Complexity for Sustainable Development

Systems that are Complex

Classical statistics assume

• Linearity
• Gaussian distributions
• Smooth changes

1. When you have feedback

2. When you have tipping

3. When you have chaos

4. When you have long-tails

5. When you have clusters

6. When you have fractals

• Machine learning
• Genetic algorithms

The noise spikes in SOC systems are called flicker noise, but are actual events, rather than `measurement errors.' Here, usually insignicant events sometimes cause complexity cascades that propagate within a system to produce very large `noise' spikes that appear to us as unexpected events. These cascades are situations where an initially small, and perhaps insignicant-seeming action generates a macro-level event, such as a currency collapse, war, market bubble, riot, bank run, electoral landslide, or a government collapse. - Brunk (2002)

smaller tipping points

Complexity for Sustainable Development

James Rising

Science and Policy Summer School

new language

networked systems, incomplete systems, overlapping systems, hierarchical systems

how do we make networks dynamic?

May 31, 2018

new tools

how do we make systems precise?

The coming revolution

data analysis, estimators

for research, communication

how do we understand complex drivers?

applying many tools

combining agents and systems and networks

• catastrophe
• data and history
• emergence
• fractal complexity

• drive toward heterogeneity
• Dialogue Wiki Engine

• Fat-tailed distributions

Complexity

Regressions can be tricked

understanding element and whole

Insights for Sustainable Develelopment

problems of statistical significance

testible hypotheses

Problems of Econometrics

You can't know everything, but knowing nothing tells you a lot.

The crumbling ediface

incomplete

evolutionary, cross-scale

• non-linearity, chaos
• "state" and evolution
• cybernetics, equifinality, teleology
• structures and feedback
• open systems
• continued dynamics
• Prezi

• not used

rank-methods (e.g. copula)

Information Theory

Systems Studies

Space, time, and history matter.

Complexity done Right

endogenous

A complex system's basic properties are much more likely to be a function of its content than context.

vs. complicated

These make a difference!

Levels of Complexity

self-organized criticality

Emergence

Linearity is not innocuous.

system regressions

small-world networks

scales and scale-free

opportunities for change

Variable errors are ubiquitous

history matters, in societies and ecosystems; you can't get places but by a path

Everything is endogenous

historical

better models

new tipping points

Adaptive Networks

Historical Physics

better communication

Misspecified models

• linearity
• memoryless
• causality
• unorganized complexity (chance)
• closed systems
• thermodynamic drive to homogeneity
• PowerPoint

• Gaussian

Classical

heterogenous

spatiality matters, and most interesting systems don't tend toward equilibrium

Not Gaussian

Agent-Based Modeling

Network Theory

GCMs

Not least squres-- L1 norm?

Behavior grows better before it grows worse.

See beyond events

connections to reality

The easy way out usually leads back in.

What are complex systems?

Counterintuitiveness

Today's problems come from yesterday's "solutions"

Problems are self-created

Dividing an elephant in half doesn't make two small elephants.

System archetypes

and mental models

When placed in the same system, people, however different, tend to produce similar results

Systems thinking

Structure influence behavior

Simulation

Insights for Sustainable Develelopment

• The computer scientist's dream
• Incomplete work, sloppy thinking
• Dogmatic complexity-mongers
• A focus on techniques
• Ill-defined terms:

Cause and effect are not closely related in time and space.

incomplete

simplistic approaches,

disconnected from reality

The harder you push, the harder the system pushes back.

Policy resistance

We are boiled frogs

The problems with the field

Leverage points

Small changes can produce big results-- but the areas of highest leverate are often the least obvious.

1. Constants, parameters, numbers (subsidies, taxes, standards)

2. Material flows and nodes of material intersection

3. Regulating negative feedback loops

4. Driving positive feedback loops

5. Information flows

6. The rules of the system (incentives, punishments, constraints)

7. The distribution of power over the rules of the system

8. The goals of the system

9. The mindset or paradigm out of which the system– its goals, power structure, rules, its culture– arises

calibration, validation

credibility

social embeddedness

big push development

gender, family, evolution

circular causality

meaning of parts

homeostasis and overdeterminism

Problems with Complexity

particle

physical

economic

SOC, networks, ABM

big models, unverified models

methodological

social

18th c.: integrity of wholes

ecological

biological

cosmology

music

understanding

management, communication, understanding

Sets of elements standing in interaction

isomorphisms between contexts

Ludwig von Bertalanffy

A.I.?

