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340
Multiobjective Evolutionary Algorithms: Analyzing the StateoftheArt
, 2000
"... Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mideighties in an attempt to stochastically solve problems of this generic class. During the past decade, ..."
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Cited by 425 (7 self)
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Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mideighties in an attempt to stochastically solve problems of this generic class. During the past decade, a variety of multiobjective EA (MOEA) techniques have been proposed and applied to many scientific and engineering applications. Our discussion's intent is to rigorously define multiobjective optimization problems and certain related concepts, present an MOEA classification scheme, and evaluate the variety of contemporary MOEAs. Current MOEA theoretical developments are evaluated; specific topics addressed include fitness functions, Pareto ranking, niching, fitness sharing, mating restriction, and secondary populations. Since the development and application of MOEAs is a dynamic and rapidly growing activity, we focus on key analytical insights based upon critical MOEA evaluation of c...
An experimental unification of reservoir computing methods
, 2007
"... Three different uses of a recurrent neural network (RNN) as a reservoir that is not trained but instead read out by a simple external classification layer have been described in the literature: Liquid State Machines (LSMs), Echo State Networks (ESNs) and the Backpropagation Decorrelation (BPDC) lea ..."
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Cited by 70 (10 self)
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Three different uses of a recurrent neural network (RNN) as a reservoir that is not trained but instead read out by a simple external classification layer have been described in the literature: Liquid State Machines (LSMs), Echo State Networks (ESNs) and the Backpropagation Decorrelation (BPDC) learning rule. Individual descriptions of these techniques exist, but a overview is still lacking. Here, we present a series of experimental results that compares all three implementations, and draw conclusions about the relation between a broad range of reservoir parameters and network dynamics, memory, node complexity and performance on a variety of benchmark tests with different characteristics. Next, we introduce a new measure for the reservoir dynamics based on Lyapunov exponents. Unlike previous measures in the literature, this measure is dependent on the dynamics of the reservoir in response to the inputs, and in the cases we tried, it indicates an optimal value for the global scaling of the weight matrix, irrespective of the standard measures. We also describe the Reservoir Computing Toolbox that was used for these experiments, which implements all the types of Reservoir Computing and allows the easy simulation of a wide range of reservoir topologies for a number of benchmarks.
A mathematical framework for critical transitions: bifurcations, fastslow systems and stochastic dynamics
 Physica D
"... ar ..."
Rényi Information Dimension: Fundamental Limits . . .
, 2010
"... In Shannon theory, lossless source coding deals with the optimal compression of discrete sources. Compressed sensing is a lossless coding strategy for analog sources by means of multiplication by realvalued matrices. In this paper we study almost lossless analog compression for analog memoryless so ..."
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Cited by 42 (10 self)
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In Shannon theory, lossless source coding deals with the optimal compression of discrete sources. Compressed sensing is a lossless coding strategy for analog sources by means of multiplication by realvalued matrices. In this paper we study almost lossless analog compression for analog memoryless sources in an informationtheoretic framework, in which the compressor or decompressor is constrained by various regularity conditions, in particular linearity of the compressor and Lipschitz continuity of the decompressor. The fundamental limit is shown to be the information dimension proposed by Rényi in 1959.
The Control Of Chaos: Theory And Applications
 Physics Reports
, 2000
"... Control of chaos refers to a process wherein a tiny perturbation is applied to a chaotic system, in order to realize a desirable (chaotic, periodic, or stationary) behavior. We review the major ideas involved in the control of chaos, and present in detail two methods: the Ott}Grebogi}Yorke (OGY) met ..."
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Cited by 33 (3 self)
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Control of chaos refers to a process wherein a tiny perturbation is applied to a chaotic system, in order to realize a desirable (chaotic, periodic, or stationary) behavior. We review the major ideas involved in the control of chaos, and present in detail two methods: the Ott}Grebogi}Yorke (OGY) method and the adaptive method. We also discuss a series of relevant issues connected with chaos control, such as the targeting problem, i.e., how to bring a trajectory to a small neighborhood of a desired location in the chaotic attractor in both low and high dimensions, and point out applications for controlling fractal basin boundaries. In short, we describe procedures for stabilizing desired chaotic orbits embedded in a chaotic attractor and discuss the issues of communicating with chaos by controlling symbolic sequences and of synchronizing chaotic systems. Finally, we give a review of relevant experimental applications of these ideas and techniques. # 2000 Elsevier Science B.V. All rights...
