Complex Systems and Emergence Gilberto Cmara Tiago Carneiro

Complex Systems and Emergence Gilberto Câmara Tiago Carneiro Pedro 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, Sci. Am, 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 Foto: National Cancer Institute, EUA http: //visualsonline. cancer. gov/ White cells attact a cancer cell (cooperative activity)

Information flows in planet Earth Mass and energy transfer between points in the planet

Complex adaptative systems How come that an ecosystem with all its diverse species functions and exhibits patterns of regularity? How come that a city with many inhabitants 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 studies information flows in natural systems. . . and how to represent and work with information flows in artificial systems

Computational Modelling with Cell Spaces n 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 Neighbourhood Rules Space and Time t States t 1

Most important neighborhoods Von Neumann Neighborhood Moore Neighborhood

Conway’s Game of Life 1. 2. 3. 4. 5. At each step in time, the following effects occur: Any live cell with fewer than two neighbors dies, as if by loneliness. Any live cell with more than three neighbors dies, as if by overcrowding. Any live cell with two or three neighbors lives, unchanged, to the next generation. 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 twodimensional 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 models the basic CA principles too constrained to be useful Extending the basic CA paradigm From binary (active/inactive) values to a set of inhomogeneous local states From discrete to continuous values (30% cultivated land, 40% grassland 30% forest) Transition rules: diverse combinations Neighborhood definitions from a stationary 8 -cell to generalized neighbourhood From system closure to external events to external output during transitions

Agents as basis for complex systems An agent is any actor within an environment, any entity that can affect itself, the environment and other agents. Agent: flexible, interacting and autonomous

Agent-Based Modelling Representations Goal Communication Action Perception Environment 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 landcover change.

Four types of agents Artificial agents, artificial environment Artificial agents, natural environment Natural agents, artificial environment Natural Agents, natural environment fonte: Helen Couclelis (UCSB)

Four types of agents e-science Artificial agents, artificial environment Behavioral Experiments Natural agents, artificial environment Engineering Applications Artificial agents, natural environment Descriptive Model Natural Agents, natural environment fonte: Helen Couclelis (UCSB)

Is computer science universal? Modelling information flows in nature is computer science http: //www. red 3 d. com/cwr/boids/

Bird Flocking (Reynolds) Example of a computational model 1. No central autority 2. Each bird reacts to its neighbor 3. Model based on bottom up interactions http: //www. red 3 d. com/cwr/boids/

Bird Flocking: Reynolds Model (1987) 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 www. red 3 d. com/cwr/boids/

Agents moving

Agents moving

Agents moving

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 neighbours White cells change to black if there are X or more black neighbours Black 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 Micro-level rules of the game Stay if at least a third of neighbors are “kin” < 1/3 Move to random location otherwise

Schelling’s Model of Segregation Tolerance values above 30%: formation of ghettos

The Modified Majority Model for Segregation Include random individual variation Some individuals are more susceptible to their neighbours than others In 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” neighbours – Variation of individual difference What happens in this case after 50 iterations and 500 iterations?

Zhang: Residential segregation in an allintegrationist 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 allintegrationist world. Journal of Economic Behaviour & Organization, v. 54 pp. 533 -550. 2004 • T. C. Shelling. Micromotives and Macrobehavior. Norton, New York. 1978

Land use change in Amazonia Some photos from Diógenes Alves (www. dpi. inpe. br/dalves)

INPE: Clear-cut deforestation mapping of Amazonia since 1988 ~230 scenes Landsat/year Yearly detailed estimates of clear-cut areas LANDSAT-class data (wall-to-wall)

Is this sound science? W. Laurance et al, “The Future of the Brazilian Amazon? ”, Science, 2001 Scenarios for Amazônia in 2020 Otimistic 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”.

The Future of Brazilian Amazonia? Optimistic scenario: 28% of deforestation (1 million km 2) by 2020 Complete degradation up to 20 km from roads (existing and projected) Moderate degradation up to 50 km from roads Reduced degradation up to 100 km from roads

Yearly rates of deforestation: 1998 -2009 Smallest yearly increase since the 1970 s

Doomsday scenario and actual data. . . Laurance et al. , 2001 Optimistic scenario(2020) Savannas and deforestation Moderate degradation Degradação leve Floresta intocada Data from INPE (Prodes, 2008) Savannas, non-forested areas, deforested or heavely degrated Deforestation Forest

Doomsday scenario and actual data. . . Laurance et al. , 2001 Optimistic scenario(2020) About 1 million km 2 deforested in 2020 Data from INPE (Prodes, 2008) About 500. 000 km 2 deforested in 2010 For Laurance´s optimistic scenario to occur, there should be 50. 000 km 2 of deforestation yearly from 2010 to 2020!

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 agentbased models Decision MODEL Parameters

São Felix do Xingu study: multiscale analysis of the coevolutio of land use dynamics and beef and milk market chains São Felix do Xingu INPE/PRODES 2003/2004: Deforestation Forest Non-forest Clouds/no data

Change 1997 -2006: deforestation and cattle Forest River Deforest Not Forest

Agents example: small farmers in Amazonia Sustainability path (alternative uses, technology) Settlement/ invaded land Diversify use money surplus Subsistence agriculture Create pasture/ Deforest Sustainability path (technology) Manage cattle bad land management Move towards the frontier Abandon/Sell the property Buy new land Speculator/ large/small

Agents example: large farmers in Amazonia Diversify use money surplus/bank loan Buy land from small farmers Create pasture/ plantation/ deforest Manage cattle/ plantation Buy calves from small Buy new land Speculator/ large/small

Observed deforestation from 1997 to 2006 Forest River Deforest Not Forest

Regional scale Frontier INDIVIDUAL AGENTS Large and small farmers Local scale SCENARIOS LANDSCAPE DYNAMICS MODEL - Front - Medium - Rear Local farmers Region CATTLE CHAIN MODEL Flows: goods, information, etc. . Connections: Agents

Landscape model: different rules for two main types of actors Landscape metrics model Beef and milk market chain model Land use Change model Small farmers agents Medium and large farmers agents Pasture degradation model Several workshops in 2007 to define model rules and variables

Landscape model: different rules of behavior at different partitions SÃO FÉLIX DO XINGU - 1997 FRONT MIDDLE BACK Forest River Deforest Not Forest

Landscape model: different rules of behavior at different partitions which also change in time SÃO FÉLIX DO XINGU - 2006 FRONT FRENTE MIDDLE MEIO BACK RETAGUARDA Forest River Deforest Not Forest

Modeling results 97 to 2006 Observed 97 to 2006