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150
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 285 (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 38 (7 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.
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 20 (1 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
Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics
 J. Comp. Neurosci
, 2003
"... Abstract. Behavior of a network of neurons is closely tied to the properties of the individual neurons. We study this relationship in models of layer II stellate cells (SCs) of the medial entorhinal cortex. SCs are thought to contribute to the mammalian theta rhythm (4–12 Hz), and are notable for th ..."
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Cited by 17 (5 self)
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Abstract. Behavior of a network of neurons is closely tied to the properties of the individual neurons. We study this relationship in models of layer II stellate cells (SCs) of the medial entorhinal cortex. SCs are thought to contribute to the mammalian theta rhythm (4–12 Hz), and are notable for the slow ionic conductances that constrain them to fire at rates within this frequency range. We apply “spike time response ” (STR) methods, in which the effects of synaptic perturbations on the timing of subsequent spikes are used to predict how these neurons may synchronize at theta frequencies. Predictions from STR methods are verified using network simulations. Slow conductances often make small inputs “effectively large”; we suggest that this is due to reduced attractiveness or stability of the spiking limit cycle. When inputs are (effectively) large, changes in firing times depend nonlinearly on synaptic strength. One consequence of nonlinearity is to make a periodically firing model skip one or more beats, often leading to the elimination of the antisynchronous state in bistable models. Biologically realistic membrane noise makes such “cycle skipping ” more prevalent, and thus can eradicate bistability. Membrane noise also supports “sparse synchrony, ” a phenomenon in which subthreshold behavior is uncorrelated, but there are brief periods of synchronous spiking.
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 17 (2 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...
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 17 (5 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...
An overview of semantics for the validation of numerical programs
, 2005
"... Abstract. In this article, we introduce a simple formal semantics for floatingpoint numbers with errors which is expressive enough to be formally compared to the other methods. Next, we define formal semantics for interval, stochastic, automatic differentiation and error series methods. This enable ..."
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Cited by 15 (5 self)
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Abstract. In this article, we introduce a simple formal semantics for floatingpoint numbers with errors which is expressive enough to be formally compared to the other methods. Next, we define formal semantics for interval, stochastic, automatic differentiation and error series methods. This enables us to formally compare the properties calculated in each semantics to our reference, simple semantics. Most of these methods having been developed to verify numerical intensive codes, we also discuss their adequacy to the formal validation of softwares and to static analysis. Finally, this study is completed by experimental results. 1
Border collision bifurcations in twodimensional piecewise smooth maps, Phys
 Rev. E
, 1999
"... Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps which can not be classified among the generic cases like saddlenode, pitchfork or Hopf bifurcations occurring in smooth maps. In this paper we first present ..."
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Cited by 12 (0 self)
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Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps which can not be classified among the generic cases like saddlenode, pitchfork or Hopf bifurcations occurring in smooth maps. In this paper we first present experimental results to establish the need for the development of a theoretical framework and classification of the bifurcations resulting from border collision. We then 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 eleven qualitatively different types of border collision bifurcations depending on the parameters of the normal form, and these are classified under six cases. We present a partitioning of the parameter space of the normal form showing the regions where different types of bifurcations occur. This theoretical framework will help in explaining bifurcations in all systems which can be represented by two dimensional piecewise smooth maps. 1
Semantics of roundoff error propagation in finite precision computations
 Journal of Higher Order and Symbolic Computation
, 2006
"... Abstract. We introduce a concrete semantics for floatingpoint operations which describes the propagation of roundoff errors throughout a calculation. This semantics is used to assert the correctness of a static analysis which can be straightforwardly derived from it. In our model, every elementary ..."
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Cited by 11 (6 self)
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Abstract. We introduce a concrete semantics for floatingpoint operations which describes the propagation of roundoff errors throughout a calculation. This semantics is used to assert the correctness of a static analysis which can be straightforwardly derived from it. In our model, every elementary operation introduces a new first order error term, which is later propagated and combined with other error terms, yielding higher order error terms. The semantics is parameterized by the maximal order of error to be examined and verifies whether higher order errors actually are negligible. We consider also coarser semantics computing the contribution, to the final error, of the errors due to some intermediate computations. As a result, we obtain a family of semantics and we show that the less precise ones are abstractions of the more precise ones.
Modeling Variation in Cooperative Coevolution Using Evolutionary Game Theory
"... Though coevolutionary algorithms are currently used for optimization purposes, practitioners are often plagued with difficulties due to the fact that such systems frequently behave in counter intuitive ways that are not well understood. This paper seeks to extend work which uses evolutionary game ..."
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Cited by 11 (3 self)
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Though coevolutionary algorithms are currently used for optimization purposes, practitioners are often plagued with difficulties due to the fact that such systems frequently behave in counter intuitive ways that are not well understood. This paper seeks to extend work which uses evolutionary game theory (EGT) as a form of dynamical systems modeling of coevolutionary algorithms in order to begin to answer questions regarding how these systems work. It does this by concentrating on a particular subclass of cooperative coevolutionary algorithms, for which multipopulation symmetric evolutionary game theoretic models are known to apply. We examine dynamical behaviors of this model in the context of static function optimization, by both formal analysis, as well as model validation study. Finally, we begin looking at the effects of variation by extending traditional EGT, offering some introductory analysis, as well as model validation. In the course of this study, we investigate the effects of parameterized uniform crossover and bitflip mutation.