A Garden of ModelsSteps Toward Growing the Topology of the Possible In Public

Policy Modeling

Carl Tollandercarl@plektyx.com

4th Lake Arrowhead Conference on Human Complex SystemsApril 25-29, 2007

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Build a modelComposed of statements about

Changing object classesWith changing relationshipsWhen background setting and geometry is dynamic

What we usually start out doing…

…but over time,much more of our task demands…

Simulate a modelComposed of statements

aboutA population of given objectsWith known relationshipsIn some specified geometry.

Modeling Complexity is a Complex Activity!

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Public Policy Making - Some Observations

• Policies are constraints that mediate the evolution of future system (community) physical and social structure.

• New candidate policies must be situated relative to a mix of other existing and contemplated policies.

• In novel situations where new policies are contemplated, the availability and semantics of requisite data are likely to be in some flux.

• Policy mix is cross-jurisdictional and multi-constituency.

• Policy makers no longer directly control information availability, analyses and tempo.

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Multi-source,continuously

refined, environmental

data

Heterogeneous,

Highly dynamic

ConstraintSets

Policy Mix

Constituency Mix

EmergentCommunityStructure

Some Implementation Challenges• Representation of emergent structure• Composability and reusability• Model Maintenance• Validation, verification, calibration

Messy,Messy,ContingentContingentConstantly Constantly EvolvingEvolving

Messy,Messy,ContingentContingentConstantly Constantly EvolvingEvolving

Adaptive Modeling Problem

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Approaching Adaptive Modeling

Improve ways to relate informal notions about models and structure to a variety of formal representations.

Leverage knowledge about growth and regeneration toolkits from developmental biology, industrial design, CAS practice….

Derek Wise (UCR Math) defines mathematical gadgets as:

• Specifying some stuff, • Equipped with structure,• Satisfying some properties

StuffStuffStructureProperties

Two-stage modeling processAdaptiv

e Structur

eModelin

g

ModelsOf

Agents

(structure agents continuously co-create

model)

(domain agents, familiar ABM

methodology and analysis)

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Toolkits and Emergent Structure

Toolkitsmediate the developmentof future system structure

•Switching•Encapsulating•Promoting,•Inhibiting,•Repressing•Repairing

Genetic toolkits, e.g. HOX(Caporale, Margulis, Carrol)

Artificial Genomes for auto styling (BiosGroup, Plektyx)

RNA shape space (Fontana, et al)

Evolution of banking in Renaissance Florence (Padgett)

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are needed to see this picture.QuickTime™ and a

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Usually multiple toolkits, overlapping, multi-purpose…

They emerge, evolve, disappear…

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Creating Topologies of the Possible

Agents carrying policy toolkits co-construct (grow) ensembles of possible model topology Adaptive Structure ModelingAdaptive Structure Modeling Models of

AgentsModels of

Agents

Well-situated “spot” ABMs created from this topology when needed for analysis.

Still messy, contingent, constantly

evolving… A Community Resource:• Self-maintaining, easier validatation,• Increased policy transparency, interoperability, componentry.• Faster, more targeted ABM creation.

But…

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Garden of Models: Research Program in Adaptive Modeling

How can heterogeneous populations of structure-buildingagents jointly and continuously create, regenerateand navigate a common model context?

Jointly grownmodel structure

Jointly grownmodel structure

Models runnable in existing modeling frameworksModels runnable in existing modeling frameworks

AAAA

AA

AA

AA

DD

DD

DD

DD

DD

DD

DynamicHeterogeneous

Structure-buildingPolicyAgents

DynamicHeterogeneous

Data

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Resartus Testbed

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.– Models building models– Policies as structure-building agency– Agents with identity and multiple agency– Heterogeneous agents, heterogeneous

policies

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• Background independence of emergent structure

• Stuff, Structure, Properties Category Theory

• Rich Partial Equivalence, detection and navigation

• Structure Agent Scheduling

• Emergent Structure Model Feeds

• Workbench user interaction mechanisms

• Toolkit packaging and exchange in Workbench

Resartus areas of investigation

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Category Theory - a set of gadgets useful for working with complex structure• Category - objects + morphisms (transformations)

that preserve structure of the objects.• Functor - bundle of transformations between

categories: object to object, morphism to morphism.• N-category - category of categories, internal

morphisms all functors.• Natural Transformations - transformations

between paths (functors of functors) that are equivalent.

• Equivalence - items are equivalent if there is a transformation between them (many available kinds of transformations)

Resartus areas of investigation - Category Theory

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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.

Resartus areas of investigation - Rich Partial Equivalence

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Aa

An Agent carries one or more horizons, which are its agencies.

Agency can be delegated, rewarded, recombined, etc.

aa

On opportunity,Agent may selectone or more ofits agencies for the situation at hand.

• Policy agents• Constituency agents

The identity of an agent is the sum of its agencies and any heuristics for their application.

Resartus areas of investigation - Agency and Identity

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Finding Equivalence

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??Aa

aa

C1 C2

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Ea

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Ea

!

Navigating Equivalence

Resartus areas of investigation - Equivalence Examples

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Since we don’t know what local topologies we will find, we must minimize pre-specification of that topology in the scheduler. A

a

aa

Aa

aa

Randomjumps incategory-memoryspace(a là Tierra,StarCat)

Resartus areas of investigation - Scheduling Structure Agents

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Similar to RSS (syndicated) news feeds on the Web.

AggregatorAggregatorFeedFeedFeedFeed

FeedFeed

FeedFeed

FeedFeedAggregatorAggregatorFeedFeed

AggregatorAggregatorFeedFeedFeedFeed

Difference: • Feeds are/deliver Categories (new local model topologies)• Aggregation is (here) an adaptive modeling process containing structure-building agents.

Resartus areas of investigation - Model Feeds

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QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

• CAP Workbench for cross-jurisdictional policy in rural communities

• Policy Component Webs - distributed policy making.• Multiple language implementation of Resartus

elements.• Learning - Hierarchical Reactive Planning

– Agent learns choice of horizon– Path equivalence / plan equivalence

• Advanced Schedulers (e.g. Cartan-geometry based)• Analytic Journalism - modeling possible story

spaces• Model recombination

Future Directions

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Category TheoryVery 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 MathematicsCorfield, 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)

References

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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?

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Some General Questions