1,014 research outputs found

    Estimation of matrices with row sparsity

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    An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of convergence for estimating matrices with row sparsity. A major focus in the present paper is on the derivation of lower bounds

    Understanding the Random Displacement Model: From Ground-State Properties to Localization

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    We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an electron in a structurally disordered medium. These results started by identifying configurations which characterize minimal energy, then led to Lifshitz tail bounds on the integrated density of states as well as a Wegner estimate near the spectral minimum, which ultimately resulted in a proof of spectral and dynamical localization at low energy for the multi-dimensional random displacement model.Comment: 31 pages, 7 figures, final version, to appear in Proceedings of "Spectral Days 2010", Santiago, Chile, September 20-24, 201

    Localization on quantum graphs with random vertex couplings

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    We consider Schr\"odinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. Using the technique of self-adjoint extensions we obtain conditions for localization on quantum graphs in terms of finite volume criteria for some energy-dependent discrete Hamiltonians. These conditions hold in the strong disorder limit and at the spectral edges

    Orbital imagery for planetary exploration. Volume 1 - Technical summary

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    Orbital imagery for planetary exploration - objectives, measurements, orbit selection results, and imaging sensor system scaling law

    Orbital imagery for planetary exploration. Volume 2 - Definitions of scientific objectives

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    Orbital imagery for planetary exploration- objective outlines for planetary and atmospheric structure and composition, fields, and extraterrestrial lif

    The weak localization for the alloy-type Anderson model on a cubic lattice

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    We consider alloy type random Schr\"odinger operators on a cubic lattice whose randomness is generated by the sign-indefinite single-site potential. We derive Anderson localization for this class of models in the Lifshitz tails regime, i.e. when the coupling parameter λ\lambda is small, for the energies ECλ2E \le -C \lambda^2.Comment: 45 pages, 2 figures. To appear in J. Stat. Phy

    Lifshitz tails for alloy type models in a constant magnetic field

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    In this note, we study Lifshitz tails for a 2D Landau Hamiltonian perturbed by a random alloy-type potential constructed with single site potentials decaying at least at a Gaussian speed. We prove that, if the Landau level stays preserved as a band edge for the perturbed Hamiltonian, at the Landau levels, the integrated density of states has a Lifshitz behavior of the type elog2E2bqe^{-\log^2|E-2bq|}

    Prediction of neutron induced activation. Volume 2 - NAP, physical models and experimental validation Final report, May 14, 1964 - Jan. 31, 1966

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    Mathematical models for IBM 7094 computer program prediction of neutron induced activatio

    Orbital imagery for planetary exploration. Volume 4 - Imaging sensor system scaling laws

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    Orbital imagery for planetary exploration - imaging sensor system scaling law
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