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1,902
NonStandard Phase Space Variables, Quantization, and Path Integrals, or Little Ado about Much
, 1993
"... In this article we want to describe a longterm research project that the authors plan to carry out over a period in the immediate future. We would like to outline the basic ideas of the project and give a few preliminary calculations the bear on the validity of our ideas as well as some speculation ..."
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In this article we want to describe a longterm research project that the authors plan to carry out over a period in the immediate future. We would like to outline the basic ideas of the project and give a few preliminary calculations the bear on the validity of our ideas as well as some speculations on where the research will lead. We
Leptons, quarks, and their antiparticles: a phasespace view
, 2009
"... Recently, a correspondence has been shown to exist between the structure of a single Standard Model generation of elementary particles and the properties of the Clifford algebra of nonrelativistic phase space. Here, this correspondence is spelled out in terms of phasespace variables. Thus, a phase ..."
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Recently, a correspondence has been shown to exist between the structure of a single Standard Model generation of elementary particles and the properties of the Clifford algebra of nonrelativistic phase space. Here, this correspondence is spelled out in terms of phasespace variables. Thus, a phasespace
Impulses and Physiological States in Theoretical Models of Nerve Membrane
 Biophysical Journal
, 1961
"... ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of nonlinear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing excitabi ..."
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Cited by 505 (0 self)
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the 4dimensional HH phase space onto a plane produces a similar diagram which shows the underlying relationship between the two models. Impulse trains occur in the BVP and HH models for a range of constant applied currents which make the singular point representing the resting state unstable.
Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging
 MAGNETIC RESONANCE IN MEDICINE 58:1182–1195
, 2007
"... The sparsity which is implicit in MR images is exploited to significantly undersample kspace. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain–for example, in terms of spatial finit ..."
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Cited by 538 (11 self)
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undersampling schemes are developed and analyzed by means of their aliasing interference. Incoherence is introduced by pseudorandom variabledensity undersampling of phaseencodes. The reconstruction is performed by minimizing the ℓ1 norm of a transformed image, subject to data fidelity constraints. Examples
PhaseSpace Structure in Plasma Turbulence
"... Plasma turbulence driven by the ion temperature gradient (ITG) is theoretically studied with highresolution Eulerian kinetic simulations. A spectral analysis of the velocity distribution function in the slab ITG turbulence clarifies how the entropy variable associated with the finescale structure ..."
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of the distribution function is produced by the turbulent heat transport in the presence of the temperature gradient, transferred from macro to microscales in the velocity space through phasemixing processes, and dissipated by collisions. The entropy spectral function is analytically derived and confirmed
A combined discontinuous Galerkin and finite volume scheme for multidimensional VPFP system
 Proceedings of 27th RGD
, 2010
"... Abstract. We construct a numerical scheme for the multidimensional VlasovPoissonFokkerPlanck system based on a combined finite volume (FV) method for the Poisson equation in spatial domain and the streamline diffusion (SD) and discontinuous Galerkin (DG) finite element in time, phasespace varia ..."
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Cited by 1 (1 self)
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Abstract. We construct a numerical scheme for the multidimensional VlasovPoissonFokkerPlanck system based on a combined finite volume (FV) method for the Poisson equation in spatial domain and the streamline diffusion (SD) and discontinuous Galerkin (DG) finite element in time, phasespace
GTM: The generative topographic mapping
 Neural Computation
, 1998
"... Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis which is based on a linear transformations between the latent space and the data space. In this paper ..."
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Cited by 361 (6 self)
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Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis which is based on a linear transformations between the latent space and the data space. In this paper
Phasespace approach to Berry’s phases
, 2004
"... We propose a new formula for the adiabatic Berry phase which is based on phasespace formulation of quantum mechanics. This approach sheds a new light into the correspondence between classical and quantum adiabatic phases — both phases are related with the averaging procedure: Hannay’s angle with av ..."
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We propose a new formula for the adiabatic Berry phase which is based on phasespace formulation of quantum mechanics. This approach sheds a new light into the correspondence between classical and quantum adiabatic phases — both phases are related with the averaging procedure: Hannay’s angle
A qDeformation of the Harmonic Oscillator
 Z. Phys. C
, 1997
"... The qdeformed harmonic oscillator is studied in the light of qdeformed phase space variables. This allows a formulation of the corresponding Hamiltonian in terms of the ordinary canonical variables x and p. The spectrum shows unexpected features such as degeneracy and an additional part that canno ..."
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Cited by 9 (1 self)
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The qdeformed harmonic oscillator is studied in the light of qdeformed phase space variables. This allows a formulation of the corresponding Hamiltonian in terms of the ordinary canonical variables x and p. The spectrum shows unexpected features such as degeneracy and an additional part
Reduced phasespace quantization of constrained systems
, 2008
"... The HamiltonJacobi method of constrained systems is discussed. The equations of motion for three singular systems are obtained as total differential equations in many variables. The integrability conditions for these systems lead us to obtain the canonical reduced phase space coordinates with out u ..."
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The HamiltonJacobi method of constrained systems is discussed. The equations of motion for three singular systems are obtained as total differential equations in many variables. The integrability conditions for these systems lead us to obtain the canonical reduced phase space coordinates with out
Results 1  10
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1,902