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-rw-r--r--docs/reference/add_err.html13
-rw-r--r--docs/reference/index.html9
-rw-r--r--docs/reference/synthetic_data_for_UBA.html290
3 files changed, 118 insertions, 194 deletions
diff --git a/docs/reference/add_err.html b/docs/reference/add_err.html
index 046eabf5..d56a8728 100644
--- a/docs/reference/add_err.html
+++ b/docs/reference/add_err.html
@@ -86,12 +86,7 @@
</ul>
<ul class="nav navbar-nav navbar-right">
- <li>
- <a href="http://github.com/jranke/mkin">
- <span class="fa fa-github fa-lg"></span>
-
- </a>
-</li>
+
</ul>
</div><!--/.nav-collapse -->
</div><!--/.container -->
@@ -112,7 +107,7 @@
may depend on the predicted value and is specified as a standard deviation.</p>
- <pre class="usage"><span class='fu'>add_err</span>(<span class='no'>prediction</span>, <span class='no'>sdfunc</span>,
+ <pre class="usage"><span class='fu'>add_err</span>(<span class='no'>prediction</span>, <span class='no'>sdfunc</span>, <span class='kw'>secondary</span> <span class='kw'>=</span> <span class='fu'>c</span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>),
<span class='kw'>n</span> <span class='kw'>=</span> <span class='fl'>1000</span>, <span class='kw'>LOD</span> <span class='kw'>=</span> <span class='fl'>0.1</span>, <span class='kw'>reps</span> <span class='kw'>=</span> <span class='fl'>2</span>,
<span class='kw'>digits</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='kw'>seed</span> <span class='kw'>=</span> <span class='fl'>NA</span>)</pre>
@@ -130,6 +125,10 @@
terms for this value.</p></td>
</tr>
<tr>
+ <th>secondary</th>
+ <td><p>The names of state variables that should have an initial value of zero</p></td>
+ </tr>
+ <tr>
<th>n</th>
<td><p>The number of datasets to be generated.</p></td>
</tr>
diff --git a/docs/reference/index.html b/docs/reference/index.html
index 511a6aaa..dbcd5ba0 100644
--- a/docs/reference/index.html
+++ b/docs/reference/index.html
@@ -86,12 +86,7 @@
</ul>
<ul class="nav navbar-nav navbar-right">
- <li>
- <a href="http://github.com/jranke/mkin">
- <span class="fa fa-github fa-lg"></span>
-
- </a>
-</li>
+
</ul>
</div><!--/.nav-collapse -->
</div><!--/.container -->
@@ -105,7 +100,7 @@
<div class="page-header">
<h1>
Reference
- <small>version&nbsp;0.9.46.2</small>
+ <small>version&nbsp;0.9.46.3</small>
</h1>
</div>
diff --git a/docs/reference/synthetic_data_for_UBA.html b/docs/reference/synthetic_data_for_UBA.html
index 173af92e..9ff18876 100644
--- a/docs/reference/synthetic_data_for_UBA.html
+++ b/docs/reference/synthetic_data_for_UBA.html
@@ -70,6 +70,9 @@
<a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
</li>
<li>
+ <a href="../articles/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
+ </li>
+ <li>
<a href="../articles/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
</li>
<li>
@@ -83,12 +86,7 @@
</ul>
<ul class="nav navbar-nav navbar-right">
- <li>
- <a href="http://github.com/jranke/mkin">
- <span class="fa fa-github fa-lg"></span>
-
- </a>
-</li>
+
</ul>
</div><!--/.nav-collapse -->
</div><!--/.container -->
@@ -109,7 +107,7 @@
two sequential or two parallel metabolites.</p>
<p>Variance component 'a' is based on a normal distribution with standard deviation of 3,
Variance component 'b' is also based on a normal distribution, but with a standard deviation of 7.
