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343
A neuropsychological theory of multiple systems in category learning
 PSYCHOLOGICAL REVIEW
, 1998
"... A neuropsychological theory is proposed that assumes category learning is a competition between separate verbal and implicit (i.e., procedurallearningbased) categorization systems. The theory assumes that the caudate nucleus is an important component of the implicit system and that the anterior ci ..."
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Cited by 229 (24 self)
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A neuropsychological theory is proposed that assumes category learning is a competition between separate verbal and implicit (i.e., procedurallearningbased) categorization systems. The theory assumes that the caudate nucleus is an important component of the implicit system and that the anterior cingulate and prefrontal cortices are critical to the verbal system. In addition to making predictions for normal human adults, the theory makes specific predictions for children, elderly people, and patients suffering from Parkinson's disease, Huntington's disease, major depression, amnesia, or lesions of the prefrontal cortex. Two separate formal descriptions of the theory are also provided. One describes trialbytrial learning, and the other describes global dynamics. The theory is tested on published neuropsychological data and on category learning data with normal adults.
Sparse signal reconstruction from limited data using FOCUSS: A reweighted minimum norm algorithm
 IEEE Trans. Signal Processing
, 1997
"... Abstract—We present a nonparametric algorithm for finding localized energy solutions from limited data. The problem we address is underdetermined, and no prior knowledge of the shape of the region on which the solution is nonzero is assumed. Termed the FOcal Underdetermined System Solver (FOCUSS), t ..."
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Cited by 218 (12 self)
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Abstract—We present a nonparametric algorithm for finding localized energy solutions from limited data. The problem we address is underdetermined, and no prior knowledge of the shape of the region on which the solution is nonzero is assumed. Termed the FOcal Underdetermined System Solver (FOCUSS), the algorithm has two integral parts: a lowresolution initial estimate of the real signal and the iteration process that refines the initial estimate to the final localized energy solution. The iterations are based on weighted norm minimization of the dependent variable with the weights being a function of the preceding iterative solutions. The algorithm is presented as a general estimation tool usable across different applications. A detailed analysis laying the theoretical foundation for the algorithm is given and includes proofs of global and local convergence and a derivation of the rate of convergence. A view of the algorithm as a novel optimization method which combines desirable characteristics of both classical optimization and learningbased algorithms is provided. Mathematical results on conditions for uniqueness of sparse solutions are also given. Applications of the algorithm are illustrated on problems in directionofarrival (DOA) estimation and neuromagnetic imaging. I.
Interaction and Intelligent Behavior
, 1994
"... This thesis addresses situated, embodied agents interacting in complex domains. It focuses on two problems: 1) synthesis and analysis of intelligent group behavior, and 2) learning in complex group environments. Basic behaviors, control laws that cluster constraints to achieve particular goals and h ..."
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Cited by 146 (20 self)
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This thesis addresses situated, embodied agents interacting in complex domains. It focuses on two problems: 1) synthesis and analysis of intelligent group behavior, and 2) learning in complex group environments. Basic behaviors, control laws that cluster constraints to achieve particular goals and have the appropriate compositional properties, are proposed as effective primitives for control and learning. The thesis describes the process of selecting such basic behaviors, formally specifying them, algorithmically implementing them, and empirically evaluating them. All of the proposed ideas are validated with a group of up to 20 mobile robots using a basic behavior set consisting of: safewandering, following, aggregation, dispersion, and homing. The set of basic behaviors acts as a substrate for achieving more complex highlevel goals and tasks. Two behavior combination operators are introduced, and verified by combining subsets of the above basic behavior set to implement collective flocking, foraging, and docking. A methodology is introduced for automatically constructing higherlevel behaviors
Issues and Approaches in Design of Collective Autonomous Agents
 Robotics and Autonomous Systems
, 1994
"... The problem of synthesizing and analyzing collective autonomous agents has only recently begun to be practically studied by the robotics community. This paper overviews the most prominent directions of research, defines key terms, and summarizes the main issues. Finally, it briefly describes our app ..."
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Cited by 123 (14 self)
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The problem of synthesizing and analyzing collective autonomous agents has only recently begun to be practically studied by the robotics community. This paper overviews the most prominent directions of research, defines key terms, and summarizes the main issues. Finally, it briefly describes our approach to controlling group behavior and its relation to the field as a whole.
The LifeSpan of Backward Error Analysis for Numerical Integrators
 Numer. Math
, 1996
"... this article we study the influence of this truncation to the difference between the numerical solution and the exact solution of the perturbed differential equation. Results on the longtime behaviour of numerical solutions are obtained in this way. We present applications to the numerical phase po ..."