ill-defined

social system dynamics

counterintuitive effects

information theory

Jay Forester

To start: A caveat

Indications for use

• Complexity science struggles to be distinguished from its methods.
• Agent-based modeling : Complexity :: Econometrics : Economics
• Many courses sadly equate the two.
• Complexity science also involves:
• Models of complexity (SOC, Ising, Network growth)
• Deep insights requiring much more discussion (What "is" complexity?)

non-linear dynamics

non-Gaussian stats

scaling

• Statistical identification/generation of
• chaos
• long-tails
• fractals
• Information theory
• Maximum entropy
• Cellular automata
• Network analysis
• Agent-based modeling
• Cross-scale analysis
• Genetic algorithms
• Machine learning

A catalog of methods

Cartesian space

arbitrary space

>1 decision-maker

>1 scale

innumerable state-space

innumerable solution-space

Alternatives under long-tails

• Take a log, if you can
• Quantile regression (quantreg in R)
• Cauchy or student-t link GLM
• Translate into ranks

Consequences:

• Std. deviation is undefined (maybe mean too).
• More data does not result in closer estimate
• Regression, correlation, ... fail

Easy to detect, if you look:

• Plot distribution of values/residuals
• Look at tails in Q-Q plot

• Small differences lead to big changes
• Easy to produce: feedback and nonlinerity
• Detect by looking at frequencies

Compare the mean to the variance across several samples.

• Random distribution: variance = mean
• Even distribution: low variance for any mean
• Clustered distribution: high variance for any mean

Methods of complexity science

Examples:

• Coastlines and rivers
• Random walks
• Market expectations
• Ecosystem niches
• Economic niches

Random network

How do networks shrink?

Scale-free network

Continually add new vertices

Attach them to nodes based on

current node attachment

Explains:

• Zipf's Laws
• Paper references
• Success-to-successful economics

Preferential attachment model

Scale-free networks

Scale-free

network

Complex Statistics

• Degree distributions
• Connectedness
• Average distance
• Clustering

Random

network

Look at how networks grow or shrink.

• Dynamic networks

• Statistics on Networks

Regular lattice

Few things behave this way.

When is the complexity important?

Networks are a kind of data, like spatial grids.

Only interesting if you can do something with them.

• Influence: connections, average-distance, small-world, communities, eigen-connectivity, ...
• Infection:

Complex Networks

• Dynamics on networks

Understanding emergence

• Traditional problems have a small parameter space.
• What if you have an infinite parameter space?

Solving problems

Big models of interactions

Any number of distinctions

Small models of assumptions

ABMs are like analytical models:

• Each agent has a set of rules
• The system as a whole evolves
• Could write out that evolution as a single dynamic equation (in theory)

Good for falsifying theories of emergence

Example model: Zombie apocalypse

Population of agents:

• Each is either infected or not
• Every time a zombie interacts with a non-zombie, there's a probability p that the non-zombie becomes a zombie.

Agent-based model

Analytical Model

• Zombies and non-zombies randomly move to adjacent unoccupied squares.
• If zombie next to non-zombie, consider as interacting.

z is the population of zombies

s is the population of non-zombies

Interaction equation says:

dz / dt = z (p - z)

Variance-bias trade-off

Sandpiles:

A cellular automata

importance of "noise"

importance of instability

locally and globally unstable

agent bias and alternatives

collapse and avalanche

towards a critical limit

build-up and collapse equilibrium

driven by a force

importance of scale, or scaling

endogenous but unpredictable

instability serves self-organized resilience

1. Solow Growth

Insights for Sustainable Development

historical and heterogenous

2. Distributed Model

SOC found in riot and strike growth (Bohstedt and Williams, 1988, Midlarsky, 1978) and urban collapse (Brunk, 2002b, Tainter, 1990).

Model of SOC economy (Brunk 2002)

Poverty Traps

distributed in space/network

Solow Model

but collapses of nodes can avalanche

Is the process that causes development to fail external to the process of development itself?

Characteristics of

SOC

Poverty Traps

emergent behavior

e.g. behavior of a sandpile

Do traps represent too much instability or too little?

but too much instability undermines cooperation (Perry 1995)

Distributed Solow Model

no fine parameter tuning

Circular graph of firms

Each firm has individual capital stock, L/N labor, and Cobb-Douglas production

development pushes toward interconnectedness

Growth is "distributed Solow"

growth term:

decay term:

if

and probability of collapse

Every time step, some firms get connections.

Connections increase "technology" (specialization) multiple in production.

When collapse, capital set to 0 and connections severed.

