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Dear Darrin:

I like to pick up on your example since it is a real one frequently
encountered (even in SBML). I modified it a little to conform with the
definition of the kineticLaw of SBML, i.e., it looks like

k * V * X(X-1)/2

Here k is the kinetic constant in the appropriate units and V the volume
of the reaction compartment. The MathML for this rate law may be found
below

<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<divide/>
<apply>
<times/>
<ci> k </ci>
<ci> V </ci>
<ci> X </ci>
<apply>
<minus/>
<ci> X </ci>
<cn> 1 </cn>
</apply>
</apply>
<cn> 2 </cn>
</apply>
</math>

This MathML includes two cn elements of which one <cn> 2 </cn> is
dimensionless and the other <cn> 1 </cn> must have the same units as X.
It is easy for a human to detect the needed units for the above example.

As Mike stated in his initial post to the mailing list defining the
units of numbers in MathML implicitly has at least one major problem.
Let us assume that the units of k are incorrectly given in the SBML
document. In this case the implicit unit definition of <cn> 2 </cn>
would correct for this obvious error and thus preventing the unit
checking which SBML facilitates. This is clearly not the intent of
implicit unit definition for numbers.

Please note that the above example can be written in SBML without any
problems. We just need to replace <cn> 1 </cn> with <ci> ONE_ITEM </ci>
and define ONE_ITEM as a global parameter with the appropriate units.
This approach is clearly cumbersome but the only correct way in SBML as
it stands now. Implicit unit definitions where brought up to make
writing correct SBML easier. However, the above problem (at least in my
opinion) makes them unfeasible.

What other options do we have:
1) We could add an attribute to the cn element similar to CellML
<cn sbml:units="UnitSId"> 1.0 </cn>
In this case the default value should be sbml:units="dimensionless",
which currently exist only as unit kind and not as UnitSId. This
however is only a minor problem

2) We can adopt the proposal for MathML which can be found at:
http://www.w3.org/TR/mathml-units/
This is basically introducing text into the content markup, i.e., it is
by itself not structured enough for SBML needs.

3) We could allow UnitSId to be valid within a ci element. This creates
the problem that UnitSIds and SIds are in separate name spaces and thus
we may have ambiguity. However, we could remove this problem by having
just one name space for all SIds.

4) We define a third csymbol:
http://www.sbml.org/sbml/symbols/units
and allow only UnitSIds as values for this csymbol. In case that we need
a number with units in MathML this expands to:
<apply>
<times/>
<cn> 1 </cn>
<csymbol encoding="text"
definitionURL="http://www.sbml.org/sbml/symbols/units">
SUBSTANCE_UNITS
</csymbol>
</apply>

I would like to hear about your thoughts an the suggested solutions or
even better other simpler ones :)

Thanks,
Stefan


On Sun, 11 Feb 2007 21:59:40 +0000 (GMT)
Darren Wilkinson <darrenjwilkinson@btinternet.com> wrote:

