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period of time. Emerging hot spot analysis combines the Getis-Ord Gi* statistic
with the Mann-Kendall trend test to determine if there is a temporal trend
associated with local clustering of hot and cold spots."><title>Emerging Hot Spot Analysis — emerging_hotspot_analysis • sfdep</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Noto_Sans_Display-0.4.8/font.css" rel="stylesheet"><link href="../deps/Noto_Sans_Mono-0.4.8/font.css" rel="stylesheet"><link href="../deps/Merriweather-0.4.8/font.css" rel="stylesheet"><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- bootstrap-toc --><script src="https://cdn.jsdelivr.net/gh/afeld/bootstrap-toc@v1.0.1/dist/bootstrap-toc.min.js" integrity="sha256-4veVQbu7//Lk5TSmc7YV48MxtMy98e26cf5MrgZYnwo=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- search --><script src="https://cdnjs.cloudflare.com/ajax/libs/fuse.js/6.4.6/fuse.js" integrity="sha512-zv6Ywkjyktsohkbp9bb45V6tEMoWhzFzXis+LrMehmJZZSys19Yxf1dopHx7WzIKxr5tK2dVcYmaCk2uqdjF4A==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/autocomplete.js/0.38.0/autocomplete.jquery.min.js" integrity="sha512-GU9ayf+66Xx2TmpxqJpliWbT5PiGYxpaG8rfnBEk1LL8l1KGkRShhngwdXK1UgqhAzWpZHSiYPc09/NwDQIGyg==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mark.js/8.11.1/mark.min.js" integrity="sha512-5CYOlHXGh6QpOFA/TeTylKLWfB3ftPsde7AnmhuitiTX4K5SqCLBeKro6sPS8ilsz1Q4NRx3v8Ko2IBiszzdww==" crossorigin="anonymous"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Emerging Hot Spot Analysis — emerging_hotspot_analysis"><meta property="og:description" content="Emerging Hot Spot Analysis identifies trends in spatial clustering over a
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associated with local clustering of hot and cold spots."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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  <main id="main" class="col-md-9"><div class="page-header">
      <img src="" class="logo" alt=""><h1>Emerging Hot Spot Analysis</h1>
      <small class="dont-index">Source: <a href="https://github.com/josiahparry/sfdep/blob/HEAD/R/emerging-hostpot-analysis.R" class="external-link"><code>R/emerging-hostpot-analysis.R</code></a></small>
      <div class="d-none name"><code>emerging_hotspot_analysis.Rd</code></div>
    </div>

    <div class="ref-description section level2">
    <p>Emerging Hot Spot Analysis identifies trends in spatial clustering over a
period of time. Emerging hot spot analysis combines the Getis-Ord Gi* statistic
with the Mann-Kendall trend test to determine if there is a temporal trend
associated with local clustering of hot and cold spots.</p>
    </div>

    <div class="section level2">
    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">emerging_hotspot_analysis</span><span class="op">(</span></span>
<span>  <span class="va">x</span>,</span>
<span>  <span class="va">.var</span>,</span>
<span>  k <span class="op">=</span> <span class="fl">1</span>,</span>
<span>  include_gi <span class="op">=</span> <span class="cn">FALSE</span>,</span>
<span>  nb_col <span class="op">=</span> <span class="cn">NULL</span>,</span>
<span>  wt_col <span class="op">=</span> <span class="cn">NULL</span>,</span>
<span>  nsim <span class="op">=</span> <span class="fl">199</span>,</span>
<span>  threshold <span class="op">=</span> <span class="fl">0.01</span>,</span>
<span>  <span class="va">...</span></span>
<span><span class="op">)</span></span></code></pre></div>
    </div>

    <div class="section level2">
    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
    <dl><dt>x</dt>
<dd><p>a spacetime object and must be a spacetime cube see details for more.</p></dd>


<dt>.var</dt>
<dd><p>a numeric vector in the spacetime cube with no missing values.</p></dd>


<dt>k</dt>
<dd><p>default <code>1</code>. The number of time lags to include in the neighborhood
for calculating the local Gi*. See details for more.</p></dd>


