+HLltCCCEeDvCF+L/GxWzfWDDGGF+SeGVH3DZTt6n1BWPMwo318+m+1Dk/e5zyPvrRTq3qMSIM0H7yhLO+kE90cyHm1x6S1CJy8IV18SDYKfN8HXb73gwyTnZ9jef/Hrua7bqky1tigd9fl2/BGJeQd3HjoZwX4GhqihFCZgsO8IXkk1QnrOyoZMnZ/MsjSyi9vHWws5EcY3Flp8hbLxmI0j//6areArd/+8sPpA5gi8AobcJ9U1hfcPsihppjL/gaz+EsmSN3SZe3stnBC/KDM7E2IeT8GGvtpPtQSVxyUdYcJpPjcHNpYX2fP0JCyLmggi+BSarJxGFibULIBeAAX4av1skUlmRCiOs/x3dCyPngAF8Kk1STScLE2oSQi0EbPCGEEFJDqOAJIYSQGsIBnhBCCKkhHOAJIYSQGtKYdAcuD2PMpLtAJsyt7/97AO78nn816Y5cEpX1sOHNSB5//HEAr3jFKybdkctgUnfiDA3wqPDfO3I53P6Bv4+Z+RlUfBCdkW+BlPHEE09gNn4GE7wTZ8iL3pgZOtlZ4+R7vxmAlRsp8xoAsGFowwYA22gmr3GzBSButJI1d3/rP5pE38dFlX/wVe4buSAycl+El7/85SPpSUWY4K99hm4z/k2ZLjqrbwIA+cZCGacbABCGAGwQIAgB2DBMVrpBHQaAdYsBAASBG+Bl30YDgA1Ua2EDQOyH/xd82z+9hBMcN1X+wVe5byTPxcfsc1ODwX6Cv3Y62RFCCCE1ZIaeoykaKsLRO74NgOm0AZj2mXptm3YbgIk6ABDHgFfwgSj4IFkGjOh1p+AD9ZGsV1P0CAIbyGZe/SdtBuncgFP2jVbcnAPw/L/3z8d3ES6BKv/gq9y3mWKC0nwoplrHU8ETQgghZJTMlhc9GSvPvOt7kUhz99oROW6cHI8BGBsD3l4uZnULiOYWbd0JgUTB23Rj7YxqrXxkoijZ2KoNsp6r/p3apfkj7x7ViRNSKaZFlydMtUCvMlTwhBBCSA2ZIUsYzX6Xz8n3frMT4oIIaPkW3GsMAHEEwEQxnNxPRTli/ZXp3cVZ3n9gtHkeQPJpeQSqfBKkXvS22QRgmy3bmoOPo5MIuju/64eGOO1qUOUffJX7VkumTtP3YOrkPm3whBBCCBklM/QcTdHQl49/ZA/AlePnAMwdPwegeXIbQPP4OQDh6RGAxvFtAM3Pfvrag//H4C23//7fgFfD3pSe6ngnyuMYYlDPC31R88qOjjgW8e1a09odeoZANraZCQP9M5AdJRpeJHuzKQreCXqXCacBYKhTnjhV/sFXuW8VYSjNPZSorYGany4RTwVPCCGEkFEyQ8/RFA1lfOyxXwNwpXPr6tHnAFx99jMAwvYJgMbpMYDPe9s/nGgHByX6+tcBXu6LNI/Eut9x8fRHxwCCnZsT6uClUuUffJX7NkH6auspUq4DzhNM0RmdGyp4QgghhIySGXqOpmgo47G9JwHcaZ+5cvQMgLmjZ+Dt7mJxv/b7/y+AuDUHoPG5zwCwzdaVf/ajAE7+p28EYJyvu7q83lLu4tS18dt9CwaA6drF5s3nUdp+3oKeHFOb50W1dzoAIKnxztrOun96BsCcnAEw7z84x7WaIqr8g69y3ybIua3jooOn17hebx1PBU8IIYSQUTJDz9EUDXUifstL7LVrQJIRzyeoR1b6tzsAcNZGp4Mk7V2kZgIkF30jBIBmEwBaTTvXSt66CrPNBgA0utfM/YufGvOJnp8q/+Cr3DcyFBWZNqjyHAAVPCGEEEJGyQw9R1M01AP71/4SADvXwpU5ICkVr2LinT9ADMB0IgA4aztjvAh6l75eFLwBgIbEwTcBoNlw2l3eNtJCc5llOWIUNd/16FjP99xU+Qdf5b6RAamIdtdUU8dTwRNCCCFklMzQczRFw+XT/o77fI12AImXvU1eXJU5sZeftcMf/eWLHC7+6pcB2dJzYm7vtJ12l9dOsYJH02ekF4u7s8HntLu8yo5nbXN6CiD89x+6SM/HQZV/8FXuWy05h9q+oBqeoL6vmo6ngieEEELIKJmh52iKhvFx9vavhc/lDtMl2XOh7QWp5iXfXISOD1sHTPsMAM5cXXkA4gnfHQev68Xl5wmcgu+k7vQo0vGyWWgA4Ooc5loQMz+8Xm8qBS/6Xmh3TLudtBa8+8lBLtflUOUffJX7Nu1U0DQ+Eaqj46ngCSGEEDJKZug5mqJhtJw98DeRVGATE7Uzt8trIqxTi3tWwUswegypBA8g6hhR8C793BkAtM/UslSLd5XlLEz2QO4wLu2ds+7HbkfZV9T2mfKlF6TnzRAAWi3b8u708A72ofKcD9VjcbvLut8BEPz8Jwa6gmOmyj/4KvdtGqFqL6MKOp4KHrurxrG6CxxuLhmjVxBCLgvejITUg0b/TcbP4ebSjZsbB3Zt3v1xAVZ27N4yAFmxtHGwtzY/4V7WhU98+EPw5d7nTm4BaB7L63ON0yMA4ckRgEBez06SV6OKtSMI7B13Ab6SuuSDkwLtgUoqp9U1sgpeKWzjbPAd22kAMGEDgGk0AJh26tAudm4r0r/wENYCsF015gFEMSKls50lPrX3448/C8Dc/BPV7ozCm/HSoOwuowqyux5UQcEfPvrw/uL998nfjOW3rgCLGw8s+0+XH9hY3H/40cOJdY+Q2YE3IyH1oQoK/uCpfVx/UGuC6/eod/P3XMf+UwcAVcNI+NLXvm6QzW79y7fDm9hjkeais52ANs7irrR73gZvjemS2Mhq60S7y6txpu4GAHTEcb0JwDTb6JpCKMSmRe1sxuofi5nfSkb6TqrgnaZ/3l0A7N94ieuYdFlOJ0ynJVy+vIbKmhfFGQ9/V8IuAhC855Ol/awuvBkvj8F16qxp/dGe7yzPB1RhgF+4dxEPP32I5eSPxk397vDpm1i8f2FCnasHT370MQBXj54B0Dq5lbw2Tm4DCMS1Le4EkRpu73wBgCBKo9Tc+tj5plnTa4D3ywUDvJ6izw3wHSST850m/GBso1Z66MIBXq9UyyYZ5+VwnQ4AK5PzHR0yl76adtvF5n32WQDmV397kCtcF3gzjp1ZG61HyCwP1eejClP08/fdn8777T6yDeyvvzNx5snMGRJCxglvRkLqQ1WCVXZXzY1tAMDKjt1a2FxaWN93H63s2K3l8j0HhpE5mj/6qX+DJPrLxgCCKNJ6OoiUao+6Fbyx1sokvHKsczpeK/tEwesUNBIaV6DgIzdhIG/VtIGEtBmrFHz3N9mt4I1aBrx9oaNaFgXf6U6kY9odX5mmnRzaIR6FMkUv0/VwSXJcC2raX4fPmfcfFH4LY+XcP3jejJcJBf1lMpE5gAn+2mfoNuPfFA0HeA7wE6TKfbtkOMBfJhzgawv/pgif+rmfBBJDeAQgkJ7PSgQAACAASURBVMEvzg7wZYO9M4THMoZ667uywavlnJMd4N30MgO8P1bB84Qf+5Md0zHbZv6X+Si1vvv1cjjXWlo6Vpahhnw1wEuu3DMA5vQMgLl1BMC87z+XXVu7+IWAc7JznZEcPuJd+OQfle04Dqr8g69y3y4NDu0XpPdo3ePyXvIwz0Q3vTjcXGKCDUKqAG9GQqaIuj1HG9MrSUnNTnZYDt/3s1B6PXntUvDOlz7upMtOu2sx7RLFWiOZXLt1vPXBclZN0Rs9Ra91vJ8bKLILpP30OyZfop6r706Ia7o+dRMGeopeqfYoEz5nlIJ3mXBEx8s8vLQYJtMVFnBJeHpP1OOsYz78u/2/pxExWZXc+07EzN+MlO8T59J0/ATvxCqEyY2SHtex718cQsio6P0XjTcjIZdA3RR8D2bT7Pdb738PgChsAgiUKA+KFHxmpXap01Z59+ryxeoktXHeHt8jDj5niQ8SG3yuA15/x12NIBX0uXK07oBujbPfJ3Vpi7R7Uuomq+C7a96IPR4nJwDM0UnBRRfRf6oj7CMAOD7DrVMA5g+PC/YaNVX+wVe5b+ODqr2CXIKOpw0eXTUtFDT4EXLJ8GYkpA5UYor+cHNpYX1/cePA7uVSaOyuGmMWWd/iXDy292TrjhcCCKMzAGEkajsCYJVt27rIt8gqgSty3Kn2sAHAZsLkYqeZJVguY4NPg+VyYXIqVa1bTq3+NgiNOqi04yS+BMjF2rhutd09q+OVqd7b4DO1bSRfXhgCCERhu2A//5pOP7hXk2bedSfj1rRabjPnMx8ByJSm9dZ3ALjSwrW5wb66icGbcRxQu5OJUAUFf/jow/ulfzWWtw5Y34KQS4I3IyH1oQoKPl/fIgPrW5yboGFdnRi04FW1s8Gb1Poei4yO41iM30FO3MtmYQOpJT4WoeyLyqTaPQ50LvpAm560XdzZ4K3s6HS8KHiZKgiUgof1rvt+d8CajP+8nhuIuze21r+VKYoQgFGq3QRB+mqCQPsN6EWTHM/935zEOD4BYG4fA74+jej4Tuo94KLhO5EraPvFfwaA+c3PdH9hk4c3I5ktZHKlrlnuq6DgF+5dxM2nS1XB4dM3sXgv61sQMn54MxJSH6qg4Ofvu39xfX1h9Z6iNNe7qwvr+4sbD1ExDMVHfvXXAZjQwAYAbCM1ITvreCyvIbyFO45jL+hjJOI+62av1ngFL5gAqXZXCWuzcfDOXq4t5XEMIJAJABOJn78oaavc9b0PfKx2d/9ldXy3dk+S3/katREAIxMGyvPfmCB5DYyJU+M7AmV3h1ryOt643s61koN6vS7++UrNdzrOJN9W6W+rBW/GEUPrO5kgVRjgMb+2Z9d2VwtjYxc3DqzlHxRCLgfejITUhkoM8ACA5S1rtybdidoQtwOIlnWiFgDQkKxzaaa5OBCxLhboOI5DAIGNoZV6smy1jo+N0tOZuYFsPXibz0WvreYmBgCx+kdG2glET2e86EWIy6tvRGn3Muu7UvCyEMKHCbiDOru7ARAEBkBsTKD852MYFJmysjre+wrcPgZgjo4BHw0vGyZWeXGnPznLtVcpeDMSUgeqYIMnhBBCyIipjoIno+FX3v0UgPCK153WS3l4URtaADY08GJdNLexsQlEr8dITNSy7I300InruzPDd+l4EcGBdQJe2bC12pbNYgPAwLi3oqpFEwcqcX3Gi74gh12hdpf1eg5AIghisfebVMHDe9Hr2HfxqBd3g0Cfij9BmO5Tk7kF02wAOS96KTUrUyl/6W4A5j//F5CpRSdB6GIqrO8vf8Uryj564vHHL7Mnk6WuvvRU8IQQQkgNoYKvG1EnAGDaXsuKZhUXcpf0DekaV8E9AGAQiwANghiAFeO30/QhfHx8HAcAgjjUyeS9MTo1XWs1n7x1BnvXDVeNDtrOLWZvadOkqj0jx7u96FMdn1XwWau87q2odvE8MB14V/k4UfPOFUD1zU00iLJPXe7TmHntpX/WBmB2P1n2HdkvuJp+H2Samd6E+j20+4AbXJBLmyE4d9n4GkAFTwghhNSQGarpVLMCVh98z014v/I33LierH/ff/gtAGErBhA24qBhAciracQAgtDCp5gzIZJlGB+7Dp1pTuzuetnlotf+7SZ3Yb0NvtSL3klzlWrexLFurcuIni77qu/ZqPoSX/rkWPlTyJS9TyvQB1FHysoFrsTcGYBAqsm1u5fN2ak5OwUQSHG5Y/GiPwKA20eALz3nasrFPjV9GwBO2gBw+xSA+dQtjJoq/+Cr3LdzkKhALRYrKw3HLc3PR0VM/uMww7OaHCGEEEJGCW3wI+bm3gcAXF9647gP9Po3Xy9cH7VTOzEA7wAOAEae55QvvdPKLm28EauwdRHsaZJ2a8SQr13uo0DZyJ1oznXGwhStVa7m4gPgnNSNtSbtlfQjb1wvrAfvPhLRnwscgDUmzUUfK8/5IEoN7cbPOhgVB28Sb/nkqurQ+eR04rTevES9ywyBc2WQOHgDhAEAiIO9XJqQD9lj4TL9ouUoxlTdJF9N7S5I3yqi42sD/7gQQgghNaRWlrDe1Mzs9wv/99PJ8l//H+4B8B9/6HcBXHthG4kNvhkHTQsgFOt7I9XuzhKv7fGB87BPs8jDedt723zGHp+3l+ct8YXkLeWJvd+UWdz7a/d8BDz0eu1SIMn4gihNzOes737ZG+blrbLHt9sAgvZp+np2Yk5PkNjgT08AmJNjpPb4Y8DXmjs6xqkqEi82+KMzAPjMMQBzqzPIBRyQKv/gq9y3c9Blg6f1/YJMXMePduJngr92TtFPK3FkALz5G9PKXl/7D78QwM9t/zagp8tl8jxQyykuZYsPn3Pz+vJbDNSG8uMMJLutzKIHBQ5x+eovSAbg7ErfJZtJIWNkZ6uGeaum6K0PsJMGizaToT1NPpLurqLy/HWRGfj08D4KzgRRACA2kglHT9Grwjn+7IJYTdFnU/EgOYBxpgfzwf8PpKYko0LFh/nqox9ExjfY1y+tTR5O0RNCCCE1pFYTZb2p2azgz279NoDTWyGAr3v7F8JP0TfmYgANmaJvxWHTAgiaEjUnIXMxiifqk7n6dFreTdGrqXsnoI1fmcszk1vTczM1wW6sLZpv794RrhfZlvvO7bvJedksraNjVCVc/xr7dLwSOyfz+elEfeCC5dwUfSDT8mfubbJsTtWrTOAfHbnYuaMTwE/UR0r6i/veRz7V+6sfkCr/4Kvct6GQCZrHH+cU/XiZyKT9qCQ+w+QIIYQQMkpog59aLACIQBeijgFgQgPABEkplDQ5q66Z4tPFpFb5oPsRU7SvZJxNj5iYy62PKYNvQmt642LqbKYkTM9XmwazqY/ya9K0uLmVJnXf8/3LGsXlJG16LXzhmDS2MDBRXFJsxh9KHyWWt/lctoFKA+w+TmIGJWru9gkAPHMEwBx+DoD9/DmQyqMLzMhrVRV7N6KDp1HHM4jufFDBE0IIITWECn76ED/5zlkA70svyHLcMQAil4wldtrUbZIue0Vv1LL1jvMZN3Eg8TW3AEzsNb1R25p0M6vkr7FxRmGL6s348etym3YQoZ99TZrrzufj/Of9pnqlI1AdiFNX+dgnujGqDqwPL7AAYpVDN+2AyoQTuHADVZMmyYojBWYkAE+mVe6+C0A8/yIAaDS6Lg+pINqcWllzey2hjh8WKnhCCCGkhlDBTx9ftfLfJMs/+f2/lyyLgnflYoMYQGSMk4nKEm9MKqOlImoiSGzm/6mSFL96G6socGONUeb5EjUPE/jWlCtAgUHd717iaqp9APxyxgbvBHp+hsDtYzLdSPwI/KsVtS2e9sYESrt71S4uDzGAAE3o5lRhXG13lyy/QZozGNZadCIA6LQBV4HGHJ0CrqSN6Pv4rS8FEDzyZPG1IFXi0qrLvOIVg3p0Jy79ZUyvJf6Sucxsx2OCCp4QQgipITWJRh2E2oTeCj/5A78HoHMawPvPNyQrrYS8++WwaCV82lpJYWsaLia+IH9t6KLe4Z3kE92r3xql3Y0y8htjBw6XB2CLQuTj3BrnCV/UZpzbzFviSw6aLUorkfGxy2XrMtpmKsmma1yUfMdlsZWPOlJJVmW0PZNEtscAguMjc3QbQHB0G4C5fQQAp6dJB8QGL6/BT3+05JsflCr/4Pv2rbBwS8Zho0qMVrsPLtYHobegn1Idf5lm+IsreMbBE0IIIWSU0AY/rZw814BPRSf4IG0DwLoE6ZK0zfnHS/1Vl0xexW0HPk17gUHd2axzVnlYq3zybd5s7yrPav/9ftjMZq5lV7w2FeUuBb0X40YdWXdJ98ha7zGgdvFp6QO1tVuhDyTmedgwOU0XQO+S2BsX+x4EyVox4cf+BABfOrbTNs0mANtqAd6XXs5DbPNhCMA2wgEuVs0pFDwV1O6jYrSqPd9ymY5/4vHHp1HE051+QKjgCSGEkBpCBT+t6ERaqmJZ1lJenHstI/HVeptX8C6THdQa8aj3EtrvYpJD2yDd2sTW6qp0RmWXywW1G1ib8XVP+2KVHE/WOIusuhxGzQDoRHYwie4v1vGZeQZrrJPnEjofJofxye+0TDcmyiW8A5AkzYtjALGY7Ttt20r9510WekmJHx0DCP7jx0BmhvGp9t7H6lLz0+tUPz4dP9We8xoqeEIIIaSGUMEDwE/9wO/BV2CTqurVR5sjja