# Tables

Open the file `examples/cain/CaoPetzold2006_Schlogl.xml` 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.

We can view the populations or reaction counts in a table. Click on the table button to bring up a choice dialog shown below.

Choosing to display a table with species populations will bring up another choice dialog (shown below) where we can select the information to display.

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.

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.

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 to bring up the following choice dialog.

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 t = 0 where the initial condition fixes the population at X = 250. 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.)

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.

Finally we choose to display the histogram bin values. This brings up the following dialog to choose a species and frame.

We choose the final frame t = 10, 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).