We survey conditions for rapid mixing of certain Markov chains, called Gibbs samplers, and uniqueness of certain probability measures with prescribed finite dimensional conditional distributions, called Gibbs measures...
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ISBN:
(纸本)9781604237924
We survey conditions for rapid mixing of certain Markov chains, called Gibbs samplers, and uniqueness of certain probability measures with prescribed finite dimensional conditional distributions, called Gibbs measures. By Tatikonda and Jordan's [1] sufficiency result, these criteria translate into conditions for convergence of the Sum-Product algorithm. The basic idea, which goes back to Dobrushin [2], is to show that the transition kernels (in the Gibbs sampler case) or the prescribed conditional distributions (in the Gibbs measure case) act as contractions on spaces of functions or measures, provided they are weakly influenced by neighboring sites. The contributions of this paper are as follows: We compare various notions of influence, unifying notation and terminology currently scattered across a large body of literature. We survey, generalize and extend existing proof techniques which fall in three broad categories: analytic arguments, coupling arguments, and arguments using path coupling. In particular, we extend all arguments from single sites to finite blocks and from total variation to Wasserstein distance;we introduce new matrix methods;we answer an open question by Weitz [3];and we provide evidence to support the superiority of path coupling, addressing a question raised by Sokal [4] regarding the dual relationship of analytic and coupling techniques.
Fully Polarimetric radar systems are capable of simultaneously transmitting and receiving in two orthogonal polarizations. Instantaneous radar polarimetry exploits both polarization modes of a dually-polarized radar t...
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ISBN:
(纸本)1424407850
Fully Polarimetric radar systems are capable of simultaneously transmitting and receiving in two orthogonal polarizations. Instantaneous radar polarimetry exploits both polarization modes of a dually-polarized radar transmitter and receiver on a pulse by pulse basis, and can improve the radar detection performance and suppress range sidelobes. In this paper, we extend the use of instantaneous radar polarimetry for radar systems with multiple dually-polarized transmit and receive antennas. Alamouti signal processing is used to coordinate transmission of Golay pairs of phase codes waveforms across polarizations and multiple antennas. The integration of multi-antenna signal processing with instantaneous radar polarimetry can further improve the detection performance, at a computational cost comparable to single channel matched filtering.
We provide a new way of understanding Golay pairs (of length N) of sequences in terms of the (2N + 1)-dimensional discrete Heisenberg-Weyl group over the field Z2. Our methodology provides a different insight into the...
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We present an equation-free computational approach to the study of the coarse-grained dynamics of finite assemblies of nonidentical coupled oscillators at and near full synchronization. We use coarse-grained observabl...
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We present an equation-free computational approach to the study of the coarse-grained dynamics of finite assemblies of nonidentical coupled oscillators at and near full synchronization. We use coarse-grained observables which account for the (rapidly developing) correlations between phase angles and natural frequencies. Exploiting short bursts of appropriately initialized detailed simulations, we circumvent the derivation of closures for the long-term dynamics of the assembly statistics.
This paper presents domain decomposition (DD) technique for efficient simulation of large-scale linear circuits such as power distribution networks. Simulation results show that by integrating the proposed DD framewor...
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ISBN:
(纸本)9783981080100
This paper presents domain decomposition (DD) technique for efficient simulation of large-scale linear circuits such as power distribution networks. Simulation results show that by integrating the proposed DD framework, existing linear circuit simulators can be extended to handle otherwise intractable systems
Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implement...
Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implementation of this approach provides a means for constructing effective free-energy landscapes of structural transitions in condensed matter. The predictions of the approach for the thermodynamic melting point of a model silicon system are in excellent agreement with those of “traditional” techniques for melting-point calculations, as well as with literature values.
In this paper, we describe how an active radar/sonar imaging problem may be formulated as a virtual passive sensor array processing problem. We consider an active sensing problem where it is desired to form a range-Do...
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In this paper, we describe how an active radar/sonar imaging problem may be formulated as a virtual passive sensor array processing problem. We consider an active sensing problem where it is desired to form a range-Doppler image at a slow- time rate, even though the radar/sonar can transmit pulses at a fast time rate. By transmitting pulses at the fast time rate we can estimate the second-order statistics of an ambiguity vector, calculated at a coarse resolution. As we show this ambiguity vector plays the role of an array snapshot vector in passive sensor array processing. The noise free version of this ambiguity vector acts as a signature vector or steering vector, which can be steered around in delay and Doppler at a fine resolution to produce an image. We employ a MVDR-like principle to generate high resolution delay-Doppler images.
Fully polarimetric radar systems are capable of simultaneously transmitting and receiving in two orthogonal polarizations. Instantaneous radar polarimetry exploits both polarization modes of a dually-polarized radar t...
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Fully polarimetric radar systems are capable of simultaneously transmitting and receiving in two orthogonal polarizations. Instantaneous radar polarimetry exploits both polarization modes of a dually-polarized radar transmitter and receiver on a pulse by pulse basis, and can improve the radar detection performance and suppress range sidelobes . In this paper, we extend the use of instantaneous radar polarimetry for radar systems with multiple dually-polarized transmit and receive antennas. Alamouti signal processing is used to coordinate transmission of Golay pairs of phase codes waveforms across polarizations and multiple antennas. The integration of multi- antenna signal processing with instantaneous radar polarimetry can further improve the detection performance, at a computational cost comparable to single channel matched filtering.
In this paper we study convergence of the max-product (MP) algorithm on general graphs with cycles. Our analysis follows analogously to that given for the convergence of the sum-product algorithm. We do not work with ...
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ISBN:
(纸本)142440505X
In this paper we study convergence of the max-product (MP) algorithm on general graphs with cycles. Our analysis follows analogously to that given for the convergence of the sum-product algorithm. We do not work with Gibbs measures but instead we introduce and work with local maxifiers. The contributions of this paper include: reformulation of the MP algorithm on cyclic graphs as max-marginalization on an associated computation tree; existence of local maxifiers and proof that uniqueness of the local maxifier is sufficient for convergence of MP; a Gibbsian theory of local maxifiers and interpretation as operators; an example of non-uniqueness which does not exhibit a phase transition like its Gibbs measure counterpart; and insights into the limitations of Dobrushin-type uniqueness conditions
Legged robots can, in principle, traverse a large variety of obstacles and terrains. In this paper, we describe a successful application of reinforcement learning to the problem of negotiating obstacles with a quadrup...
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Legged robots can, in principle, traverse a large variety of obstacles and terrains. In this paper, we describe a successful application of reinforcement learning to the problem of negotiating obstacles with a quadruped robot. Our algorithm is based on a two-level hierarchical decomposition of the task, in which the high-level controller selects the sequence of foot-placement positions, and the low-level controller generates the continuous motions to move each foot to the specified positions. The high-level controller uses an estimate of the value function to guide its search; this estimate is learned partially from supervised data. The low-level controller is obtained via policy search. We demonstrate that our robot can successfully climb over a variety of obstacles which were not seen at training time
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