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Learning distance to subspace for the nearest subspace methods in high-dimensional data classification
The nearest subspace methods (NSM) are a category of classification methods widely applied to classify high-dimensional data. In this paper, we propose to improve the classification performance of NSM through learning tailored distance metrics from samples to class subspaces. The learned distance metric is termed as ‘learned distance to subspace’ (LD2S). Using LD2S in the classification rule of NSM can make the samples closer to their correct class subspaces while farther away from their wrong class subspaces. In this way, the classification task becomes easier and the classification performance of NSM can be improved. The superior classification performance of using LD2S for NSM is demonstrated on three real-world high-dimensional spectral datasets
Z-graded weak modules and regularity
It is proved that if any Z-graded weak module for vertex operator algebra V
is completely reducible, then V is rational and C_2-cofinite. That is, V is
regular. This gives a natural characterization of regular vertex operator
algebras.Comment: 9 page
Polarizations in decays B_{u,d}\to VV and possible implications for R-parity violating SUSY
Recently BABAR and Belle have measured anomalous large transverse
polarizations in some pure penguin decays, which might be
inconsistent with the Standard Model expectations. We try to explore its
implications for R-parity violating (RPV) supersymmetry. The QCD factorization
approach is employed for the hadronic dynamics of B decays. We find that it is
possible to have parameter spaces solving the anomaly. Furthermore, we have
derived stringent bounds on relevant RPV couplings from the experimental data,
which is useful for further studies of RPV phenomena.Comment: 26 pages, 12 eps figures. Typos corrected and references added. Final
version to appear in PR
Stationary and dynamical properties of a zero range process on scale-free networks
We study the condensation phenomenon in a zero range process on scale-free
networks. We show that the stationary state property depends only on the degree
distribution of underlying networks. The model displays a stationary state
phase transition between a condensed phase and an uncondensed phase, and the
phase diagram is obtained analytically. As for the dynamical property, we find
that the relaxation dynamics depends on the global structure of underlying
networks. The relaxation time follows the power law with the
network size in the condensed phase. The dynamic exponent is found to
take a different value depending on whether underlying networks have a tree
structure or not.Comment: 9 pages, 6 eps figures, accepted version in PR
Hydrogen-bonded liquid crystals with broad-range blue phases
We report a modular supramolecular approach for the investigation of chirality induction in hydrogen-bonded liquid crystals. An exceptionally broad blue phase with a temperature range of 25 °C was found, which enabled its structural investigation by solid state 19F-NMR studies and allowed us to report order parameters of the blue phase I for the first time
Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra
The purpose of this paper is to generalize Zhu's theorem about characters of
modules over a vertex operator algebra graded by integer conformal weights, to
the setting of a vertex operator superalgebra graded by rational conformal
weights. To recover SL_2(Z)-invariance of the characters it turns out to be
necessary to consider twisted modules alongside ordinary ones. It also turns
out to be necessary, in describing the space of conformal blocks in the
supersymmetric case, to include certain `odd traces' on modules alongside
traces and supertraces. We prove that the set of supertrace functions, thus
supplemented, spans a finite dimensional SL_2(Z)-invariant space. We close the
paper with several examples.Comment: 42 pages. Published versio
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