New SOC Relations

Agent Bias

Requirements:

critical state

between chaos and order

near threshold of instability

far out of equilibrium

missing information

fractal patches or

scale-free networks

• self-organization support
• critical value support
• collapse facilitation
• critical competition

spatial self-similarity

e.g. sand slope instability

e.g. slope area affected

power-law temporal fluctuations

large fluctuations

no "normal size" of events

variance is undefined

scale-independent

unpredictable

e.g. size of avalanches

Self-organized criticality in SD

intense adaptive forces

society collapse follows a power law (Brunk, 2002)

city size/abundance follows power law (Eeckhout, 2004), corporations too

price fluctuations follow 1/f noise (Pleurou et al, 1999)

Examples of Self-Organized Criticality

Classic examples

Biology and Economy

Are economies SOC?

But not everywhere...

SOC Examples: human-impacted vegetation patterns (Barbier et al, 2006), academic papers (Barabasi and Albert, 1999), market prices (Cootner, 1964), politial popularity (Byers, 1991), war and conflict (Conybeare, 1990)

Price fluctuations in developing countries do not have scale-independence (Matia et al, 2004)

City size distribution differs by country (Soo, 2005, Mulianta et al, 2004)

economic networks are small-world (scale-free?)

evolutionary, path-dependent, multiple equilibria

similar behaviors a many scales (global to personal)

City distribution characteristics, vs. HDI

According to theory, log-log slope for Zipf law is 1.

• High HDI countries have higher power-law slopes (greater decrease in abundance for increase in size)
• High HDI countries more closely approximate a power-law (?)

2

Data: GapMinder

• 497 indicators
• 259 countries/territories

1. normalized year-to-year differences

2. HDI or

3. sort into bins by HDI deciles

4. estimate PDF by indicator-bin

5. calculate R for log-log regression

Where is SOC?

Peru's year-to-year indicator differences

• Air accidents killed
• DOTS all new case detection rate (%)
• DOTS new smear-positive case detection rate (%)
• DOTS treatment success (%)
• Lung Female Mortality
• Male 15-64 labour to population (%)
• Male 15+ labour to population (%)
• Male above 15 employment to population (%)
• Neonates protected at birth against neonatal tetanus (PAB) (%)
• Total 15+ labour to population (%)
• Total 25-54 labour to population (%)
• Total expenditure on health as percentage of GDP (gross domestic product)
• Whole country all new case detection rate (%)
• Whole country new smear-positive case detection rate (%)

High SOC (R > .5)

2

• 0-4 years- number
• 10-14 years- number
• 15-19 years- number
• 20-39 years- number
• 50+ yrs sex ratio
• Annual population growth rate (%)
• Crude death rate (deaths per 1-000 population)
• DOTS population coverage (%)
• Energe use- total (toe)
• Epidemic affected
• Female 10-14 years (%)
• Female 15-19 years (%)
• Female 20-39 years (%)
• Female 40-59 years (%)
• Flood affected
• Flood killed
• Forest coverage (%)
• HDI
• Income share held by highest 20%
• Lung Male Mortality
• Median age
• Prostate Male Mortality
• Road traffic total deaths
• RTI 0-14 all age adj
• SBP male (mm Hg)- age standardized mean
• Storm affected
• Storm killed
• Surface area (sq. km)
• Total sex ratio
• Water resources: total renewable per capita (actual) (m3/inhab/yr)

Falling SOC

• 40-59 years- number
• Crude oil production- total (toe)
• Electricity consumption- total (kWh)
• Fixed broadband Internet subscribers
• GDP per employee- (constant 1990$)
• Homicide 0-14 all age adj
• Hydro production- total (toe)
• Natural Gas Production total (tonnes oil equivalent)
• Per capita government expenditure on health (PPP int. $)
• Per capita government expenditure on health at average exchange rate (US$)
• Per capita total expenditure on health (PPP int. $)
• Population density (per square km)
• Proportion of the population using improved sanitation facilities- total
• Residential electricity consumption- total (kWh)
• Suicide 15-29 all age adj
• Suicide 45-59 all age adj
• Tax revenue (% of GDP)
• TB incidence- all forms in HIV+ (per year)
• Total above 60- number
• Total CO2 emissions from fossil-fuels (metric tons)
• Total water withdrawal per capita (m3/inhab/yr)
• Urban population (% of total)

2

Moderate SOC (R < .5, > .1)

Rising SOC

2

Low SOC (R < .1)