75llHzRbZvJ/3FtVyMzYAY7HMKPmNcN9llFSzujNZetUPpeG2Md5vp9PUZc3jyVtvF02z5mVNOZy/SXmU2cE2Je3zSVeWy4DpgcqdpfAyATTsT6ivjtDsAY4zW7gFU0LzMGcQRANtoArDNlpUI+FYn+QiygdjgifJIr42KKuQy5XvhoanjZwEqeEIIIaSGVDdSduQMFYz4nh8/APDmb1wYZ48uxI/9kz8AXGq4UIq7q9B2txzaoJF+lKxEV1V4HwcvMwGBLw8PPzfgq8Kna4zJrNTV5DLLQdYzIMhtpm3w1sfB5+rB5wPck40zIezIrfHbFNWYh1rOHMsdTqzjqp2kYDzgi8pHkcmEy6uy8Z00Gj48PQYQnByFx7cBmOMj+OB4Vyr+9AQAztoAzNkZAHvXneGP/Urxdz8YUx0Hn1DZbGJqAqt/8jjNBLV7nsKeT6OOF8an4y/yC2QcPCGEEEJGSXWf8UdOlQXNUPz4//z78JnnRU+HBQLdrQ+UoA+yer3r1XgFr7W70TI9q+Mz2etUcvduHa9Ue4HcT6PHxQtAK2ytqvV6J6mzae+UzkbB+qJcePoo0EcsSG/nk9ypZVHzURDlFLzKahe0zwAEpycAwtOjwGl3peBPTwCYs1MA5qwNIPyx9wOIvn4p/Pd7hT+AAanyD77KfRuKc+Swq5SCT8hLeep4Ue0Xn0OigieEEELIKKnJc/QgTLtoePe/+W0Ab/l2V0ru333f78OFahcY15WCL9HuspnT7gAQBFar9vIk8245I+7LdXxeqReY6pP89lq1Q8voAh1fsFLr+GwjRVnutY6HXpO17pfp+AiAiSJJWe+T1bfTV2eDP4PPSB+eHjvtLiZ5p93PABjxrm+3k+XG9i90vvUrADT+7S/iXFT5B1/lvvUlL+mG0vHVVPBCPXT8aC3xF9fxVPCEEEIIGSVT/Bw9LFMtGjQ/+uAfwNvdQyXKwyKH+d42eKNt8IHNeM7rFG+5wnHGWHQ51ScbZCYAbKnFPWOV98vKtb6s8luqxZXnfB8db+OyQnZJJrz0ZK0tMv+X2+D7eNGfAQjbJwCCsxNR7YFY3NvymhagE+0uy4g65vQUQOPf/lLuJzAQVf7BV7lvQ1Eb7Z5Hq3nqeIEKnhBCCCGTpyoD/O6qMWZ1V94cbi6ZhKXNw8l2rXJ88zte9M3veJExXvIa5JddIfbAmnRN5l9mRyGb9M7JaaPW2/SfCyy3YrA21nrda2FjY2ODGIi7N3MrY9jYVa/zO8qy3xjGwlgjOeEN/HLXP5hAvPlL1ss/Y42xQVC0cWBNYIPABsnGfo1+qzcuOJbJ9zZ/uW0Q2iC0YdM2W7bZiltzcWvOtq7Y1hU7V/KvNQf5d+nwZhycl7/85RWM0R8Jr3jFy5Mphycef5yp4qaRSqSq3V01N7ZXduzWMoDDzaWFh+8/sHvzyYdm1X02Lj7yq78O4DVveEnhpx/98K8BeNVrXzbGHgyDpLgJJHmqTPzkHeKS1XrYLshbm6XvBqpSi0tMK8lui5PJwsTWmjScL1NhNpZpeYMkoaxBZuOCjLbyPKpLusDYAIA1mZWKJOttnH3bfUJ6jc+8q3eJAXeJdUZfC2NMr6sm1WZt2ICksHXflPhGBoCrM2tMCCBwNWfdp5IN9+w7/zsArR/+Tz2OMkImfjP28GaqYNKbc4TJTRc6r+2U1pYdIRX8BfamCgp+95FtLG48IH80dt+5vr/y4Np88unyAxuL2++gciDkEuDNSEh9qISCB3D9Hvkrcvj0TSzen0kQO3/Pdew/dQDMF+45Csq0u1Ad7S6cHocA5q5GSMSeq/0KwBVRsRjep8Nm1Gyi1NNVqnSrNck7VUUGetnt6N7GWsdLY2k/k+Uk4Q3KdbyTzl0GBafjlV8eYmSkutbu+jXfZ9+muxDd0xJWz5ek7egNAgDWzbEAaWWaQFYGJoQX94F6jZ2aF2XvzCfihXeZTPZmFHlkDPJuSZVSTvIDmJF560THT0VNGloTEqqg4JffuoLtR8TkN3/f/Yv7Tx3ojw+fvonFe6ubFJ6Q+sCbkZD6UIUBHstbOyvbN8SvZ37toY2bN1Jnnt3VhXVsPLQ2PsUwpUTtIGoHccfEHRN1TNQxcST/EEfO003KptgY4sum/3nft3QZXQ5xaoPsjka2dG+d35xyrJPldHfVWvdH3a522b4Vu91ZF89X5HmX26zMOS5tJ/FINFlHueRfxhGxG1ek1mtNGxgbOJe6uNGMG8240Ur/NVtxcy5uzomTXdy6EreuxK2rcetq1Loata5657s525qzzTnxyEPYQHh5M20VuRmrH0PnfquzBH3upo6KTNEvb1m7tbua+ivtL5h1AMDKjrVbk+sYIbMGb0ZCakJN0k0MQo9sA3u/+AkAS1/xpZfbo3Oy8W1/CuDqnRGARjMG0GhaAI1WDCCU5aZblkQ3+Rw4JYluurPWZIu6ZtbrHDilRWODxG9cfZQvGuv9/wcqYOOy0MRlNWkK1vhysb6KjDqpXOlYA59CJ44BBPn0tJLZJs6mqnUty8Y6LY/aPXa1ZX1e2w7gktv4yjSnAAJJXtv2WXGkPs3tWwCa/+rnMDBVTibTo29djsom7whRJWqc6KYHU5EDZ9xzDIN7hDDRDSGEEEJGSUWm6HtxuLm0sH59rMG3ot0/8OgnAbzxvi8Z23HOidSH/cZ/+ufkbRwbAJ0zV/tF1gGJ5o2RRFqbWDYwEiaupbnsrBzm0yUnna3a2HTtaKx1zuQZZ3hpQ/mlW2MyzbvgeAA26HZfN10O9nGq4zNt+oK1UKLcZvqmTsp33D1Ai4N6zmc+E8VvfYiAxOhLmIDbQkfASwCD95DXWXIDpeDjGAACUfOhk/KBeNHr2PfuaZPAxrbTAZKCQpV4Fr+EmzGp7SELldLu5w6Dro12F7qC41FJHZ90aZbdBaZggJ9f27Nrg27cO+sIIeQiDH4z8k4kZOJU10o3cnoYQj703t8A8Lo3/eXL7dGFEEu82N2brdTu3sguh83UBi/LeUt8tw2+3EaulvtvgIwNvuijdHc7UJvZjg1SWzapDFtWKNaNQmq9kagDIMiXlsmY1Z29P2v4Vx/pjaX9OM5Y8cUS35FXZYNvnwIIT47Co1sAwtvPAQhuPwegufkIBqYeNvipoIclvmbaPc9U2OMxBh1PGzwhhBBCJkN1nvEPN5cW1vfz61dGZfC7nMeoS3PIf+e3/Bd4pS4KvtkS1Z7R8eJgH3qnegB5v3rnS58tF5vxqFfSudvjvegjtaO3mBd9pNb7RvI+833nBgbT8fkStNqXPqPvXah+tjhspgRtepR0L9dN3QHtfu9bjnMKPkqryoqOD89OAIQnt8Oj5wCEt54DENx6FkBwdASgsf1eDMAFfvBTdjMWpr27zJmAQgVfe+2umU0dP+Cva9YV/OHmkjELD99/YPPs4AaLWBFyWfBmJKQ2VEHBu5JVeyUJsvp8PDBVNkkOxf/6jZ8FEEcGXrXLa2vOIrXKu/h4HRyfsccXxcQHQSroM/Z4pbbT5RKzencsu9qsKMx9KLt+0cbSw0zsu0vKr9ZYZBQ81HKR3M/p9YyTfFfSejUTkNHuWes7lIIPVBx8oOLgQ2eDFwV/1BAFLzb4554FENx6DuNV8LwZh4PaXTNrOp4KfhAOntpP6lsUkNS3IISMGd6MhNSHKoTJLdy7iIefPsRyiWjI17QaDx/4+U8CeONXVi4Ovot//OMvBPDdX/UcgGt3AL78mpWIcG1lttaLUpt8JPHlsnGY6lIEFggBb04O3BOn/M+kq2Jf2U3Vect8JDrex7KbIA2Uh2tLh7lnwujz9egKi85lNlZR9d4nPoAX0Gl8vGtO5UXz55HZzLXcnV3AOmnefS7pXupyFUwAGOeK70raSd/kWwtUzH2mHnxogwaSqnSheh0jVbkZkzj4ipNE7cvbmdXuAovHV40qKPj5++5f3F9fWN0t+nB3dWF9f/H++1hshpDxw5uRkPpQBQUv2TN0dQvF4saBteP7g6JVe9iKk/V77/sNAEt/rYqR8W9fvgWg0QCA0+MAQBxbAHFqBYbPjG69W7dIxgAAJLeaDZKt3UYel95OCVzfaLqNTQq9AwCME6MFOj6v1IVCHV+QC09vXFg8HmkiOV083ul4VxU+6W3q8a5leJeO9xvoEvJx5pNk2e/iBbyo9nQKQUS/9DlIplJkVkBl25ee+1cpJx/YMARgGw0AttEEYJtNjJkJ3oyFfu8VD4sfKhf9jDBdxePrTSUGeACuhtWkO0EI4c1ISD2oiS/rINTGcVf4tjceAbgyZwG0WjGAK1diAHNzqUd9cy7WbvYu4Z0OlxfveudpH5cWnVMe9c6VHWnoN7JO8pkUdYEtioCXjfu43PePie+dHS8b+J5WikMmUL7Yiz63Wb70nLOaIyN0y3zpA+c8H7mo96gNINT+8y6TnfKlPzsJT44AhMe3AEhWu+DoFgBzfAyg+a9/Hj2p8g++yn07B6LjZ9wAn6eyTvWXHA0/4170hBBCCBkx1ZminyQffO9NAK9/0/VJd2QgvvNNtwBYGwDY+IU7APzdLzuCrzLnXhOP+lTTel/uwAAIQgMgFpmeqNycf7jyN88um8RvPOdYntnFIO8A73wAUnt2oct9X3t8QSE7qzZW9nijLPZIXOnhPko77vewajN1Tglpy9Z1J9lC3ojBPn16tka6FPtkgZkZie42/afiVG/DBgDbbAGI564ACGqkffNU3OjeBbV7D6ai6Fy9oYInhBBCasisK/gPf+DjAF7/phcDeP8jTwFoXIkBvP7N1VXzP/zeO7vW/Ov3XwPwHV92lKwRERgYK0o9bBgAoQuXT1+hXq212tBcpt2zajmj4+FrwCfLxiZW6oF0fGFwPEp0fEFwvIoP8DMNJtk6Od3MHIM7K5ucizW+Te0sr5b9DlqFJ4I+7RLUB6mTvLLc6xasbsV1LICUjW80AcTNFoAgigDYOBP1UBu0dk+80ysu5QuL1rNSriav4wWq+UuACp4QQgipIbOu4CU9u+j45tUA2arw7/+Z3wTwZV/9xRPqXX++6t42gJ97qgng5NQAaIQGQKNhADSaphmlhnkfHF/yahNZn0a9O+1ekMHNR5araHAdko7UrJ5+1FfH90hyl7bvdXxpkjub29GY0rx1EpiuTODGGmvUvnkdj3TNwHizeibewF8RZEVfYoPXcfBRE4BtRQCiRp1v20LtPhWG+cKidqSMiVjlR14VvuLUKlilNzWLzMnzNV96BuDz7+4AuPOOCMC1a/HVaxGAK1djAHNXJYIuAtC8EgNozqW1ZcNmnKkqG/YMkzMDhLHlg9n61JYt/0gfK2mk5KC6EG3aPTek9gyQS9d0f5SpA5ts6t6Yro/8sgqWiyVYriMFZvIBci40zi2fATCdtoup67QBGNng9CRpOQ6bAO56+w+ihCr/4Kvct4vDKfoydOCc5hKG+XEP7T2ePhkmRwghhJBRUue5vkF4bO9JAHE7APDav/LiZP2v7t4E8Ibl6wD2f/kTABa//Esn08WB+X8+0QKw8oYIachcNnYuBoBYZrAz6y2AIDau/EkE+Hlsl3bWHUFFjwXJVHmB+xvUfH7BhLxroWC6Xn+kpXJmij52UXAyr5A/aNagkPGl64qdQ3a6PqHoozTxrRbo6ryhPkqXM8V/0gMgvZLQy6lHngmMpBZ2FWjCNGGtqHnbahV0fZrRaV8TPZT3vKv4RD2KwiyJoB3uNIm8HoeUn7Vpec3ACv5wc8mY4hIUhBBCCKkYeQW/u2pubJdsvX/DbAPAyo7dWh5nty6NZqsNoBM04NW8aK03LL8UacmZqmt3TRwBiViPTdaZrlu72yh9jUMrNWNEZyOyQFI2NTE1J7okKRebqhWXQMZ0u8ih2yEu7YzbPcjqbOmGJIfJxNG5AwMwsJm0NvooBT56ptvnLnmj8MLd+PasO/vsBtpCn6LeFmS6zaj5bj2veiCvLojOqNozRirQNFsAOnNXkvV1pcvVblq0OxmEMh2PkcbRzbJwT8j/jVje2lmBKxylONhYBFZ25E1NRndCCCGkrhTZ4Je3rH3rqlkwD28c7K3Vu/bz6dEcgKCRqrRXv+6lyfL4ysX+6qOfBPCG+75E3v7Uv/g9AH/ru//84C18wytPADx7OwTws081ASz/xTaAP3s3AESFNngR9wWvBoCJTMbzXClc9xgoqxMDudLuMNmP4IrXGmNcDVm/Dwoj37xZPd+O+6hIx+uPSnW8iOAgyWuLdGM366Bnpi61LwAAIABJREFUGjL28oIcPmomQwn0bj2uxb0vOeM2djMqhXMA6bFkMVnutvFLTZr2nS8A8Omf+BEAn/8N/yDX1NSj9fr4tHt+bkBnnx3Q9znZhdb3wemh44UB1XxFlHo1J5nKZvmWt6zdub6+YJY2Dy+1Q4QQQgi5OL286Je37MG9Swui5O+7tC5dHh//yP4dzQjAWesagGtHn+va4MmPfgTAS1/1mvy++7/0CQCLf7XbPC8PpH2LTyTaXRhKuws/8bErXWt2f6sJ4BteGQGIfH4bWYicYV50fPoaOe0OAKaTKPhiAeIUu3/VZVNkrTOKB1mzuhj7M5MAqn0teQK3gd+lj463uY/KnPlN7HPXOC8BZePXngXeK0Dnr3Ud0C717gq4MHdT6CfvT81Fw8eudGyykJ57Zkct/W1e6EvCWhN1AEStKwDaV+/qPu4Uov3ne2xQJo+eeOKJ/EcDKqr8BoXZZwdpJHWxoI4fmL46XihU8xXR7lWmj5/O/NqePdjA+oJ528OX0yFCCCGEXJwBM+wcbi4trO9Pt/d8Pp3QY3tPitx81WtfBuCjH/k1AK96zcsm0r3R8m1vPAJw5x3xNZ3Jbi4G0JIcdi15tQAaLUlgFzckh13DAgilkqzOZ6ey2gWBV+qienXyuMCqV5+czmXBkxe1o5oASLPj5VrLr4fP+lqQUC8oaL8sO15BvjzYrOFcktBFQJqQLlkTxJGJU7M6VMMFCj6Ojd436sAnqtNJ6ySfXeAz2ZlO+ipx8C/49u8D8Ec/+S54Hf/nvuZbkKPK2eK6+paPgC8U5dMIdfyA9BXxFaSrMBJKZowqlclud7Ug3n1+bY/e84QQQsjUkH+yUHHwUy3Yc+Qfox5//AkxhoYmAhDZEMgkMHvlq18GYO8XPwFg6SumKRr+ba8+AXD3CzrXrsUArlyJAcyp/POtVpqFvtGMATSaVueizyv4rrz0iZRXK1OxnqwxBfnn5TV1iffKu0CI692zSeaLxHcmMb7sUrhxnx21dtcKPvMq+jvuZMzqgspnpxMRBHFs1L5+uY0uNe8k+5l+K5kNXBz8lWsATu+6G8DZtecD+KLlr0GOKVXwhUxvNDwV/FBMo47XVF/BL28lYe/bN4wxho70hBBCyLTR98kiFfSLUx4VX/gYlX9g7OsAPxRPfuwxAC995asLP/3Q+34DwNlzjdNbDQCnzzUAnNyS1xDA0XMNAM890wDw3T96t+z1PW95Ft4lXtzgT08NgHZHOcYbALhyJb56RSn4Oa3gU+u7mN4b3gYfOht8DG+P9woe8Jb4ILBaYQdBaqTXQj8IuyziallOJrs+q9fT5QI1b5CpblfUmm6qSLuX6HifZj+r3XPWd9HcUUdWZnV86v2emQzwCj6r4ztpa50OAOPs8WeBsr7L2bav3QXg8775AQC/9+6fAHB8590ATq/e+ZcX34AsU6TghS4dP3Kl3mMCoO8UgiYfNN+D0f49qT3TpeDzNni9PqFSCr4LEfTW7qzsry8YY5iQnhBCCKk+A1eTW96ydgtwTnj1MM4/8fjjgY0BvOyVrwLw8Y/sj/wQZdpdaMxFADrHofcYB4C4YwB80z9/Udle3//u5w149L/z+uNmwwLotA2AIEgPI4XRrDzhOTtxII+ZVsy9NgAQxKmmd7nh3LYmkfIAEAI+9N0qTWxjK0u+8pvElMtm+pHWB7iLABalrpatTbPjwYe8W6v31Ms6Jl6OaP0GOpVeSVo9a12gvKrtZlUAvYteV74AyeF09feMK75bExnlje+1ewTARKmyT7aRlTZs+APBNloA/vCn/08AnTvvBhA1WgBOW3