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Re: Semantic information for math representations of physics

From: JB Collins <joebmath@yahoo.com>
Date: Wed, 9 Feb 2005 11:42:35 -0800 (PST)
Message-ID: <20050209194235.83064.qmail@web31104.mail.mud.yahoo.com>
To: Roger I Martin PhD <hypernexdev@hypernexinc.com>
Cc: www-math@w3.org

It seems to me that what you are offering supports
translation into available numerical library calls.
The problem I am facing is that physicists often "roll
their own" numerical methods - and for good reason.
General purpose methods, say for example a Runge-Kutta
integrator, works well for general use. When high
performance is required, however, an integrator
specific to the equation of interest will generally
work more efficiently. This latter case happens all of
the time. Don't get me wrong: physicists use the
general purpose libraries all of the time, also. But
support for documenting the translation of
mathematical descriptions to discrete representations
is required for both cases.

Regards,
Joe Collins
Naval Research Lab

--- Roger I Martin PhD <hypernexdev@hypernexinc.com>
wrote:

> 
> Do you have an example illustrating the full scope? 
> Partial 
> differentials and solutions?  My example was of only
> an equation for a 
> NURBS curve or surface.  There are many diciplines
> and equation systems 
> that can be accomplished between abstract math in
> mathml to working 
> solutions.  I realize I'm talking from a detail
> perspective trying to 
> understand a more global view of achieving
> your "interested in
> 
> representing and supporting the validation of
> physics-based numerical models generally, from the
> conceptual, mathematical statements, encapsulated as
> a
> coherent model, to the translation of that model so
> as
> to incorporate mathematical approximations, and then
> to the translation of an encapsulated, approximative
> model to a discrete, numerical model."
> 
> And I'm trying to gain an understanding of your
> perspective.  I think I understand the above
> paragraph:-) When your talking of translation to
> discrete numerical model I understand it in terms of
> the difficulties of solving partial differential
> systems where the abstract level does little to
> describe the domain and solution spatial resolution.
>  However mathml does have domain
>
http://www.w3.org/TR/MathML2/chapter4.html#contm.domain
> and exists
>
http://www.w3.org/TR/MathML2/chapter4.html#contm.elem
> etc. tags that I use to define where a solution is
> wanted:
> 
>     <apply>
>       <exists/>
>       <bvar><ci>x</ci></bvar>
>       <lowlimit><cn>-1</cn></lowlimit>
>       <uplimit><cn>1</cn></uplimit>
>       <true/>
>     </apply>
>     <apply>
>       <exists/>
>       <bvar><ci>y</ci></bvar>
>       <lowlimit><cn>-1</cn></lowlimit>
>       <uplimit><cn>1</cn></uplimit>
>       <true/>
>     </apply>
> 
> Working on more complex boundary definitions(hence
> NURBS and femml.) I think of resolution and say
> variable/optimized meshes as values which an end
> user may want to control.  For example a dynamic
> membrane ending up in a 3D display is greatly
> effected by spatial and time resolution for a given
> cpu power; 3GHz can easily be swamped with a
> practical problem. (An example is modeling cellular
> locomotion from multiphoton confocal microscopy
> data)
> 
> Another way to put it, I'm looking to take mathml
> 2.0(especially content) from any Editor that
> produces it(Mathematica, MathCad, etc.) or from raw
> data reduction to mathematical modeling and be able
> to incorporate in a reliable way via open source
> transforms in systems that then can use the results
> for the end users purposes.  I use it for example in
> peak analysis, specifically x-ray diffraction
> peaks(gaussian etc.), least squares fitting, solving
> for Avrami equation parameters, etc as peaks change
> over time.
> 
> http://sourceforge.net/projects/mathml-x/ has the
> stylesheets(not about examples of use yet) but
> before the site would be useful we would need to
> define a number of systems that interest you and see
> whether there is implementation for it.  Mathml-x is
>  yet a playground to explore mathml and xslt so I'm
> not suggesting it plugs in and solves everything. 
> It currently is being applied in dynamic calibration
> curves for instrumentation, visualization and
> electro-physiological modeling.  Recently upgraded
> to XSLT 2.0 applying Michael Kay's Saxon 8.2 and it
> overcame nearly all of difficulties I was having
> with xslt 1.0 and custom extensions.
> 
> Haven't implemented as much for integrals but for
> example instead of going numerical immediately I use
> the pattern matching capability of xslt to go to
> mathematical solutions/tables.  ie. integral of 1/x
> goes to ln(x) and depending on the domain readily
> compute the solution.  Likewise for sin(x)/x where
> numerical solutions fail at zero, use abstract
> analytical limits to find solutions.
> 
> Part of what started my efforts with mathml-x is
> getting away from writing for and while loops at the
> code level(tired of it); codifying what a
> physicists/scientists does on a tablet by hand is
> error prone and the connection between the tablet
> and software gets lost over time and memory fades. 
> As I talked about before there is a lot of code that
> does not do what physicists/scientists think it is
> doing; Seen code that was used for finding a
> supposedly optimal minimum applied for 25 years
> where numbers came out but there was no minimum any
> more than the Peano Surface's
> http://mathworld.wolfram.com/PeanoSurface.html 
> minimum:-)  I also know that it is difficult
> preventing a programmer from inserting what may be
> an optimization for speed but eventually functions
> as a bug.  Impossible; part of our genetics I
> guess:-) And when a non-programmer gets into the
> code look out!
> 
> But I'm writing details again.  If you have the time
> I would like to hear more of the global perspective
> of what is needed.  Am also interested in a larger
> group of collaborators because it is an immense
> topic.
> 
> r,
> Roger
> 
> JB Collins wrote:
> 
> >This sounds interesting and useful, but I'm not
> sure
> >it provides the full scope of what I'd like to do.
> >
> >Unfortunately, I was unable to investigate by
> >accessing the website you gave, i.e.
> >http://sourceforge.net/projects/mathml-x/ .
> >
> >Regards,
> >Joe Collins	
> >
> >  
> >
> 
> 
> 
> 



		
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Received on Wednesday, 9 February 2005 19:43:06 GMT

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