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Autonomous Agents, AI and Chaos Theory
"... Agent theory in AI and related disciplines deals with the structure and behaviour of autonomous, intelligent systems, capable of adaptive action to pursue their interests. In this paper it is proposed that a natural reinterpretation of agenttheoretic intentional concepts like knowing, wanting, liki ..."
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Cited by 12 (1 self)
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Agent theory in AI and related disciplines deals with the structure and behaviour of autonomous, intelligent systems, capable of adaptive action to pursue their interests. In this paper it is proposed that a natural reinterpretation of agenttheoretic intentional concepts like knowing, wanting, liking, etc., can be found in process dynamics. This reinterpretation of agent theory serves two purposes. On the one hand we gain a well established mathematical theory which can be used as the formal mathematical interpretation (semantics) of the abstract agent theory. On the other hand, since process dynamics is a theory that can also be applied to physical systems of various kinds, we gain an implementation route for the construction of artificial agents as bundles of processes in machines. The paper is intended as a basis for dialogue with workers in dynamics, AI, ethology and cognitive science. 1 Introduction Agent theory is a branch of artificial intelligence (Kiss, 1988). Its domain is...
Prior Information and Generalized Questions
, 1996
"... In learning problems available information is usually divided into two categories: examples of function values (or training data) and prior information (e.g. a smoothness constraint). ..."
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Cited by 7 (4 self)
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In learning problems available information is usually divided into two categories: examples of function values (or training data) and prior information (e.g. a smoothness constraint).
Time Series of Rational Partitions and Complexity of Onedimensional Processes
"... Abstract. Time series based on couples of partitions, and a related reduction algorithm, are used to develop indicators of complexity for general onedimensional processes with discretizable states. After introducing the calculation scheme, we provide algorithms for some typical examples (cellular a ..."
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Abstract. Time series based on couples of partitions, and a related reduction algorithm, are used to develop indicators of complexity for general onedimensional processes with discretizable states. After introducing the calculation scheme, we provide algorithms for some typical examples (cellular automata and iterated maps). Experiments show the sensitivity of these indicatorsto complexity in the intuitive sense, and to hidden features distinguishing complexity from ordinary randomness. 1. Rational partitions The concept of a rational partition (rpartition) was introduced in [1], with the purpose of estimating the complexity of objects or situations endowed, in a broad sense, with a dynamics (cellular automata (CAs) , mappings, shifts, patterns depending on a parameter, and so on). The idea illustrated there may be summarized in the following main points. • Inasmuch as finite measurable partitions in probability spaces give a
The Correspondence Principle and Structural Stability in NonMaximum Systems
, 2004
"... The correspondence principle suggests a link between asymptotic stability properties of equilibria of economic models and the equilibrium response to data that describe the model or the model environment. However, this link has been impaired by a logicalmathematical deficiency. This paper, by intro ..."
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The correspondence principle suggests a link between asymptotic stability properties of equilibria of economic models and the equilibrium response to data that describe the model or the model environment. However, this link has been impaired by a logicalmathematical deficiency. This paper, by introducing a conceptual requirement of (local) structural stability as part of the principle hypotheses, rectifies the relation between qualitative properties of equilibria and the analysis of variations. Two related examples are given. The first completes Dierkers’ proof of a unique equilibrium in regular Arrow–Debreu economies, where all price systems are locally stable relative to a tâtonnement process. The second validates linear approximation analysis of deterministic continuous time rational expectation models. The paper’s focus on local analysis makes it possible to handle potentially difficult problems in a straightforward manner.
An extension of Markov partitions for a certain toral endomorphism
, 1999
"... We define and construct Markov partition for a certain toral endomorphism and then we use it to obtain a symbolic representation of the semidynamical system induced by the endomorphism. ..."
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We define and construct Markov partition for a certain toral endomorphism and then we use it to obtain a symbolic representation of the semidynamical system induced by the endomorphism.
Published by Parus Analytical Systems
, 2004
"... where it all began. Table of Contents Acknowledgements..................................................................................... vii Preface to the Second Edition..................................................................... ix Chapter 1 Introduction and Overview................... ..."
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where it all began. Table of Contents Acknowledgements..................................................................................... vii Preface to the Second Edition..................................................................... ix Chapter 1 Introduction and Overview.......................................................... 1 ASSUMPTION 1: Individuals understand international events using pattern
On the extension of the Painleve ́ property to difference equations
, 2000
"... Abstract. It is well known that the integrability (solvability) of a differential equation is related to the singularity structure of its solutions in the complex domain—an observation that lies behind the Painleve ́ test. A number of ways of extending this philosophy to discrete equations are explo ..."
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Abstract. It is well known that the integrability (solvability) of a differential equation is related to the singularity structure of its solutions in the complex domain—an observation that lies behind the Painleve ́ test. A number of ways of extending this philosophy to discrete equations are explored. First, following the classical work of Julia, Birkhoff and others, a natural interpretation of these equations in the complex domain as difference or delay equations is described and it is noted that arbitrary periodic functions play an analogous role for difference equations to that played by arbitrary constants in the solution of differential equations. These periodic functions can produce spurious branching in solutions and are factored out of the analysis which concentrates on branching from other sources. Second, examples and theorems from the theory of difference equations are presented which show that, modulo these periodic functions, solutions of a large class of difference equations are meromorphic, regardless of their integrability. It is argued that the integrability of many difference equations is related to the structure of their solutions at infinity in the complex plane and that Nevanlinna theory provides many of the concepts necessary to detect integrability in a large class of equations. A perturbative method is then constructed and used to develop series in z and the derivative of log(z), where z is the independent variable of the difference equation. This method provides an analogue of the series developed in the Painleve ́ test for differential equations. Finally, the implications of these observations are discussed for two tests which have been studied in the literature regarding the integrability of discrete equations. AMS classification scheme numbers: 30D35, 39A10, 39A12 1.
Accurate Computation of Chaotic Dynamical Systems
"... Abstract: The computation of orbits of dynamical systems is known to be highly unstable if the system exhibits chaotic behavior. In this case, even for the very simplest systems, ordinary floatingpoint computations will eventually deliver results which are completely wrong quantitatively, when com ..."
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Abstract: The computation of orbits of dynamical systems is known to be highly unstable if the system exhibits chaotic behavior. In this case, even for the very simplest systems, ordinary floatingpoint computations will eventually deliver results which are completely wrong quantitatively, when compared with the true trajectory on which the computation began. Similarly, ordinary interval arithmetic (i. e. intervals of floatingpoint numbers) yield poor enclosures after few iterations. In most cases the computation breaks down because of overflow. Using intpakX’s multiple precision intervals, we can compute enclosures of orbits for a considerably longer time with high accuracy. Statements concerning the sensitivity with respect to small changes in the seed value of the numerical computations are possible with mathematical rigor. We also show that computing an orbit using a rational arithmetic as e.g. provided by the computer algebra system Maple is not possible due to computing time and computer memory limitations. Key–Words: Dynamical system, logistic equation, chaotic behaviour, verified numerical results, intpakX 1