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A Garden of Models Steps Toward Growing the Topology of the Possible In Public Policy Modeling. Carl Tollander firstname.lastname@example.org 4th Lake Arrowhead Conference on Human Complex Systems April 25-29, 2007. Modeling Complexity is a Complex Activity!. What we usually start out doing….
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4th Lake Arrowhead Conference on Human Complex Systems
April 25-29, 2007
What we usually start out doing…
Simulate a model
Composed of statements about
A population of given objects
With known relationships
In some specified geometry.
…but over time,
much more of our task demands…
continuously refined, environmental
Adaptive Modeling Problem
Two-stage modeling process
(structure agents continuously co-create model)
(domain agents, familiar ABM methodology and analysis)Approaching Adaptive Modeling
Improve ways to relate informal notions about models and structure to a variety of formal representations.
Derek Wise (UCR Math) defines mathematical gadgets as:
Leverage knowledge about growth and regeneration toolkits from developmental biology, industrial design, CAS practice….
Artificial Genomes for auto styling (BiosGroup, Plektyx)
Genetic toolkits, e.g. HOX
(Caporale, Margulis, Carrol)
Usually multiple toolkits, overlapping, multi-purpose…
They emerge, evolve, disappear…
RNA shape space (Fontana, et al)
Evolution of banking in Renaissance Florence (Padgett)
Still messy, contingent, constantly evolving…
Agents carrying policy toolkits co-construct (grow) ensembles of possible model topology
Well-situated “spot” ABMs created from this topology when needed for analysis.
Adaptive Structure Modeling
Models of Agents
How can heterogeneous populations of structure-building
agents jointly and continuously create, regenerate
and navigate a common model context?
Models runnable in existing modeling frameworks
Purpose: test computational embodiments of Garden of Models research program in order to drive effort towards a well-engineered Policymaker’s Workbench software architecture and implementation.
Agents use policy constraints to detect, establish, degrade or navigate rich partial equivalence in a model based on policy constraints.
In practical terms, these constraints take the form of one or more N-categories, called Horizons, which describe the depth and scope of the policy.
Comparing two N-categories for equivalence with respect to a Horizon yields a (possibly empty) functor, which constitutes new agent-navigable structure in the growing model.
Properties of a policy horizon determine the role of the equivalence vis-à-vis toolkits, i.e., promote, inhibit, repress, activate, etc.
Agent may select
one or more of
its agencies for the
situation at hand.
An Agent carries one or more horizons, which are its agencies.
Agency can be delegated, rewarded, recombined, etc.
The identity of an agent is the sum of its agencies and any heuristics for their application.
Resartus areas of investigation - Scheduling Structure Agents
Since we don’t know what local topologies we will find, we must minimize pre-specification of that topology in the scheduler.
(a là Tierra,
Similar to RSS (syndicated) news feeds on the Web.
Very fast introduction by John Baez: http://math.ucr.edu/home/baez/planck/node5.html
Notions of Equivalence by Barry Mazur: http://www.math.harvard.edu/~mazur/preprints/when_is_one.pdf
Research Programs and Mathematics
Corfield, David, “How Mathemeticians may Fail to be Fully Rational”, 2006 http://www.dcorfield.pwp.blueyonder.co.uk/HowMathematicians.pdf
Wise, Derek, “Properties, Structure and Stuff”, UCR Quantum Gravity Seminar notes, Spring, 2004, http://math.ucr.edu/home/baez/qg-spring2004/s04week01.pdf
Developmental and Molecular Biology, Constructive Social Models (Toolkits, etc.)
Caporale, Helena Lynnn , “Darwin in the Genome: Molecular Strategies in Biological Evolution”, McGraw-Hill, 2003
Carroll, Sean B., “Endless Forms Most Beautiful: The New Science of Evo Devo”, W.W. Norton Company, 2005
Margulis, Lynn and Dorion Sagan, “Acquiring Genomes: A Theory of the Origins of Species”, Basic Books, 2002
Padgett, John, and Paul McLean, “Organizational Invention and Elite Transformation: The Birth of Partnership Systems in Renaissance Florence”, AJS Volume 111 Number 5 (March 2006): pp 1463-1568
B. M. R. Stadler, P. F. Stadler, G. Wagner and W. Fontana “The Topology of the Possible: Formal spaces underlying patterns of evolutionary change”, Journal of Theoretical Biology, 213 (2), 241-274 (2001)
How to transform structural asymmetry to ‘gradients’ (non-commutative flows along equivalence)
Organizations of dimensionality vs. ‘levels’?
Next implementation languages after Java?
Relationships vs Transformations?
More meta the model the lower the required cognition?