mumot.MuMoTmodel

class mumot.MuMoTmodel

Bases: object

Model class.

__init__()

Initialize self. See help(type(self)) for accurate signature.

Methods

SSA([initWidgets])	Construct interactive Stochastic Simulation Algorithm (SSA) plot (simulation run of the Gillespie algorithm to approximate the Master Equation solution).
__init__()	Initialize self.
bifurcation(bifurcationParameter, stateVariable1)	Construct and display bifurcation plot of stateVariable1 (y-axis), or stateVariable1 +/- stateVariable2 (y-axis), depending on bifurcationParameter (x-axis).
getFokkerPlanckEquation()	Get Fokker-Planck equation derived from term ~ O(1) in van Kampen expansion (linear noise approximation).
getMasterEquation()	Gets Master Equation expressed with step operators, and substitutions.
getNoiseEquations()	Get equations of motion of first and second order moments of noise.
getNoiseSolutions()	Gets noise in the stationary state.
getODEs([method])	Get symbolic equations for the model system of ODEs.
getStoichiometry()	Get stoichiometry as a dictionary
getVanKampenExpansion()	Get van Kampen expansion when the operators are expanded up to second order.
integrate([showStateVars, initWidgets])	Construct interactive time evolution plot for state variables.
multiagent([initWidgets])	Construct interactive multiagent plot (simulation of agents locally interacting with each other).
noiseCorrelations([initWidgets])	Construct interactive time evolution plot for noise correlations around fixed points.
show()	Show a LaTeX representation of the model.
showConstantReactants()	Show a sorted LaTeX representation of the model’s constant reactants.
showFokkerPlanckEquation()	Show Fokker-Planck equation derived from term ~ O(1) in van Kampen expansion (linear noise approximation).
showMasterEquation()	Displays Master equation expressed with step operators.
showNoiseEquations()	Display equations of motion of first and second order moments of noise.
showNoiseSolutions()	Display noise in the stationary state.
showODEs([method])	Show a LaTeX representation of the model system of ODEs.
showRates()	Show a sorted LaTeX representation of the model’s rate parameters.
showReactants()	Show a sorted LaTeX representation of the model’s reactants.
showSingleAgentRules()	Show the probabilistic transitions of the agents in each possible reactant-state.
showStoichiometry()	Display stoichiometry as a dictionary with keys ReactionNr, ReactionNr represents another dictionary with reaction rate, reactants and corresponding stoichiometry.
showVanKampenExpansion()	Show van Kampen expansion when the operators are expanded up to second order.
stream(stateVariable1[, stateVariable2, …])	Display interactive stream plot of stateVariable1 (x-axis), stateVariable2 (y-axis), and optionally stateVariable3 (z-axis; not currently supported - see below).
substitute(subsString)	Create a new model with variable substitutions.
vector(stateVariable1, stateVariable2[, …])	Display interactive vector plot of stateVariable1 (x-axis), stateVariable2 (y-axis), and optionally stateVariable3 (z-axis)
visualise()	Build a graphical representation of the model.

SSA(initWidgets=None, **kwargs)

Construct interactive Stochastic Simulation Algorithm (SSA) plot (simulation run of the Gillespie algorithm to approximate the Master Equation solution).

Parameters:

• initWidgets (dict {str,list}, optional) – Keys are the free-parameter or any other specific parameter, and values are four values as [initial-value, min-value, max-value, step-size]
• Keywords
• ——–
• params (list [(str,num)], optional) – List of parameters defined as pairs (‘parameter name’, value). See ‘Partial controllers’ in the docs/MuMoTuserManual.ipynb. Rates defaults to mumot.MuMoTdefault._initialRateValue. System size defaults to mumot.MuMoTdefault._systemSize.
• initialState (dictionary {str:float}, optional) – Initial proportions of the reactants (type: dictionary with reactants as keys and floats in range [0,1] as values). See the bookmark of and example. Defaults to a dictionary with the (alphabetically) first reactant to 1 and the rest to 0.
• maxTime (float, optional) – Simulation time. Must be strictly positive. Defaults to mumot.MuMoTdefault._maxTime.
• randomSeed (int, optional) – Random seed. Must be strictly positive in range [0, mumot.MAX_RANDOM_SEED]). Defaults to a random number.
• plotProportions (bool, optional) – Flag to plot proportions or full populations. Defaults to False.
• realtimePlot (bool, optional) – Flag to plot results in realtime (True = the plot is updated each timestep of the simulation; False = the plot is updated once at the end of the simulation). Defaults to False.
• visualisationType (str, optional) – Type of visualisation ('evo',``’final’`` or 'barplot'). See docs/MuMoTuserManual.ipynb for more details. Defaults to ‘evo’.
• final_x (object, optional) – Which reactant is shown on x-axis when visualisation type is ‘final’. Defaults to the alphabetically first reactant.
• final_y (object, optional) – Which reactant is shown on y-axis when visualisation type is ‘final’. Defaults to the alphabetically second reactant.
• runs (int, optional) – Number of simulation runs to be executed. Must be strictly positive. Defaults to 1.
• aggregateResults (bool, optional) – Flag to aggregate or not the results from several runs. Defaults to True.
• legend_loc (str, optional) – Specify legend location: combinations like ‘upper left’ (default), ‘lower right’, or ‘center center’ are allowed (9 options in total).
• fontsize (integer, optional) – Specify fontsize for axis-labels. If not specified, the fontsize is automatically derived from the length of axis label.
• xlab (str, optional) – Specify label on x-axis. Defaults to ‘time t’.
• ylab (str, optional) – Specify label on y-axis. Defaults to ‘reactants’.
• choose_xrange (list of float, optional) – Specify range plotted on x-axis as a two-element iterable of the form [xmin, xmax]. If not given uses data values to set axis limits.
• silent (bool, optional) – Switch on/off widgets and plot. Important for use with multicontrollers. Defaults to False.

Returns:

MuMoTstochasticSimulationController – A MuMoT controller object

bifurcation(bifurcationParameter, stateVariable1, stateVariable2=None, initWidgets=None, **kwargs)

Construct and display bifurcation plot of stateVariable1 (y-axis), or stateVariable1 +/- stateVariable2 (y-axis), depending on bifurcationParameter (x-axis).

1D and 2D systems are currently supported. Only limit points and branch points can be detected.

Parameters:

• bifurcationParameter – Critical parameter plotted on x-axis. Type?
• stateVariable1 – State variable expression to be plotted on the y-axis; allowed are: reactant1, reactant1-reactant2, or reactant1+reactant2. Type?
• stateVariable2 (optional) – State variable if system is larger than 2D (not currently supported). Type?
• initWidgets (dict, optional) – Keys are the free-parameter or any other specific parameter, and values are four values, e.g. 'parameter': [initial-value, min-value, max-value, step-size].
• Keywords
• ——–
• initialState (dict, optional) – Initial proportions of the reactants. State variables are the keys the values of which must be in range [0, 1]. Can also be set via initWidgets argument. Defaults to an empty dictionary.
• initBifParam (float, optional) – Initial value of bifurcation parameter. Can also be set via initWidgets argument. Defaults to 2.0.
• conserved (bool, optional) – Whether a system is conserved to make proportions of state variables (at time t=0) sum up to 1, or not. Defaults to False.
• contMaxNumPoints (int, optional) – Maximum number of continuation points. Defaults to 100.
• fontsize (int, optional) – Font size for axis labels. If not given, font size is automatically derived from length of axis label.
• xlab (str, optional) – Label for x-axis. If not given uses symbol for bifurcationParameter in arguments as default label.
• ylab (str, optional) – Label for y-axis. If not given, defaults to '\Phi_{stateVariable1}', where stateVariable1 is another argument to this method. If stateVariable1 is a sum/difference of the form ‘Reactant1 +/- Reactant2’ the default label is '\Phi_{Reactant1} - \Phi_{Reactant2}'.
• choose_xrange (list of float, optional) – Range plotted on x-axis as [xmin, xmax]. If not given, uses data values to set axis limits.
• choose_yrange (list of float, optional) – Range plotted on y-axis as [ymin, ymax]. If not given, uses data values to set axis limits.
• silent (bool, optional) – Switch on/off widgets and plot. Important for use with multi controllers.

Returns:

MuMoTbifurcationController

Notes

Plotting keywords are also described in the user manual.

getFokkerPlanckEquation()

Get Fokker-Planck equation derived from term ~ O(1) in van Kampen expansion (linear noise approximation).

