Optical metasurfaces (subwavelength-patterned surfaces typically described by variable effective surface impedances) are typically modeled by an approximation akin to ray optics: the reflection or transmission of an i...
In this paper, we develop a stochastic algorithm based on the Euler–Maruyama scheme to approximate the invariant measure of the limiting multidimensional diffusion of G/P h/n + GI queues in the Halfin-Whitt regime. S...
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One of the leading approaches to collaborative filtering is to use matrix factorization to discover a set of latent factors that explain the pattern of preferences. In this paper, we apply a resilient stochastic gradi...
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One of the leading approaches to collaborative filtering is to use matrix factorization to discover a set of latent factors that explain the pattern of preferences. In this paper, we apply a resilient stochastic gradient descent approach that uses only the sign of the gradient, similar to the R-Prop algorithm in neural network training, to matrix factorization for collaborative filtering. We evaluate the performance of our approach on the MovieLens 1M dataset, and find that test set accuracy markedly improves compared to standard gradient descent. As a follow-up experiment, we apply clustering to the learned item-factor matrix in factor space, and attempt to manually characterize each cluster of movies.
Given a closed linear relation T between two Hilbert spaces H and K, the corresponding first and second coordinate projections PT and QT are both linear contractions from T to H, and to K, respectively. In this paper ...
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The correlated electron momentum distribution for nonsequential double ionization (NSDI) of Ne in a strong linearly polarized laser field is studied by quantum S-matrix and semiclassical theories. At low intensity, wh...
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The correlated electron momentum distribution for nonsequential double ionization (NSDI) of Ne in a strong linearly polarized laser field is studied by quantum S-matrix and semiclassical theories. At low intensity, where the single-return-collision NSDI process dominates, a good agreement between two theories is found. However, at high intensity, two theories are inconsistent with each other, and the semiclassical calculation is qualitatively in agreement with the experimental observation. Our analysis shows that this can be attributed to the neglect of the ion potential in the present S-matrix theory, and hence the multiple-return-collision NSDI process, which becomes important at high intensity, is underestimated in the current S-matrix theory.
We investigate the theory of the finite discrete Heisenberg-Weyl group in relation to the development of adaptive radar. We contend that this group can form the basis for the representation of the radar environment in...
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We investigate the theory of the finite discrete Heisenberg-Weyl group in relation to the development of adaptive radar. We contend that this group can form the basis for the representation of the radar environment in terms of operators on the space of waveforms. We also demonstrate, following recent developments in the theory of error correcting codes, that the finite discrete Heisenberg-Weyl group provides a unified basis for the construction of useful waveforms/sequences for radar, communications and the theory of error correcting codes.
It is known that Hall’s sextic residue sequence has some desirable features of pseudorandomness: an ideal two-level autocorrelation and linear complexity of the order of magnitude of its period p. Here we study its c...
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We introduce a high-order weight-adjusted discontinuous Galerkin (WADG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in anisotropic porous media. We use a coupled first-order s...
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In this paper we review and derive hyperbolic and trigonometric double summation addition theorems for Jacobi functions of the first and second kind. In connection with these addition theorems, we perform a full analy...
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