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Discrete solitons and vortices on anisotropic lattices
The two-dimensional nonlinear lattice discrete nonlinear schrodinger equation the vortex solitons
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2014/12/25
We consider the effects of anisotropy on solitons of various types in two-dimensional nonlinear lattices, using the discrete nonlinear Schrödinger equation as a paradigm model. For fundamental so...
From Feshbach-resonance managed Bose-Einstein condensates to anisotropic universes: Applications of the Ermakov-Pinney equation with time-dependent nonlinearity
Two-dimensional condensate time-varying magnetic confinement scattering wave function ordinary differential equations
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2014/12/25
In this work we revisit the topic of two-dimensional Bose–Einstein condensates under the influence of time-dependent magnetic confinement and time-dependent scattering length. A moment approach reduce...
Anisotropic oracle inequalities in noisy quantization
Quantization Deconvolution Fast rates Margin assumption,k-means clus-tering
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2013/6/13
The effect of errors in variables in quantization is investigated. We prove general exact and non-exact oracle inequalities with fast rates for an empirical minimization based on a noisy sample $Z_i=X...
Aggregation of autoregressive random fields and anisotropic long memory
Aggregation autoregressive random fields anisotropic long memory
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2013/4/27
We introduce the notion of anisotropic long memory for random fields on $\mathbb{Z}^2$ whose partial sums on incommensurate rectangles with sides growing at different rates O(n) and $O(n^{H_1/H_2})$, ...
A Directional Gradient-Curvature Method for Gap Filling of Gridded Environmental Spatial Data with Potentially Anisotropic Correlations
correlation anisotropy spatial interpolation stochastic estimation optimization simulation
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2013/4/27
We introduce the Directional Gradient-Curvature (DGC) method, a novel approach for filling gaps in gridded environmental data. DGC is based on an objective function that measures the distance between ...
Polar sets of anisotropic Gaussian random fields
Anisotropic Gaussian fields Hitting probabilities Polar sets Hausdorff dimension European option Jump diffusion Calibration
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2012/9/18
This paper studies polar sets of anisotropic Gaussian random fields,i.e. sets which a Gaussian random field does not hit almost surely. The main assumptions are that the eigenvalues of the covariance ...
Reconstruction from anisotropic random measurements
Reconstruction anisotropic random measurements
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2011/7/5
Random matrices are widely used in sparse recovery problems, and the relevant properties of matrices with i.i.d. entries are well understood.
On the fractional anisotropic Wiener field
the fractional anisotropic Wiener field the local properties
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2009/9/22
In this paper we study the local properties of
the fractional anisotropic Wiener field {~("(t): i E Rd}, where
a = (a,, . . . , a,), 0 < a, < 2. It is proved that, with probability 1, the
realizati...