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<html>
<head>
<title>Methods</title>
</head>
<body>
<h1>Methods</h1>

<p>
A solver is described with four indices which specify: time
dependence, category, method, and options. The
mapping from these fourindices to the name of a command line solver is defined
in <code>state/simulationMethods.py</code>. The <i>time dependence</i>
indicates whether the solver
may simulate time homogeneous or time inhomogeneous models.
Time inhomogeneous models have reaction propensity functions that have
explicit time dependence. The <i>category</i> indicates what kind of
output the solver produces. There are seven possibilities:
<ul>
  <li> Time series data that is recorded at uniformly-spaced intervals.
  <li> Time series data that records every reaction event.
  <li> Time series data for deterministic solvers, which is also recorded
  at uniformly-spaced intervals.
  <li> Histograms for recording the transient behavior of the species
  populations. These record the state at uniformly-spaced intervals in time.
  <li> Histograms for recording the steady state behavior of the species
  populations.
  <li> Statistics for recording the transient behavior of the species
  populations. These record the mean and standard deviation at
  uniformly-spaced intervals in time. The two statistics categories
  are used only for importing externally-generated solutions.
  <li> Statistics for recording the steady state behavior of the species
  populations.
</ul>
Next is the
simulation <i>method</i>: direct, next reaction, tau-leaping, etc. Most methods
have a number of <i>options</i>. For instance, with tau-leaping you may choose
to use adaptive step size or a fixed step size.
</p>

<p>
Below are the attributes for the method element. The identifier as
well as the indices describing the time dependence, category, method,
and options and mandatory. The rest of the attributes are optional.
</p>

<pre>  &lt;method id=&quot;Identifier&quot; timeDependence=&quot;Integer&quot; category=&quot;Integer&quot;
   method=&quot;Integer&quot; options=&quot;Integer&quot; <font color="#777777">startTime=&quot;Number&quot; equilibrationTime=&quot;Number&quot;
   recordingTime=&quot;Number&quot; maximumSteps=&quot;Integer&quot; numberOfFrames=&quot;Integer&quot;
   numberOfBins=&quot;Integer&quot; multiplicity=&quot;Integer&quot; solverParameter=&quot;Number&quot;</font>/&gt;</pre>

<p>
The starting time is of course when the simulation begins. The
equilibration time is how long the simulation is advanced before
recording the solution. The recording time is the length of time that
the simulation is advanced while recording the solution.
If a maximum number of steps is specified, then the solver will abort
if this limit is exceeded.
For solvers that record data at
uniformly-spaced intervals, the number of frames defines the frame times.
For solvers that generate histograms
one needs to specify the number of bins. The solvers dynamically adjust the
bin width to maintain this constant number of bins.
For histogram output one may also specify the histogram
multiplicity. A higher multiplicity allows one to more accurately
assess the error in the empirical probablity distributions for the
species populations. The default multiplicity is four.
Some solvers require
a parameter value. For example tau-leaping with an adaptive step size needs
an error tolerance. Which solvers require a parameter is
indicated in <code>state/simulationMethods.py</code>.
</p>

</body>
</html>