<dt>include_gi</dt>
<dd><p>default <code>FALSE</code>. If <code>TRUE</code>, includes the local Gi* calculations
in the attribute <code>gi_star</code>.</p></dd>


<dt>nb_col</dt>
<dd><p>Optional. Default <code>NULL</code>. The name of the column in the <code>geometry</code>
context of <code>x</code> containing spatial neighbors. If <code>NULL</code>, Queen's contiguity
neighbors are identified.</p></dd>


<dt>wt_col</dt>
<dd><p>Optional. Default <code>NULL</code>. The name of the column in the <code>geometry</code>
context of <code>x</code> containing spatial weights. If <code>NULL</code>, row standardized weights
are used.</p></dd>


<dt>nsim</dt>
<dd><p>default <code>199</code>. The number of simulations to run in calculating the
simulated p-value for the local Gi*.</p></dd>


<dt>threshold</dt>
<dd><p>default <code>0.01</code>. The significance threshold to use.</p></dd>


<dt>...</dt>
<dd><p>unused.</p></dd>

</dl></div>
    <div class="section level2">
    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
    

<p>Returns a data.frame.</p>
    </div>
    <div class="section level2">
    <h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></a></h2>
    
<div class="section">
<h3 id="how-emerging-hot-spot-analysis-works">How Emerging Hot Spot Analysis Works<a class="anchor" aria-label="anchor" href="#how-emerging-hot-spot-analysis-works"></a></h3>


<p>Emerging Hot Spot Analysis is a somewhat simple process. It works by first
calculating the Gi* statistic for each location in each time period (time-slice).
Next, for each location across all time-periods, the Mann-Kendall trend test
is done to identify any temporal trend in Gi* values over all time periods.
Additionally, each location is classified into one of seventeen categories based
on <a href="https://pro.arcgis.com/en/pro-app/2.8/tool-reference/space-time-pattern-mining/learnmoreemerging.htm" class="external-link">ESRI's emerging hot spot classification criteria</a>.</p>
<p>The Mann-Kendall trend test is done using <code><a href="https://rdrr.io/pkg/Kendall/man/MannKendall.html" class="external-link">Kendall::MannKendall()</a></code>. <code>Kendall</code>
is not installed with sfdep and should be installed prior to use.</p>
</div>

<div class="section">
<h3 id="using-your-own-neighbors-and-weights">Using your own neighbors and weights<a class="anchor" aria-label="anchor" href="#using-your-own-neighbors-and-weights"></a></h3>


<p>If you would like to use your own neighbors and weights, they must be created
in the <code>geometry</code> context of a spacetime object. The arguments <code>nb_col</code>
and <code>wt_col</code> must both be populated in order to use your own neighbor and weights
definitions.</p>
</div>

<div class="section">
<h3 id="time-lagged-neighbors">Time lagged neighbors<a class="anchor" aria-label="anchor" href="#time-lagged-neighbors"></a></h3>


<p>In addition to identifying neighbors in space, emerging hotspot analysis also
incorporates the same observations from <code>k</code> periods ago-called a time lag. If
the time lag k is 1 and the unit of time is month, the neighbors for the
calculation of Gi* would include the spatial neighbors' values at time <code>t</code>
and the same spatial neighbors' values at time <code>t-1</code>. If <code>k = 2</code>, it would include
<code>t</code>, <code>t-1</code>, and <code>t-2</code>.</p>
</div>

<div class="section">
<h3 id="missing-values">Missing values<a class="anchor" aria-label="anchor" href="#missing-values"></a></h3>


<p>Presently, there is no method of missing value handling. If there are missing
values, the emerging hot spot analysis will fail. Be sure to fill or omit
time-slices with missing values <em>prior</em> to using emerging hot spot analysis.</p>
</div>

    </div>
    <div class="section level2">
    <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
    <div class="dont-index"><p><a href="https://pro.arcgis.com/en/pro-app/2.8/tool-reference/space-time-pattern-mining/learnmoreemerging.htm" class="external-link">How Emerging Hot Spot Analysis works</a>, <a href="https://pro.arcgis.com/en/pro-app/2.8/tool-reference/space-time-pattern-mining/emerginghotspots.htm" class="external-link">Emerging Hot Spot Analysis (Space Time Pattern Mining)</a>, and the video <a href="https://www.youtube.com/watch?v=0aV6HHwJuo4&amp;t=3848s&amp;ab_channel=EsriEvents" class="external-link">Spatial Data Mining II: A Deep Dive into Space-Time Analysis</a> by ESRI.</p></div>
    </div>

