## MathML

Home page: http://www.w3.org/Math

MathML is "MathML is a low-level specification for describing mathematics as a basis for machine to machine communication".

In the context of a markup langauge for System Dynamics models, MathML allows the equations to be expressed in a symbolic, software-independent and standards-compliant manner. The particular syntax required by particular software tools (e.g. in the representation of IF...THEN...ELSE constructs) can then be generated from the MathML - for example, by the use of XSLT stylesheets. This can of course also be done by writing specific parsers for equations represented as plain text strings, but that means that two technologies (something to handle the XMILE XML, and something to parse the equations) is needed to produce software-specific model-representations.

The downside of MathML is that it is much more verbose. This is only an issue if XMILE is intended to be a human-editable format.

MathML is used by other modelling languages, e.g. SBML and CellML.

## SBML

Home page: http://www.sbml.org

This is a language developed for describing biochemical pathways and biological signalling pathways. The models are continuous-systems models, hence can be expressed in terms of differential equations, but the language works in terms which are meaningful to biologists and biochemists: e.g. chemical species and reactions.

SBML is the *de facto* standard for the biological modelling community, and currently some **120 software tools** support it to a lesser or greater extent.

The current vesion of SBML is restricted to flat models (no disaggregation), but there is considerable avtivity within the community towards the development of extensions to the language which will allow (for example) the representation of grid space and dynamic populations of cells.

SBML is closely allied with BioModels, http://www.ebi.ac.uk/biomodels/, an online database of several 100 curated and uncurated models expresed in SBML.

## CellML

Home page: http://www.cellml.org

This covers similar ground to SBML, but is engineered rather differently.

## ModelicaML

Key paper: http://www.modelica.org/events/Conference2003/papers/h39_Pop.pdf

"The language was designed as a standard format for storage, analysis and exchange of models." - specifically, Modelica models (http://www.modelica.org)

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