Complex Systems and Emergence

Gilberto CâmaraTiago CarneiroPedro Andrade

Where does this image come from?

Where does this image come from?

Map of the web (Barabasi) (could be brain connections)

Information flows in Nature

Ant colonies live in a chemical world

Conections and flows are universal

Interactions yeast proteins(Barabasi e Boneabau, SciAm, 2003)

Interaction btw scientits in Silicon Valley(Fleming e Marx, Calif Mngt Rew, 2006)

Information flows in the brain

Neurons transmit electrical information, which generate conscience and emotions

Information flows generate cooperation

White cells attact a cancer cell (cooperative activity)

Foto: National Cancer Institute, EUA http://visualsonline.cancer.gov/

Information flows in planet Earth

Mass and energy transfer between points in the planet

Complex adaptative systems

How come that a city with many inhabitants functions and exhibits patterns of regularity?

How come that an ecosystem with all its diverse species functions and exhibits patterns of regularity?

What are complex adaptive systems?

Systems composed of many interacting parts that evolve and adapt over time.

Organized behavior emerges from the simultaneous interactions of parts without any global plan.

What are complex adaptive systems?

Universal Computing

Computing studies information flows in natural systems...

...and how to represent and work with information flows in artificial systems

Computational Modelling with Cell SpacesCell Spaces

Components Cell Spaces Generalizes Proximity Matriz – GPM Hybrid Automata model Nested enviroment

Cell Spaces

Cellular Automata: Humans as Ants

Cellular Automata: Matrix, Neighbourhood, Set of discrete states,Set of transition rules,Discrete time.

“CAs contain enough complexity to simulate surprising and novel change as reflected in emergent phenomena”(Mike Batty)

2-Dimensional Automata

2-dimensional cellular automaton consists of an infinite (or finite) grid of cells, each in one of a finite number of states. Time is discrete and the state of a cell at time t is a function of the states of its neighbors at time t-1.

Cellular Automata

RulesNeighbourhood

States

Space and Time

t

t1

Von Neumann Neighborhood

Moore Neighborhood

Most important neighborhoods

Conway’s Game of Life

1. At each step in time, the following effects occur:2. Any live cell with fewer than two neighbors dies, as

if by loneliness. 3. Any live cell with more than three neighbors dies,

as if by overcrowding. 4. Any live cell with two or three neighbors lives,

unchanged, to the next generation. 5. Any dead cell with exactly three neighbors comes to

life.

Game of Life

Static Life

Oscillating Life

Migrating Life

Conway’s Game of Life

The universe of the Game of Life is an infinite two-dimensional grid of cells, each of which is either alive or dead. Cells interact with their eight neighbors.

Characteristics of CA models

Self-organising systems with emergent properties: locally defined rules resulting in macroscopic ordered structures. Massive amounts of individual actions result in the spatial structures that we know and recognise;

Which Cellular Automata?

For realistic geographical modelsthe basic CA principles too constrained to be useful

Extending the basic CA paradigm From binary (active/inactive) values to a set of

inhomogeneous local statesFrom discrete to continuous values (30% cultivated land, 40%

grassland and 30% forest)Transition rules: diverse combinations Neighborhood definitions from a stationary 8-cell to

generalized neighbourhoodFrom system closure to external events to external output

during transitions

Agents as basis for complex systems

Agent: flexible, interacting and autonomous

An agent is any actor within an environment, any entity that can affect itself, the environment and other agents.

Agent-Based Modelling

Goal

Environment

Representations

Communication

ActionPerception

Communication

Gilbert, 2003

Agents: autonomy, flexibility, interaction

Synchronization of fireflies

Agents changing the landscape

It is the agent (an individual, household, or institution) that takes specific actions according to its own decision rules which drive land-cover change.

Four types of agents

Natural agents, artificial environment

Artificial agents, artificial environment Artificial agents, natural environment

Natural Agents, natural environment

fonte: Helen Couclelis (UCSB)

Four types of agents

Natural agents, artificial environment

Artificial agents, artificial environment Artificial agents, natural environment

Natural Agents, natural environment

fonte: Helen Couclelis (UCSB)

e-science Engineering Applications

BehavioralExperiments

Descriptive Model

Is computer science universal?

Modelling information flows in nature is computer science

http://www.red3d.com/cwr/boids/

Bird Flocking (Reynolds)

Example of a computational model1. No central autority2. Each bird reacts to its neighbor3. Model based on bottom up

interactionshttp://www.red3d.com/cwr/boids/

Bird Flocking: Reynolds Model (1987)

www.red3d.com/cwr/boids/

Cohesion: steer to move toward the average position of local flockmates

Separation: steer to avoid crowding local flockmates

Alignment: steer towards the average heading of local flockmates

Agents moving

Agents moving

Agents moving

Segregation

Segregation is an outcome of individual choices

But high levels of segregation indicate mean that people are prejudiced?

Schelling Model for Segregation

Start with a CA with “white” and “black” cells (random)The new cell state is the state of the majority of the

cell’s Moore neighboursWhite cells change to black if there are X or more black

neighboursBlack cells change to white if there are X or more white

neighbours

How long will it take for a stable state to occur?