    <div class="section level2">
    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span></span></span>
<span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/ns-load.html" class="external-link">requireNamespace</a></span><span class="op">(</span><span class="st">"Kendall"</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span></span>
<span class="r-in"><span><span class="va">df_fp</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span><span class="st">"extdata"</span>, <span class="st">"bos-ecometric.csv"</span>, package <span class="op">=</span> <span class="st">"sfdep"</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="va">geo_fp</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span><span class="st">"extdata"</span>, <span class="st">"bos-ecometric.geojson"</span>, package <span class="op">=</span> <span class="st">"sfdep"</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># read in data</span></span></span>
<span class="r-in"><span><span class="va">df</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/utils/read.table.html" class="external-link">read.csv</a></span><span class="op">(</span><span class="va">df_fp</span>, colClasses <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"character"</span>, <span class="st">"character"</span>, <span class="st">"integer"</span>, <span class="st">"double"</span>, <span class="st">"Date"</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="va">geo</span> <span class="op">&lt;-</span> <span class="fu">sf</span><span class="fu">::</span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="va">geo_fp</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># Create spacetime object called `bos`</span></span></span>
<span class="r-in"><span><span class="va">bos</span> <span class="op">&lt;-</span> <span class="fu"><a href="spacetime.html">spacetime</a></span><span class="op">(</span><span class="va">df</span>, <span class="va">geo</span>,</span></span>
<span class="r-in"><span>                 .loc_col <span class="op">=</span> <span class="st">".region_id"</span>,</span></span>
<span class="r-in"><span>                 .time_col <span class="op">=</span> <span class="st">"time_period"</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># conduct EHSA</span></span></span>
<span class="r-in"><span><span class="va">ehsa</span> <span class="op">&lt;-</span> <span class="fu">emerging_hotspot_analysis</span><span class="op">(</span></span></span>
<span class="r-in"><span>  x <span class="op">=</span> <span class="va">bos</span>,</span></span>
<span class="r-in"><span>  .var <span class="op">=</span> <span class="st">"value"</span>,</span></span>
<span class="r-in"><span>  k <span class="op">=</span> <span class="fl">1</span>,</span></span>
<span class="r-in"><span>  nsim <span class="op">=</span> <span class="fl">9</span></span></span>
<span class="r-in"><span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="va">ehsa</span></span></span>
<span class="r-in"><span><span class="op">}</span></span></span>
<span class="r-msg co"><span class="r-pr">#&gt;</span> Loading required namespace: Kendall</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Reading layer `bos-ecometric' from data source </span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   `/private/var/folders/zc/tg2xwck53dg9sls8x4ndzdc00000gn/T/Rtmp2RGXTr/temp_libpath2b6f5ea0db20/sfdep/extdata/bos-ecometric.geojson' </span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   using driver `GeoJSON'</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Simple feature collection with 168 features and 1 field</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Geometry type: POLYGON</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Dimension:     XY</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Bounding box:  xmin: -71.19115 ymin: 42.22788 xmax: -70.99445 ymax: 42.3974</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Geodetic CRS:  NAD83</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>        location         tau     p_value      classification</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 1   25025010405  0.11111111 0.720514774 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 2   25025010404 -0.33333334 0.210497662 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 3   25025010801 -0.20000000 0.474274337 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 4   25025010702 -0.60000002 0.020044670 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 5   25025010204 -0.46666667 0.073638275 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 6   25025010802 -0.33333334 0.210497662 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 7   25025010104 -0.33333334 0.210497662 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 8   25025000703 -0.60000002 0.020044670 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 9   25025000504 -0.33333334 0.210497662 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 10  25025000704 -0.42222223 0.107404657 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 11  25025010103  0.02222222 1.000000000 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 12  25025000803 -0.37777779 0.152406260 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 13  25025120201 -0.33333334 0.210497662 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 14  25025120104  0.46666667 0.073638320 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 15  25025110607  0.28888890 0.283130884 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 16  25025000302  0.37777779 0.152406216 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 17  25025000301  0.37777779 0.152406216 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 18  25025140400  0.06666667 0.858027697 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 19  25025140300  0.37777779 0.152406216 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 20  25025140201  0.46666667 0.073638320 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 21  25025140202  0.15555556 0.591505051 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 22  25025140102 -0.24444444 0.371093363 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 23  25025130402  0.46666667 0.073638320 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 24  25025130300  0.33333334 0.210497618 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 25  25025130200  0.33333334 0.210497618 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 26  25025130100 -0.20000000 0.474274337 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 27  25025120700  0.37777779 0.152406216 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 