- Variance component 'c' is based on the error model from Rocke and Lorenzato (1995), with the
+ Variance component 'c' is based on the error model from Rocke and Lorenzato (1995), with the
minimum standard deviation (for small y values) of 0.5, and a proportionality constant of 0.07
for the increase of the standard deviation with y.</p>
<p>Initial concentrations for metabolites and all values where adding the variance component resulted
@@ -133,184 +131,116 @@
<h2 class="hasAnchor" id="source"><a class="anchor" href="#source"></a>Source</h2>
<p>Ranke (2014) Prüfung und Validierung von Modellierungssoftware als Alternative
- zu ModelMaker 4.0, Umweltbundesamt Projektnummer 27452
- Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for
+ zu ModelMaker 4.0, Umweltbundesamt Projektnummer 27452</p>
+<p>Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for
measurement error in analytical chemistry. Technometrics 37(2), 176-184.</p>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'>
-<span class='no'>m_synth_SFO_lin</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"M1"</span>),
- <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"M2"</span>),
- <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
-
-<span class='no'>m_synth_SFO_par</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fu'>c</span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>),
- <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>),
- <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>),
- <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
-<span class='no'>m_synth_DFOP_lin</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"DFOP"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"M1"</span>),
- <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"M2"</span>),
- <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
-<span class='no'>m_synth_DFOP_par</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"DFOP"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fu'>c</span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>),
- <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>),
- <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>),
- <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
-<span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>m_synth_SFO_lin</span>, <span class='no'>synthetic_data_for_UBA_2014</span><span class='kw'>[[</span><span class='fl'>1</span>]]$<span class='no'>data</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='fu'><a href='plot.mkinfit.html'>plot_sep</a></span>(<span class='no'>fit</span>)</div><img src='synthetic_data_for_UBA_2014-10.png' alt='' width='540' height='400' /><div class='input'><span class='fu'>summary</span>(<span class='no'>fit</span>)</div><div class='output co'>#&gt; mkin version: 0.9.46
-#&gt; R version: 3.4.1
-#&gt; Date of fit: Sat Jul 29 15:15:33 2017
-#&gt; Date of summary: Sat Jul 29 15:15:34 2017
-#&gt;
-#&gt; Equations:
-#&gt; d_parent/dt = - k_parent * parent
-#&gt; d_M1/dt = + f_parent_to_M1 * k_parent * parent - k_M1 * M1
-#&gt; d_M2/dt = + f_M1_to_M2 * k_M1 * M1 - k_M2 * M2
-#&gt;
-#&gt; Model predictions using solution type deSolve
-#&gt;
-#&gt; Fitted with method Port using 381 model solutions performed in 2.241 s
-#&gt;
-#&gt; Weighting: none
-#&gt;
-#&gt; Starting values for parameters to be optimised:
-#&gt; value type
-#&gt; parent_0 101.3500 state
-#&gt; k_parent 0.1000 deparm
-#&gt; k_M1 0.1001 deparm
-#&gt; k_M2 0.1002 deparm
-#&gt; f_parent_to_M1 0.5000 deparm
-#&gt; f_M1_to_M2 0.5000 deparm
-#&gt;
-#&gt; Starting values for the transformed parameters actually optimised:
-#&gt; value lower upper
-#&gt; parent_0 101.350000 -Inf Inf
-#&gt; log_k_parent -2.302585 -Inf Inf
-#&gt; log_k_M1 -2.301586 -Inf Inf
-#&gt; log_k_M2 -2.300587 -Inf Inf
-#&gt; f_parent_ilr_1 0.000000 -Inf Inf
-#&gt; f_M1_ilr_1 0.000000 -Inf Inf
-#&gt;
-#&gt; Fixed parameter values:
-#&gt; value type
-#&gt; M1_0 0 state
-#&gt; M2_0 0 state
-#&gt;
-#&gt; Optimised, transformed parameters with symmetric confidence intervals:
-#&gt; Estimate Std. Error Lower Upper
-#&gt; parent_0 102.1000 1.71400 98.5800 105.5000
-#&gt; log_k_parent -0.3020 0.04294 -0.3894 -0.2147
-#&gt; log_k_M1 -1.2070 0.07599 -1.3610 -1.0520
-#&gt; log_k_M2 -3.9010 0.06952 -4.0420 -3.7590
-#&gt; f_parent_ilr_1 0.8492 0.18090 0.4812 1.2170
-#&gt; f_M1_ilr_1 0.6780 0.18860 0.2943 1.0620
-#&gt;
-#&gt; Parameter correlation:
-#&gt; parent_0 log_k_parent log_k_M1 log_k_M2 f_parent_ilr_1
-#&gt; parent_0 1.00000 0.40213 -0.1693 0.02912 -0.4726
-#&gt; log_k_parent 0.40213 1.00000 -0.4210 0.07241 -0.5837
-#&gt; log_k_M1 -0.16931 -0.42103 1.0000 -0.37657 0.7438
-#&gt; log_k_M2 0.02912 0.07241 -0.3766 1.00000 -0.2518
-#&gt; f_parent_ilr_1 -0.47263 -0.58367 0.7438 -0.25177 1.0000
-#&gt; f_M1_ilr_1 0.17148 0.42643 -0.8054 0.52647 -0.8602
-#&gt; f_M1_ilr_1
-#&gt; parent_0 0.1715
-#&gt; log_k_parent 0.4264
-#&gt; log_k_M1 -0.8054
-#&gt; log_k_M2 0.5265
-#&gt; f_parent_ilr_1 -0.8602
-#&gt; f_M1_ilr_1 1.0000
-#&gt;
-#&gt; Residual standard error: 2.471 on 33 degrees of freedom
-#&gt;
-#&gt; Backtransformed parameters:
-#&gt; Confidence intervals for internally transformed parameters are asymmetric.
-#&gt; t-test (unrealistically) based on the assumption of normal distribution
-#&gt; for estimators of untransformed parameters.
-#&gt; Estimate t value Pr(&gt;t) Lower Upper
-#&gt; parent_0 102.10000 59.55 1.815e-35 98.58000 105.5000
-#&gt; k_parent 0.73930 23.29 2.337e-22 0.67750 0.8068
-#&gt; k_M1 0.29920 13.16 5.552e-15 0.25630 0.3492
-#&gt; k_M2 0.02023 14.38 4.497e-16 0.01756 0.0233
-#&gt; f_parent_to_M1 0.76870 16.90 4.093e-18 0.66380 0.8483
-#&gt; f_M1_to_M2 0.72290 13.53 2.557e-15 0.60260 0.8178
-#&gt;
-#&gt; Chi2 error levels in percent:
-#&gt; err.min n.optim df
-#&gt; All data 8.454 6 17
-#&gt; parent 8.660 2 6
-#&gt; M1 10.583 2 5
-#&gt; M2 3.586 2 6
-#&gt;
-#&gt; Resulting formation fractions:
-#&gt; ff
-#&gt; parent_M1 0.7687