dgmin0oh/5Uc43JdB7r75tMia+xozjVzpaBq5XsbtqhHfce1CL0Z0QQgipMbNug68937J4DODuF0TwnvNifXdx8M10udG0iTEeqSW+1KPeLeiP1MaFpvqM2VtWaHN4Py9614j3pc/a2nPtd9vg+wTK6x29z3/eEp9q7sQe3/UWqYldltX6yCn4IM7p9Si1xBvvUR+cHgN43tr3J5frT/7dDwP4r/7H7wRw+L6fBXB0xwsBHEV3veb1L+n66qv8g69y38YHdfyAVNYS3+V+Mb02+MPNJRHsN7Z9YbmpHt0JIYSQmaJnPfh6xcHn+dhHfk3XkdNG06tHzwA4vvY8eL0VhS1RaZ2gBSC0HQCRaQB4xStfLq0BaARtAC99VS/T+yUgteZaTdsIAeDkJEBaJN6my5HV6/VHDfdR+hqGGbEe6shvAIkPQbaQvCw4U7cuPZe3wccWKts8YrXszPtiz5bE9TZra5dWUrO6btlYv7G3/6ctq80Se7z7oMASH8AnybcI5QTdyjgEEFuV8C4UUR4CsCLKTTvoyHnEyWWAcrOHMuHDxpJ5XvjTh34IQPuO5wH47ff+DID2lTsBtFtXAcTPTndt+FHZMgfMLHaZ6M5I6nT61fegstpdk3yn1bfBFzvZ1X1kJ4QQQmrODFnCehhC9n/5EwBad7UBRO0AwKsXXwrgyY8+hgrI8VGx8vpj+Gj4uZZNlhOrfFPZ4L09vjsyPrHKu4R32mDfFOWqbPNJJrtMGvn8mowN3q0si4NPdsy3UJ6dviCzvY62R7aRTA8tEqt53kkeLu2dFuI+aD61wYdJ0LzOW5fJP6+z0J8BMFFkgwCADZsAzu58AbxqP7nj+QBOrj4PwEnnGoCTzzXf+JWZ+oSotp27R98Ko+GnMYddb2iPL2QqFHxfqm+DJ4QQQsgUU91n/JEzqseoc8j6itSp+1svPQVw9YoFcGUuTl7n5iyAVivWDvZOwStpLssNL9x1Hnufvr4g+V0mTX1eu2fWFySh68psr9cMqN2h5X7eJ78oSb4pkPi6vpyLhPd7266PvNDX6eud+32g89ZpHR+1AYSi49tnAMKz48/7pu8a4FstZUoV/FCcQ9lXpE4dFXwhlVXwF/nNUMETQgghZJRU9xl/5BQ+Rn3kg7+eLIv0dGZaWRNGAKJ2CF8zvga8aaEN4POeHwO4pjLVX5lzCr6lQuRFrzebqvScLyTv89inct+Fy4uOl9x2oS0Q33lpnqhtFZveo0IdtNzPJqhPdtfSPJX7A+l4mxX08pK27zDJ/3Pa3S3rJPYu5D3IxcFnNH2nDSD0uehf9LV/G8AfPrwN4OQuyTl/F3z2utvhCwC0b4coKXU4dQp+QJ/kKujvkUARn6fiCn7AsoddTPBOHDhVbU2R9CCPf+wJAKFtA4iDEMC1288AOLl6J4CmPZGNn/rgLwM4uvp8AO1bDQCv/Ssvnki3u3jH138WQKcdwBeeOT0NAJyeBe5t2wA4PTMArs4ZALeODYBOFADoRK5KTSeK4cvVRFEMoKni6HT4WWBiiXkzkvjWpCFzkv7WZb21ydgsuXJtsmxiPXIDMsjqAd6mr0UTTS6mTtpxyWVdQtk0JC+t/avS31odehenXUpS2Lrz1AVg9diuHyDSQ0ubkgZYBvgAgDURfHydCYI4DgEEqhCtUU8AQaMDIHLT9WdytC+4f6XrzD/x4T0Ar3rtSwuuyjQzVJLacVemOR+DdJ5hctNL18+s+r6fnKInhBBCakh1J/FGTpVnLC+T1/2FDoBmCABzTQvg2pwFcMfV+Opc6n+nI+hcZN2VGEBrzr021Yy9drILi5zsgvKZ9nTZFKzMFqLN7J511gMSGQ2k67sC8FTLpdP1cDMJuUQ+SdOZ9gt8/XTLSAPnjI27QuyQzOeLjrdpjtsgaouIF/Uvk/OS1qYdzgGITkMAUdsAWPyygpmkKv/gq9y3S4NT9GWUTdQXTn5Uala/alP0FVbwh5tLrE1LSBXgzUjIFFKF52iVHLeUEeTW6/EY9bHHfg1Aw7Th1dVLXv3aix1tmviLL4wBzP/X0V3XUs87HU139Wqq4BMdL754DRVT553slIIPXE0akbOB1u6hWpO4wuUkvq5wY/RyUOC4lzGUd7nd9XPZS3exrjqtlZy4+ieTd98rz7dTME+A2Et5HWinvfOUPT6KRME3z44AfNHy1wK4ufcBwCXVkTQ4nUYLwEtf9Zr813ou3TD5m7GaxvXLgZpe0KJ8KJeFy1HzPZxFqODzLG/trAC+pk3CwcYisLIjb5g5l5BLgDcjIfWhGl70y1vWvnXVLJiHJ1OS9pWvrkkI3Pn4rc+6Oqzy9q3XzwA837vOIytwA+c0box6OpTnU1eTJi5X8H4lACP++eIJ78ztRuvpIPfb9AVsVF+RyNnUi1467Zzb5X3iGa9fNdZtJv+zkfENFyh475/vuxoDWtADVnnsO/98d16BzbjZax2fmupd9RoYiaAT7S5cX3pjruujZtI340xJ9i7yMm+WNf05wg1kl/HpeP3jnIofahUUvLC8Ze3O9fUFs7R5OOm+EDLT8GYkpA5UQ8F7lrfswb1LCyIe7rvso0s0fODcnjvJerGJzp3cOrl6FxKBZQL4oHlnso0MgLgjr8HIQ+R/+od+F0DnLGgfhwBOTwIAZ8cBgFO1xkXAuzh4c3ZmALTbBsBZ2wDodAyAdiRx8AZA5MrFIrap6j06NgACF8AtMd8S8g64jWL4qPeGU/AxgDgCgCB0ge/aiB5INLw2qAdpzHocWLdXqLRzzpfd63gbiOIO0m197Hyqetxq47RRUKLd/QfO9O4UfJxTT5ncOABg4i5Br2LrTTo54dYHVg6UDZ2XHsqPKrXBA+hgLtfdy2OyN+NoC3GOVmxdsG+Mg+/LBS/RuHX8FFEdBe+YX9uzBxtYXzBve3jSfSFkpuHNSMhUUwUv+kION5cW1vdHWZmeobdvvqcNr29FtUexQZqozml3UZvNhgVw51ULQLzr77gawXvUX7kSz12x8HltfWWaTJJaAGGYVfDqo0A5ySc+9sbvBe+NLxH2QZgvY1Pgcp9PN5e8cZHuEkmvJw+kA1I0xs/ExFHqP291azpoPomD14K+d7Gc0Jbmx9XOBy7HbZRIeQCdxhyAl73ylRiY0f3geTOOnlk2rvdAZPdIJjnGreAHnxZiqto882t7dm3SnSCE8GYkZEqp7ACfcri5tLB+fXTiYXZ5z9PN8+341dfP4CzLzk4fW6Mt7pKyPmqkFvTQ6+xQafdskjul452aN6LRM3Z3rZ2RscfrZPU543vWU95k8tuL2o/DtF2x5ovRPVHw+pnbeIt7srFX3kaS4Wey6LuU+MoGH7qjuzz8NjXSO+O92PtDCyAOXc8anTaA60tvQGXgzTgqzqfoqPsHZxyW+KnwnNdMwQA/lHwwvAMIGRuD34y8EwmZOFMwwA9FD1NHLf/i/C/f8FkAJ8chgGeeDQH8yPvuGPlRfuZmC8BXfnEbQBQBQBQ77S6l51qdtMJsqAR6GLq3ot31a94SHzasd5/P6fXMerGX20CL41j5pRd9z86nPUx/HtljpMnn40iM4M4k73fX9nJ1rFiHFfijaPd47b0fGOdF72z5SP7n2pfQeZknCMNKafdh6W10rOXNeAk5+Gxupqo2VNzpfeq0u1A5L3pCCCGEXJzqKHjnqZtjhK67F+Xglx4FcHTHC5FEwEsAN3Q0PADY2MTtAOMpGL/19j8G0D4LAFy9FsBVIXda+Xve8ix8HPzZmTlrB/AR8G2JgO8APgK+EwFAHPuodgBeAGuVIG72Ymt+9nYAIIpN5FqI4WPrm80YQKMBKEt8Qyn4Rk7Ha4f5OLZWirtbna1Oou1TXER7DBu6BaTO6uoEsmgbvG5Ob5tkMnDGeOVAn5HmKnUdjBejmQT1PurdfzUuYV9o3RRDnFrfffeUwT5OXyfEFNyM5whGH4cI69EN/RFj33vTJd9H6Es/41RCwR9uLhmz8PD92fTXwg5uGObTIuSS4M1ISG2ogoI/fPTh/cWyvNfLWwcbNxcefvRwbQJpsbtY+KuXndBr58cOAXRc0rpQXltX08cyMYR3GgaJJu4YeGUchiZ0+eGBRIiHBoBVAd6xGIa9Ygy0lziQfOQS3lkD4NaxEfUvswJXpUh80yCR6aFIdoiC14HyuvSc2ziyAGxskdPusuwMutZvBtjYBrKgg9oDrdMz+Apv3et1bru4SMF7l3h1TbRMT+vBK1O6ykWvk+2bONPDjB3adS/V7tGtiTx8T83NeMk20dFm1iMJ4zO9V9yofzlUQcEfPLWP6/eU/sWYv+c69p86uMweETKj8GYkpD5UQcEv3LuIh58+xHLxn5XDp29i8f6FS+5UNbjxTd3X5Mf+yR9E7QBAxyWWT5fbZwbA6akBcHwSADg5DU7P0iz0orbPlCXerZFpgMi0IwA4bRsANz8zxMPf1734DMC1qzGAlpLmjYaVBcmL1xSJ35RleU01vbVx1n8+XQ5TAe9mI2zsJiTEBm+9kRupMs7qeDGLi4DOxtMnLXsbvBR10/slOezSVcoGn761KlzehbzHKnVdYIxOWa97p9YHJgZw5QXtJz/6GHxq+jgIAERBEz5e/5WvGkcJRN6MxeQnDC5T0w8VND8tPvZ9FXalLPE9vu4qO9hXQcHP33f/4v76wupu0Ye7qwvr+4v33zfxKUFCZgDejITUh+pkhN5dNTe286tL7YFDU5v011vf9ccA2lIv7jgAcHwUAjg6CgB87pkGgHe9/5reRbLQN0Ig6xIfK7O68QnbQ8mIbtJX2ViM7rdPAwAf+lSY75hIh7d8yRmAKy0LoNW0rUaq11tKu0sS+9acBTDnluNmKwbQbFkAjVYMn4s+73IfdGW5zySWTzujOpcqaReI7zLny+SBQcYGr3dMW0vyzyOj4JXdPZOLvvu4JjHYy9u8N78FgC//mi/OX9tzcIEfPG/GQemr4/PybrQKu/AqVlzEn8M6PqCOr2beOuaih5Sg3pp0JwghvBkJqQc1eY4ehHM/Rj22/yScZIwAhHGE1MArXughkmhyiTt/rvn6N18/Xz/33vcbADqnAYD2UQjg7KgB4EyWb4eu+vtRCK/gM/XgdVX4M9NWNniJVu+oSvBazSOJgNcKXnmZy8UTuZ9eSJu8ODd73TKAZgh47S6votevzFkAV67EyevclXhuLgbQnEt1fNiIUZgCL1Xw0CuR+KJrEWOSU0vnAKQ1l9tOTq3jdHymEnxWr6Mrq53JHE4XtTPo3kUZ7CWWX29mAZw82wTwlX/7v8UoqLJKPl/fzm32PrcUG62hvSLm5Etmer3Za6Dgq2CDJ4QQQsiIqe4z/sipsqAZhP/0I78DoH0SSED8qQuLD+Bz0YuaPzlJX0/PzNlZAKAtXvSi3TuAzyGvq8IXXhvZ4N2fbI3wRL7mS8+Q1piPAVy75irNX7kaA9A6vpG3wXtLfOZtmKaN0yXetfKGV9jeBp/uaMsVfN7u3mVc16JcF3rP7O7eFBSJF9709fcMexn7UuUffJX71pcLyvqL6PiRX7OxWuunUbuPwyV+gr/2Kb7NhmWq/6Yk/If/7VPiXtc+UdPyMlGv1pylqWoNkpg6PTkvpWJkvj0bNWbU5HxBuhv/ZNBRQXefeS4A8IHfKXDpeNFVC+BFL4gBXG1aANfmLIA7rlgAd16NAdx5Rwzgjmvx1atupAfQuiIFbMqm6FEwwKsp+iA7iOop9EBlz/VT9CY5NRuVOtkVDvPavc4vuwuW7J70wW3miufGABpymtc6AFp3dgC85g0vyV/Gc1DlH3yV+zYg5x7mL2GivuzSXo7z3TSO64Vwip4QQgghVaQ6XvSkDw//4KcANK84dSnTyOLLJhlarHsDJO5yxkhql06YavdIu9cVTc5rhRoY65t0G5+1AeChD10dsNt/cCx9KQir6+LvvO44Uw1TRY7J828cZybqY9HBzsnOIKvjY5W8NpXOgUlak6YDWzRFry9IJuhOWtNedZncNVknuwJPPe/AmG7m+ty0AIJWdwYeUkEuOEWfCNyhpHyZLB5KZQ4oI7XQr40cn02o4AkhhJAaMvWWsMGZRrPfB99zE77YTNsHy7mqM0epk93ZiVo+1Tb4QMLkXIBcp5+CV/5iPkwuXeNiAmWawDrXPGnz5NQA+JPPNgD87FPNYU/zTQttAH/2z0R33REBuONa6nk3N2cBNJQlPnDCPZPoJlTpbmQDbW43JmuD1xZ9VWjHJbqJjOS98ZdET4moRZeyxmpjf8bVTm8GfxkDAHjrd3zRsJfoHFT5B1/lvhUyXcVmZG7gHBc4b6SvvYK/hESztMETQgghZJRM2XP0RZg60dDFe3/iaQCds6B9HMJ70WcUvAh9peDbZ8Zp93aq3bWCt11ZawCkNnjli26QbCaiv902P7hz51jP9x98xW0Ad9/dAdCSkLlssFxYkuhG63hfRjajs7UXfSZVbcddmayCVyj3+KT+rHfa745/ywQgxADwdW//wpFcmQGp8g++yn3rSwXV/LhlaAVP+SJccnkYKnhCCCGEjJIpfo4elqkWDTPO993/DAApRRM6o3tGr/dV89pUny02A+Rt8Gp6o4zElz4fiK9t/KHUw51zr82rEYDmtQhA844OgObVDoArx88C+JLXf/lorpfrYXV/8FXuG+lBzaR8GaOV+FTwhBBCCBklM/QcXWPR8H/94z+Et767pHWdAEAceYu7s7uX+M8XetFLxHZJPrs4dklwP/3pJnLVaevNu9Y+DW9u//Yf/vxBdvmZ//13ADSvRnN3deAVfKMVwct9qLS1i1/24pH0s8o/+Cr37SJUQeBesoF5guirPeBZD/UFMZMdIYQQQqpIPZ+jC5ku0fDhX/k4gKAZw3tlS7q6zkkoAfFSSVZ71LeVF33Hqfmgc2YARB31qjS9XA9JimeRqXCq3cJ15jUhjpx/vg+7NwBE05/6NPgAOh0jtWgD73MOoKHN4aGFd49vNm2zaeFt7VIuttVKS850F2PNzzfoyPisITxsphZxvSxdEqO786LvBFFHTXvoZfUq+f+/9fu/YOCv9LKp8g++yn3rogqinPSlyvMWVPCEEEIIGSVT8xx9caZINJCEzW//UwBzYrRupDq+OzmdKhQbald2L9ldLrxWTsFLHHysxHrbK3iXQiAAcHo7BPDf/6M/f3lnfmGq/IOvct9IGdWZzKiyXs9DBU8IIYSQUTJDz9H1EA2PfejJ6DS1u3eOlSX+OK0T7+3xoaS6O74VAvi7PzKQy/e4+Z63PAug1Uqt72IpbzStVH9vaEu8RJC30s18YvxMxj2jFHyBDb4Vu3j0ltLxrVTBw2bM7bEvDI800CAXE++P68vBydxADCCcS2Pfw7kIQDM6BfDi1yyO6hoOQpV/8FXu24BcUM5WRINWR5RfJsxkRwghhJApZuqfowenBqJh5Lxr/dP5lTrz/HdsVEL0Txfv/5nfBHD1807hNb0Pc3el6cRpX2YFXrX40jF1o8o/+Cr3bSL0VdIVUfxTx0QC37uggieEEELIKJmh5+jpEg0f/8geAOtKi4sBONP5OAgBRHEDQEfZ46V4vNjpO2dBJHHw7QA+Dj52Se5UTbk4WzJNWbV1RncdMh61A5cy7yxNnxdJy5205Tg2LtQ+Z8lOcrnrY+nDCVUONM/zwffcBPD6N1+fdEeAav/gq9y3LmbTSl3IdM0iyBdXhT5TwRNCCCFklEzNc/TFmSLRUMgnP/h+AHEYakEfhU0AnaAFr+MjUfOnAYDoLIjOAngFH6t8dvkEbZ2z4G8+8Bcu/bTIuKjyD77KfevL5Wj6KkhPMhKo4AkhhBAyShqT7gDpz80P/QqAqDkHIA4CreDFSP//t3c/r42k+R3Hv4/k2cwhEEKOCYQFySFGZIfNZGemFHZJTpH6EBOIb6HJRSLkIEGYW8NefEpfpKN18zGCgSZgCQIL2WSs+cEMszNrnNBVl+QPSG67mWm7nhyqSqrSD1u2VT/0rfeLppFKJflbpXrqo6d+GhOc2G0k2qFu3hgR+fO/+sN8Ki6Bn330HyLyO7/3v++8l+nZ7cjRo/vudMfT84h7ypUHPXgAABTa4z1hD7XXu/0K7p/+8b8lusa7xA6bt9FR9OHt5/3gkH4jIn/z09/Np9ZsffX5ZyJSvX0jIn/0wZ9m+aeLvMAXubZ999DNDCXp9ebY0c9xaS9RMyvsOuWzj39hqotbl8oiJUX8xdVSzfwUs/CBnT8JTl0LLq36/o/fyaLo7Xw0+C8TO+ctyv7gyD4Rkb/+h9/PpbAyKOwCL0WtbbdHzxUqOLmQTo44yA4AAOxSEX9Hp6SYnQYgJUVe4ItcG7Bb9OABAMAucZrcfvvk519LdK/S8OS52C/F95pp3chk7vNPvpLo+rj+m8VFcG10CZ3gwDobu6LOr/7neyLyl3/3/bRrS8kvPvtERKq3NyJS8W8q/q2IGN8XEWN9EfmDP/uLXAtEPu7Yz53NHu7HHUOwv3vft5ne/Z26naAHDwCAQiXaE8ZuP5RKkRf4ItcG7Bb74MUbNk2kO119aWkYgLTQGAEdCrEP3hs2630ZuLZXE5Fp1xjTmdizVt515e/jf/nl/HHlILhnqw3PLI/d4jXYz/3BT36QcXnQh8a41oN2b5d8vy+Kowg9eO9iPHMG571a8LR1Zt3BVds0h16+dQGlQ2ME9ChCD969nknjRS02pNa7tIddU2+Ke9nLra6sfPPJx36lKtGdY6wx8//f/u2KRIegh4ej++G7guvBhZez81c+FHiMUjfGbO4DC2SmCD34+pEjV6+XewitMztp9Ovs7wOyQ2ME9CjEsazesFnvN9bt6Jt2TXskIrKD3YAcuItSedwCT2MEdqvsR9HXepfu4Kq95vDc1pl1B9xuG8gKjRFQo0S/owvVafjq809jz8y6UWI3iwtvJGdExDeV+P1Y48zqh93xwRL/ELM0XGI7+0VEgv39FSvRwfzvvstxwkVXqAV+SXFq2/f97hyxX3xl78EDAIDdKsrv6Dts3in4MMXpNAAZSGOBpzECD5Xj0q6tmRmzdqt0SNnEAnfIN0TvbolCY0Rp5NgSi3Ae/C7dMR/vXeMA2JW712g0RiAD7IM7JJKJAAASKklEQVQHAECh4gR8/A4XcVxcA8gYjRHQoBAB7w2bxtTHJ65dNZG24UrYQEZojIAaRTjIzhs26+MT97JXe8zLW+PA3Xt98vOvRaRSXcylcIaF/xsREWNF5P0fv5N5dXiYRy3wNMai2PIEfc6DL76SnwfvXs+kcbhxjVE7bMjs2s2yIqCkaIyAHkU4ir5+5Mj4tSetDZ2G11finNQzLqqUuKN86dEYi4KuOZ6uCD342rMTZ7bpVlXTbr0/c06ePXGTIIAt0BgBPYrQg5da79L2pt2158Y6A9daViibfP3pTERuDr4nIia2w7zi3wYjmMS+HyvhPnQx8WvNB+OY+Q3pKyIS3KI++UYrIu+890EqU4JioDE+WsaXtaeLj3uV6FAXjutBqRR5gS9ybcBulfwgOwAAsGOF2ESPTX45+zeJtpZbUxWR2+qBf1sREXtrRMT6Rhab2EUkvKlrdIPZYHO7GGNFxAQvWV9Eqrc3Em11D05/s6Z6W62KiPUrIuLfhkPXFmYqNvh71cqNiPzwT3604ykHimSP7irLpnvM0YMHAEChEu0JY7cfSqXIC3yRawN2i33wAABglwh4AAAUIuABAFCIgMdjfDP797xLACBffvnlHh3hj4wR8AAAKFSiY1k5cBelUuQFvsi1AbvFUfQAAGCXCHgAABQi4AEAUIiABwBAIQIeAACFuJscFr74InZCrRUR8d9URMT6IiLBXew++MkPnvhXvv50JtEt8t74b4nIj97/4RM/E1Dm3rPbd3LXuKW/wp3olKEHDwCAQvTgS+SbTz4WkerNdyJSsb6I+KYqIn61KiJ+5aBSPRAR31ZFxL+piMjtm4pE/fjb74yI/Os/X4uI9YPbyocdfRu7bXylakWkcuCLyMHbvjnwRaT6lhURU/VFxJi3RUSCt/vr7zcP6Pb0y89xATvcix48AAAKleh6Ulw8C6VS5AW+yLUBu8WV7AAAwC6xDx4LwVH0/neLve83/1cRkdtvqyLy5tdVEXnzq6qItP+2lmOdgHpb7mLnuHfcgR48AAAKlWhPGLv9Hu1nH/2niNx+WxGRm2/D/v3tjRERe2tEJD5fg6Poj//++3lUioUiL/BFrq3IHnHkPF383LEPHgAA7FKJfkfTaUCpFHmBL3JtwG7luLSX6yA7Y7isClAINEYgbfyOTtF+dVOoNiV7VKpie/Qt7FGpQrXFxj54AAAUIuABAFCIgAcAQCECHgAAhQh4AAAUIuABAFCIgAcAQCECHgAAhQh4AAAUKtdlfQAAKAl68AAAKETAAwCgEAEPAIBCBDwAAAoR8AAAKETAAwCgEAEPAIBCBDwAAAoR8AAAKETAAwCgEAEPAIBCBDwAAAoR8E827ZpQc+htGskbNo3ZYrzUbVVtcvQcy92y2vjc7U6zKy9uu1KLUKlme9QYaYnpoTHOWTzFpCPiDNyVxwnuwJH5S8ET6UwyrTOwVbVL498/Vlq2rHbSib0y6eQyb7cr1R04ydHyWQrU2qPGSEtMD40xhoB/CnfgJBafSWfdYuIOnOTglQHZ2K5am3g9v9XKltUuj5bHvH1AqfHh981/PMgeNUZaYnpojAlson8C72I8k8ZhbT6gfuTI6NXyxp5a79Las1ZswGFD5Op1xpvbtqx2PvrwdOQMBp1silv989tV612MZ87Js8VoKzM7fQ+csUjFHjVGWmJ6aIxJBPwTOUf1xZPaYWOb90xfjSSxEGZm62q94fO+DM57hxkUtdEW1brXM2kc1h64P3P3tpmxtWcnjoxOwwKn3fZIOsdZrwBV26PGSEtMD41xgYB/Avd6tmbofb2Babc9EmfwYdZL0wOqjVYqOfwEiWxXrff6SmTUNq+Owy1S7sm4nvUBM1vP2Frv0k4a/boxxpj21cDNvoOj1x41RlpiemiMSQR8tqZd0x5JZ3KZZ5O9RwFWKg/iDNx526z1XnQKu0Vu2jWmLZPYCjDP8ylQ+MZIS0xPSRojAf8E9SNnzdDNm/umXdMeOXn9Vtyy2oKsVB4wb5MDs9/ntvWMPR1JZxJ997Xe+cCZ9V8Wdg24Z/aoMdIS00NjTCLgn2h27S6eeK+vNo3nDZvBCiXX7sL91XoX45nMwi1XxrRHEjzL4zzR+6vdsIMtsRMuE1ssBu71bM3ewcyPtdRsjxojLTE9NMYFAv4Jas9OnMRC4V7P1h6q4Q2b9f6sM7F5pvt21dZ6l/GzLObnkWbdz9ly3raOl7cDhgf7ZFJkYMtS60dOctUjIjkda6nRHjVGWmJ6aIxL0jwHrwS2uahC4pIKuXro5TW2HSsd21+wYvHK8lmwGdmu1MTlNIqzVKixR42RlpgeGmMMAf9U4cWwRJJLyOJCCrER4vK7aMWd1S7Jc7WyfbXRhUBym61blxqrVOcKJV971BhpiemhMc4Za+26JR4AAOwx9sEDAKAQAQ8AgEIEPAAAChHwAAAoRMADAKAQAQ8AgEIEPJ7IGzbNhgtoesPm4pVgvJzvJAloRmNEAgGPJ6r1XnRk7V0lpi/70WUivWGz3m+E15iYNPp1VivAztEYkZTbJXagR+Kyj4mh4QWili7DtfFyXQCehsaIBXrweLrW8Zpuw/TVSJyTZzURkdaZzfVGO0BZ0BixQMBjB1ofDpbv/RxfpSR5w+f9mTP4MPP7cAMlQGPEHAGPXag9O0muVNavUqZdY0y9P3MG53QhgFTQGBEh4LETyZWKNzwdSefFynqjdWattdY9Gdc5ehdIB40RIQIeu1HrvehEKxXvYhwdsbt53Nn4gpUKkAIaIwIEPHalddyR0enQu3eVIiL1I0dm125mtQGlQmOECAGPHWodd2Q2vphejJcO20lcY0NERNzr+9Y6AB6PxggRMdbavGuAGt6wWR+LM5MTN3kizrRr2leDaKA3bNbHy6MA2CEaIwh47JQ3bNb7M2ewZn0x7Zr2KHzcmdgzegxAmmiMIOABAFCIffAAAChEwAMAoBABDwCAQgQ8AAAKEfAAAChEwAMAoBABDwCAQgQ8AAAKEfAAAChEwAMAoBABDwCAQgQ8AAAKEfAAAChEwAMAoBABDwCAQgd5F1A4v3Vgf/Mtefst+xsH8r0DeatqD6pyULUHFTmoSrViqxU5qNpqRSqV8Gkl/H/+wAaPKyYcGPxvzPyxGJMYaGIDTcVWjJhgoLFmMSTxkjHBu6wJhqy8xSTHjJ6uDI+GyGLMtcPDlyT+4cmn4ZjGGusbG/zvG2uN7y8exx/4iyEyf8m3xvoSjSPRkPk44sdesnbd02hMa40fDbe+8X0JH1iJPjB4u0QfK9aXsIDFR4m/+KjFW4Knwch++AmrT8O/69v5U/GjMYMHtzYa4stt9H/8340vN7dycytvbuXbW/n1beVba63Nu6Gkz5i8K0jdl198kXcJKXr33T/Ou4QMmCI3RnrwAAAoRMADAKAQAQ8AgEIEPAAAChHwAAAoRMADAKAQAQ8AgEIEPAAAChHwAAAoRMADAKAQAQ8AgEIEPAAAChHwAAAoRMADAKAQAQ8AgEIEPAAAChX6ZvW5MMbkXQJwjzI0W1oi9kKRG+NB3gUUUZG/sDljCvrjrLCF3WtfKi9J8mX8XezLt/8U6qdR/QQ+FJvoAQBQiIAHAEAhAh4AAIUIeAAAFCLgAQBQiIAHAEAhAh4AAIUIeAAAFOKyAAAAKEQPHgAAhQh4AAAUIuABAFCIgAcAQCECHgAAhQh4AAAUIuABAFCIgAcAQCECHgAAhQh4AAAUIuABAFCIgAcAQCECHgAAhQh4AAAUIuABAFCIgAcAQKHyBvy0awLdaTjEGzaXByV5w2Zz6GVX4sK0G9W0KNIYY8xSPasTlXWZOf71+8Vm3rzEzTXnPDNXJBa/os9qlabdzNr/9uuax4wZNoTu8ClrtJ3MDW/YTGEZfsCaOsPvNBe2nCYd6UwSj9yB4wxcGzyKXoxzB45IOEqmJh0RWa1otczVicrUpBPMng3zL3exuuYPN9ccvRJfMvKUWPyKPqt1KsaCsAM7mZDdzI28l2A13+kGZQ34hTAL7/ui3YHjdDrZLwzuwOlM1gX2nRmeR8AnfiEVvdGEJW6uOf68ANOTXPz2alanyx04nU4n6KwEi/zqzAlnnoiIM5gMwgeutdGP58R7gzHDdULs1ejZ/JeVxD4n+cbdTJczcFenLlbU8iIQTktnMHDCetfPmdg0z9+bnNQ1A5Y/LTE3Hjd9IiJOp+PEeiV3/cVEVSuzPfnNbpx7uX6neSjvJnoJN1S1ZXLWEnGvZw25aG7Y7ukNn49Pzj88yr7GWu/yrLU62BueXg0+XPNCYqIy5V7PGoc1EZHaYWN27Wb85x9k+rLfeNGr3VFz7bAxG18E2zMvxrN8yowsL377NKvTN5Jja62ddEavNm7rnV0dnVvrDqR/KsGD8YXnDZunR+EmEWmHjT4Y0561vOHz8Ym7+ORa73zgOAP3slfzhs/7jYm11k4a/efhFt75G1OduunL8C/bSaP/Mja90277auBaa4+v+7P17w21zsJcn5c67dbDSXUHV+3uVJanffXTYnPjERM1n4HnR1ezcMia72Kp/jtm+9I3u2nuFeQ7zVCpA77Wu7TWHr8KA300lvOlJSwQrF8ftSSnZPqyLyfP1ha0NFFYMe2a0yP3vkbbOps0+nVjjHl+3XDuHjddxVv8isU5qouI1I+cq9eb9qY6UWtxYs3GvZ7Ngq/YtEcSvnk+Qq13eS7Pky8u3tg5bomItI470Q8sZ0ODfKKlqasfOaO2McZ05SwePN7rq7CA1nFnw3s3WbxXar1Le9ZaP+1bftoWvIuxBN2TWu9FUO367yL5F++e7Wvn/9InFOQ7zVCJAn5+zNRS9M0X2M6LcCW6tAh7F+Ng4av3Z7N+Pe1jMjbVGR/l1Whe7Ho7aIUPtfiT3uursGEVjjdsmtOjeb/jzppbZ8FWrstjiTrMeViz+O3FrM6fe33vlpfYxtflvui0a+rXL4LeXmolPljw+90dBDGf1o/4XKb9ju9iV4r5naapRAEfra+tPWvFDksPt3e2jhfbohZbQEUkalM22oeV1sK3ts61Nq3VVyYqvSLXmG/U9i7GeQbiZt6wWb9+EV973FHzfGZ6w9NR+Ns+F2sWv+LP6nwFHTDv9dXdo9WPnNHp0JONx3IHX/v01WjNG4OVxfTVKNMfWGGhtd6ltZNOrBO62KW0Wu59YrujZNoNz8zZNO27UHt2IuH+hegP3PtdyI5me/G+01SVKOATWmcTaQf95HBzbevMPTpNDIkHZqEsp3dU5+pEZSraqF3vN7I/AmAL05f9mYzaiTMMV2temZlFnJyiz+o81XovOqP2NrtWar3LcDfMuvnYOg4+xrySTvCToXbYCDah1Hrng6u2Mca0ZZL2D/6VkqM23r4axHbczHcpvZIHd05bZ+7JONw+LpPLXm112teUEs2NR01GNANPr5z5hG3+Lpbf9djZXsjvNFXGWpt3DQCAnfCGzedyriei8BRl7cEDgB7zQ3fqHJGJOXrwAAAoRA8eAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUOj/AbU9SpDtWcPnAAAAAElFTkSuQmCC" /></p>
<p>The gating process took about 19.1 seconds on a machine with the
features listed at the end of the vignette (4 variables, 2 gates, 2
cytokines, 400,000 observations). The corrected significance level in
the first gate was . The histograms for the two cytokines are the same
as above.</p>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Plot of Cytokine 1</span></span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">2</span>), <span class="at">pty =</span> <span class="st">"s"</span>)</span>
<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(out_gate<span class="sc">$</span>obs<span class="sc">$</span>Z1[out_gate<span class="sc">$</span>obs<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span></span>
<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> out_gate<span class="sc">$</span>obs<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"2"</span>]),</span>
<span id="cb13-5"><a href="#cb13-5" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"red"</span>, <span class="at">main =</span> <span class="st">"Cytokine 1 of cases</span><span class="sc">\n</span><span class="st">post-gating"</span>,</span>
<span id="cb13-6"><a href="#cb13-6" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">30</span>),</span>
<span id="cb13-7"><a href="#cb13-7" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.2</span>))</span>