Returns:dict, dict – Dictionary of Fokker-Planck right hand sides Dictionary of substitutions used, this defaults to None if no substitutions were made

getMasterEquation()

Gets Master Equation expressed with step operators, and substitutions.

Returns:dict, dict – Dictionary showing all terms of the right hand side of the Master Equation Dictionary of substitutions used, this defaults to None if no substitutions were made

getNoiseEquations()

Get equations of motion of first and second order moments of noise.

Returns:dict, dict, dict, dict – Dictionary of first order moments equations of motion right hand sides (derived using Fokker-Planck equation) Dictionary of substitutions used for first order moments equations Dictionary of second order moments equations of motion right hand sides (derived using Fokker-Planck equation) Dictionary of substitutions used for second order moments equations

getNoiseSolutions()

Gets noise in the stationary state.

Returns:dict, dict, dict, dict – Dictionary of first order moments noise solution right hand sides Dictionary of substitutions used for first order moments solutions Dictionary of second order moments noise solution right hand sides Dictionary of substitutions used for second order moments solutions

getODEs(method='massAction')

Get symbolic equations for the model system of ODEs.

Parameters:method (str, optional) – Can be 'massAction' (default) or 'vanKampen'. Returns:dict – Dictionary of ODE right hand sides with reactant (left hand side) as key

getStoichiometry()

Get stoichiometry as a dictionary

Returns:dict – Dictionary with key ReactionNr; ReactionNr represents another dictionary with reaction rate, reactants and corresponding stoichiometry.

getVanKampenExpansion()

Get van Kampen expansion when the operators are expanded up to second order.

Returns:Add, Add, dict – van Kampen expansion left hand side van Kampen expansion right hand side Dictionary of substitutions used, this defaults to None if no substitutions were made

integrate(showStateVars=None, initWidgets=None, **kwargs)

Construct interactive time evolution plot for state variables.

Parameters:

• showStateVars (optional) – Select reactants (state variables) to be shown in plot, if not specified all reactants are plotted. Type?
• initWidgets (dict, optional) – Dictionary where keys are the free-parameter or any other specific parameter, and values are four values, e.g. 'parameter':[initial-value, min-value, max-value, step-size]
• Keywords
• ——–
• maxTime (float, optional) – Simulation time for noise correlations. Must be strictly positive. Defaults to 3.0.
• tstep (float, optional) – Time step of numerical integration of reactants. Defaults to 0.01.
• plotProportions (bool, optional) – Flag to plot proportions or full populations. Defaults to False
• initialState (dict, optional) – Initial proportions of the reactants (type: float in range [0,1]), can also be set via initWidgets argument. Defaults to an empty dictionary.
• conserved (bool, optional) – Specify if a system is conserved to make proportions of state variables (at time t=0) sum up to 1, or not. Defaults to False.
• legend_fontsize (int, optional) – Specify fontsize of legend. Defaults to 14.
• legend_loc (str, optional) – Specify legend location: combinations like ‘upper left’ (default), ‘lower right’, or ‘center center’ are allowed (9 options in total).
• fontsize (integer, optional) – Specify fontsize for axis-labels. If not specified, the fontsize is automatically derived from the length of axis label.
• xlab (str, optional) – Specify label on x-axis. Defaults to ‘time t’.
• ylab (str, optional) – Specify label on y-axis. Defaults to ‘reactants’.
• choose_xrange (list of float, optional) – Specify range plotted on x-axis as a two-element iterable of the form [xmin, xmax]. If not given uses data values to set axis limits.
• choose_trange (list of float, optional) – Specify range plotted on y-axis as a two-element iterable of the form [ymin, ymax]. If not given uses data values to set axis limits.
• silent (bool, optional) – Switch on/off widgets and plot. Important for use with multi controllers. Defaults to False.

Returns:

MuMoTtimeEvolutionController

Notes

Plotting keywords are also described in the user manual.

multiagent(initWidgets=None, **kwargs)

Construct interactive multiagent plot (simulation of agents locally interacting with each other).