-#&gt; parent_sink 0.2313
-#&gt; M1_M2 0.7229
-#&gt; M1_sink 0.2771
-#&gt;
-#&gt; Estimated disappearance times:
-#&gt; DT50 DT90
-#&gt; parent 0.9376 3.114
-#&gt; M1 2.3170 7.697
-#&gt; M2 34.2689 113.839
-#&gt;
-#&gt; Data:
-#&gt; time variable observed predicted residual
-#&gt; 0 parent 101.5 1.021e+02 -0.56248
-#&gt; 0 parent 101.2 1.021e+02 -0.86248
-#&gt; 1 parent 53.9 4.873e+01 5.17118
-#&gt; 1 parent 47.5 4.873e+01 -1.22882
-#&gt; 3 parent 10.4 1.111e+01 -0.70773
-#&gt; 3 parent 7.6 1.111e+01 -3.50773
-#&gt; 7 parent 1.1 5.772e-01 0.52283
-#&gt; 7 parent 0.3 5.772e-01 -0.27717
-#&gt; 14 parent NA 3.264e-03 NA
-#&gt; 14 parent 3.5 3.264e-03 3.49674
-#&gt; 28 parent NA 1.045e-07 NA
-#&gt; 28 parent 3.2 1.045e-07 3.20000
-#&gt; 60 parent NA -1.054e-10 NA
-#&gt; 60 parent NA -1.054e-10 NA
-#&gt; 90 parent 0.6 -1.875e-11 0.60000
-#&gt; 90 parent NA -1.875e-11 NA
-#&gt; 120 parent NA -2.805e-11 NA
-#&gt; 120 parent 3.5 -2.805e-11 3.50000
-#&gt; 0 M1 NA 0.000e+00 NA
-#&gt; 0 M1 NA 0.000e+00 NA
-#&gt; 1 M1 36.4 3.479e+01 1.61088
-#&gt; 1 M1 37.4 3.479e+01 2.61088
-#&gt; 3 M1 34.3 3.937e+01 -5.07027
-#&gt; 3 M1 39.8 3.937e+01 0.42973
-#&gt; 7 M1 15.1 1.549e+01 -0.38715
-#&gt; 7 M1 17.8 1.549e+01 2.31285
-#&gt; 14 M1 5.8 1.995e+00 3.80469
-#&gt; 14 M1 1.2 1.995e+00 -0.79531
-#&gt; 28 M1 NA 3.034e-02 NA
-#&gt; 28 M1 NA 3.034e-02 NA
-#&gt; 60 M1 0.5 2.111e-06 0.50000
-#&gt; 60 M1 NA 2.111e-06 NA
-#&gt; 90 M1 NA 2.913e-10 NA
-#&gt; 90 M1 3.2 2.913e-10 3.20000
-#&gt; 120 M1 1.5 3.625e-11 1.50000
-#&gt; 120 M1 0.6 3.625e-11 0.60000
-#&gt; 0 M2 NA 0.000e+00 NA
-#&gt; 0 M2 NA 0.000e+00 NA
-#&gt; 1 M2 NA 4.455e+00 NA
-#&gt; 1 M2 4.8 4.455e+00 0.34517
-#&gt; 3 M2 20.9 2.153e+01 -0.62527
-#&gt; 3 M2 19.3 2.153e+01 -2.22527
-#&gt; 7 M2 42.0 4.192e+01 0.07941
-#&gt; 7 M2 43.1 4.192e+01 1.17941
-#&gt; 14 M2 49.4 4.557e+01 3.83353
-#&gt; 14 M2 44.3 4.557e+01 -1.26647
-#&gt; 28 M2 34.6 3.547e+01 -0.87275
-#&gt; 28 M2 33.0 3.547e+01 -2.47275
-#&gt; 60 M2 18.8 1.858e+01 0.21837
-#&gt; 60 M2 17.6 1.858e+01 -0.98163
-#&gt; 90 M2 10.6 1.013e+01 0.47130
-#&gt; 90 M2 10.8 1.013e+01 0.67130
-#&gt; 120 M2 9.8 5.521e+00 4.27893
-#&gt; 120 M2 3.3 5.521e+00 -2.22107</div><div class='input'>
-</div></pre>
+# The data have been generated using the following kinetic models
+m_synth_SFO_lin <- mkinmod(parent = list(type = "SFO", to = "M1"),
+ M1 = list(type = "SFO", to = "M2"),
+ M2 = list(type = "SFO"), use_of_ff = "max")
+
+
+m_synth_SFO_par <- mkinmod(parent = list(type = "SFO", to = c("M1", "M2"),
+ sink = FALSE),
+ M1 = list(type = "SFO"),
+ M2 = list(type = "SFO"), use_of_ff = "max")
+
+m_synth_DFOP_lin <- mkinmod(parent = list(type = "DFOP", to = "M1"),
+ M1 = list(type = "SFO", to = "M2"),
+ M2 = list(type = "SFO"), use_of_ff = "max")
+
+m_synth_DFOP_par <- mkinmod(parent = list(type = "DFOP", to = c("M1", "M2"),
+ sink = FALSE),
+ M1 = list(type = "SFO"),
+ M2 = list(type = "SFO"), use_of_ff = "max")
+