<span id="cb13-8"><a href="#cb13-8" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(out_gate<span class="sc">$</span>obs<span class="sc">$</span>Z1[out_gate<span class="sc">$</span>obs<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"control"</span> </span>
<span id="cb13-9"><a href="#cb13-9" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> out_gate<span class="sc">$</span>obs<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"2"</span>]),</span>
<span id="cb13-10"><a href="#cb13-10" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"blue"</span>,</span>
<span id="cb13-11"><a href="#cb13-11" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 1 of controls</span><span class="sc">\n</span><span class="st">post-gating"</span>,</span>
<span id="cb13-12"><a href="#cb13-12" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">30</span>),</span>
<span id="cb13-13"><a href="#cb13-13" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.2</span>))</span>
<span id="cb13-14"><a href="#cb13-14" aria-hidden="true" tabindex="-1"></a><span class="co"># Plot of Cytokine 2</span></span>
<span id="cb13-15"><a href="#cb13-15" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">2</span>), <span class="at">pty =</span> <span class="st">"s"</span>)</span>
<span id="cb13-16"><a href="#cb13-16" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(out_gate<span class="sc">$</span>obs<span class="sc">$</span>Z2[out_gate<span class="sc">$</span>obs<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span></span>
<span id="cb13-17"><a href="#cb13-17" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> out_gate<span class="sc">$</span>obs<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"2"</span>]),</span>
<span id="cb13-18"><a href="#cb13-18" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"red"</span>,</span>
<span id="cb13-19"><a href="#cb13-19" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 2 of cases</span><span class="sc">\n</span><span class="st">post-gating"</span>,</span>
<span id="cb13-20"><a href="#cb13-20" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">5</span>),</span>
<span id="cb13-21"><a href="#cb13-21" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.5</span>))</span>
<span id="cb13-22"><a href="#cb13-22" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(out_gate<span class="sc">$</span>obs<span class="sc">$</span>Z2[out_gate<span class="sc">$</span>obs<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"control"</span> </span>
<span id="cb13-23"><a href="#cb13-23" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> out_gate<span class="sc">$</span>obs<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"2"</span>]),</span>
<span id="cb13-24"><a href="#cb13-24" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"blue"</span>,</span>
<span id="cb13-25"><a href="#cb13-25" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 2 of controls</span><span class="sc">\n</span><span class="st">post-gating"</span>,</span>
<span id="cb13-26"><a href="#cb13-26" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">5</span>),</span>
<span id="cb13-27"><a href="#cb13-27" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.5</span>))</span></code></pre></div>
<p><img src="data:image/png;base64,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" /><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAqAAAAKgCAMAAABz4j/3AAAA2FBMVEUAAAAAADoAAGYAAP8AOjoAOmYAOpAAZpAAZrY6AAA6ADo6AGY6OgA6OmY6OpA6ZpA6ZrY6kLY6kNtmAABmADpmOgBmOjpmZgBmZmZmkJBmkLZmkNtmtrZmtttmtv+QOgCQOjqQZgCQZjqQkGaQkLaQtpCQttuQtv+Q29uQ2/+2ZgC2Zjq2ZpC2kDq2kGa225C227a229u22/+2/7a2/9u2//++vr7bkDrbkGbbtmbbtpDb27bb29vb2//b/7bb/9vb////AAD/tmb/25D/27b//7b//9v///+E821cAAAACXBIWXMAAA7DAAAOwwHHb6hkAAAcp0lEQVR4nO2dC3vkSHlG2+Mdx14WWMbLkoTgCRAIbkISBjYdQtjY7bH7//+j6N6lbkmty1elt6RzHphty3Kp9PaRVLpVbQ4AwmzmrgBAFwgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIE0IQd/+8tVms/nhp7Pp//ZdfcJ2866Y8vZxc/PUXernbxsLzf7693ebzdfjKquKeohn9SinX65EJwEEff3pJudDffrnn76bkO3+Livz6rHpdw1Lixz1EM/rcehbiW78C5rUsOSh9otjku1Tukp993h4uWtc+11z5BEjH2LrUvUF3W0273+bbGJJxDf/93Fzm05Lts6HbZp2ulb/kxxmvvjHdCWytXy937z7lK9WktHvfp/8eRbUW/Lp6utyXV+/vbs91HOpytnW9grpofGLX2QzpHuhH2bT/zuZePXjTyflOlPF0AnRWZJTclGPZMpvfpos2ZmrEHR0tN4FTbfSbPXf/vnrvyXrlP2QRlJmu8t3DDdP+eRk/iSWMttNdQhKIk95X99OnWyP5dSy3VZHxv2xsGLe9G+dcp2pYuiE6C7JKbkStPjdca5aJUZE613QJJPb40/J4eShnJbnkh9gdtnaJ1P+/DE7iFWr9f7T8Xef0plrrSLn6OSW4xydEit/8vT5Pv/S/u4pLyFd/tPhLyflulPFkAnxZI5ayfkmfvPp8L/uXFklJkTrXdB6HG/Z4Wmf5Zev0/a4O0j/+Vm+ElW2D1kJt+nXkW+/7kaY7hDKJplbjpNtEdyP/5j99Nd/T440t2mJ7/9YFVGW60xVQyfE+hxVyUdBH07KySoxIdrAgubhbKtjUdWG3lUHiiyWqvn0WOwqXu6cI1VBsk1X236tnGO2bhP97Vd5CbfFKUfWRHLKdaaqIRNiwxzunnznLjj/Mfs8IdrAh/js8FRsyGVrvmrxF02dm6eGbIsGpJttGndlX62cWrbl0tOQ3v/LX7P5PucXba7+tVbucaoaMiE2zNEgqDtXXonx0YY8SUpP4tKVLVajceO/+UOt+eRu/PXrK/Voe2z8+V6ozO7zr7/KvsZ6ueVUb2mMRCbEkXvQw/how15myk79rr7K69nYfPouWV/n3K9K4GQfkjed3NXtbD7tf/jbos3mHCzffpkvrl5uNtVTFONRCbFhjgZBz9qgeTGjog1+oT5rB2WO5GtzcgL6XS7SWbbJ765+kTaYyrXdnmyO7SegX2dNoIdshvQbvs3PStPDTnY5pSzXnaqGSogNc+Ql74rLd/nfnJ7FT4g25K3O7MZuup75drTfNF3CO5St6pNsi0t4ZWhVe7/hEl7tJsi2fmaUfTz8/tgUc8p1psohEmLDHHnJeT2qvzm9Djo+2oAPixTXGfab4jiT3tV4X950+Hk6pbqo9+E828PnXyVxVvciyovEpzdBfp7/0kkiuwmSTk7P4t//Nr/G4jx54ZTb8jyGBCIhns+Rl5zX4/g31VzFIX50tOEft9uf3k6G4awnxOCCJg0RwZOQyFhRiIEFzRpBercS42JVIYYX9OonYRe5PFYVIq98gDQICtIgKEiDoCANgoI0MQna9mbrySxTX9NaDVHkGZGgrW+2nsyCoP2II8+IBO3xPu2AV24hjjxVBE2i+M9v8+ceDu6rrcf3Vbe1pxqyhxMe8wCr14nzWf7c/LZtOfc6WEyeOoI6D2Sdv9qaPYjrBJo/O3f1VfHsY/GX9UCPBbpzr4TF5Ckk6LtP6Yupt7XHXU9eEK7ySB83e3pL/8h9ndh9AcJ9J9aZe851DMli8hQS9OHgvLRQfHbfV3UD3ZadLuSTiteJTwI9eSe2mnsNLCZPHUGzlXVfs9qdvApcvsCY9/5yfCPn+DpxPdDqado3d+6VsJg8xQRNH8StvdrqvK/qBPp9MUvxVlb1OnFzoK/O3POtYVgWk6eYoKdb/MF5X7Vli3dfJxbY4kVYTJ46gja2mfJf5u+rtrSZ3NeJmwOlDRpxnkKCNp11uu+rum9xOeeRzuvE+SzngXIWH2+eQoIe3y90rts576vum6/bua8T72sXlo+vHK73Omj0eeoI+u7Pv6reiD2+2uq8r1q+YZuR/vCjT9VZZ/E6cTbLH8/ftnXmXgmLyVNI0BErux30GMOwueNmMXlGKug262Ijv2xsPfciWEyekQpadiTYry+VYXMvgsXkGamgh8/f3g3olX/Y3EtgMXmqCArQCIKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgzRBBX+/ToSXcNwVgCuTZg8GC7tKnqF/vVzKMlFfIswdDBS2i3LU87L9ZLBZhk+eRviENFfTlLgt033JQWmyT1peg5Gk146HfFj+guKiYaw/qYbESeBI03TffHsrm/cTiosKPoORpN2NOOgrfY3Li2TZSJIEOgzzNZpylOB1mWjHyRNB+IKgtvgXdcdZpCnlOnrG7lMGXt2Ij7IqR5/AZZylOBw7xtiCoMQhqiydBy74jWx9uINBBkKfdjCm78npd64U7Ah0CeRrOeEi39ypGbs0ZQJ6WMx5qD4XxcIMB5Gk544Et3hrytJwxZbcpNnnaTCaQp+GMGfnzN5v2vskJdBDkaTfjLMXpwHVQWxDUGAS1BUGNQVBbENQYBLUFQY1BUFsQ1BgEtQVBjUFQWxDUGAS1BUGNQVBbENQYBLUFQY1BUFsQ1BgEtQVBjUFQWxDUGAS1BUGNWbig19eBFlSCoMYsW9BrBI2dhQua/S8kCGoMgtqCoMYsXtDAhiKoMYsW9Lr6JxgIagyC2uJV0GJkCqviosDnis2e51IELV+S7ejuCkEHIJPnUgQt+xeYfYufAS8rppLntfNvILx13JB2MTB7oDPgq+MGhTyva/8Jg7c26PbqcfZA58DXiinkuShB0z4t5w50DrytmECeyxI02d6/QFBD5s/z+uS/IfB5ment4wZBDZk9z6UJGrA4HRZ8of767EMAfAvKwFO2zJnnIgU9LYWBp2yXFjLPNQjqqzgd1nCID2koghqDoLZ4EpSBp2yRyHNBguoNPPX8HGhBXlZMI8/lCCo1bMpzSZjF+VgxkTyXI6jSwFOpmJmcEQsqkud140fPLH4P+tzwySfL3YNet3z2i682qMrAU8+NHz3iqQ0qkOeSBJUZeOq55bM/fD0POn+eixI0dHFtPLf+4IvlXge9bv3BJ8sW9LnjJ08gqC0IagyC2rImQYMYuhJBgxm6aEFPhUTQCVx3/ugNBDVmNYIGMnTJgp77GMDQtQgaaheKoMYgqC0Iasx6BA1j6IIFbbARQcdz5iOCTqTJRv+GLlXQBh2DGIqgxiCoLcsVtNFFBB1Lk40hDEVQYxDUlpUJ6t/QNQkawtDFCtpiIoKOBEGNQVBTWlT0byiCGoOgtixV0DYREXQcbYJ6N3Rtgno3dF2C+t+F+hR0v9lcPdoVN4glCjpnnksTdLvZfHj50ZPb5cCU4gbTrmGcgs6dZ7uIvg31I+j25ikblmK2jgYWJujseS5M0Gw7f/kyDXSmrlo6NPRsqI8Vmz/PmAR9vd/cXpj39T7t/+LtbwfBPaicoFHk2a6hnqBpRyybth5YyjnK7TyPdspyR9EloZqgMeTZpaFnQ0ce4i9lustPN/et46YgaA3xPOMTNI+0tb9fw+WOolNCv4aOXTHpPKMTdJ+k+XB4+9jal5XdckcRm6DqecYlaNrTWp5k2ymlwyzj+lxQ0Kuhw1dMP89uCf0aOuYsvvV2Ro9SgozrE5WgEeQZmaDf5Hn22NwtljuGuATVzzNOQdsONsbLHUOUggrnGZOg2+NBpeuyyKzj+lwU0KehA1cshjwvOejV0PF70C7mHdcnJkFjyPOSgWKC9mDmUSniErQHc4/ysThB5x3X57J+sQk69zhJEQn6ev+hHHCi477HvFt8D/08GjpsxWLIMypBezLruD4xCdqTmcdJumSgT0M9PVE/57g+CxR05nGSIhM0feRr15GV7XKHE5ug6nle9k9M0O3N08vd7WF76TFbm+UOJzZB1fOMTdD0lDJ9LlH11lwv+fwZOuJevHaeffzzaOg4QbdJmKq35mIUVDnPPvZJCZoci17vb55e70UPSbEJqp5nfIImZ5RXj28fJ+WJoEfE84xP0LDLHUx0gqovFkFN6acegvaml3z+DB0h6MVHv0yXO5Se6nkzdPiKaecZoaDbSUkOXe5Q4hNUO8/4BG3tO8DPcocSnaDiefZTT0vQts4DvCx3KBEKKp1nT/W8GTpc0KkXRAYudyB9xdMRVDvPCAXt6H/Fx3IHEp+g2nlGKGiPB2wtlzuQ3uL5MnTEIV45z77iCQkaeLkDiU9Q7cUiqDEIakuUgiYHpZun7bSLI54CHaCdJ0NHrJhwnv2982XomJOkq8dd+vTNpEQRtEI5zxgFTV8xTN8tlHx+MUJBpfOMUdD0wnIaaOcT4Lusw8tD8O4CIxRUOc8B1ukIWm7x2463vNIeq/MncBH0Esp5DrHOk6Gj26C7jsvLeUcDWYfBYQMdJJ0fQ8e2QSXzjFPQ/NJyV6+r5e3lZKeAoJeRzXOQc0KCXqTqqmV7i6AGzJXnYgWtDkTJvgFBDZgpz2HO+TF07L34C/1glC2qt48IegHhPKMUdFtc7rgwNprZcocwUDkvhg5dMeU8YxR0XzbmX+4mPSSGoDnSeUYoqPN0bb++hII26uMTVDrPgcZJCOrcMR51a87ruD5DhRMQVDrPOAW92Bm18XIHMFg4H4YOFVQ4z6HGeTEUQY1BUFs8CTrLuD4LFnSOPAf7FpGg84zrs1xBZ8kzUkGPzXK1USmG66YgqG6ew33zYaiXW53zjOszQjcPhvo4NMyT54IFjWUPGoug7EEtZ0yZZVyf5Qo6S54jbItH0FnG9VmwoHPkOcY2D4Z6EjR0cYdxskUj6AyLRVBjRslmbyiC2oKgxiCoLQhqzKoF9WAoghqzFEHHqYagrYxUzdxQBLUFQY1BUFsQ1BgEtWXtgpobiqC2LEXQ0Z4haCNjTTM3FEEta3FAUNNaHBAUQZtBUNviENS4PAS1LW6CZ8aGrlxQc0MXIugEyxC0gfGaIWgjCGpbHILaFjdFMgRtAEF1BDU2dO2CWhuKoAjaAIIiqC22i50iGYI2gKAIqizoRMVMDV29oMaGehG0R4cuCDqA0HkuXtD2vv7HFXeJpQsaOs/lC+p2bW1R3AUWL2jgPFcg6GHfMbLfiOI6mSyYpaGe2qAh85yqmKmhSzhJWoOgQReLoAhqDYLqCjpdLwStM9UwS0N9CxpgXB8DvQwN9SxoiHGSJvsVk6CnpXgY12dVgp4uzcc4SWsW1EdxFnbZGbqAQ/x0vwwNjV9QE7cQ9IiBXfqCBhzXZxWChhwnaQ2ChhzXx8YtM0O9CBp0nCQLu+wM9SJo0FEpViBo2FE+ViBoyHF9jMySFjTsOEkrEDTkFm9lllU50e9BbdwyM9RXGzTUuD5mez5lQYOOk7QKQcON62N3+m1Ukp+z+HDjJF2vQ9Bgxa1E0HCLtTLLqpzIBTW8R4mgGQhqWpzlc0g2ZUUuqNmhGUEzENR4sXbXh4xKiltQ07eJENTsFCkryqYYBDUuLXJBbYoxLCtqQZ8R1HixCGpanHX33RblRS2o7RvDJqXFLKjxDhRBEdS2OPuRYA1KjFlQ685nLcqLWFDzHSiCWhRiXF7Mgk4v4qzI6WVGLKj5EDIWF63iFdSDnxaFIqhtidEK6uEAb1JqvIIaXqQ/ljm5hHgFtaiFh2IjFnR6ER4KjVVQPzvQw3RDoxXUi5/Td8vRCmpSCw8FxyqojwO8RbmRCurNz8lFRyuoRS0aC55WMoKeFT2t7EgF9eZnauiUwuMU1KOfUw2NU1BfB/jppXsS1G9XLd7OkAyK9yOo565v/Po5aQG+Xjv22lWLXz+nGerptWOveXr3c8IivAjqt6MBz/vPiYvwIajnjhsC+Dm+JepFUK9dtQTwc8pCfAjqNc8geo5fUHR70CB+TlhMZHvQYHqOXZavNqivrloC+Tl+QZ7aoH7ynHYFKMjiPJ3Fe+qqJZie4xfm5yzeT55h9Ry3xJiugz4H9fMwTtF4roOG13PMUqMR9Dm4nuMWGomggQ/u45fsW1CLcX2en2exc9zCPQs6Mc/rCsM6DWbI4gPvQathff5rsZjkRJ4VvaMwTta2OB0iOcRHQzRt0FhAUFuifFhEmSgfFhEmyodFlInxYRFlorvVqU5ktzrlie9hEXGie1hEHPagxrAHtWW2h0UWy5CcyPMyfTMyfljEZFF9Z5xrPjvIM0whxouKOtBwrCNPBB0+nwjryBNBh88nwjryRNDh84mwjjwRdPh8IqwjTwQdPp8I68gTQYfPJ8I68kTQ4fOJsI48EXT4fCKsI8/IvhRYGwgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNGEF3fZ5vzbrUavlPfEj+83m6tGqsJxetZNiBXkGFXTf5wXwt49JULvN7YWikpn2lxPtV9iA2kmxhjxDCvp636fKL3dpdxttfWIX5L3GbC8G1auwIbVTYhV5hhR0d/PL3lW+sDUPCOpyYTlDaqfBKvIMKOjLl4/9WyXb7qySsg7tfcINLKwsMbI26DryDCdoehTpXeXW3rTK32fbcK8t+XJhKYNqJ8FK8gwnaNrDYN8q7/u06fsGerGwlCG102AleQYTNDuI9Kzy5U10wCGpz/Y+qHYarCXPEILu0ktnu6JfyIdLMzpdt7fTv1Hfo7BiyZdqJ8Oq8hS8UL/rsVp9L4v0Kqwkqj1oxgry1BP05a7PJtrzwnK/wgqWKWjkeeoJWhwdLoW163Vrrmdh/WunxQry5GERkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRojQd8+5h2jNfd28nK3yfuUrPpXOZ/S1PXK9lI/K/XehF7vH5zp+wdnwvlfuuXuTyqxP/bN5tZvjr7vOoM9DrlRrcHpqtQIlWfy/f7gu6ISeWidX3MnZoLmvjXmuE8mvt4nv98mdcs6+jufUn1wyUvbta9RW3dXyfQ0zPZAa31lVT/UKpHVL+2QMPtVWon9DIZ2BXsccqNag+pDVXGXQHmm2WWbVRVa99fciZmgX2RdoDbnmG7kSWKv99mHm6fzKdWH2l/mpeW/a2RsoLXeBqsf6pVIv+JsytvH2+z/vbontKYr2KpTz2oN6quSV9ohTJ7Z7jQVtArtwtfciZmgt7usNk05funsqbJ/z6c0d0FdBprGss2PFq/3/3SfHzbSg8Wvr36XhpBvpTff3x+n/yZpQyQT/uGu8cBc66+1+qFWiWNHgzML2h5sTppnuQb1fmhbBfWbZ9oH874m6IWvuRM7QbP1LnJMm5hVa2f/7k/3WVOpqN7moWFK+aFWanFIKt1Ijxiv9+lhLfl/OtLEPllCujmmh7lkI85rUEzPt/hi5tMq1Xq8rn6oVeI4ksVu3kN8e7A5SUWrNaj35H12LA+T56H6WIZ24WvuxE7Q1n7zd+n+Pp2h2M42D+dTqg+1v8wb9el4UK/fPObbaXaQSD7kf7DNN8rt3988JRmlGVbT80A/HBqbPLUt+bhjdypRHQf3p6chYekKNiPtMr5xD7U/H7IwTJ7ZhNzVIrQLX3MnhoK2jTySb3JplfMmciLo2ZTjB5e8tHJUiX16dMm26uSfPIG8bfT6zW9+8N0+bdE+HNzp1cxnVWoW1K2EE/bbx1SQpNxB3Qsb0RVsyr48R2o4hGYVdwmTZzYh+7MqtO6vuRNDQdNaNQqaVTY/iUtaz3/65vF8ivPBoSgtXc+kJfTuP+6OGe3K4A7bDy8/+v6bx6wt/nDY9Qq0+RDvVsJdEbeVZxNXf7qCPZRDbrQc4lva9L7zPJQfndA6v+ZOLAVN1q25DfrdwTlVesm2zpMpJx8KitLK1v/LXcMWnxwA/3B72P7kY/671i2+3mZqPElyKlE7001mGNG6t6Er2GrIjZaTpLOjcZg8U7I/Owmt9WvuxFTQly+/atjQ8zWqNq/sasPplJMPBeUWf/OUr7BzSCoiSY8YP/jZh8MuvRhzbDPtLmzxzZeZnEoUX23+n335zfcdKtCQrmCrxtz5Zabm+obJ83Co7UEvf82dmAqa7MAbc0wmpquQXfrOLyOfTjn+yqVsMz0UG/vmwzGj/AyxPA/Nhn7OfldOT/eBrYE2X6h3KlH+bltUdNY26KEl2GN9zi/UVxV3CZTn4bQNeuFr7sRW0Nf7xo1jX9yRSyI53pGrTzn+ysG5NZfdIitOJovksutzj447r851u8f0O/2+NdDyllte791ZJaqj1ba8WbfdnJ8VB6ArWGfIjfNbiVXFHULlWe02t72+5k54WASkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWn+H0NS8bZekPDFAAAAAElFTkSuQmCC" /></p>
<p>Compare histograms before and after gating. Gating reduced the
overall sample size of observations from 400,000 (cases & controls
and Condition 1 & Condition 2) to 73,316 observations (cases &
controls and Condition 1 & Condition 2).</p>
<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Plot of Cytokine 1</span></span>
<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">2</span>), <span class="at">pty =</span> <span class="st">"s"</span>)</span>
<span id="cb14-3"><a href="#cb14-3" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(df_full<span class="sc">$</span>Z1[df_full<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span></span>
<span id="cb14-4"><a href="#cb14-4" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> df_full<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"2"</span>]),</span>
<span id="cb14-5"><a href="#cb14-5" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"black"</span>,</span>
<span id="cb14-6"><a href="#cb14-6" aria-hidden="true" tabindex="-1"></a> <span class="at">lty =</span> <span class="dv">1</span>,</span>
<span id="cb14-7"><a href="#cb14-7" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 1 of cases</span><span class="sc">\n</span><span class="st">pre-gating"</span>,</span>
<span id="cb14-8"><a href="#cb14-8" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">30</span>),</span>
<span id="cb14-9"><a href="#cb14-9" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.2</span>))</span>
<span id="cb14-10"><a href="#cb14-10" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(out_gate<span class="sc">$</span>obs<span class="sc">$</span>Z1[out_gate<span class="sc">$</span>obs<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span></span>
<span id="cb14-11"><a href="#cb14-11" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> out_gate<span class="sc">$</span>obs<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"2"</span>]),</span>
<span id="cb14-12"><a href="#cb14-12" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"black"</span>,</span>
<span id="cb14-13"><a href="#cb14-13" aria-hidden="true" tabindex="-1"></a> <span class="at">lty =</span> <span class="dv">1</span>,</span>
<span id="cb14-14"><a href="#cb14-14" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 1 of cases</span><span class="sc">\n</span><span class="st">post-gating"</span>,</span>
<span id="cb14-15"><a href="#cb14-15" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">30</span>),</span>
<span id="cb14-16"><a href="#cb14-16" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.2</span>))</span>
<span id="cb14-17"><a href="#cb14-17" aria-hidden="true" tabindex="-1"></a><span class="co"># Plot of Cytokine 2</span></span>
<span id="cb14-18"><a href="#cb14-18" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">2</span>), <span class="at">pty =</span> <span class="st">"s"</span>)</span>
<span id="cb14-19"><a href="#cb14-19" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(df_full<span class="sc">$</span>Z2[df_full<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span> </span>
<span id="cb14-20"><a href="#cb14-20" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> df_full<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"2"</span>]),</span>
<span id="cb14-21"><a href="#cb14-21" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"black"</span>,</span>
<span id="cb14-22"><a href="#cb14-22" aria-hidden="true" tabindex="-1"></a> <span class="at">lty =</span> <span class="dv">1</span>,</span>
<span id="cb14-23"><a href="#cb14-23" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 2 of cases</span><span class="sc">\n</span><span class="st">pre-gating"</span>,</span>
<span id="cb14-24"><a href="#cb14-24" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">5</span>),</span>
<span id="cb14-25"><a href="#cb14-25" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.5</span>))</span>