28  25025120600  0.60000002 0.020044684 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 29  25025120500  0.55555558 0.031823158 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 30  25025120400  0.55555558 0.031823158 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 31  25025110601  0.55555558 0.031823158 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 32  25025110502  0.42222223 0.107404709 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 33  25025110501 -0.02222222 1.000000000 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 34  25025110401 -0.20000000 0.474274337 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 35  25025101102  0.02222222 1.000000000 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 36  25025101101  0.37777779 0.152406216 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 37  25025101002  0.24444444 0.371093392 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 38  25025101001  0.46666667 0.073638320 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 39  25025100900  0.51111114 0.049098015 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 40  25025100800  0.46666667 0.073638320 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 41  25025100601  0.46666667 0.073638320 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 42  25025100500  0.37777779 0.152406216 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 43  25025100400 -0.24444444 0.371093363 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 44  25025100300 -0.28888890 0.283130825 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 45  25025100200 -0.15555556 0.591504991 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 46  25025100100 -0.06666667 0.858027637 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 47  25025092400 -0.15555556 0.591504991 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 48  25025092300  0.15555556 0.591505051 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 49  25025092200  0.06666667 0.858027697 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 50  25025092000  0.06666667 0.858027697 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 51  25025091900 -0.02222222 1.000000000 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 52  25025091800 -0.02222222 1.000000000 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 53  25025091700 -0.33333334 0.210497662 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 54  25025091600 -0.15555556 0.591504991 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 55  25025981100 -0.15555556 0.591504991 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 56  25025140105  0.02222222 1.000000000 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 57  25025120105  0.02222222 1.000000000 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 58  25025120301 -0.11111111 0.720514774 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 59  25025071201  0.02222222 1.000000000 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 60  25025091001 -0.06666667 0.858027637 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 61  25025091500 -0.24444444 0.371093363 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 62  25025091400  0.15555556 0.591505051 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 63  25025091300  0.46666667 0.073638320 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 64  25025091200  0.33333334 0.210497618 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 65  25025091100  0.77777779 0.002357483 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 66  25025090700  0.64444447 0.012266040 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 67  25025090600  0.60000002 0.020044684 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 68  25025090400  0.60000002 0.020044684 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 69  25025090300  0.73333335 0.004207492 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 70  25025090200  0.73333335 0.004207492 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 71  25025040801  0.46666667 0.073638320 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 72  25025010203  0.60000002 0.020044684 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 73  25025110403  0.60000002 0.020044684 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 74  25025110201  0.60000002 0.020044684 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 75  25025090100  0.51111114 0.049098015 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 76  25025082100  0.06666667 0.858027697 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 77  25025082000  0.37777779 0.152406216 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 78  25025081900  0.24444444 0.371093392 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 79  25025081800  0.42222223 0.107404709 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 80  25025081700  0.64444447 0.012266040 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 81  25025081500  0.68888891 0.007290363 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 82  25025081400  0.64444447 0.012266040 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 83  25025081300  0.64444447 0.012266040 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 84  25025110103  0.51111114 0.049098015 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 85  25025110301  0.60000002 0.020044684 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 86  25025140106  0.24444444 0.371093392 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 87  25025010701  0.42222223 0.107404709 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 88  25025010408  0.33333334 0.210497618 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 89  25025000503  0.64444447 0.012266040 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 90  25025081200  0.82222223 0.001282215 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 91  25025081100  0.82222223 0.001282215 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 92  25025080900  0.73333335 0.004207492 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 93  25025080801  0.82222223 0.001282215 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 94  25025080601  0.46666667 0.073638320 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 95  25025080500  0.51111114 0.049098015 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 96  25025080401  0.20000000 0.474274397 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 97  25025080300  0.20000000 0.474274397 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 98  25025071101 -0.20000000 0.474274337 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 99  