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Cited by 61 (3 self)
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this article we study the influence of this truncation to the difference between the numerical solution and the exact solution of the perturbed differential equation. Results on the longtime behaviour of numerical solutions are obtained in this way. We present applications to the numerical phase portrait near hyperbolic equilibrium points, to asymptotically stable periodic orbits and Hopf bifurcation, and to energy conservation and approximation of invariant tori in Hamiltonian systems.
Sequential Behavior and Learning in Evolved Dynamical Neural Networks
, 1994
"... This paper explores the use of a realvalued modular genetic algorithm to evolve continuoustime recurrent neural networks capable of sequential behavior and learning. We evolve networks that can generate a fixed sequence of outputs in response to an external trigger occurring at varying intervals o ..."
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Cited by 52 (3 self)
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This paper explores the use of a realvalued modular genetic algorithm to evolve continuoustime recurrent neural networks capable of sequential behavior and learning. We evolve networks that can generate a fixed sequence of outputs in response to an external trigger occurring at varying intervals of time. We also evolve networks that can learn to generate one of a set of possible sequences based upon reinforcement from the environment. Finally, we utilize concepts from dynamical systems theory to understand the operation of some of these evolved networks. A novel feature of our approach is that we assume neither an a priori discretization of states or time nor an a priori learning algorithm that explicitly modifies network parameters during learning. Rather, we merely expose dynamical neural networks to tasks that require sequential behavior and learning and allow the genetic algorithm to evolve network dynamics capable of accomplishing these tasks. 2 1. Introduction Much of the rec...
Extracting macroscopic dynamics: model problems and algorithms
 NONLINEARITY
, 2004
"... In many applications, the primary objective of numerical simulation of timeevolving systems is the prediction of macroscopic, or coarsegrained, quantities. A representative example is the prediction of biomolecular conformations from molecular dynamics. In recent years a number of new algorithmic ..."
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Cited by 48 (8 self)
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In many applications, the primary objective of numerical simulation of timeevolving systems is the prediction of macroscopic, or coarsegrained, quantities. A representative example is the prediction of biomolecular conformations from molecular dynamics. In recent years a number of new algorithmic approaches have been introduced to extract effective, lowerdimensional, models for the macroscopic dynamics; the starting point is the full, detailed, evolution equations. In many cases the effective lowdimensional dynamics may be stochastic, even when the original starting point is deterministic. This review surveys a number of these new approaches to the problem of extracting effective dynamics, highlighting similarities and differences between them. The importance of model problems for the evaluation of these new approaches is stressed, and a number of model problems are described. When the macroscopic dynamics is stochastic, these model problems are either obtained through a clear separation of timescales, leading to a stochastic effect of the fast dynamics on the slow dynamics, or by considering high dimensional ordinary differential equations which, when projected onto a low dimensional subspace, exhibit stochastic behaviour through the presence of a broad frequency spectrum. Models whose stochastic microscopic behaviour leads to deterministic macroscopic dynamics are also introduced. The algorithms we overview include SVDbased methods for nonlinear problems, model reduction for linear control systems, optimal prediction techniques, asymptoticsbased mode elimination, coarse timestepping methods and transferoperator based methodologies.
Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics
, 2000
"... This paper applies dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted threebody problem. These related phenomena have been of concern for some time in topics such as the capture of comets and asteroids and with the des ..."
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Cited by 45 (19 self)
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This paper applies dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted threebody problem. These related phenomena have been of concern for some time in topics such as the capture of comets and asteroids and with the design of trajectories for space missions such as the Genesis Discovery Mission. The main new technical result in this paper is the numerical demonstration of the existence of a heteroclinic connection between pairs of periodic orbits, one around the libration point L1 and the other around L2, withthe two periodic orbits having the same energy. This result is applied to the resonance transition problem and to the explicit numerical construction of interesting orbits with prescribed itineraries. The point of view developed in this paper is that the invariant manifold structures associated to L1 and L2 as well as the aforementioned heteroclinic connection are fundamental tools that can aid in understanding dynamical channels throughout the solar system as well as transport between the “interior ” and “exterior”
Complex Behavior of Switching Power Converters
 PROC. IEEE
, 2002
"... Power electronics circuits are rich in nonlinear dynamics. Their operation is characterized by cyclic switching of circuit topologies, which gives rise to a variety of nonlinear behavior. This paper provides an overview of the chaotic dynamics and bifurcation scenarios observed in power converter ci ..."
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Cited by 33 (21 self)
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Power electronics circuits are rich in nonlinear dynamics. Their operation is characterized by cyclic switching of circuit topologies, which gives rise to a variety of nonlinear behavior. This paper provides an overview of the chaotic dynamics and bifurcation scenarios observed in power converter circuits, emphasizing the salient features of the circuit operation and the modeling strategies. In particular, this paper surveys the key publications in this field, reviews the main modeling approaches, and discusses the salient bifurcation behaviors of power converters with particular emphasis on the disruption of standard bifurcation patterns by border collisions.