32,715 research outputs found
Difficulty in the Fermi-Liquid-Based Theory for the In-Plane Magnetic Anisotropy in Untwinned High-T_c Superconductor
Recently, Eremin and Manske [1] presented a oneband Fermi-liquid theory for
the in-plane magnetic anisotropy in untwinned high-Tc superconductor
YBa2Cu3O6:85 (YBCO). They claimed that they found good agreement with inelastic
neutron scattering (INS) spectra. In this Comment, we point out that their
conclusion on this important problem may be questionable due to an error in
logic about the orthorhombicity delta_0 characterizing the lattice structure of
YBCO. In Ref. [1], a single band at delta_0>0 is proved to be in accordance
with the angle resolved photoemission spectroscopy (ARPES) on untwinned YBCO.
But in their Erratum in PRL[3], they admit that delta_0= -0.03 was used to fit
the INS data. Hence publications [1,3] contain errors that we believe
invalidate their approach.Comment: This is a Comment on the paper of I. Eremin, and D. Manske, Phys.
Rev. Lett. 94, 067006(2005
Exact heat kernel on a hypersphere and its applications in kernel SVM
Many contemporary statistical learning methods assume a Euclidean feature
space. This paper presents a method for defining similarity based on
hyperspherical geometry and shows that it often improves the performance of
support vector machine compared to other competing similarity measures.
Specifically, the idea of using heat diffusion on a hypersphere to measure
similarity has been previously proposed, demonstrating promising results based
on a heuristic heat kernel obtained from the zeroth order parametrix expansion;
however, how well this heuristic kernel agrees with the exact hyperspherical
heat kernel remains unknown. This paper presents a higher order parametrix
expansion of the heat kernel on a unit hypersphere and discusses several
problems associated with this expansion method. We then compare the heuristic
kernel with an exact form of the heat kernel expressed in terms of a uniformly
and absolutely convergent series in high-dimensional angular momentum
eigenmodes. Being a natural measure of similarity between sample points
dwelling on a hypersphere, the exact kernel often shows superior performance in
kernel SVM classifications applied to text mining, tumor somatic mutation
imputation, and stock market analysis
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