Schelling’s Model of Segregation

Schelling (1971) demonstrates a theory to explain the persistence of racial segregation in an environment of growing tolerance

If individuals will tolerate racial diversity, but will not tolerate being in a minority in their locality, segregation will still be the equilibrium situation

Schelling’s Model of Segregation

< 1/3

Micro-level rules of the game

Stay if at least a third of neighbors are “kin”

Move to random location otherwise

Tolerance values above 30%: formation of ghettos

http://ccl.northwestern.edu/netlogo/models/Segregation

Schelling’s Model of Segregation

The Modified Majority Model for Segregation

Include random individual variationSome individuals are more susceptible to their neighbours

than othersIn general, white cells with five neighbours change to black,

but: Some “white” cells change to black if there are only four “black”

neighbours Some “white” cells change to black only if there are six “black”

neighboursVariation of individual difference

What happens in this case after 50 iterations and 500 iterations?

Zhang: Residential segregation in an all-integrationist world

Some studies show that most people prefer to live in a non-segregated society. Why there is so much segregation?

References

J. Zhang. Residential segregation in an all-integrationist world. Journal of Economic Behaviour & Organization, v. 54 pp. 533-550. 2004

T. C. Shelling. Micromotives and Macrobehavior. Norton, New York. 1978

Some photos from Diógenes Alves (www.dpi.inpe.br/dalves)

Land use change in Amazonia

~230 scenes Landsat/year

Yearly detailed estimates of clear-cut areas LANDSAT-class data (wall-to-wall)

INPE: Clear-cut deforestation mapping of Amazonia since 1988

Is this sound science?

Scenarios for Amazônia in 2020Otimistic scenario: 28% of

deforestation Pessimistic scenario: 42% of

deforestation

“We generated two models with realistic but differing assumptions--termed the "optimistic" and "nonoptimistic" scenarios--for the future of the Brazilian Amazon. The models predict the spatial distribution of deforested or heavily degraded land, as well as moderately degraded, lightly degraded, and pristine forests”.

W. Laurance et al, “The Future of the Brazilian Amazon?”, Science, 2001

The Future of Brazilian Amazonia?

Optimistic scenario: 28% of deforestation (1 million km2) by 2020Complete degradation up to 20 km from roads (existing and

projected)Moderate degradation up to 50 km from roadsReduced degradation up to 100 km from roads

Smallest yearly increase since the 1970s

Yearly rates of deforestation: 1998-2009

Laurance et al., 2001Optimistic scenario(2020)

Savannas and deforestation

Moderate degradation

Degradação leve

Floresta intocada

Doomsday scenario and actual data...

Data from INPE (Prodes, 2008)

Savannas, non-forested areas, deforested or heavely degrated

Deforestation

Forest

Laurance et al., 2001Optimistic scenario(2020)

Doomsday scenario and actual data...

Data from INPE (Prodes, 2008)

About 1 million km2 deforested in 2020

For Laurance´s optimistic scenario to occur, there should be 50.000 km2 of deforestation yearly from 2010 to 2020!

About 500.000 km2 deforested in 2010

Brazilian scientists write to Science

Amazon Deforestation Models: Challenging the Only-Roads Approach“Deforestation predictions presented by Laurance et al. are based on the assumption that the governmental road infrastructure is the prime factor driving deforestation. Simplistic models such as Laurance et al. may deviate attention from real deforestation causes, being potentially misleading in terms of deforestation control.”

Improving deforestation prediction using agent-based models

Decision

MODEL

Parameters

São Felix do Xingu study: multiscale analysis of the coevolution of land use dynamics and beef and milk market chains

São Felix do Xingu

Deforestation

Forest

Non-forest

Clouds/no data

INPE/PRODES 2003/2004:

Forest

Not ForestDeforest

River

Change 1997-2006: deforestation and cattle

Land use Change model

Beef and milk market chain model

Small farmersagents

Medium and largefarmersagents

Land use Change model

Beef and milk market chain model

Small farmersagents

Medium and largefarmersagents

Create pasture/Deforest

Speculator/large/small

bad land management

money surplus

Subsistenceagriculture

Diversify use

Manage cattle

Move towardsthe frontier

Abandon/Sellthe property

Buy newland

Settlement/invaded land

Sustainability path(alternative uses, technology)

Sustainability path (technology)

Agents example: small farmers in Amazonia

Create pasture/plantation/deforest

Speculator/large/small

money surplus/bank loan

Diversify use

Buy newland

Manage cattle/plantation

Buy calvesfrom small

Buy landfrom smallfarmers

Agents example: large farmers in Amazonia

Forest

Not ForestDeforest

River

Observed deforestation from 1997 to 2006

Local scale

Regional scale

CATTLE CHAIN MODEL Flows: goods, information, etc.. Connections: Agents

LANDSCAPE DYNAMICS MODEL - Front- Medium- Rear

INDIVIDUAL AGENTSLarge and small farmers

Loca

l far

mer

sFr

ontie

r Re

gion

SCENARIO

S

Land use Change model

Beef and milk market chain model

Small farmersagents

Medium and largefarmersagents

Land use Change model

Small farmersagents

Medium and largefarmersagents

Landscapemetrics model

Pasture degradation

model

Several workshops in 2007 to define model rules and variables

Landscape model: different rules for two main types of actors

Landscape model: different rules of behavior at different partitions

Forest

Not ForestDeforest

River

FRONT

MIDDLE

BACK

SÃO FÉLIX DO XINGU - 1997

Landscape model: different rules of behavior at different partitions which also change in time

FRENTE

MEIO

RETAGUARDA

Forest

Not ForestDeforest

River

FRONT

MIDDLE

BACK

SÃO FÉLIX DO XINGU - 2006

Modeling results 97 to 2006

Observed 97 to 2006