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Kevin Burrage wrote:
> Andrew
>
> I have lots of ideas on this - but email not a good way of doing it.
> Am in oxford at the moment but could skype you if you were interested.

Hi Kevin,

Sorry for the delay in getting back to you about this.

There seems to be a lot of interest amongst members of the CellML
community in Auckland about hearing your views on this; one suggestion I
heard was to use the BestGRID rather than Skype so more people could be
involved at this end (although I am not sure how convenient it would be
for you to access the BestGRID facilities in Oxford so the timezones
would work out).

When would be the most convenient for you? Given that there are a number
of people who have indicated a desire to be involved in these
discussion, and also a few that are interested in sitting in to listen,
I would suggest making it at earliest next week, to ensure everyone can
get their schedules to fit, and to ensure that software is working ahead
of time. Since you are, I presume, in a GMT+1 timezone, and we are in
GMT+12, the best time would probably be early in the morning for you /
night time for us, e.g. 7-8 AM Oxford / 6-7 PM NZ, 8-9 AM Oxford / 7-8
PM NZ , or 9-10 AM Oxford / 8-9 PM NZ.

Best regards,
Andrew

>
> BW
>
> Kevin
> -------------------------------------------------
> Kevin Burrage
> Professor of Computational Systems Biology, COMLAB, University of Oxford
> and Professor of Computational Mathematics, IMB, University of Queensland
> -------------------------------------------------
>
>
>
> On Wed, 23 Apr 2008 17:31:26 +1200
> Andrew Miller <ak.miller at auckland.ac.nz> wrote:
> Hi all,
>
> I have spent some time looking into how we might be able
> to represent stochastic models in CellML. This is
> something that would be useful to ensure we have properly
> contemplated for CellML 1.2. I have pasted in the notes I
> wrote on this below.
>
> Please let me know if you have any suggestions, comments,
> or criticisms of the below document. At some point, this
> will obviously need to be transformed into a more robust
> proposal, but for now, I just want to make sure we keep
> the option open to use the CellML 1.2 core to represent
> stochastic models.
>
> Best regards,
> Andrew
>
> -----
>
> Overall goal:
> Describe a framework which can be used in CellML 1.2 to
> represent a
> range of
> different systems which require stochastic differential
> equations to
> describe.
>
> Constraints:
> Do not want to describe the procedure for solving the
> model in core
> CellML,
> only the underlying mathematical / statistical model.
> Want to express the model in such a way that the
> procedure is computable
> from the model.
> Want there to be only one interpretation of the model.
> Want the representation to be abstract enough that it is
> meaningful for a
> number of different fields, and not just chemical
> equations in a well
> stirred vessel.
> Want the representation to work naturally when mixed
> with systems of
> ordinary
> differential equations.
>
> Use cases:
> Chemical reactions under the Chemical Master Equation
> model of Gillespie:
> We need to split these into separate species. This is
> a Poisson process,
> so there are simple ways to represent it.
>
> It is more efficient to represent models using Weiner
> processes when
> this
> there are large enough numbers of molecules to justify
> this but ODEs are
> not being used.
>
> However, Poisson and Weiner processes are both Levy
> Processes, that is,
> they have stationary independent increments, are zero
> at time zero, and
> are cadlag. This is not necessarily a good thing
> because some things we
> want to model might have memory of past events or a
> time dependence.
>
> How we can represent this in CellML:
> For the continuous case, integral equations for the
> increment in terms of
> built in processes like Weiner and Poisson processes (I
> don't believe
> there
> is a clean way to represent increments in MathML).
>
> Implementations will need to identify these and work out
> the
> distribution of
> the time until the next event (good implementations
> might be able to
> perform
> symbolic algebra to work this out, but most
> implementations would probably
> just recognise common cases like Poisson distributions
> with arbitrary
> parameters, and deal with expressions involving a Weiner
> process by
> sampling
> from the increment distribution in each time step),
> which could be put
> into a
> slightly generalised Gibson-Bruck type of framework
> where we store the
> time of
> the next event.
>
> None of this helps for non stationary independent
> processes, however.
>
> How could this be related to the standards:
> It has been proposed that CellML 1.2 have a core
> specification which
> describes
> the basic way of representing the mathematical structure
> in very general
> terms, and secondary specifications be used to narrow
> CellML down to
> specific
> subsets which can be implemented in their entirety by a
> actual software
> packages.
>
> Core CellML 1.2 should be general enough to represent
> concepts like
> probability distributions (MathML allows new operators
> to be defined,
> so we
> could create ones for our base types of stochastic
> process). The ODE IV
> secondary specification would not allow stochastic
> models, while we would
> have another alternative secondary specification which
> extended the ODE IV
> one to allow certain limited types of stochastic model
> (limited to
> types we
> know how to solve).
>
> In terms of interaction with the typing system, in a
> stochastic system we
> have both reals and real-valued random variables. Once
> we have one random
> variable in our system, this will propagate to
> everything else which
> is affected by it, so most of the model will technically
> be a random
> variable.
> However, we want to be able to easily mix stochastic
> models with
> existing ODE
> IV models to create hybrid models, so we don't really
> want the required
> datatype to change just to connect up a random variable
> to a non-random
> variable. For this reason, I don't think it is
> worthwhile to consider a
> random variable of a certain type a different datatype,
> and instead we
> would
> require tools to deduce this information if they require
> it.
>

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• [cellml-discussion] Representing stochastic models in CellML, Andrew Miller, 05/14/2008
  • [cellml-discussion] Representing stochastic models in CellML, Randall Britten, 05/14/2008
  • Message not available
    • [cellml-discussion] Representing stochastic models in CellML, Andrew, 05/19/2008
      • [cellml-discussion] Representing stochastic models in CellML, Mike Cooling, 05/19/2008
      • [cellml-discussion] Representing stochastic models in CellML, Randall Britten, 05/19/2008

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