o que são sistemas complexos? renato vicente complex systems each usp jan/10
TRANSCRIPT
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O que são Sistemas Complexos?
Renato VicenteComplex Systems EACH USP jan/10
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I. Problemas Contemporâneos
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Problemas e PerguntasContemporâneos
Tráfego urbano
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Problemas e PerguntasContemporâneos
Crescimento urbano e energia
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Problemas e PerguntasContemporâneos
Estabilidade política e econômica
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Problemas e PerguntasContemporâneos
Impactos climáticos
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Problemas e PerguntasContemporâneos
Controle de epidemias
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Problemas e PerguntasContemporâneos
Preservação de ecossistemas
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Problemas e Perguntas Contemporâneos
É possível evitar o colapso de uma civilização?
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II. Sistemas Complexos: Idéias/Características Centrais
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Dinâmica Evolucionária
Complexidade resulta de replicação/imitação, mutação/tweaking e seleção.
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Caos
Mapa logístico
1 (1 )t t tx rx x
r = 2.8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 5 10 15 20 25
n
x(n
)
x(0)=0.1
x(0)=0.2
x(0)=0.3
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Caos
A população final pode ser imprevisível
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Emergência
Estorninhos: sem coordenação central
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Emergência
Cardume de sardinhas
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Emergência
Ola
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Emergência
Congestionamento fantasma
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Emergência
Segregação Racial: Micromotivos conhecidos gerando macrocomportamentos inesperados.
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Transição de Fase
Incêndios em florestas
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Transição de Fase
Predador-presa
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Auto-similaridade
Estruturas fractais
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Auto-similaridade
Batimentos cardíacos
http://www.physionet.org/tutorials/ndc/
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Auto-similaridade
Batimentos cardíacos
http://www.physionet.org/tutorials/ndc/
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Auto-similaridade
Leis de potência
Tamanho de assentamos maias
Mortes em ataques insurgentes
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Auto-similaridade
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Auto-similaridade
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Redes Complexas
Cadeia alimentar
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Redes Complexas
10000 neurônios em uma coluna neocortical
proteoma
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Redes Complexas
internet
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Redes Complexas
Espaço de produtos
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Redes Complexas
Padrões de votação no senado americano
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Redes Complexas
Relacionamentos em uma high-school
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Redes Complexas
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Redes Complexas
http://www.nytimes.com/interactive/2008/05/05/science/20080506_DISEASE.html
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Outras características:
1. Capacidade adaptativa2. Auto-referência3. Dependência com relação ao
caminho/história4. Competição e cooperação
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Tentativa de definição
Sistema Complexo = Sistema composto por agentes adaptativos em interação.
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III. Metáforas Científicas
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Metáforas
Isaac Newton (Sécs. 17 -18)
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Metáforas
Sadi Carnot (Sécs. 18 -19)
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Metáforas
James Clerk Maxwell (Sécs. 19, segunda metade)
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Metáforas
John von Neumann Séc. 20
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Metáforas