Parameters:

• initWidgets (dict {str,list}, optional) – Keys are the free-parameter or any other specific parameter, and values are four values as [initial-value, min-value, max-value, step-size]

• Keywords

• ——–

• params (list [(str,num)], optional) – List of parameters defined as pairs (‘parameter name’, value). See ‘Partial controllers’ in the docs/MuMoTuserManual.ipynb. Rates defaults to mumot.MuMoTdefault._initialRateValue. System size defaults to mumot.MuMoTdefault._systemSize.

• initialState (dictionary {str:float}, optional) – Initial proportions of the reactants (type: dictionary with reactants as keys and floats in range [0,1] as values). See the bookmark of and example. Defaults to a dictionary with the (alphabetically) first reactant to 1 and the rest to 0.

• maxTime (float, optional) – Simulation time. Must be strictly positive. Defaults to mumot.MuMoTdefault._maxTime.

• randomSeed (int, optional) – Random seed. Must be strictly positive in range [0, mumot.MAX_RANDOM_SEED]). Defaults to a random number.

• plotProportions (bool, optional) – Flag to plot proportions or full populations. Defaults to False.

• realtimePlot (bool, optional) – Flag to plot results in realtime (True = the plot is updated each timestep of the simulation; False = the plot is updated once at the end of the simulation). Defaults to False.

• visualisationType (str, optional) – Type of visualisation ('evo',``’graph’,’final’`` or 'barplot'). See docs/MuMoTuserManual.ipynb for more details. Defaults to ‘evo’.

• final_x (object, optional) – Which reactant is shown on x-axis when visualisation type is ‘final’. Defaults to the alphabetically first reactant.

• final_y (object, optional) – Which reactant is shown on y-axis when visualisation type is ‘final’. Defaults to the alphabetically second reactant.

• runs (int, optional) – Number of simulation runs to be executed. Must be strictly positive. Defaults to 1.

• aggregateResults (bool, optional) – Flag to aggregate or not the results from several runs. Defaults to True.

• netType (str, optional) – Type of network ('full', 'erdos-renyi', 'barabasi-albert' or 'dynamic'. See docs/MuMoTuserManual.ipynb for more details. Defaults to ‘full’.

• netParam (float, optional) – Property of the network ralated to connectivity. The precise meaning and range of this parameter varies depending on the netType. See docs/MuMoTuserManual.ipynb for more details and defaults.

• motionCorrelatedness (float, optional) – (active only for netType=’dynamic’) level of inertia in the random walk, with 0 the reactants do a completely uncorrelated random walk and with 1 they move on straight trajectories. Must be in range [0, 1]. Defaults to 0.5.

• particleSpeed (float, optional) – (active only for netType=’dynamic’) speed of the moving particle, i.e. displacement in one timestep. Must be in range [0,1]. Defaults to 0.01.

• timestepSize (float, optional) – Length of one timestep, the maximum size is automatically determined by the rates. Must be strictly positive. Defaults to the maximum value.

• showTrace (bool, optional) – (active only for netType=’dynamic’) flag to plot the trajectory of each reactant. Defaults to False.

• showInteractions (bool, optional) –

  (active only for netType=’dynamic’) flag to plot the interaction range between particles. Defaults to False.

  legend_fontsize: int, optional

  Specify fontsize of legend. Defaults to 14.

• legend_loc (str, optional) – Specify legend location: combinations like ‘upper left’ (default), ‘lower right’, or ‘center center’ are allowed (9 options in total).

• fontsize (integer, optional) – Specify fontsize for axis-labels. If not specified, the fontsize is automatically derived from the length of axis label.

• xlab (str, optional) – Specify label on x-axis. Defaults to ‘time t’.

• ylab (str, optional) – Specify label on y-axis. Defaults to ‘reactants’.

• choose_xrange (list of float, optional) – Specify range plotted on x-axis as a two-element iterable of the form [xmin, xmax]. If not given uses data values to set axis limits.

• silent (bool, optional) – Switch on/off widgets and plot. Important for use with multicontrollers. Defaults to False.

Returns:

MuMoTmultiagentController – A MuMoT controller object

noiseCorrelations(initWidgets=None, **kwargs)

Construct interactive time evolution plot for noise correlations around fixed points.