> Yes, units really are tricky! I don't have a strong view on what
> to do about them (yet!), but I always think its helps clarify
> things to think about my favourite rate law:
>
> X(X-1)/2
>
> Here it is assumed that X has units of "item". Then the "1" also
> has units of "item", but the "2" is dimensionless. This
> difference really matters if you decide to convert units to
> (say) moles, as then the "1" needs converting (to become the
> reciprocal of avogadros constant), but the 2 remains unchanged.
> It would obviously be highly desirable for any unit
> checking/conversion capability in SBML/libSBML to be able to
> cope with such issues... However, it would be a bit messy to
> have to define a "one" and a "two" externally with appropriate
> units just to be able to construct this rate law...
>
> Regards,
>
> Darren
>
>
>
> --- Michael Hucka <mhucka@caltech.edu> wrote:
>
> > The SBML editors had an off-line discussion which we
> > realized needs to be put on sbml-discuss. It concerns an
> > issue that Sarah Keating ran into while implementing unit
> > validation in libSBML.
> >
> > The issue is how the units of pure numbers in MathML should
> > be treated. Here's an example, in the case of the 'delay'
> > field on Events:
> >
> > <delay>
> > <math xmlns="http://www.w3.org/1998/Math/MathML">
> > <cn> 1 </cn>
> > </math>
> > </delay>
> >
> > Note the literal "1". What units, if any, should be
> > assumed for the number?
> >
> > One option is to treat literal numbers as always being
> > without units. This is a valid viewpoint, but it leads to
> > more model validation failures. Although modelers should
> > define parameters (which can have defined units) for a lot
> > of the cases where they often write numbers directly, the
> > practical reality is that many people won't think of doing
> > that.
> >
> > A second option is to take the units to be whatever units
> > are defined as the default for the field in question, or if
> > there is an associated field definining the units, then
> > whatever that field says the units are. (For instance,
> > there is a 'timeUnits' field on Events that could apply in
> > this example.) The logic behind this idea is that even
> > though the user didn't specify the units explicitly, a
> > reasonable interpretation of their intention is that the
> > units are meant to be whatever the defaults are. In other
> > words, the modeler didn't mean "1" without units, they meant
> > "1 in the units of time" for this example.
> >
> > Sounds reasonable? But it gets more complicated. Imagine
> > now something like
> >
> > <math xmlns="http://www.w3.org/1998/Math/MathML">
> > <apply>
> > <plus/>
> > <ci> S </ci>
> > <cn> 2 </cn>
> > </apply>
> > </math>
> >
> > For the purpose of this second example, the "S" can be
> > anything (e.g., a species identifier) and the context can be
> > anything, not just the Events example above.
> >
> > The question is, what should be assumed for the units of "2"?
> >
> > If we follow the same guideline, i.e., that the literal
> > number has whatever units are appropriate for the situation,
> > then it creates validation problems. First, it implies a
> > unit validator must deduce the expected units somehow, and
> > this may sometimes be impossible due to ambiguities in a
> > given situation. Second, Stefan Hoops pointed out it opens
> > a hole in validation: it effectively means that numbers in
> > MathML are assumed to always have the appropriate units, so
> > unit checking becomes worthless.
> >
> > To cope with this, we are tentatively thinking of using the
> > following set of guidelines:
> >
> > 1) If the number is the only thing contained inside a <math>
> > (such as the original example involving a delay on
> > Events), assume that the units of the number are the
> > units defined for that field (so, timeUnits for delays).
> >
> > 2) In all other cases, assume pure numbers have no units.
> >
> > This handles the first case, and also addresses the second
> > case. (In the second case, there would be a unit validation
> > failure because the "2" would not have units and therefore
> > the overall expression could not have consistent units.)
> >
> > The downside is that this "rule" is defined with an
> > exception.
> >
> > What do the rest of you SBMLers think?
> >
> > Whatever is decided, the next SBML specification will have
> > to spell out the guidelines precisely.
> >
> > MH
> >
> > ____________________________________________________________
> > To manage your sbml-discuss list subscription, visit
> > https://utils.its.caltech.edu/mailman/listinfo/sbml-discuss
> >
> > For a web interface to the sbml-discuss mailing list, visit
> > http://sbml.org/forums/
> >
> > For questions or feedback about the sbml-discuss list,
> > contact sbml-team@caltech.edu.
> >
>
>
> --
> Darren Wilkinson
> email: darrenjwilkinson@btinternet.com
> home www: http://www.darrenjwilkinson.btinternet.co.uk/
> work www: http://www.staff.ncl.ac.uk/d.j.wilkinson/
> ____________________________________________________________
> To manage your sbml-discuss list subscription, visit
> https://utils.its.caltech.edu/mailman/listinfo/sbml-discuss
>
> For a web interface to the sbml-discuss mailing list, visit
> http://sbml.org/forums/
>
> For questions or feedback about the sbml-discuss list,
> contact sbml-team@caltech.edu.


--
Stefan Hoops, Ph.D.
Senior Project Associate
Virginia Bioinformatics Institute - 0477
Virginia Tech
Bioinformatics Facility I
Blacksburg, Va 24061, USA

Phone: (540) 231-1799
Fax: (540) 231-2606
Email: shoops@vbi.vt.edu
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