107,680 research outputs found
A new proof of a theorem of Mansour and Sun
We give a new proof of a theorem of Mansour and Sun by using number theory
and Rothe's identity.Comment: 3 pages, to appear in European J. Combin., see also
http://math.univ-lyon1.fr/~gu
The Schrodinger-like Equation for a Nonrelativistic Electron in a Photon Field of Arbitrary Intensity
The ordinary Schrodinger equation with minimal coupling for a nonrelativistic
electron interacting with a single-mode photon field is not satisfied by the
nonrelativistic limit of the exact solutions to the corresponding Dirac
equation. A Schrodinger-like equation valid for arbitrary photon intensity is
derived from the Dirac equation without the weak-field assumption. The
"eigenvalue" in the new equation is an operator in a Cartan subalgebra. An
approximation consistent with the nonrelativistic energy level derived from its
relativistic value replaces the "eigenvalue" operator by an ordinary number,
recovering the ordinary Schrodinger eigenvalue equation used in the formal
scattering formalism. The Schrodinger-like equation for the multimode case is
also presented.Comment: Tex file, 13 pages, no figur
Information filtering via biased heat conduction
Heat conduction process has recently found its application in personalized
recommendation [T. Zhou \emph{et al.}, PNAS 107, 4511 (2010)], which is of high
diversity but low accuracy. By decreasing the temperatures of small-degree
objects, we present an improved algorithm, called biased heat conduction (BHC),
which could simultaneously enhance the accuracy and diversity. Extensive
experimental analyses demonstrate that the accuracy on MovieLens, Netflix and
Delicious datasets could be improved by 43.5%, 55.4% and 19.2% compared with
the standard heat conduction algorithm, and the diversity is also increased or
approximately unchanged. Further statistical analyses suggest that the present
algorithm could simultaneously identify users' mainstream and special tastes,
resulting in better performance than the standard heat conduction algorithm.
This work provides a creditable way for highly efficient information filtering.Comment: 4 pages, 3 figure
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