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INNOVATION AND COMPLEXITY

INNOVATION AND COMPLEXITY. Carlos Eduardo Maldonado Research Professor Universidad del Rosario. INNOVATION ENTAILS COMPLEXITY. Complex systems contain and lead to surprise ( emergence) They are unpredictable ( chaotic , catastrophic )

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INNOVATION AND COMPLEXITY

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  1. INNOVATION AND COMPLEXITY Carlos Eduardo Maldonado ResearchProfessor Universidad del Rosario

  2. INNOVATION ENTAILS COMPLEXITY • Complex systems contain and lead to surprise (emergence) • They are unpredictable (chaotic, catastrophic) • They do nothavecentralityorhierarchy (local control) (self-organization) • They are essentially open systems (complexnetworks) (NET)

  3. INNOVATION AND PROBLEM SOLVING • Innovation and problemsolving: two faces of one and thesametoken • Theyroot in biology, notjust in culture

  4. INNOVATION AND/AS RESEARCH • Basic Research • Experimental Research • AppliedResearch  Alldependson de themode and degree of innovation • Incremental Innovation • Radical Innovation • Targets-basedResearch • Researchgroundedonhabilities and skills

  5. Twokind of problems Decidible Indecidible Cannot be solved algorithmically, not even with unlimited or infinite time and space resources Difficult RelevantProblems P N-P Easy/IrrevelevantProblems N-P Complete Hyper-computation N-P Hard • Simulation • Metaheurístics

  6. SIMULATION MODELING COMPUTER REAL SYSTEM (REAL WORLD )

  7. OPTIMIZATION(COMBINATORIAL COMPLEXITY) • Local Optimization (orpartial) • Global Optimization

  8. P and N-P: COMPLEXITY •  Itiseasiertofind a solutionthanverifyingit: • P: Itisnecessarythat a problemadmits a methodtofind a solution in a P time. • N-P: Itissufficientthat a problemadmits a methodtoverifythesolution in a P time.

  9. P, N-P and OPTIMIZATION • Problems: P = N-P P ≠ N-P P ≤ N-P P C N-P

  10. MODERN METHODS OF HEURISTICS • FuzzySystems • Neural Networks • GeneticProgramming • Agents (multi-agents)- basedSystems

  11. TECHNIQUES FOR LOCAL OPTIMIZATION • (Stochastic) Hill climbing • SimulatedAnnealing • TabooSearch • EvolutionaryAlgorithms • ConstraintHandling

  12. METHODS OF GLOBAL OPTIMIZATION • Problems of combinatorialcomplexity Heuristics: Algorithmthat looks forgoodsolutions at a reasonablecomputationalcost, withoutthoughguarantee of optimality (orevenfeasibility). Usuallyworkswithspecificproblems Metaheuristics: They are heuristics in a larger and deeperscope  Bio-inspiredComputation

  13. MODELING, SIMULATION, OPTIMIZATION • Data mining • EvolutiveComputation • SwarmIntelligence • Artificial Life • Sciences of Complexity • . • . • . • Other • Optimization Metaheuristics • Multi-AgentModels • CellularAutomata • Artificial Chemistry • . • . • . • Other Prediction

  14. METAHEURISTICS • Single-SolutionBased • Population-Based • MetaheuristicsforMultiobjectiveOptimization • HybridMetaheuristics • ParallelMetaheuristics • DistinctionbetweenDecidable and IndecidableProblems (Computationally)

  15. COMPLEXITY OF ALGORITHMS AND PROBLEMS DECIDIBLE PROBLEMS INDECIDIBLE PROBLEMS Ej.: The Halting Problem (Turing)

  16. COMPLEXITY OF ALGORITHMS • An algorithm needs two important resources to solve a problem: space and time • The time complexity of an algorithm is the number of steps required to solve a problem of size n

  17. ALGORITHM AND TIME • Polynomial-time algorithm p(n) = ak . nk + … + aj . nj + … + al . n + ao • Exponential-time algorithm Its complexity is: O(cn), where c is a real constant superior to 1

  18. COMPLEXITY OF PROBLEMS • The complexity of a problem is equivalent to the complexity of the best algorithm solving that problem • A problem is tractable (or easy) if there exists a P-time algorithm to solve it • A problem is intractable (or difficult) if no P-time algorithm exists to solve the problem • C/A complexitytheory of problemsdealswithdecisionproblems. A decisionproblemalways has a yes or no answer

  19. OptimizationMethods ExactMethods ApproximateMethods Branchand x RestrictedProgramming DynamicProgramming A*, IDA* HeuristicAlgorithms and ApproximateAlgorithms Metaheuristics Specificheuristicproblems Single-basedsolutionsMetaheuristics Population-basedMetaheuristics

  20. METAHEURISTICS • Metaheuristics • P Metaheuristics • HybridMetaheuristics • ParallelMetaheuristics

  21. WHAT IS COMPUTABLE? • Thatwe can know • Thatwe can say • Thatwe can decide upon  Thatwe can solve

  22. NEW PROBLEMS IN COMPUTATION • Conversations • Numbering • Proves • Finite Time • Infinite Time • Continuous Time • Discrete Time New Computational Paradigms. Changing Conceptions of What is Computable. S. Barry Cooper, B. Löwe, A. Sorbi (Eds.), Springer Verlag, 2008

  23. LOGICS AND COMPUTATION • IntuitionBubbles • Non-ClassicalLogics: ParaconsistentLogics RelevantLogics Quantum Logics Time Logics Many-ValuedLogics EpistemicLogics FuzzyLogics • ComputationalComplexity • AlgorithmicComplexity

  24. INNOVATION AND KNOWLEDGE • Innovatingandsolvingproblems as a matter of pushing-back thefrontiers of knowledge • Makinglifeevery time more possible • Gainingdegrees of freedom • Pushing-back cenralcontrols and rigidhierarchies • Trusting in local controls and dynamic centers • Working in a small-world: complexnetworks

  25. INNOVATION AND AESTHETICS • Spearheadsciencedoesnotpretendto control orpredict, anylonger • Sciencedistrustsconclusivearguments and yetstrivesforthem • Scienceassessesharmony

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