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| <slide title="System Models">
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| * Aggregate System: population, land use, water flows
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| * Sentiments: Pro-market vs. pro-environment, inequality, conflict
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| * Spatial water flow
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| * Spatial population movement
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| * Water demand economic model
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| * Infrastructure building
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| * Diet Model: livestock, wild-caught, nourishment, prices
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| * Politicized dynamic optimization of decisions
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| * Linear programming for spatial optimization
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| </slide>
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|
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| <slide title="Model Connections">
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| [[File:Allmods.png|center]]
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| </slide>
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|
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| <slide title="Aggregate System 1">
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| [[File:Agg1.png|center]]
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| </slide>
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|
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| <slide title="Aggregate System 1">
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| [[File:Politics.png|center]]
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| </slide>
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|
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| <slide title="Aggregate System 1 Calibration">
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| * 12.7-37 kg ha-1 per mm = 25: French, R. J., & Schultz, J. E. (1984). Water use efficiency of wheat in a Mediterranean-type environment. I. The relation between yield, water use and climate.
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| Crop and Pasture Science, 35(6), 743-764.
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| * 1961: 49% agriculture, 1.66% urban = 2.6% urban in 2002 * 183.7e6 pop / 287.6e6 pop (Major Uses of Land in the United States, 2002)
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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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| * Open Interface
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| * Smart Variables
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|
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| [[File:Elements.png|center]]
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| </slide>
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|
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| <slide title="District Population Shifts">
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| [[File:Districtnetwork2.png|center]]
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| </slide>
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|
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| <slide title="Smart Variables: Dimensions">
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| * <math>3</math> vs. <math>3</math> [tonnes] vs. <math>1350487537</math> [seconds since Jan. 1, 1970]
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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="Smart Variables: Maps" fs="1.5em">
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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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| <syntaxhighlight lang="cpp">
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| GeographicMap<double>& degreeDayMelt =
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| (degreeDayFactor + degreeDaySlope * elevation)
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| * (snowCover / 100) * (surfaceTemp - ZERO_CELSIUS)
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| * (surfaceTemp >= ZERO_CELSIUS);
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| </syntaxhighlight>
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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="Case Study: Hydrological Modeling">
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| {img src="/images/9/91/Flowcauses.png" width="500" height="333" /}
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| </slide>
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|
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| <slide title="Case Study: Hydrological Modeling">
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| [[File:Bhakramap.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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|
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| <slide title="Smart 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="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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| {img src="/images/d/db/Solow.png" width="300" height="160" /}
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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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| </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="Amalgamated Modeling" fs="1.6em">
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| Amalgamated modeling allows models to interact, specialize, and "overlap".
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|
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| Every model is incomplete; applies to a constrained context.
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| :'''Let's embrace partial models!'''
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| Want a "plugin architecture", where models can easily be allowed to interact
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|
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| Coupling causes feedback, and models are defined at different scales.
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| :'''Need a new way to couple models!'''
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|
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| Allow overlapping-- models inform different variables, at different scales.
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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="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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|
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| [[File:Amalgcombo.png|center]]
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| </slide>
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|
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| <slide title="Amalgamation Challenges">
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| * How do I test it?
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| * Efficient probability function calculations
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| * Smooth or spectrally-informed transitions?
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| * What does downsampling contribute?
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| * How to ensure that different scales add up?
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| * How do we understand a multi-scale model?
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|
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| [[File:Trialestimate.png|left]]
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| </slide>
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|
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| <slide title="A New System Dynamics">
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| Coupling natural and human systems makes things complex:
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| : feedback, non-linearity, resilience, and spacial heterogeneity
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|
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| Combine the temporal sophistication of system dynamics,
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| : with spatial heterogeneity
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|
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| [[File:ssdarch-mod.png]]
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| (Ahmad et al 2004; flood management, water resources modeling, invasive species spread)
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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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| * Disaggregations into structured 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="Disaggregating System Models">
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| [[File:Popmod-vensim.png|center]]
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|
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| [[File:Popmod.png|center]]
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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="Self-Similar Networks">
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| [[File:Selfsimodel.jpeg|center]]
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| </slide>
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|
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| <slide title="Networking Challenges">
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| * Ensure that the separate blocks match the aggregate
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| * What is a full language of networked system dynamics?
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| * Can a model only apply to part of a network?
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| * How to ensure that missing models "fail gracefully"?
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| </slide>
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|
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| <slide title="Computational Tools">
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| * Evaluate model performance (Barlas 1996)
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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="Integrating Data" fs="2em">
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| * Calibration
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| * Validation
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| * Filling in missing models
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| :'''We need a smart (context-aware and incomplete-welcoming) data library!'''
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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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| <syntaxhighlight lang="cpp">
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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 *
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| (1 - biomass / capacity) - catches;
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|
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| print(biomass[0:100], "\t");
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| </syntaxhighlight>
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| </slide>
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|
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| <slide title="Extensions">
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| * Memetic propagation of models
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| * Integration with climate models
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| * Importing Vensim models
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| </slide>
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|
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| <slide title="Model for Climate Behaviors">
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| Overdetermined status-quo:
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| * Politicians won't make unpopular changes
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| * Businesses won't take action alone
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| * Consumers have great difficulty without support
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| * Carbon leakage
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| * Rebound effects
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| </slide>
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|
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| <slide title="Model for Climate Behaviors">
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| * Climate behaviors as aggregate activity
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| * Looking for leverage points
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| * Not trying to predict future states
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| </slide>
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|
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| <slide title="Model for Climate Behaviors">
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| [[File:Architecture.png]]
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|
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| (Self-similar Meadows 2004 regionally, Forrester 1971 for urban)
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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="Multimanaged Fisheries Project">
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| * Collapsing fisheries, despite new management
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| * Perverse economic incentives
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| * Multiple scales of uncertainty
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| * Unintended policy consequences
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| </slide>
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|
| |
| <slide title="Multimanaged Fisheries Project">
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| [[File:Food_web_600.jpg]]
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| </slide>
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|
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| <slide title="Multimanaged Fisheries Project">
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| * <math>g_t^i = r^i s_t^i \left(1 - \frac{s_t^i}{K_t^i}\right)</math>
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| * <math>K_t^i = \sum_{j \in q(i)} w^{ij} s_t^j</math>
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|
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| * Nature: ecosystem and regional models
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| * Social: Fishing community, policy-makers, NGOs
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| * Plug-in different "fish" and "policy" modules
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| * Working with stakeholders
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| </slide>
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