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| <slide header="none" center="both">
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| = Open World Project =
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| Friday Forum
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| Oct. 19, 2012
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| James Rising, Upmanu Lall,
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| Bruce Shaw, Pierre Gentine
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| </slide>
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|
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| <slide title="Talk Plan">
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| * Other Projects of Interest
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| * Motivation and Vision
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| * Core Elements
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| * Case Study Projects
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| * Climate Behaviors
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| * Fisheries Model
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| * Next Steps
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| </slide>
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|
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| <slide title="Other Projects of Interest">
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| * [http://www.existencia.org/carbon/ Carbon Transition Working Group]
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| * [http://sdresearch.wikischolars.columbia.edu/jar2234+Peruvian+Fisheries Peruvian Spatial Fisheries]
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| * [http://sdresearch.wikischolars.columbia.edu/Ocean+Health Ocean Health Metric]
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|
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| * [http://sdresearch.wikischolars.columbia.edu/jar2234+Marine+Protected+Areas Empirical Benefits from Marine Protected Areas]
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| * [http://existencia.org/weaver/ Web-Weaver Data Extractor]
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| * [http://cantovario.com CantoVario]
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| * [http://openworld.existencia.org/index.php?title=Friday_Forum_Presentation Slider Extension]
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| </slide>
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|
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| <slide title="Introduction" fs="2em">
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| Many of the human behaviors that drive climate change and
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| environmental degradation are deeply embedded in our society,
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| economy, and government, and are mutually reinforcing. Better
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| modeling of human-natural systems can help in many ways:
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| * Analyzing feedback loops can help identify '''leverage points''', where small policy changes can have pervasive impacts.
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| * Allowing models at diverse scales and contexts to interact can help scientists '''integrate knowledge'''.
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| * Interactive models can facilitate '''communication''' with policymakers and make complex problems intelligible.
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|
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| The Open Model is a modeling framework aimed at these issues.
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| </slide>
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|
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| <slide title="Applicability" fs="2em">
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| * Systemically intractable due over-determined, reinforcing drives, and spatially heterogeneous.
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| * Environmental and public health issues: environmental degradation, agricultural practices in poor countries, obesity, substance abuse, groundwater use, and fishery management
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| * Rebound effects and cross-border shifts (e.g., carbon leakage)
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|
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|
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|
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| <center>'''Something for everyone!'''</center>
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| </slide>
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|
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| <slide title="Core Elements">
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| * Amalgamated Modeling
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| * Multiple Network Maps
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| * Networked System Dynamics
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| * Computational Tools
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| * Integrating Data
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| * Open Interface
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| </slide>
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|
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| <slide title="Amalgamated Modeling">
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| [[File:Blobs.png]]
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| </slide>
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|
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| <slide title="Amalgamated Modeling">
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| Coupling causes feedback, and models are defined at different scales.
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|
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| Amalgamated modeling allows models to interact, specialize, and "overlap".
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| </slide>
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|
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| <slide title="Bayesian Coupling">
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| [[File:Amalgelt.png]]
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| </slide>
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|
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| <slide title="Bayesian Coupling">
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| For a variable <math>\theta</math> described by multiple models, each
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| model provides both a PDF across values at a given time <math>t</math>
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| when run in isolation, <math>p(\theta, \bar{S}^i)</math>, and a
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| distribution that includes feedback effects, <math>p(\theta, \tilde{S}^i)</math>. The final distribution is
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| <math>
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| p(\theta | \cdot) \propto p(\theta) \prod_i p(\theta |
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| \bar{S}^i)^\lambda p(\theta, \tilde{S}^i)^{1-\lambda}
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| </math>
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| </slide>
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|
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| <slide title="Multiple Networks">
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| Models use multiple networks simultaneously
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| * Different paths on which stocks flow
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| * Structured disaggregations into classes
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| * Capturing network properties
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| </slide>
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|
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| <slide title="Multiple Networks in Ohio">
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| [[File:Ohionet.png]]
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| </slide>
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|
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| <slide title="Networked System Dynamics">
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| [[File:Netstocks.png]]
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| </slide>
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|
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| <slide title="Networked System Dynamics">
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| [[File:Ohiomod.png]]
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| </slide>
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|
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| <slide title="Networked System Dynamics">
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| Spatial variation matters
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|
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| [[File:ssdarch-mod.png]]
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| </slide>
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|
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| <slide title="Self-Similar Networks">
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| [[File:Selfsimodel.jpeg]]
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| </slide>
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|
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| <slide title="Computational Tools">
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| * Evaluate model performance
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| * Identify driving feedback loops
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| * Identify tipping and leverage points
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| * Construct simplified models for communication
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| * System Regression: construct models from data
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| </slide>
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|
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| <slide title="Open Interface">
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| * A '''Website Interface''' would allow researchers to explore
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| the model, run tests, and contribute models. For
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| policy-makers, the online interface would provide ways to
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| interact with the model, see results, and outline scenarios.