+# The model predictions without intentional error were generated as follows
+sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+
+d_synth_SFO_lin <- mkinpredict(m_synth_SFO_lin,
+ c(k_parent = 0.7, f_parent_to_M1 = 0.8,
+ k_M1 = 0.3, f_M1_to_M2 = 0.7,
+ k_M2 = 0.02),
+ c(parent = 100, M1 = 0, M2 = 0),
+ sampling_times)
+
+d_synth_DFOP_lin <- mkinpredict(m_synth_DFOP_lin,
+ c(k1 = 0.2, k2 = 0.02, g = 0.5,
+ f_parent_to_M1 = 0.5, k_M1 = 0.3,
+ f_M1_to_M2 = 0.7, k_M2 = 0.02),
+ c(parent = 100, M1 = 0, M2 = 0),
+ sampling_times)
+
+d_synth_SFO_par <- mkinpredict(m_synth_SFO_par,
+ c(k_parent = 0.2,
+ f_parent_to_M1 = 0.8, k_M1 = 0.01,
+ f_parent_to_M2 = 0.2, k_M2 = 0.02),
+ c(parent = 100, M1 = 0, M2 = 0),
+ sampling_times)
+
+d_synth_DFOP_par <- mkinpredict(m_synth_DFOP_par,
+ c(k1 = 0.3, k2 = 0.02, g = 0.7,
+ f_parent_to_M1 = 0.6, k_M1 = 0.04,
+ f_parent_to_M2 = 0.4, k_M2 = 0.01),
+ c(parent = 100, M1 = 0, M2 = 0),
+ sampling_times)
+
+# Construct names for datasets with errors
+d_synth_names = paste0("d_synth_", c("SFO_lin", "SFO_par",
+ "DFOP_lin", "DFOP_par"))
+
+# Function for adding errors. The add_err function now published with this
+# package is a slightly generalised version where the names of secondary
+# compartments that should have an initial value of zero (M1 and M2 in this
+# case) are not hardcoded any more.
+add_err = function(d, sdfunc, LOD = 0.1, reps = 2, seed = 123456789)
+{
+ set.seed(seed)
+ d_long = mkin_wide_to_long(d, time = "time")
+ d_rep = data.frame(lapply(d_long, rep, each = 2))
+ d_rep$value = rnorm(length(d_rep$value), d_rep$value, sdfunc(d_rep$value))
+
+ d_rep[d_rep$time == 0 & d_rep$name <!-- %in% c("M1", "M2"), "value"] &lt;- 0 -->
+ d_NA <- transform(d_rep, value = ifelse(value < LOD, NA, value))
+ d_NA$value <- round(d_NA$value, 1)
+ return(d_NA)
+}
+
+# The following is the two-component model of Rocke and Lorenzato (1995)
+sdfunc_twocomp = function(value, sd_low, rsd_high) {
+ sqrt(sd_low^2 + value^2 * rsd_high^2)
+}
+
+# Add the errors.
+for (d_synth_name in d_synth_names)
+{
+ d_synth = get(d_synth_name)
+ assign(paste0(d_synth_name, "_a"), add_err(d_synth, function(value) 3))
+ assign(paste0(d_synth_name, "_b"), add_err(d_synth, function(value) 7))
+ assign(paste0(d_synth_name, "_c"), add_err(d_synth,
+ function(value) sdfunc_twocomp(value, 0.5, 0.07)))
+
+}
+
+d_synth_err_names = c(
+ paste(rep(d_synth_names, each = 3), letters[1:3], sep = "_")
+)
+
+# This is just one example of an evaluation using the kinetic model used for
+# the generation of the data
+fit <- mkinfit(m_synth_SFO_lin, synthetic_data_for_UBA_2014[[1]]$data,
+ quiet = TRUE)
+plot_sep(fit)
+summary(fit)
+
+</div><div class='output co'>#&gt; <span class='error'>Error: &lt;text&gt;:68:43: Unerwartete(s) SPECIAL</span>
+#&gt; <span class='error'>67: </span>
+#&gt; <span class='error'>68: d_rep[d_rep$time == 0 &amp; d_rep$name &lt;!-- %in%</span>
+#&gt; <span class='error'> ^</span></div></pre>
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