Re: [Swarm-Modelling] Mean Field Theory

[Russell Standish]

I would agree with Glen that fully connected is more appropriate term
for agent based models, than something with an implied spatial
dimension mixed up by an implied mixing process.

I think panmictic is still appropriate for population models like
EcoLab, as in the real world system it is attempting to model, the
ecology is distributed over some area, and the species roam around
that area.

Incidently, as another illustration of the difference between mean
field and panmictic, I introduce a model called EcoLab-- as a
theoretical device in my "Statistics of Certain Models of Evolution"
paper. EcoLab-- turns out to be a mean field approximation of a
panmictic model.

                                                Cheers

address@hidden wrote:
> 
> 
> 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 (")
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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             
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> http://parallel.hpc.unsw.edu.au/rks
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> -- 
> glen e. p. ropella              =><=                           Hail Eris!
> H: 503.630.4505                              http://www.ropella.net/~gepr
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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
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