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| </slide>
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|
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| <slide title="Intelligent Variables: Dimensions">
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| * <math>3</math> vs. <math>3 [tonnes]</math> vs. <math>1350487537 [seconds since Jan. 1, 1970]</math>
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| * Dimensional analysis at the heart of science
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| * Automatic model checking, unit conversion
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| </slide>
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|
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| <slide title="Intelligent Variables: Maps">
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| "Maps" are dimension-aware functions in space-time, often tied to data streams (e.g., IRI tsvs, geotiffs).
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| Maps of different resolutions can be manipulated transparently. Example:
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|
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| GeographicMap<double>& degreeDayMelt = (degreeDayFactor + degreeDaySlope * elevation) * (snowCover / 100) * (surfaceTemp - ZERO_CELSIUS) * (surfaceTemp >= ZERO_CELSIUS);
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|
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| * elevation is a static map at <math>1 km</math> resolution
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| * surfaceTemp is a daily varying map at <math>.25^\circ</math> resolution, read from the file 1 day at a time
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| * snowCover is a weekly varying map at <math>.33^\circ</math> resolution, reconstructed for past years
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| </slide>
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|
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| <slide title="Intelligent Variables: Relations">
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| Variables can represent relationships or differential equations between other variables.
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|
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| Example (the heat equations):
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| <syntaxhighlight lang="cpp">
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| q = -k * Grad(u);
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| Diff(u) = (-1 / c_p * rho) * Div(q);
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| </syntaxhighlight>
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|
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| The equations themselves are saved within <code>q</code> and <code>Diff(u)</code>, so the model can be run.
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| </slide>
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|
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| <slide title="Networked Equations Language">
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| Custom '''Modeling Language''' combines a units-aware equation-like syntax with networks and GIS.
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|
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| capacity = 1e10 [tons];
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| rate = 0.0077 [tons/year];
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| biomass = Stock(1e7 [tons]);
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| catches = TimeSeries("catches.tsv", [tons/year]);
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| biomass += rate * biomass * (1 - biomass / capacity) - catches;
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|
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| print(biomass[0:100], "\t");
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| </slide>
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|
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| <slide title="Toolbox">
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| Transparently combine Matlab, R, shell scripting, Mathematica and other code.
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|
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| [[File:Toolbox.png]]
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| </slide>
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|
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| <slide title="Integrating Data">
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| * Calibration
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| * Validation
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| * Filling in missing models
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| </slide>
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|
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| <slide title="Unified Model of Everything">
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| [[File:Architecture.png]]
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| </slide>
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|
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| <slide title="How Many Variables?">
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| {| World3/2000 || 283 |-
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| | System Dynamics National Model || 2000+ |-
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| | Encyclopedia of World Problems and Human Potential || 56,135 |-
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| | environmental feedback loops || 2,675 |}
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| </slide>
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|
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| <slide title="Case Study: Networked Economics">
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| Step 1: Reconstruct Solow Growth (with some random shocks):
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|
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| * <math>\frac{d L}{d t} = \lambda L(t)</math>
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| * <math>Y(t) = K(t)^\alpha L(t)^{1-\alpha} \epsilon(t)</math>
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| * <math>\frac{d K}{d t} = s Y(t) - \delta K(t)</math>
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|
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| [[File:Solow.png|200px]]
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| </slide>
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|
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| <slide title="Case Study: Networked Economics">
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| Step 2: Make a "distributed" analog to Solow growth:
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|
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| * Multiple firms, with individual capital stocks
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| * Separate growth and decay: <math>g[t] = s Y[t]</math>, <math>d[t] = \delta K[t]</math>
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| * If <math>g[t] \ge d[t]</math>, growth: <math>K[t+1] = K[t] + g[t]</math>
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| * If <math>g[t] < d[t]</math>, stagnation: <math>K[t+1] = K[t]</math>
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| ** And probability of collapse, so expected value follows Solow
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| ** <math>K[t+1] = K[t] + g[t] - d[t] = (1 - P(c)) K[t] \implies P(c) = (d[t] - g[t]) / K[t]</math>
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| * Firms can make connections to each other, which increase "technology" (specialization) factor
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|
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| [[File:Smallworld.png]]
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|
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| * But when collapse, connections severed, capital goes to 0
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|
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| </slide>
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|
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| <slide title="Case Study: Networked Economics">
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| [[File:Distrib.png]]
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|
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| [[File:Economies.png]]
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| </slide>
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|
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| <slide title="Case Study: Hydrological Modeling">
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| [[File:Netmap_ext.png]]
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| </slide>
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