Parameters:

• initWidgets (dict, optional) – Dictionary where keys are the free-parameter or any other specific parameter, and values are four values, e.g. 'parameter': [initial-value, min-value, max-value, step-size].
• Keywords
• ——–
• maxTime (float, optional) – Simulation time for noise correlations. Must be strictly positive. Defaults to 3.0.
• tstep (float, optional) – Time step of numerical integration of noise correlations. Defaults to 0.01.
• maxTimeDS (float, optional) – Simulation time for ODE system. Must be strictly positive. Defaults to 50.
• tstepDS (float, optional) – Time step of numerical integration of ODE system. Defaults to 0.01.
• initialState (dict, optional) – Initial proportions of the reactants. Must be in range [0, 1]. Can also be set via initWidgets argument. Defaults to an empty dictionary.
• conserved (bool, optional) – Whether a system is conserved to make proportions of state variables (at time t=0) sum up to 1. Defaults to False.
• legend_fontsize (int, optional) – Font size of legend. Defaults to 14.
• legend_loc (str, optional) – Legend location. Combinations like 'upper left', 'lower right', or 'center center' are allowed (9 options in total). Defaults to 'upper left'.
• fontsize (int, optional) – Font size for axis labels If not given, font size is automatically derived from length of axis label.
• xlab = str, optional – Label on x-axis. Defaults to 'time t'.
• ylab (str, optional) – Label on y-axis. Defaults to 'noise correlations'.
• choose_xrange (list of float, optional) – Range to be plotted on x-axis. Specified as [xmin, xmax]. If not given uses data values to set axis limits.
• choose_yrange (list of float, optional) – Range to be plotted on y-axis. Specified as [ymin, ymax]. If not given uses data values to set axis limits.
• silent (bool, optional) – Switch on/off widgets and plot. Important for use with multi controllers. Defaults to False.

Returns:

MuMoTtimeEvolutionController

Notes

Plotting keywords are also described in the user manual.

show()

Show a LaTeX representation of the model.

Display all rules in the model as rendered LaTeX in the Jupyter Notebook.

Returns:None

Notes

If rules are rendered in the Notebook with extraneous | characters on the right-hand-side then try:

• Switching web browser and/or
• Updating the notebook package: pip install --upgrade --no-deps notebook

showConstantReactants()

Show a sorted LaTeX representation of the model’s constant reactants.

Displays the LaTeX representation in the Jupyter Notebook if there are constant reactants in the model, otherwise prints an error.

Returns:None

showFokkerPlanckEquation()

Show Fokker-Planck equation derived from term ~ O(1) in van Kampen expansion (linear noise approximation).

Displays rendered LaTeX in the Jupyter Notebook.

Returns:None

showMasterEquation()

Displays Master equation expressed with step operators.

Displays rendered LaTeX in the Jupyter Notebook.

Returns:None

showNoiseEquations()

Display equations of motion of first and second order moments of noise.

Displays rendered LaTeX in the Jupyter Notebook.

Returns:None

showNoiseSolutions()

Display noise in the stationary state.

Displays rendered LaTeX in the Jupyter Notebook.

Returns:None

showODEs(method='massAction')

Show a LaTeX representation of the model system of ODEs.

Displays rendered LaTeX in the Jupyter Notebook.

Parameters:method (str, optional) – Can be 'massAction' (default) or 'vanKampen'. Returns:None

showRates()

Show a sorted LaTeX representation of the model’s rate parameters.

Displays rendered LaTeX in the Jupyter Notebook.

Returns:None

showReactants()

Show a sorted LaTeX representation of the model’s reactants.

Displays rendered LaTeX in the Jupyter Notebook.

Returns:None

showSingleAgentRules()

Show the probabilistic transitions of the agents in each possible reactant-state.

Returns:None

showStoichiometry()

Display stoichiometry as a dictionary with keys ReactionNr, ReactionNr represents another dictionary with reaction rate, reactants and corresponding stoichiometry.

Displays rendered LaTeX in the Jupyter Notebook.

Returns:None

showVanKampenExpansion()

Show van Kampen expansion when the operators are expanded up to second order.

Displays rendered LaTeX in the Jupyter Notebook.

Returns:None

stream(stateVariable1, stateVariable2=None, stateVariable3=None, params=None, initWidgets=None, **kwargs)

Display interactive stream plot of stateVariable1 (x-axis), stateVariable2 (y-axis), and optionally stateVariable3 (z-axis; not currently supported - see below).

