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50
Path planning using Laplace’s equation
, 1990
"... A method for planning smooth robot paths is presented. The method relies on the use of Laplace’s Equation to constrain the generation of a potential function over regions of the configuration space of an effector. Once the function is computed, paths may be found very quickly. These functions do not ..."
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Cited by 132 (8 self)
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A method for planning smooth robot paths is presented. The method relies on the use of Laplace’s Equation to constrain the generation of a potential function over regions of the configuration space of an effector. Once the function is computed, paths may be found very quickly. These functions do not exhibit the local minima which plague the potential field method. Unlike decompositional and algebraic techniques, Laplace’s Equation is very well suited to computation on massively parallel architectures. 1
Range Estimation by Optical Differentiation
 JOURNAL OF THE OPTICAL SOCIETY OF AMERICA, 15(7):17771786
, 1988
"... We describe a novel formulation of the range recovery problem based on computation of the differential variation in image intensities with respect to changes in camera position. This method uses a single stationary camera and a pair of calibrated optical masks to directly measure this differential q ..."
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Cited by 41 (0 self)
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We describe a novel formulation of the range recovery problem based on computation of the differential variation in image intensities with respect to changes in camera position. This method uses a single stationary camera and a pair of calibrated optical masks to directly measure this differential quantity. We also describe a variant based on changes in aperture size. The subsequent computation of the range image involves simple arithmetic operations, and is suitable for realtime implementation. We present the theory of this technique and show results from a prototype camera which we have constructed.
Maximizing network lifetime of broadcasting over wireless stationary ad hoc networks
 Mobile Networks and Applications (MONET), Special Issue on Energy Constraints and Lifetime Performance in Wireless Sensor Networks
, 2005
"... Abstract — We investigate the problem of energyefficient broadcast routing over stationary wireless adhoc networks where the host is not mobile. We define the lifetime of a network as the duration of time from the network initialization until the first node failure due to the battery exhaustion. We ..."
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Cited by 22 (0 self)
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Abstract — We investigate the problem of energyefficient broadcast routing over stationary wireless adhoc networks where the host is not mobile. We define the lifetime of a network as the duration of time from the network initialization until the first node failure due to the battery exhaustion. We provide a globally optimal solution to the problem of maximizing a static network lifetime through a graph theoretic approach. We make use of this solution to develop a periodic tree update strategy for dynamic load balancing and show that a significant gain in network lifetime can be achieved. We also provide extensive comparative simulation studies on parameters that affect the lifetime of a network. I.
Harmonic functions and collision probabilities
 in Proceedings of the IEEE International Conference on Robotics and Automation
, 1994
"... There is a close relationship between harmonic functions— which have recently been proposed for path planning—and hitting probabilities for random processes. The hitting probabilities for random walks can be cast as a Dirichlet problem for harmonic functions, in much the same wa ..."
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Cited by 21 (2 self)
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There is a close relationship between harmonic functions&mdash; which have recently been proposed for path planning&mdash;and hitting probabilities for random processes. The hitting probabilities for random walks can be cast as a Dirichlet problem for harmonic functions, in much the same way as in path planning. This equivalence has implications both for uncertainty in motion planning and in the application of machinelearning techniques to some robot problems. In particular, Erdmann’s method can directly incorporate such hitting probabilities. In addition, the value functions obtained by reinforcement learning algorithms can be rapidly reconstructed by relaxation or resistive networks, once the extrema for such functions are known. 1.
Population Markov Chain Monte Carlo
 Machine Learning
, 2003
"... Stochastic search algorithms inspired by physical and biological systems are applied to the problem of learning directed graphical probability models in the presence of missing observations and hidden variables. For this class of problems, deterministic search algorithms tend to halt at local optima ..."
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Cited by 15 (2 self)
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Stochastic search algorithms inspired by physical and biological systems are applied to the problem of learning directed graphical probability models in the presence of missing observations and hidden variables. For this class of problems, deterministic search algorithms tend to halt at local optima, requiring random restarts to obtain solutions of acceptable quality. We compare three stochastic search algorithms: a MetropolisHastings Sampler (MHS), an Evolutionary Algorithm (EA), and a new hybrid algorithm called Population Markov Chain Monte Carlo, or popMCMC. PopMCMC uses statistical information from a population of MHSs to inform the proposal distributions for individual samplers in the population. Experimental results show that popMCMC and EAs learn more efficiently than the MHS with no information exchange. Populations of MCMC samplers exhibit more diversity than populations evolving according to EAs not satisfying physicsinspired local reversibility conditions. KEY WORDS: Markov Chain Monte Carlo, MetropolisHastings Algorithm, Graphical Probabilistic Models, Bayesian Networks, Bayesian Learning, Evolutionary Algorithms Machine Learning MCMC Issue 1 5/16/01 1.