<span id="cb14-26"><a href="#cb14-26" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(out_gate<span class="sc">$</span>obs<span class="sc">$</span>Z2[out_gate<span class="sc">$</span>obs<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span> </span>
<span id="cb14-27"><a href="#cb14-27" aria-hidden="true" tabindex="-1"></a> <span class="sc">&</span> out_gate<span class="sc">$</span>obs<span class="sc">$</span>condition <span class="sc">==</span> <span class="st">"2"</span>]),</span>
<span id="cb14-28"><a href="#cb14-28" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"black"</span>,</span>
<span id="cb14-29"><a href="#cb14-29" aria-hidden="true" tabindex="-1"></a> <span class="at">lty =</span> <span class="dv">1</span>, </span>
<span id="cb14-30"><a href="#cb14-30" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 2 of cases</span><span class="sc">\n</span><span class="st">post-gating"</span>,</span>
<span id="cb14-31"><a href="#cb14-31" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">5</span>),</span>
<span id="cb14-32"><a href="#cb14-32" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.5</span>))</span></code></pre></div>
<p><img src="data:image/png;base64,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" 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" /></p>
</div>
<div id="for-a-one-condition-using-only-condition-1" class="section level3">
<h3>For a one condition (using only Condition 1)</h3>
<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Data subset, only c1</span></span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a> df_sub <span class="ot"><-</span> df_full[df_full<span class="sc">$</span>condition <span class="sc">==</span> <span class="dv">1</span>, ] <span class="co"># For only condition condition = 1</span></span>
<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a><span class="co"># Initial parameters</span></span>
<span id="cb15-5"><a href="#cb15-5" aria-hidden="true" tabindex="-1"></a> alpha <span class="ot"><-</span> <span class="fl">0.05</span></span>
<span id="cb15-6"><a href="#cb15-6" aria-hidden="true" tabindex="-1"></a> vars <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">"V1"</span>, <span class="st">"V2"</span>, <span class="st">"V3"</span>, <span class="st">"V4"</span>)</span>
<span id="cb15-7"><a href="#cb15-7" aria-hidden="true" tabindex="-1"></a> p_correct <span class="ot"><-</span> <span class="st">"correlated Bonferroni"</span></span>
<span id="cb15-8"><a href="#cb15-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">set.seed</span>(<span class="dv">1234</span>) <span class="co"># for reproducibility</span></span>
<span id="cb15-9"><a href="#cb15-9" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb15-10"><a href="#cb15-10" aria-hidden="true" tabindex="-1"></a><span class="co"># Gates 1 and 2</span></span>
<span id="cb15-11"><a href="#cb15-11" aria-hidden="true" tabindex="-1"></a> start_time <span class="ot"><-</span> <span class="fu">Sys.time</span>() <span class="co"># record start time</span></span>
<span id="cb15-12"><a href="#cb15-12" aria-hidden="true" tabindex="-1"></a> out_gate <span class="ot"><-</span> gateR<span class="sc">::</span><span class="fu">gating</span>(<span class="at">dat =</span> df_sub,</span>
<span id="cb15-13"><a href="#cb15-13" aria-hidden="true" tabindex="-1"></a> <span class="at">vars =</span> vars,</span>
<span id="cb15-14"><a href="#cb15-14" aria-hidden="true" tabindex="-1"></a> <span class="at">plot_gate =</span> <span class="cn">TRUE</span>,</span>
<span id="cb15-15"><a href="#cb15-15" aria-hidden="true" tabindex="-1"></a> <span class="at">n_condition =</span> <span class="dv">1</span>,</span>
<span id="cb15-16"><a href="#cb15-16" aria-hidden="true" tabindex="-1"></a> <span class="at">alpha =</span> alpha,</span>
<span id="cb15-17"><a href="#cb15-17" aria-hidden="true" tabindex="-1"></a> <span class="at">p_correct =</span> p_correct,</span>
<span id="cb15-18"><a href="#cb15-18" aria-hidden="true" tabindex="-1"></a> <span class="at">c1n =</span> <span class="st">"case"</span>) <span class="co"># level "case" as the numerator of first condition</span></span>
<span id="cb15-19"><a href="#cb15-19" aria-hidden="true" tabindex="-1"></a> end_time <span class="ot"><-</span> <span class="fu">Sys.time</span>() <span class="co"># record end time</span></span>
<span id="cb15-20"><a href="#cb15-20" aria-hidden="true" tabindex="-1"></a> total_time <span class="ot"><-</span> end_time <span class="sc">-</span> start_time <span class="co"># calculate duration of gating() example</span></span></code></pre></div>
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" 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" /></p>
<p>The gating process took about 22.8 seconds on a machine with the
features listed at the end of the vignette (4 variables, 2 gates, 2
cytokines, 200,000 observations). The corrected significance level in
the first gate was . The histograms for the two cytokines are the same
as above.</p>
<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Plot of Cytokine 1</span></span>
<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">2</span>), <span class="at">pty =</span> <span class="st">"s"</span>)</span>
<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(out_gate<span class="sc">$</span>obs<span class="sc">$</span>Z1[out_gate<span class="sc">$</span>obs<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span>]),</span>
<span id="cb16-4"><a href="#cb16-4" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"red"</span>,</span>
<span id="cb16-5"><a href="#cb16-5" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 1 of cases</span><span class="sc">\n</span><span class="st">post-gating"</span>,</span>
<span id="cb16-6"><a href="#cb16-6" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">30</span>),</span>
<span id="cb16-7"><a href="#cb16-7" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.2</span>))</span>
<span id="cb16-8"><a href="#cb16-8" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(out_gate<span class="sc">$</span>obs<span class="sc">$</span>Z1[out_gate<span class="sc">$</span>obs<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"control"</span>]),</span>
<span id="cb16-9"><a href="#cb16-9" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"blue"</span>,</span>
<span id="cb16-10"><a href="#cb16-10" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 1 of controls</span><span class="sc">\n</span><span class="st">post-gating"</span>,</span>
<span id="cb16-11"><a href="#cb16-11" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">30</span>),</span>
<span id="cb16-12"><a href="#cb16-12" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.2</span>))</span>
<span id="cb16-13"><a href="#cb16-13" aria-hidden="true" tabindex="-1"></a><span class="co"># Plot of Cytokine 2</span></span>
<span id="cb16-14"><a href="#cb16-14" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">2</span>), <span class="at">pty =</span> <span class="st">"s"</span>)</span>
<span id="cb16-15"><a href="#cb16-15" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(out_gate<span class="sc">$</span>obs<span class="sc">$</span>Z2[out_gate<span class="sc">$</span>obs<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span>]),</span>
<span id="cb16-16"><a href="#cb16-16" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"red"</span>,</span>
<span id="cb16-17"><a href="#cb16-17" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 2 of cases</span><span class="sc">\n</span><span class="st">post-gating"</span>,</span>
<span id="cb16-18"><a href="#cb16-18" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">5</span>),</span>
<span id="cb16-19"><a href="#cb16-19" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.5</span>))</span>
<span id="cb16-20"><a href="#cb16-20" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(out_gate<span class="sc">$</span>obs<span class="sc">$</span>Z2[out_gate<span class="sc">$</span>obs<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"control"</span>]),</span>
<span id="cb16-21"><a href="#cb16-21" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"blue"</span>,</span>
