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Complex Systems and Emergence

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.

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Complex Systems and Emergence

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  1. Complex Systems and Emergence Gilberto Câmara Tiago Carneiro Pedro Andrade

  2. Where does this image come from?

  3. Where does this image come from? Map of the web (Barabasi) (could be brain connections)

  4. Information flows in Nature Ant colonies live in a chemical world

  5. 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)

  6. Information flows in the brain Neurons transmit electrical information, which generate conscience and emotions

  7. Information flows generate cooperation Foto: NationalCancerInstitute, EUA http://visualsonline.cancer.gov/ White cells attact a cancer cell (cooperative activity)

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

  9. 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?

  10. 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.

  11. What are complex adaptive systems?

  12. Universal Computing Computing studies information flows in natural systems... ...and how to represent and work with information flows in artificial systems

  13. Cell Spaces • Components • Cell Spaces • Generalizes Proximity Matriz – GPM • Hybrid Automata model • Nested enviroment Computational Modelling with Cell Spaces

  14. Cell Spaces

  15. 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)

  16. 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.

  17. Cellular Automata Neighbourhood Rules Space and Time t States t1

  18. Von Neumann Neighborhood Moore Neighborhood Most important neighborhoods

  19. Conway’s Game of Life • 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.

  20. Game of Life Static Life Oscillating Life Migrating Life

  21. 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.

  22. 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;

  23. 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 and 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

  24. Agent: flexible, interacting and autonomous 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.

  25. Representations Communication Communication Action Perception Environment Agent-Based Modelling Goal Gilbert, 2003

  26. Agents: autonomy, flexibility, interaction Synchronization of fireflies

  27. 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.

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

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

  30. Is computer science universal? Modelling information flows in nature is computer science http://www.red3d.com/cwr/boids/

  31. Bird Flocking (Reynolds) Example of a computational model No central autority Each bird reacts to its neighbor Model based on bottom up interactions http://www.red3d.com/cwr/boids/

  32. 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.red3d.com/cwr/boids/

  33. Agents moving

  34. Agents moving

  35. Agents moving

  36. Segregation Segregation is an outcome of individual choices But high levels of segregation indicate mean that people are prejudiced?

  37. 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?

  38. 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

  39. 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

  40. Schelling’s Model of Segregation Tolerance values above 30%: formation of ghettos http://ccl.northwestern.edu/netlogo/models/Segregation

  41. 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?

  42. Zhang: Residential segregation in an all-integrationist world Some studies show thatmostpeopleprefer to live in a non-segregatedsociety. Whythere is somuchsegregation?

  43. 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

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

  45. 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)

  46. Scenarios for Amazônia in 2020 Otimisticscenario: 28% ofdeforestation Pessimisticscenario: 42% ofdeforestation Is this sound science? W. Laurance et al, “The Future of the Brazilian Amazon?”, Science, 2001 “Wegeneratedtwomodelswithrealisticbutdifferingassumptions--termedthe "optimistic" and "nonoptimistic" scenarios--for the future oftheBrazilianAmazon. Themodelspredictthespatialdistributionofdeforestedorheavilydegradedland, as well as moderatelydegraded, lightlydegraded, andpristineforests”.

  47. The Future of Brazilian Amazonia? Optimistic scenario: 28% of deforestation (1 million km2) 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

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

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

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