• 0-14 yrs sex ratio
• 15-24 yrs sex ratio
• 15-49 yrs sex ratio
• Agriculture- value added (% of GDP)
• Arms imports (constant 1990 US$)
• Breast Female Mortality
• Cervix Female Mortality
• Children per woman
• Colon & Rectum Female Mortality
• Colon & Rectum Male Mortality
• Crude birth rate (births per 1000 population)
• Debt servicing costs (% of exports and net income from abroad)
• Female 0-4 years (%)
• Female 15-24 employment to population (%)
• Female 15-64 labour to population (%)
• Female 15+ labour to population (%)
• Female 25-54 labour to population(%)
• Female above 15 employment to population (%)
• General government expenditure on health as percentage of total expenditure on health
• General government expenditure on health as percentage of total government expenditure
• Income per person (PPP) with projections
• Life expectancy at brith
• Male 15-24 employment to population (%)
• Male 65+ labour to population (%)
• Malnutrition prevalence- weight for age (% of children under 5)
• Murdered men- per 100-000- age adjusted
• One-year-olds immunized with three doses of diphtheria tetanus toxoid and pertussis (DTP3) (%)
• Per capita CO2 emissions (metric tons of carbon)
• Private expenditure on health as percentage of total expenditure on health
• Stomach Female Mortality
• Stomach Male Mortality
• Suicide women age adjusted
• Suicide- age adjusted- per 100 000 standard population
• Total 15-24 employment to population (%)
• Total 15-64 labour to population (%)
• Total 65+ labour to population (%)
• Total above 15 employment to population (%)
• Under-five mortality rate

• Agricultural land (% of land area)
• CO2 emissions (kg per 2005 PPP $ of GDP)
• Crude oil production- per capita (toe)
• Electricity consumption- per capita (kWh)
• Energy production- per capita (toe)
• Energy production- total (toe)
• Energy use- per capita (toe)
• Exports of goods and services (% of GDP)
• Exports unit value (index- 2000=100)
• External debt stocks (% of GNI)
• Fixed broadband Internet subscribers (per 100 people)
• Foreign direct investment- net inflows (% of GDP)
• Foreign direct investment- net outflows (% of GDP)
• GDP per capita growth (annual %)
• Gross capital formation (% of GDP)
• High-technology exports (% of manufactured exports)
• Homicide 15-29 all
• Homicide 30-44 all age adj
• Homicide 45-59 all age adj
• Hydro production- per capita (toe)
• Import value index (2000 = 100)
• Imports of goods and services (% of GDP)
• income per person
• Industry- value added (% of GDP)
• Inflation- GDP deflator (annual %)
• Internet users (per 100 people)
• Male 15-19 years (%)
• Male 5-9 years (%)
• Male above 60 (%)
• Merchandise trade (% of GDP)
• Military expenditure (% of GDP)
• Murder per 100-000- age adjusted
• Murdered women- per 100-000- age adjusted
• Natural Gas Production per person (tonnes oil equivalent)
• Net barter terms of trade (2000 = 100)
• Out-of-pocket expenditure as percentage of total health expenditure
• People living with HIV
• Population
• Population growth (annual %)
• Residential electricity consumption- per person (kWh)
• RTI 30-44 all age adj
• RTI 45-59 all age adj
• SBP female (mm Hg)- age standardized mean
• Services- etc.- value added (% of GDP)
• Suicide 0-14 all age adj
• Suicide 30-44 all age adj
• Suicide 60+ all age adj
• TC female (mmol/L)- age standardized mean
• TC male (mmol/L)- age standardized mean
• Total 0-4 years (%)
• Total 15-19 years (%)
• Total 40-59 years (%)
• Total above 60 (%)
• Total GDP (PPP 2005 intl.D)
• Total population both sexes
• Total population female
• Total population male
• Total reserves (% of total external debt)
• Trade balance (current US$)
• Traffic mortality per 100-000- age adjusted
• Traffic mortality women- per 100-000- age adjusted
• Urban population
• Urban population growth (annual %)
• Water resources: total internal renewable per capita (m3/inhab/yr)

Uncategorized

Needed more efficiency: model it on a network!