T.: Gpubased nonlinear ray tracing
 Comput. Graph. Forum
"... In this paper, we present a mapping of nonlinear ray tracing to the GPU which avoids any data transfer back to main memory. The rendering process consists of the following parts: ray setup according to the camera parameters, ray integration, ray–object intersection, and local illumination. Bent rays ..."
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Cited by 31 (2 self)
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In this paper, we present a mapping of nonlinear ray tracing to the GPU which avoids any data transfer back to main memory. The rendering process consists of the following parts: ray setup according to the camera parameters, ray integration, ray–object intersection, and local illumination. Bent rays are approximated by polygonal lines that are represented by textures. Ray integration is based on an iterative numerical solution of ordinary differential equations whose initial values are determined during ray setup. To improve the rendering performance, we propose acceleration techniques such as early ray termination and adaptive ray integration. Finally, we discuss a variety of applications that range from the visualization of dynamical systems to the general relativistic visualization in astrophysics and the rendering of the continuous refraction in media with varying density. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Picture/Image Generation I.3.7 [Computer Graphics]: ThreeDimensional Graphics and Realism
Multiple attractors and resonance in periodically forced population
 Physica D
"... Oscillating discrete autonomous dynamical systems admit multiple oscillatory solutions in the advent of periodic forcing. The multiple cycles are out of phase, and some of their averages may resonate with the forcing amplitude while others attenuate. In application to population biology, populations ..."
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Cited by 31 (1 self)
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Oscillating discrete autonomous dynamical systems admit multiple oscillatory solutions in the advent of periodic forcing. The multiple cycles are out of phase, and some of their averages may resonate with the forcing amplitude while others attenuate. In application to population biology, populations with stable inherent oscillations in constant habitats are predicted to develop multiple attracting oscillatory final states in the presence of habitat periodicity. The average total population size may resonate or attenuate with the amplitude of the environmental fluctuation depending on the initial population size. The theory has been tested successfully in the laboratory by subjecting cultures of the flour beetle Tribolium to habitat periodicity
Detecting and Locating NearOptimal AlmostInvariant Sets and Cycles
"... The behaviours of trajectories of nonlinear dynamical systems are notoriously hard to characterise and predict. Rather than characterising dynamical behaviour at the level of trajectories, we consider following the evolution of sets. There are often collections of sets that behave in a very predicta ..."
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Cited by 31 (10 self)
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The behaviours of trajectories of nonlinear dynamical systems are notoriously hard to characterise and predict. Rather than characterising dynamical behaviour at the level of trajectories, we consider following the evolution of sets. There are often collections of sets that behave in a very predictable way, in spite of the fact that individual trajectories are entirely unpredictable. Such special collections of sets are invisible to studies of long trajectories. We describe a global setoriented method to detect and locate these large dynamical structures. Our approach is a marriage of new ideas in modern dynamical systems theory and the novel application of graph dissection algorithms.
Bifurcations in TwoDimensional Piecewise Smooth Maps  Theory and Applications in Switching Circuits
, 2000
"... Recent investigations on the bifurcation behavior of power electronic dcdc converters has revealed that most of the observed bifurcations do not belong to generic classes like saddlenode, period doubling or Hopf bifurcations. Since these systems yield piecewise smooth maps under stroboscopic sampl ..."
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Cited by 31 (9 self)
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Recent investigations on the bifurcation behavior of power electronic dcdc converters has revealed that most of the observed bifurcations do not belong to generic classes like saddlenode, period doubling or Hopf bifurcations. Since these systems yield piecewise smooth maps under stroboscopic sampling, a new class of bifurcations occur in such systems when a fixed point crosses the "border" between the smooth regions in the state space. In this paper we present a systematic analysis of such bifurcations by deriving a normal form  the piecewise linear approximation in the neighborhood of the border. We show that there can be many qualitatively different types of border collision bifurcations depending on the parameters of the normal form. We present a partitioning of the parameter space of the normal form showing the regions where different types of bifurcations occur. We then use this theoretical framework to explain the bifurcation behavior of the current programmed boost converte...