By Peter Korosec
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Additional info for New Achievements in Evolutionary Computation
1 Particle swarm optimization Particle Swarm Optimization is a Swarm Intelligence technique which shares many features with Evolutionary Algorithms. Swarm Intelligence is used to designate the artificial intelligence techniques based on the study of collective behavior in decentralized, selforganized systems. Swarm Intelligence systems are typically made up of a population of simple autonomous agents interacting locally with one another and with their environment. Although there is no centralized control, the local interactions between agents lead to the emergence of global behavior.
Constraint Processing, Selected Papers 923: 121–137. X. , Eberhart, R. & Shi, Y. (2003). Swarm intelligence for permutation optimization: a case study on n-queens problem, Proceedings of the IEEE Swarm Intelligence Symposium, pp. 243–246. 3 Morphological-Rank-Linear Models for Financial Time Series Forecasting 1Information 2Systems Ricardo de A. Araújo1, Gláucio G. de M. Melo1, Adriano L. I. de Oliveira2 and Sergio C. B. Soares2 Technology Department, [gm]2 Intelligent Systems, Campinas, SP, and Computing Department, University of Pernambuco, Recife, PE, Brazil 1.
In a mathematical sense, such a relationship involving time series historical data defines a ddimensional phase space, where d is the minimum dimension capable of representing such relationship. Therefore, a d- dimensional phase space can be built so that it is possible to unfold its corresponding time series. Takens  proved that if d is sufficiently large, such phase space is homeomorphic to the phase space that generated the time series. Takens' Theorem  is the theoretical justification that it is possible to build a state space using the correct time lags, and if this space is correctly rebuilt, Takens' Theorem  also guarantees that the dynamics of this space is topologically identical to the dynamics of the real system state space.
New Achievements in Evolutionary Computation by Peter Korosec