Hydrological model for Himalayan glaciers

integration with climate modeling

• 5-9 years- number
• Adult literacy rate (%). Female
• Adult literacy rate (%). Male
• Adult literacy rate (%). Total
• Agricultural water withdrawal as % of total water withdrawal (%)
• Aid received % of GNI
• Aid received per person (current US$)
• Air accidents affected
• Annual number of AIDS deaths
• Arms exports (constant 1990 US$)
• Births attended by skilled health staff (% of total)
• Contraceptive prevalence (% of women ages 15-49)
• Democracy score
• Dependency ratio
• Drought affected
• Epidemic killed
• Estimated ART Coverage (CD4 < 350)
• Estimated HIV Prevalence% - (Ages 15-49)
• Estimated new births
• Estimated new HIV infections (All ages)
• External debt stocks- total (DOD- current US$)
• Female 5-9 years (%)
• Female 65+ labour to population (%)
• Female above 60 (%)
• Forest area (sq. km)
• GINI index
• Homicide 60+ all age adj
• Income share held by fourth 20%
• Income share held by highest 10%
• Income share held by lowest 10%
• Income share held by lowest 20%
• Income share held by second 20%
• Income share held by third 20%
• Industrial water withdrawal as % of total water withdrawal (%)
• Infant Mortality Rate
• Male 0-4 years (%)
• Male 10-14 years (%)
• Male 20-39 years (%)
• Male 25-54 labour to population (%)
• Male 40-59 years (%)
• Mobile cellular subscriptions (per 100 people)
• Mobile cellular subscriptions- total number
• Municipal water withdrawal as % of total withdrawal (%)
• Municipal water withdrawal per capita (m3/inhab/yr)
• New and relapse cases
• New and relapse cases (per 100 000 population)
• New smear-positive cases (per 100 000 population)
• One-year-olds immunized with MCV (%)
• One-year-olds immunized with three doses of Hepatitis B (HepB3) (%)
• PC per 100
• Per capita total expenditure on health at average exchange rate (US$)
• Personal computers
• Population in urban agglomerations of more than 1 million (% of total population)
• Poverty headcount ratio at $1.25 a day (PPP) (% of population)
• Poverty headcount ratio at $2 a day (PPP) (% of population)
• Proportion of the population using improved drinking water sources- rural
• Proportion of the population using improved drinking water sources- total
• Proportion of the population using improved drinking water sources- urban
• Proportion of the population using improved sanitation facilities- rural
• Proportion of the population using improved sanitation facilities- urban
• Reported Cases
• Reported cases per 100000
• Reported Deaths
• Reported Deaths per 100000
• Roads- paved (% of total roads)
• RTI 15-29 all age adj
• RTI 60+ all age adj
• Stillbirth rate
• Suicide among men- per 100 000- age adjusted
• TB incidence- all forms (per 100 000 population per year)
• TB incidence- all forms in HIV+ (per 100 000 population per year)
• TB incidence- smear-positive (per 100 000 population per year)
• TB mortality- all forms (per 100 000 population per year)
• TB mortality- all forms in HIV+ (per 100 000 population per year)
• TB mortality- all forms in HIV+ (per year)
• TB prevalence- all forms (per 100 000 population per year)
• TB prevalence- all forms in HIV+ (per 100 000 population per year)
• TB prevalence- all forms in HIV+ (per year)
• Total 10-14 years (%)
• Total 20-39 years (%)
• Total 5-9 years (%)
• Total fertility rate
• Total water withdrawal (summed by sector) (10^9 m3/yr)
• Trade balance (% of GDP)
• Traffic mortality men- per 100-000- age adjusted
• Under 5 mortality rate from CMEinfo
• Youth literacy rate (%). Female
• Youth literacy rate (%). Male
• Youth literacy rate (%). Total

memetic propogation of models

Want to explore SOC: model it on a network!

Expanded Solow-model for poverty traps

Extras

• intractable, systemic problems
• spatially heterogenous

Challenges:

• Language of model building
• model visualization
• Modular simulation

Challenges:

• new handling of feedback
• how to adjust parameters
• how to determine hierarchical allotments
• missing models fail gracefully

Reasons:

• research platform
• better models
• communication tool

Reasons:

• incomplete, hierarchical, interacting

Open Interfaces

Overlapping Models

Applications

The future of modeling for SusDev

6

3

rebound and border leakage

obesity, substance abuse

Challenges:

• conceptualizing components that work along different networks
• what about when not available?

health problems

• Systems Regression
• Driving forces simplifier
• Tipping point finder
• Model evaluation

Reasons:

• Different stocks flow differently
• Deaggregating through networks
• Capture society's network properties

Why bigger models?

Computational Tools

• Precision? Debatable.
• Accuracy? Better.
• As a platform? If popular.

Multiple Network Maps

Finding tipping points for change

passanger transporation

5

groundwater use, fishery management

2

environmental degradation

environmental problems

Challenges:

• what of endogenous dynamics
• data library (contextual, incomplete)

Challenges:

• how to allow systems to vary
• how to ensure matches aggregate

Reasons:

• callibration and validation
• defining flows

Integrating Data

Reasons:

• spatial heterogeneity
• finer tipping points

Combining systems and space

importing Vensim

4

1

language? Toolbox.

transparency

systems: intelligent objects

networks

units and indicators

modular, abstractions

software framework

a context

Technical Details

Challenges and Steps Forward

uestions?