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<html>
<head>
<title>Tables</title>
</head>
<body>
<h1>Tables</h1>
<p>
Open the file <tt>examples/cain/CaoPetzold2006_Schlogl.xml</tt> and
select the "Schlogl" model and the "Time Series"
method. Select all of the species and reactions in the recorder panel
and then generate 10 trajectories. As we saw in the previous section,
the steady state distribution of species populations is
bi-modal. Below we reproduce a plot of the trajectories.
</p>
<p align="center">
<img src="VisualizationTablesSchloglTimeSeriesPlot.jpg">
</p>
<p>
We can view the populations or reaction counts in a table. Click on
the table button <img src="x-office-spreadsheet.png"> to bring
up a choice dialog shown below.
</p>
<p align="center">
<img src="VisualizationTablesSchloglTimeSeriesTableChoice.jpg">
</p>
<p>
Choosing to display a table with species populations will bring up
another choice dialog (shown below) where we can select the
information to display.
</p>
<p align="center">
<img src="VisualizationTablesSchloglTimeSeriesTableSpeciesChoice.jpg">
</p>
<p>
We select the "Statistics for all frames" option. This table
is shown below. The row headers number the frames. The columns show
the time, population mean, and population standard deviation. Because
the populations develop into a bi-modal distribution, the standard
deviation becomes relatively large as time advances.
</p>
<p align="center">
<img src="VisualizationTablesSchloglTimeSeriesTableSpeciesStatistics.jpg">
</p>
<p>
Now we will quantitatively study how the trajectories separate into
a bi-modal distribution.
Select the "Histograms Transient" method, which records
the populations in histograms
at 6 frames, and generate 10,000 trajectories. The plot from the
previous section, which shows the probability distributions at each of
frames (excluding the initial condition), is reproduced below.
</p>
<p align="center">
<!--Saved as PNG. Reduced from 8 to 6 inches and saved as JPG.-->
<img src="VisualizationPlottingHistogramsSchloglNonzero.jpg">
</p>
<p>
We can also view the histogram information in a table. With the
histogram output selected in the simulation output panel, click on the
table button <img src="x-office-spreadsheet.png"> to bring
up the following choice dialog.
</p>
<p align="center">
<img src="VisualizationTablesSchloglHistogramsTransientTableChoice.jpg">
</p>
<p>
First we display the estimated error in the probability distributions.
The estimated error in the first histogram is zero. This is because
the first histogram is recorded at time <i>t = 0</i> where the initial
condition fixes the population at <i>X = 250</i>. The rest of the
distributions have reasonably low errors. This indicates that 10,000
trajectories is adequate for our choice of histograms with 32 bins. (If
we desired higher resolution histograms we would need to generate a
greater number of trajectories.)
</p>
<p align="center">
<img src="VisualizationTablesSchloglHistogramsTransientError.jpg">
</p>
<p>
Next we display the mean and standard deviation of the species
population. For this system these statistics are not particularly
useful because the distribution is bi-modal.
</p>
<p align="center">
<img src="VisualizationTablesSchloglHistogramsTransientMean.jpg">
</p>
<p>
Finally we choose to display the histogram bin values. This brings up
the following dialog to choose a species and frame.
</p>
<p align="center">
<img src="VisualizationTablesSchloglHistogramsTransientBinsChoice.jpg">
</p>
<p>
We choose the final frame <i>t = 10</i>, which is shown below.
The bin width for the histogram is 32. From the table below we see
that the mode of the lower part of the distribution is the bin [64..96) and
the mode of the upper part is the bin [544..576).
</p>
<p align="center">
<img src="VisualizationTablesSchloglHistogramsTransientBins.jpg">
</p>
</body>
</html>
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