Computational Complexity: Theory, Techniques, and Applications
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Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The recognition that the collective behavior of the whole system cannot be simply inferred from an understanding of the behavior of the individual components has led to the development of numerous sophisticated new computational and modeling tools with applications to a wide range of scientific, engineering, and societal phenomena.
Computational Complexity: Theory, Techniques and Applications presents a detailed and integrated view of the theoretical basis, computational methods, and state-of-the-art approaches to investigating and modeling of inherently difficult problems whose solution requires extensive resources approaching the practical limits of present-day computer systems. This comprehensive and authoritative reference examines key components of computational complexity, including cellular automata, graph theory, data mining, granular computing, soft computing, wavelets, and more.
Canada LAI , MING-JUN The University of Georgia Athens USA KEINERT, FRITZ Iowa State University Ames USA LANGE, W OLFGANG University of Sussex Brighton UK Contributors XXXVII LAUBENBACHER, REINHARD Virginia Polytechnic Institute and State University Virginia USA LAURITSEN, KENT BÆKGAARD Danish Meteorological Institute Copenhagen Denmark LAVI , RON The Technion – Israel Institute of Technology Haifa Israel LEVY, MOSHE The Hebrew University Jerusalem Israel LIAU, CHURN-JUNG Academia Sinica
agent price-prediction rules. The agents become heterogeneous (adopt very diﬀerent rules). Trading volumes ﬂuctuate (large volumes correspond to bubbles and crashes). The rules evolve over time to more and more complex patterns, organized in hierarchies (rules, exceptions to rules, exceptions to exceptions, and so on ...). The successful rules are time dependent: a rule which is successful at a given time may perform poorly if reintroduced after many cycles of market co-evolution. The Lux and Lux
Physics, Locomotion, Per- ception, Behavior. In: Proceedings of SIGGRAPH‘94, 24–29 July 1994, Orlando, pp 43–50 Weisbuch G (1991) Complex Systems Dynamics: An Introduction to Automata Networks, translated from French by Ryckebusch S. Addison-Wesley, Redwood City Wiener N (1948) Cybernetics, or Control and Communication in the Animal and the Machine. Wiley, New York Wooldridge M (2000) Reasoning About Rational Agents. MIT Press, Cambridge 57 58 Agent Based Modeling and Computer Languages
developed. Functional languages oﬀer yet another alternative to the previously discussed languages. Like logic-based and object-oriented languages, functional languages often provide a form of direct support for binding data with behaviors. This support often leverages the fact that most functional languages support higher-order programming. As a result, the data is usually in the form of nested lists of values and functions while the behaviors themselves are implemented in the form of functions.
Science, University at Albany – State University of New York, New York, USA Article Outline Glossary Deﬁnition of the Subject Introduction Existing Mathematical Frameworks Finite Dynamical Systems Finite Dynamical Systems as Theoretical and Computational Tools Mathematical Results on Finite Dynamical Systems Future Directions Bibliography Glossary Agent-based simulation An agent-based simulation of a complex system is a computer model that consists of a collection of agents/variables that can