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A nonlinear dynamics perspective of Wolfram’s new kind of science. Part III: Predicting the unpredictable
 International Journal of Bifurcation and Chaos
, 2004
"... This tutorial provides a nonlinear dynamics perspective to Wolfram’s monumental work on A New Kind of Science. By mapping a Boolean local Rule, ortruth table, ontothepoint attractors of a specially tailored nonlinear dynamical system, we show how some of Wolfram’s empirical observations can be justi ..."
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Cited by 13 (0 self)
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This tutorial provides a nonlinear dynamics perspective to Wolfram’s monumental work on A New Kind of Science. By mapping a Boolean local Rule, ortruth table, ontothepoint attractors of a specially tailored nonlinear dynamical system, we show how some of Wolfram’s empirical observations can be justified on firm ground. The advantage of this new approach for studying Cellular Automata phenomena is that it is based on concepts from nonlinear dynamics and attractors where many fuzzy concepts introduced by Wolfram via brute force observations can be defined and justified via mathematical analysis. The main result of Part I is the introduction of a fundamental concept called linear separability and a complexity index κ for each local Rule which characterizes the intrinsic geometrical structure of an induced “Boolean cube ” in threedimensional Euclidean space. In particular, Wolfram’s seductive idea of a “threshold of
Intelligence and Cooperative Search by Coupled Local Minimizers
, 2001
"... this paper we propose a new methodology of coupled local minimizers (CLM) for solving continuous nonlinear optimization problems. We pose a somewhat similar challenge as for committee networks but within a di#erent and broader context of solving di#erentiable optimization problems. The aim is to (on ..."
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Cited by 8 (5 self)
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this paper we propose a new methodology of coupled local minimizers (CLM) for solving continuous nonlinear optimization problems. We pose a somewhat similar challenge as for committee networks but within a di#erent and broader context of solving di#erentiable optimization problems. The aim is to (online) combine the results from local optimizers in order to let the ensemble generate a local minimum that is better than the best result obtained from all individual local minimizers. We show how improved local minima can be obtained by having interaction and information exchange between the local search processes. This is realized through state synchronization constraints that are imposed between the local minimizers by incorporating principles of masterslave dynamics. Synchronization theory has been intensively studied within the area of chaotic systems and secure communications [Chen & Dong, 1998; Pecora & Carroll, 1990; Suykens et al., 1996, 1997, 1998; Wu & Chua, 1994]. The CLM method is related to Lagrange programming network approaches for chaos synchronization [Suykens & Vandewalle, 2000], where identical or generalized synchronization constraints are imposed on dynamical systems. CLMs also fit within the framework of Cellular Neural Networks (CNN) [Chua & Roska, 1993; Chua et al., 1995; Chua, 1998]. By considering the objective of minimizing the average cost of an ensemble of local minimizers subject to pairwise synchronization constraints, a continuoustime optimization algorithm is studied according to Lagrange programming networks [Cichocki & Unbehauen, 1994; Zhang & Constantinides, 1992]. The resulting continuoustime optimization algorithm is described by an array of coupled nonlinear cells or a onedimensional CNN with bidirectional coupling
SeckTuohMora: Phenomenology of reactiondiffusion binarystate cellular automata
 Int. J. Bifurcation and Chaos
, 2006
"... We study a binarycellstates eightcell neighborhood twodimensional cellular automaton model of a quasichemical system with a substrate and a reagent. Reactions are represented by semitotalistic transitions rules: every cell switches from state 0 to state 1 depending on if sum of neighbors in st ..."
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Cited by 7 (5 self)
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We study a binarycellstates eightcell neighborhood twodimensional cellular automaton model of a quasichemical system with a substrate and a reagent. Reactions are represented by semitotalistic transitions rules: every cell switches from state 0 to state 1 depending on if sum of neighbors in state 1 belongs to some specified interval, cell remains in state 1 if sum of neighbors in state 1 belong to another specified interval. We investigate spacetime dynamics of 1296 automata, establish morphologybases classification of the rules, explore precipitating and excitatory cases and scrutinize collisions between mobile and stationary localizations (gliders, cycle life and still life compact patterns). We explore reactiondiffusion like patterns produced in result of collisions between localizations. Also, we propose a set of rules with complex behavior called Life 2c22.
Sync in complex dynamical networks: Stability, evolution, control and application
 Int. J. Comp. Cognition
"... ..."
Feature Complex Networks: SmallWorld, ScaleFree and Beyond
"... In the past few years, the discovery of smallworld and scalefree properties of many natural and artificial complex networks has stimulated a great deal of interest in studying the underlying organizing principles of various complex networks, which has led to dramatic advances in this emerging and ..."