2007): “Nonparametric matching and efficient estimators of homothetically separable functions
 Econometrica
"... For vectors x and w, letr(x, w) be a function that can be nonparametrically estimated consistently and asymptotically normally. We provide consistent, asymptotically normal estimators for the functions g and h, where r(x, w) =h[g(x),w], g is linearly homogeneous and h is monotonic in g. This framewo ..."
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Cited by 10 (4 self)
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For vectors x and w, letr(x, w) be a function that can be nonparametrically estimated consistently and asymptotically normally. We provide consistent, asymptotically normal estimators for the functions g and h, where r(x, w) =h[g(x),w], g is linearly homogeneous and h is monotonic in g. This framework encompasses homothetic and homothetically separable functions. Such models reduce the curse of dimensionality, provide a natural generalization of linear index models, and are widely used in utility, production, and cost function applications. One of our estimator’s of g is oracle efficient, achieving the same performance as an estimator based on local least squares knowing h. We provide simulation evidence on the small sample performance of our estimators, and an empirical production function application.
An Alternative Approach to the Gaussian Noise Model and its System Implications
 J. Lightw. Technol
, 2013
"... Abstract—This paper presents an alternative derivation of the Gaussian noise (GN) model of the nonlinear interference (NLI) in strongly dispersive optical systems. The basic idea is to exploit an enhanced regular perturbation expansion of the NLI, which highlights several interesting features of the ..."
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Cited by 6 (3 self)
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Abstract—This paper presents an alternative derivation of the Gaussian noise (GN) model of the nonlinear interference (NLI) in strongly dispersive optical systems. The basic idea is to exploit an enhanced regular perturbation expansion of the NLI, which highlights several interesting features of the GN model. Using the framework, we derive a fast algorithm to evaluate the received NLI power spectral density (PSD) for any input PSD. In the paper we also provide an asymptotic expression of the NLI PSD which further speeds up the computation without losing significant accuracy. Moreover, we show how the asymptotic expression can be used to optimize system performance. For instance, we are able to prove why a flat spectrum is best to minimize the NLI variance when the input is constrained to a fixed bandwidth and power. Finally, we also provide a generalization of the NLI GN model to arbitrarily correlated X and Y polarizations. Index Terms—Gaussian Noise (GN) model, perturbation methods.
Intercalation Dynamics in LithiumIon Batteries
, 2009
"... A new continuum model has been proposed by Singh, Ceder, and Bazant for the ion intercalation dynamics in a single crystal of rechargeablebattery electrode materials. It is based on the CahnHilliard equation coupled to reaction rate laws as boundary conditions to handle the transfer of ions betwe ..."
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Cited by 5 (0 self)
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A new continuum model has been proposed by Singh, Ceder, and Bazant for the ion intercalation dynamics in a single crystal of rechargeablebattery electrode materials. It is based on the CahnHilliard equation coupled to reaction rate laws as boundary conditions to handle the transfer of ions between the crystal and the electrolyte. In this thesis, I carefully derive a second set of boundary conditions—necessary to close the original PDE system—via a variational analysis of the free energy functional; I include a thermodynamicallyconsistent treatment of the reaction rates; I develop a semidiscrete finite volume method for numerical simulations; and I include a careful asymptotic treatment of the dynamical regimes found in different limits of the governing equations. Further, I will present several new findings
Image simplification and vectorization
 In Proceedings of the 9th International Symposium on NonPhotorealistic Animation and Rendering (NPAR
"... We present an unsupervised system which takes digital photographs as input, and generates simplified, stylized vector data as output. The three component parts of our system are imagespace stylization, edge tracing, and edgebased image reconstruction. The design of each of these components is spec ..."
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Cited by 4 (0 self)
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We present an unsupervised system which takes digital photographs as input, and generates simplified, stylized vector data as output. The three component parts of our system are imagespace stylization, edge tracing, and edgebased image reconstruction. The design of each of these components is specialized, relative to their state of the art equivalents, in order to improve their effectiveness when used in such a combined stylization / vectorization pipeline. We demonstrate that the vector data generated by our system is often both an effective visual simplification of the input photographs, and an effective simplification in the sense of memory efficiency, as judged relative to state of the art lossy image compression formats.