Re: [Swarm-Modelling] Mean Field Theory

[gepr]

Neither of these terms is adequate.  They both rely too much on
metaphors that are misleading, even if they have unambiguous
definitions in their respective domains of origin.  (E.g. one could
argue that the "mixing" metaphor doesn't describe a "soup" model,
either.  I can't imagine ham-piece4000, which sits on the right top of
the stew kettle communicating with kidney-bean399, which sits on the
left bottom of the kettle.)

A much better term than "soup", "mean field", "well-stirred",
"well-mixed", or "panmictic" is "fully connnected".  This is true
especially because communication in ABMs, for the most part, is really
concerned with topology not space.  And there are equivalently more
appropriate terms for many of the other concepts like demes,
compartments, etc.  The language of graphs can also pull double duty
and fold right into the next most useful language for ABM, which is
programming and computation.

The only time that using the language of graphs brings trouble is
when talking explicitly about discretizing a (seemingly) continuous
magnitude.  At that point, things like fields are more efficient
tokens.

Of course, the caveat is that when one is popularizing a subject,
ambiguities are tolerated because bridges have to be built between
lexicons.

Russell Standish writes:
 > Actually, a panmictic model is spatially homogenous if there is a
 > spatial dimension. Also, mean field models are also spatially
 > homogenous. See Ashcroft & Mermin "Solid State Physics" for a
 > technical discussion of the term "mean field" in it original
 > application.
 > 
 > Panmictic and mean field approximations are only equivalent when the
 > effect of interactions with the other agents  can
 > be replaced by the average effect, multiplied by the interaction
 > rate. When this condition is true, the phenomenon in question is
 > called "resultant".
 > 
 > People using "mean field" to mean "panmictic" are mistaken,
 > misleading and downright obfuscatory...
 > 
 >                                      Cheers
 > 
 > Doug Donalson wrote:
 > > 
 > > I disagree.  mean fierld is used as an alternate term for well-mixed 
 > > models,
 > > not just spatially homogeneous models.  For example, implicit in ODE models
 > > are both homogeneous space and the well-mixed (your soup) assumptions.  
 > > ODEs
 > > are often refered to as mean field models for both those reason.  Then
 > > again, it is not uncommon to find different uses of terms from different
 > > groups of researchers.
 > > 
 > > Cheers
 > > ----- Original Message -----
 > > From: "Russell Standish" <address@hidden>
 > > To: <address@hidden>
 > > Sent: Tuesday, May 27, 2003 4:23 PM
 > > Subject: Re: [Swarm-Modelling] Re: [Swarm-Support] Re: Agent communication
 > > and grid models
 > > 
 > > 
 > > > No! Mean field means that agents interact solely with an average
 > > > background property, not with individual agents. A panmictic model
 > > > (dubbed "soup" model here) has each agent having equal probability of
 > > > interacting with the other agents (or simply interacting with all
 > > > other agents). A mean field approximation is really only valid when
 > > > the effect of all agents is equivalent to the sum (or average) of the
 > > > agents - pretty much when there is no complex emergence in the system.
 > > >
 > > > Cheers
 > > >
 > > > Doug Donalson wrote:
 > > > >
 > > > > Just for reference.  The more common term for "soup" models is  "mean
 > > > > field".
 > > > >
 > > > > Cheers,
 > > > >
 > > > > D4
 > > > >
 > > >
 > > >
 > > > --------------------------------------------------------------------------
 > > --
 > > > A/Prof Russell Standish            Director
 > > > High Performance Computing Support Unit, Phone 9385 6967, 8308 3119
 > > (mobile)
 > > > UNSW SYDNEY 2052                     Fax   9385 6965, 0425 253119 (")
 > > > Australia            address@hidden
 > > > Room 2075, Red Centre
 > > http://parallel.hpc.unsw.edu.au/rks
 > > >             International prefix  +612, Interstate prefix 02
 > > > --------------------------------------------------------------------------
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 > > 
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 > 
 > 
 > 
 > ----------------------------------------------------------------------------
 > A/Prof Russell Standish               Director
 > High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
 > UNSW SYDNEY 2052                              Fax   9385 6965, 0425 253119 
 > (")
 > Australia                                     address@hidden             
 > Room 2075, Red Centre                    http://parallel.hpc.unsw.edu.au/rks
 >             International prefix  +612, Interstate prefix 02
 > ----------------------------------------------------------------------------
 > _______________________________________________
 > Modelling mailing list
 > address@hidden
 > http://www.swarm.org/mailman/listinfo/modelling

-- 
glen e. p. ropella              =><=                           Hail Eris!
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