<span id="cb16-22"><a href="#cb16-22" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 2 of controls</span><span class="sc">\n</span><span class="st">post-gating"</span>,</span>
<span id="cb16-23"><a href="#cb16-23" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">5</span>),</span>
<span id="cb16-24"><a href="#cb16-24" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.5</span>))</span></code></pre></div>
<p><img 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" /><img src="data:image/png;base64,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" /></p>
<p>Compare histograms before and after gating. Gating reduced the
overall sample size of observations from 200,000 (cases & controls)
to 86,167 observations (cases & controls).</p>
<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Plot of Cytokine 1</span></span>
<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">2</span>), <span class="at">pty =</span> <span class="st">"s"</span>)</span>
<span id="cb17-3"><a href="#cb17-3" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(df_full<span class="sc">$</span>Z1[df_full<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span>]),</span>
<span id="cb17-4"><a href="#cb17-4" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"black"</span>,</span>
<span id="cb17-5"><a href="#cb17-5" aria-hidden="true" tabindex="-1"></a> <span class="at">lty =</span> <span class="dv">1</span>,</span>
<span id="cb17-6"><a href="#cb17-6" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 1 of cases</span><span class="sc">\n</span><span class="st">pre-gating"</span>,</span>
<span id="cb17-7"><a href="#cb17-7" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">30</span>),</span>
<span id="cb17-8"><a href="#cb17-8" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.2</span>))</span>
<span id="cb17-9"><a href="#cb17-9" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(out_gate<span class="sc">$</span>obs<span class="sc">$</span>Z1[out_gate<span class="sc">$</span>obs<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span>]),</span>
<span id="cb17-10"><a href="#cb17-10" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"black"</span>,</span>
<span id="cb17-11"><a href="#cb17-11" aria-hidden="true" tabindex="-1"></a> <span class="at">lty =</span> <span class="dv">1</span>,</span>
<span id="cb17-12"><a href="#cb17-12" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 1 of cases</span><span class="sc">\n</span><span class="st">post-gating"</span>,</span>
<span id="cb17-13"><a href="#cb17-13" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">30</span>),</span>
<span id="cb17-14"><a href="#cb17-14" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.2</span>))</span>
<span id="cb17-15"><a href="#cb17-15" aria-hidden="true" tabindex="-1"></a><span class="co"># Plot of Cytokine 2</span></span>
<span id="cb17-16"><a href="#cb17-16" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">2</span>), <span class="at">pty =</span> <span class="st">"s"</span>)</span>
<span id="cb17-17"><a href="#cb17-17" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(df_full<span class="sc">$</span>Z2[df_full<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span>]),</span>
<span id="cb17-18"><a href="#cb17-18" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"black"</span>,</span>
<span id="cb17-19"><a href="#cb17-19" aria-hidden="true" tabindex="-1"></a> <span class="at">lty =</span> <span class="dv">1</span>,</span>
<span id="cb17-20"><a href="#cb17-20" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 2 of cases</span><span class="sc">\n</span><span class="st">pre-gating"</span>,</span>
<span id="cb17-21"><a href="#cb17-21" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">5</span>),</span>
<span id="cb17-22"><a href="#cb17-22" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.5</span>))</span>
<span id="cb17-23"><a href="#cb17-23" aria-hidden="true" tabindex="-1"></a> graphics<span class="sc">::</span><span class="fu">plot</span>(stats<span class="sc">::</span><span class="fu">density</span>(out_gate<span class="sc">$</span>obs<span class="sc">$</span>Z2[out_gate<span class="sc">$</span>obs<span class="sc">$</span>group <span class="sc">==</span> <span class="st">"case"</span>]),</span>
<span id="cb17-24"><a href="#cb17-24" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"black"</span>,</span>
<span id="cb17-25"><a href="#cb17-25" aria-hidden="true" tabindex="-1"></a> <span class="at">lty =</span> <span class="dv">1</span>,</span>
<span id="cb17-26"><a href="#cb17-26" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Cytokine 2 of cases</span><span class="sc">\n</span><span class="st">post-gating"</span>,</span>
<span id="cb17-27"><a href="#cb17-27" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">5</span>),</span>
<span id="cb17-28"><a href="#cb17-28" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fl">0.5</span>))</span></code></pre></div>
<p><img src="data:image/png;base64,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" 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" /></p>
</div>
<div id="current-limitations" class="section level3">
<h3>Current limitations</h3>
<ol style="list-style-type: decimal">
<li>Extracts observations at <em>all</em> significant clusters (either
case or controls), and there is currently no functionality to select
cells within a specific (set of) cluster(s) for the next gate.</li>
<li>Only two dimensions (i.e., markers) per gate because the spatial
relative risk function is a two-dimensional spatial statistic.</li>
<li>Only two-group comparisons (e.g., case vs. control) per gate because
the spatial relative risk function is a ratio by nature.</li>
<li>Only comparisons of one condition or two conditions are
possible.</li>
<li>Large computational expense (i.e., run-time) to calculate the
correlated Bonferroni correction.</li>
<li>A large sample size of observations (i.e., cells) may overload the
gateR process. We are evaluating this potential limitation and
developing a possible solution (e.g., randomly subsetting the data to
estimate the clusters at each gate).</li>
</ol>
<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="fu">sessionInfo</span>()</span></code></pre></div>
<pre><code>## R version 4.2.1 (2022-06-23 ucrt)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 19045)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.utf8
## [2] LC_CTYPE=English_United States.utf8
## [3] LC_MONETARY=English_United States.utf8
## [4] LC_NUMERIC=C
## [5] LC_TIME=English_United States.utf8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] tibble_3.1.8 gateR_0.1.13
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.10 lattice_0.20-45 deldir_1.0-6
## [4] foreach_1.5.2 digest_0.6.31 utf8_1.2.2
## [7] R6_2.5.1 evaluate_0.20 spam_2.9-1
## [10] highr_0.10 ggplot2_3.4.0 tensor_1.5
## [13] pillar_1.8.1 rlang_1.0.6 misc3d_0.9-1
## [16] rstudioapi_0.14 jquerylib_0.1.4 rpart_4.1.19
## [19] Matrix_1.4-1 goftest_1.2-3 rmarkdown_2.20
## [22] splines_4.2.1 spatstat.explore_3.0-6 polyclip_1.10-4
## [25] munsell_0.5.0 spatstat.data_3.0-0 compiler_4.2.1
## [28] xfun_0.36 pkgconfig_2.0.3 mgcv_1.8-41
## [31] tcltk_4.2.1 htmltools_0.5.4 tidyselect_1.2.0
## [34] spatstat.random_3.1-3 gridExtra_2.3 codetools_0.2-18
## [37] fansi_1.0.4 viridisLite_0.4.1 dplyr_1.1.0
## [40] grid_4.2.1 nlme_3.1-157 jsonlite_1.8.4
## [43] gtable_0.3.1 lifecycle_1.0.3 magrittr_2.0.3
## [46] scales_1.2.1 cli_3.6.0 cachem_1.0.6
## [49] viridis_0.6.2 doParallel_1.0.17 fastmatrix_0.4-1245
## [52] spatstat_3.0-3 spatstat.linnet_3.0-4 bslib_0.4.2
## [55] spatstat.utils_3.0-1 generics_0.1.3 vctrs_0.5.2
## [58] iterators_1.0.14 tools_4.2.1 Cairo_1.6-0
## [61] glue_1.6.2 maps_3.4.1 fields_14.1
## [64] parallel_4.2.1 spatstat.model_3.1-2 abind_1.4-5
## [67] fastmap_1.1.0 yaml_2.3.6 terra_1.7-3
## [70] spatstat.sparse_3.0-0 colorspace_2.1-0 SpatialPack_0.4
## [73] dotCall64_1.0-2 spatstat.geom_3.0-6 sparr_2.2-17
## [76] knitr_1.42 sass_0.4.4</code></pre>
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