Parameters:

• stateVariable1 – State variable to be plotted on the x-axis. Type?
• stateVariable2 – State variable to be plotted on the y-axis. Type?
• stateVariable3 (optional) – State variable to be plotted on the z-axis. Not currently supported; use vector instead for 3-dimensional systems. Type?
• params (optional) – Parameter list (see ‘Partial controllers’ in the user manual). Type?
• initWidgets (dict, optional) – Keys are the free parameter or any other specific parameter, and values each a list of [initial-value, min-value, max-value, step-size].
• Keywords
• ——–
• showFixedPoints (bool, optional) – Plot fixed points. Defaults to False.
• showNoise (bool, optional) – Plot noise around fixed points. Defaults to False.
• runs (int, optional) – Number of simulation runs to be executed. Must be strictly positive. Defaults to 1.
• aggregateResults (bool, optional) – Flag to aggregate or not the results from several runs. Defaults to True.
• fontsize (int, optional) – Font size for axis-labels.
• xlab (str, optional) – Label for x-axis. Defaults to 'stateVariable1'.
• ylab (str, optional) – Label for y-axis. Defaults to 'stateVariable2'.
• choose_xrange (list of float, optional) – Range plotted on x-axis. Specify as [xmin, xmax]. If not given uses data values to set axis limits
• choose_yrange (list of float, optional) – Range plotted on y-axis. Specify as [ymin, ymax]. If not given uses data values to set axis limits
• silent (bool, optional) – Switch on/off widgets and plot. Important for use with multi controllers. Defaults to False.
• setNumPoints (int, optional) – Used for 3d stream plots to specify the number of streams plotted
• maxTime (float, optional) – Must be strictly positive. Used for numerical integration of ODE system in 3d stream plots. Default value is 1.0.

Returns:

MuMoTcontroller – A MuMoT controller object

Notes

Plotting keywords are also described in the user manual.

substitute(subsString: str)

Create a new model with variable substitutions.

Parameters:subsString (str) – Comma-separated string of assignments. Returns:MuMoTmodel – A new model.

vector(stateVariable1, stateVariable2, stateVariable3=None, params=None, initWidgets=None, **kwargs)

Display interactive vector plot of stateVariable1 (x-axis), stateVariable2 (y-axis), and optionally stateVariable3 (z-axis)

Parameters:

• stateVariable1 – State variable to be plotted on the x-axis. Type?
• stateVariable2 – State variable to be plotted on the y-axis. Type?
• stateVariable3 (optional) – State variable to be plotted on the z-axis. Type?
• params (optional) – Parameter list (see ‘Partial controllers’ in the user manual). Type?
• initWidgets (dict, optional) – Keys are the free parameter or any other specific parameter, and values each a list of [initial-value, min-value, max-value, step-size].
• Keywords
• ——–
• showFixedPoints (bool, optional) – Plot fixed points. Defaults to False.
• showNoise (bool, optional) – Plot noise around fixed points. Defaults to False.
• runs (int, optional) – Number of simulation runs to be executed. Must be strictly positive. Defaults to 1.
• aggregateResults (bool, optional) – Flag to aggregate or not the results from several runs. Defaults to True.
• fontsize (int, optional) – Font size for axis-labels.
• xlab (str, optional) – Label for x-axis. Defaults to 'stateVariable1'.
• ylab (str, optional) – Label for y-axis. Defaults to 'stateVariable2'.
• zlab (str, optional) – Label for z-axis (3D plots only). Defaults to 'stateVariable3'.
• choose_xrange (list of float, optional) – Range plotted on x-axis. Specify as [xmin, xmax]. If not given uses data values to set axis limits
• choose_yrange (list of float, optional) – Range plotted on y-axis. Specify as [ymin, ymax]. If not given uses data values to set axis limits
• silent (bool, optional) – Switch on/off widgets and plot. Important for use with multi controllers. Defaults to False.

Returns:

MuMoTcontroller – A MuMoT controller object

Notes

Plotting keywords are also described in the user manual.

visualise()

Build a graphical representation of the model.

Returns:graphviz.Digraph – Graphical representation of model.

Notes

If result cannot be plotted check for installation of libltdl e.g on macOS see if XQuartz needs updating or do:

brew install libtool --universal
brew link libtool