25025070900 -0.06666667 0.858027637 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 100 25025140107  0.46666667 0.073638320 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 101 25025130404  0.15555556 0.591505051 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 102 25025130406  0.20000000 0.474274397 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 103 25025120103  0.11111111 0.720514774 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 104 25025100700  0.64444447 0.012266040 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 105 25025100603  0.82222223 0.001282215 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 106 25025092101  0.11111111 0.720514774 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 107 25025061101  0.64444447 0.012266040 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 108 25025070800  0.60000002 0.020044684 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 109 25025070700  0.55555558 0.031823158 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 110 25025070600  0.60000002 0.020044684 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 111 25025070500  0.37777779 0.152406216 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 112 25025070300  0.55555558 0.031823158 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 113 25025070200  0.46666667 0.073638320 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 114 25025070101  0.51111114 0.049098015 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 115 25025061200  0.37777779 0.152406216 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 116 25025061000  0.33333334 0.210497618 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 117 25025060800  0.64444447 0.012266040 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 118 25025060700  0.37777779 0.152406216 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 119 25025080100  0.55555558 0.031823158 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 120 25025060301  0.55555558 0.031823158 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 121 25025090901  0.37777779 0.152406216 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 122 25025060101  0.20000000 0.474274397 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 123 25025060600  0.15555556 0.591505051 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 124 25025060400  0.20000000 0.474274397 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 125 25025060200  0.20000000 0.474274397 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 126 25025050700  0.37777779 0.152406216 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 127 25025050600 -0.51111114 0.049097981 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 128 25025050500 -0.42222223 0.107404657 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 129 25025050400 -0.51111114 0.049097981 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 130 25025050300 -0.37777779 0.152406260 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 131 25025050200  0.24444444 0.371093392 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 132 25025040300  0.02222222 1.000000000 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 133 25025040200  0.24444444 0.371093392 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 134 25025030500  0.06666667 0.858027697 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 135 25025051101  0.20000000 0.474274397 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 136 25025051000 -0.37777779 0.152406260 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 137 25025030400  0.11111111 0.720514774 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 138 25025030300 -0.02222222 1.000000000 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 139 25025030200  0.06666667 0.858027697 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 140 25025030100  0.33333334 0.210497618 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 141 25025020200 -0.02222222 1.000000000 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 142 25025010600  0.11111111 0.720514774 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 143 25025010500 -0.33333334 0.210497662 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 144 25025010300 -0.06666667 0.858027637 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 145 25025000802  0.20000000 0.474274397 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 146 25025000701 -0.20000000 0.474274337 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 147 25025050101 -0.02222222 1.000000000 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 148 25025050901 -0.51111114 0.049097981 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 149 25025060501 -0.02222222 1.000000000 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 150 25025040100 -0.11111111 0.720514774 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 151 25025040600  0.60000002 0.020044684 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 152 25025000602  0.73333335 0.004207492 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 153 25025000601  0.77777779 0.002357483 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 154 25025000502 -0.24444444 0.371093363 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 155 25025000402 -0.33333334 0.210497662 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 156 25025000401 -0.28888890 0.283130825 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 157 25025000202 -0.20000000 0.474274337 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 158 25025000201 -0.28888890 0.283130825 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 159 25025040401 -0.02222222 1.000000000 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 160 25025020303  0.42222223 0.107404709 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 161 25025070402  0.46666667 0.073638320 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 162 25025020302  0.15555556 0.591505051 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 163 25025020301  0.37777779 0.152406216 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 164 25025020101  0.42222223 0.107404709 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 165 25025081001  0.42222223 0.107404709 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 166 25025010403  0.33333334 0.210497618 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 167 25025000100  0.33333334 0.210497618 no pattern detected</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 168 25025051200  0.28888890 0.283130884 no pattern detected</span>
<span class="r-in"><span></span></span>
</code></pre></div>
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