Lateral diffusive spin transport in layered structures

A one dimensional theory of lateral spin-polarized transport is derived from the two dimensional flow in the vertical cross section of a stack of ferromagnetic and paramagnetic layers. This takes into account the influence of the lead on the lateral current underneath, in contrast to the conventional 1D modeling by the collinear configuration of lead/channel/lead. Our theory is convenient and appropriate for the current in plane configuration of an all-metallic spintronics structure as well as for the planar structure of a semiconductor with ferromagnetic contacts. For both systems we predict the optimal contact width for maximal magnetoresistance and propose an electrical measurement of the spin diffusion length for a wide range of materials.Comment: 4 pages, 3 figure

A Spectral Algorithm for Latent Dirichlet Allocation

The problem of topic modeling can be seen as a generalization of the clustering problem, in that it posits that observations are generated due to multiple latent factors (e.g., the words in each document are generated as a mixture of several active topics, as opposed to just one). This increased representational power comes at the cost of a more challenging unsupervised learning problem of estimating the topic probability vectors (the distributions over words for each topic), when only the words are observed and the corresponding topics are hidden. We provide a simple and efficient learning procedure that is guaranteed to recover the parameters for a wide class of mixture models, including the popular latent Dirichlet allocation (LDA) model. For LDA, the procedure correctly recovers both the topic probability vectors and the prior over the topics, using only trigram statistics (i.e., third order moments, which may be estimated with documents containing just three words). The method, termed Excess Correlation Analysis (ECA), is based on a spectral decomposition of low order moments (third and fourth order) via two singular value decompositions (SVDs). Moreover, the algorithm is scalable since the SVD operations are carried out on $k\times k$ matrices, where $k$ is the number of latent factors (e.g. the number of topics), rather than in the $d$-dimensional observed space (typically $d \gg k$).Comment: Changed title to match conference version, which appears in Advances in Neural Information Processing Systems 25, 201

A Risk Comparison of Ordinary Least Squares vs Ridge Regression

We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that the risk of this ordinary least squares method is within a constant factor (namely 4) of the risk of ridge regression.Comment: Appearing in JMLR 14, June 201

Radial oscillations and stability of compact stars in Eddington-inspired Born-Infeld gravity

We study the hydrostatic equilibrium structure of compact stars in the Eddington-inspired Born-Infeld gravity recently proposed by Banados and Ferreira [Phys. Rev. Lett. 105, 011101 (2010)]. We also develop a framework to study the radial perturbations and stability of compact stars in this theory. We find that the standard results of stellar stability still hold in this theory. The frequency square of the fundamental oscillation mode vanishes for the maximum-mass stellar configuration. The dependence of the oscillation mode frequencies on the coupling parameter \kappa of the theory is also investigated. We find that the fundamental mode is insensitive to the value of \kappa, while higher order modes depend more strongly on \kappa.Comment: Minor changes to match the published versio

Spin-dependent properties of a two-dimensional electron gas with ferromagnetic gates

A theoretical prediction of the spin-dependent electron self-energy and in-plane transport of a two-dimensional electron gas in proximity with a ferromagnetic gate is presented. The application of the predicted spin-dependent properties is illustrated by the proposal of a device configuration with two neighboring ferromagnetic gates which produces a magnetoresistance effect on the channel current generated by nonmagnetic source and drain contacts. Specific results are shown for a silicon inversion layer with iron gates. The gate leakage current is found to be beneficial to the spin effects.Comment: 3 pages, 2 figures, Replaced with revised versio