4,283 research outputs found

    Spectral tensor-train decomposition

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    The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT decomposition and analyze its properties. We obtain results on the convergence of the decomposition, revealing links between the regularity of the function, the dimension of the input space, and the TT ranks. We also show that the regularity of the target function is preserved by the univariate functions (i.e., the "cores") comprising the functional TT decomposition. This result motivates an approximation scheme employing polynomial approximations of the cores. For functions with appropriate regularity, the resulting \textit{spectral tensor-train decomposition} combines the favorable dimension-scaling of the TT decomposition with the spectral convergence rate of polynomial approximations, yielding efficient and accurate surrogates for high-dimensional functions. To construct these decompositions, we use the sampling algorithm \texttt{TT-DMRG-cross} to obtain the TT decomposition of tensors resulting from suitable discretizations of the target function. We assess the performance of the method on a range of numerical examples: a modifed set of Genz functions with dimension up to 100100, and functions with mixed Fourier modes or with local features. We observe significant improvements in performance over an anisotropic adaptive Smolyak approach. The method is also used to approximate the solution of an elliptic PDE with random input data. The open source software and examples presented in this work are available online.Comment: 33 pages, 19 figure

    New SUSYQM coherent states for Poschl-Teller potentials: a detailed mathematical analysis

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    In a recent short note [Bergeron H, Gazeau J P, Siegl P and Youssef A 2010 EPL 92 60003], we have presented the nice properties of a new family of semi-classical states for P\"oschl-Teller potentials. These states are built from a supersymmetric quantum mechanics approach and the parameters of these "coherent" states are points in the classical phase space. In this article we develop all the mathematical aspects that have been left apart in the previous article (proof of the resolution of unity, detailed calculations of quantized version of classical observables and mathematical study of the resulting operators: problems of domains, self- adjointness or self-adjoint extensions). Some additional questions as asymptotic behavior are also studied. Moreover, the framework is extended to a larger class of P\"oschl-Teller potentials

    Immunoregulatory soluble CTLA-4 modifies effector T cell responses in systemic lupus erythematosus

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    Acknowledgments This work was supported by Arthritis Research UK (Grant no. 19282). We are grateful to Dr. Nick Fluck for his invaluable support in recruiting patients for the study, and Mrs. Vivien Vaughan for her invaluable expertise in recruiting study participants and maintaining ethical documentation.Peer reviewedPublisher PD

    Thermal simulation of magnetization reversals for size-distributed assemblies of core-shell exchange biased nanoparticles

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    A temperature dependent coherent magnetization reversal model is proposed for size-distributed assemblies of ferromagnetic nanoparticles and ferromagnetic-antiferromagnetic core-shell nanoparticles. The nanoparticles are assumed to be of uniaxial anisotropy and all aligned along their easy axis. The thermal dependence is included by considering thermal fluctuations, implemented via the N\'eel-Arrhenius theory. Thermal and angular dependence of magnetization reversal loops, coercive field and exchange-bias field are obtained, showing that F-AF size-distributed exchange-coupled nanoparticles exhibit temperature-dependent asymmetric magnetization reversal. Also, non-monotonic evolutions of He and Hc with T are demonstrated. The angular dependence of Hc with T exhibits a complex behavior, with the presence of an apex, whose position and amplitude are strongly T dependent. The angular dependence of He with T exhibits complex behaviors, which depends on the AF anisotropy and exchange coupling. The resulting angular behavior demonstrates the key role of the size distribution and temperature in the magnetic response of nanoparticles.Comment: Revised arguments in Introduction and last sectio

    Magnetic properties of exchange biased and of unbiased oxide/permalloy thin layers: a ferromagnetic resonance and Brillouin scattering study

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    Microstrip ferromagnetic resonance and Brillouin scattering are used to provide a comparative determination of the magnetic parameters of thin permalloy layers interfaced with a non-magnetic (Al2O3) or with an antiferromagnetic oxide (NiO). It is shown that the perpendicular anisotropy is monitored by an interfacial surface energy term which is practically independent of the nature of the interface. In the investigated interval of thicknesses (5-25 nm) the saturation magnetisation does not significantly differ from the reported one in bulk permalloy. In-plane uniaxial anisotropy and exchange-bias anisotropy are also derived from this study of the dynamic magnetic excitations and compared to our independent evaluations using conventional magnetometryComment: 7 pages, 6 figures, submited to Journal of Physics: Condensed Matte
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