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In the past few years, the discovery of smallworld and scalefree properties of many natural and artificial complex networks has stimulated a great deal of interest in studying the underlying organizing principles of various complex networks, which has led to dramatic advances in this emerging and active field of research. The present article reviews some basic concepts, important progress, and significant results in the current studies of various complex networks, with emphasis on the relationship between the topology and the dynamics of such complex networks. Some fundamental properties and typical complex network models are described; and, as an example, epidemic dynamics are analyzed and discussed in some detail. Finally, the important issue of robustness versus fragility of dynamical synchronization in complex networks is introduced and discussed. Index terms—complex network, smallworld network, scalefree network, synchronization, robustness
Learning and Generalization by Coupled Local Minimizers
"... The purpose of this paper is to introduce a fundamentally new method of Coupled Local Minimizers (CLMs). We show how state synchronization of continuous local optimization methods (coupled backpropagation learning processes in this case) can lead to cooperative search and improved solutions. We expl ..."
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The purpose of this paper is to introduce a fundamentally new method of Coupled Local Minimizers (CLMs). We show how state synchronization of continuous local optimization methods (coupled backpropagation learning processes in this case) can lead to cooperative search and improved solutions. We explain under which conditions the method leads to good generalization when applied to the training of MLPs, without using a regularization term in the cost function. The choice of the initial states of the minimizers plays an important role at this point. In the formulation, one takes identical copies of the cost function and realizes a compacti  cation through the synchronization constraints, which is also known in string theory. It is explained how to achieve optimal cooperative search between the individual minimizers. The method is formulated in continuous time and related with Lagrange programming networks and cellular neural networks.
Stability Results for Cellular Neural Networks with Delays
"... In this paper we give a sufficient condition to imply global asymptotic stability of a delayed cellular neural network of the form n� n� ˙xi(t) = −dixi(t) + aijf(xj(t)) + bijf(xj(t − τij)) + ui, t ≥ 0, i = 1,..., n, j=1 j=1 where f(t) = 1 2 (t + 1  − t − 1). In order to prove this stability r ..."
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In this paper we give a sufficient condition to imply global asymptotic stability of a delayed cellular neural network of the form n� n� ˙xi(t) = −dixi(t) + aijf(xj(t)) + bijf(xj(t − τij)) + ui, t ≥ 0, i = 1,..., n, j=1 j=1 where f(t) = 1 2 (t + 1  − t − 1). In order to prove this stability result we need a sufficient condition which guarantees that the trivial solution of the linear delay system n� n� ˙zi(t) = aijzj(t) + bijzj(t − τij), t ≥ 0, i = 1,..., n j=1 j=1 is asymptotically stable independently of the delays τij. keywords: delayed cellular neural networks, global asymptotic stability, Mmatrix 1
Regular Student Paper Extending neuromorphic engineering beyond electronics
"... optoelectronics, optical interconnects, mechanics, embodied artificial intelligence. One of the advantages of the neuromorphic approach is energy efficiency, which comes from the exploitation of the intrinsic physics of electronic devices. Taking the intrinsic efficiency of physics as a guiding pri ..."
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optoelectronics, optical interconnects, mechanics, embodied artificial intelligence. One of the advantages of the neuromorphic approach is energy efficiency, which comes from the exploitation of the intrinsic physics of electronic devices. Taking the intrinsic efficiency of physics as a guiding principle, we can extend it beyond electronics to other technologies including optical, mechanical, and chemical. In this paper we consider the role that some of these other technologies may has to play in this area, describe some of the work that has already been done, and suggest some advantages of pursuing what we call a physical computational approach to AI. 1.
Sync in Complex Dynamical Networks: Stability, Evolution, Control, and Application
"... Abstract — In the past few years, the discoveries of smallworld and scalefree properties of many natural and artificial complex networks have stimulated significant advances in better understanding the relationship between the topology and the collective dynamics of complex networks. This paper re ..."
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Abstract — In the past few years, the discoveries of smallworld and scalefree properties of many natural and artificial complex networks have stimulated significant advances in better understanding the relationship between the topology and the collective dynamics of complex networks. This paper reports recent progresses in the literature of synchronization of complex dynamical networks including stability criteria, network synchronizability and uniform synchronous criticality in different topologies, and the connection between control and synchronization of complex networks as well. The economiccycle synchronous phenomenon in the World Trade Web, a scalefree type of social economic networks, is used to illustrate an application of the network synchronization mechanism. Copyright c ○ 2005 Yang’s Scientific