9,078 research outputs found
Classification of flat bands according to the band-crossing singularity of Bloch wave functions
We show that flat bands can be categorized into two distinct classes, that
is, singular and nonsingular flat bands, by exploiting the singular behavior of
their Bloch wave functions in momentum space. In the case of a singular flat
band, its Bloch wave function possesses immovable discontinuities generated by
the band-crossing with other bands, and thus the vector bundle associated with
the flat band cannot be defined. This singularity precludes the compact
localized states from forming a complete set spanning the flat band. Once the
degeneracy at the band crossing point is lifted, the singular flat band becomes
dispersive and can acquire a finite Chern number in general, suggesting a new
route for obtaining a nearly flat Chern band. On the other hand, the Bloch wave
function of a nonsingular flat band has no singularity, and thus forms a vector
bundle. A nonsingular flat band can be completely isolated from other bands
while preserving the perfect flatness. All one-dimensional flat bands belong to
the nonsingular class. We show that a singular flat band displays a novel
bulk-boundary correspondence such that the presence of the robust boundary mode
is guaranteed by the singularity of the Bloch wave function. Moreover, we
develop a general scheme to construct a flat band model Hamiltonian in which
one can freely design its singular or nonsingular nature. Finally, we propose a
general formula for the compact localized state spanning the flat band, which
can be easily implemented in numerics and offer a basis set useful in analyzing
correlation effects in flat bands.Comment: 23 pages, 13 figure
Hybrid Spam Filtering for Mobile Communication
Spam messages are an increasing threat to mobile communication. Several
mitigation techniques have been proposed, including white and black listing,
challenge-response and content-based filtering. However, none are perfect and
it makes sense to use a combination rather than just one. We propose an
anti-spam framework based on the hybrid of content-based filtering and
challenge-response. There is the trade-offs between accuracy of anti-spam
classifiers and the communication overhead. Experimental results show how,
depending on the proportion of spam messages, different filtering %%@
parameters should be set.Comment: 6 pages, 5 figures, 1 tabl
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