5,744 research outputs found
Of McKay Correspondence, Non-linear Sigma-model and Conformal Field Theory
The ubiquitous ADE classification has induced many proposals of often
mysterious correspondences both in mathematics and physics. The mathematics
side includes quiver theory and the McKay Correspondence which relates finite
group representation theory to Lie algebras as well as crepant resolutions of
Gorenstein singularities. On the physics side, we have the graph-theoretic
classification of the modular invariants of WZW models, as well as the relation
between the string theory nonlinear -models and Landau-Ginzburg
orbifolds. We here propose a unification scheme which naturally incorporates
all these correspondences of the ADE type in two complex dimensions. An
intricate web of inter-relations is constructed, providing a possible guideline
to establish new directions of research or alternate pathways to the standing
problems in higher dimensions.Comment: 35 pages, 4 figures; minor corrections, comments on toric geometry
and references adde
The structure of TeV-bright shell-type supernova remnants
Aims. Two-dimensional MHD simulations are used to model the emission
properties of TeV-bright shell-type supernova remnants (SNRs) and to explore
their nature. Methods. In the leptonic scenario for the TeV emission, the
-ray emission is produced via Inverse Compton scattering of background
soft photons by high-energy electrons accelerated by the shocks of the SNRs.
The TeV emissivity is proportional to the magnetic field energy density and MHD
simulations can be used to model the TeV structure of such remnants directly.
2D MHD simulations for SNRs are then performed under the assumption that the
ambient interstellar medium is turbulent with the magnetic field and density
fluctuations following a Kolmogorov-like power-law spectrum. Results. (1) As
expected, these simulations confirm early 1D and 2D modelings of these sources,
namely the hydrodynamical evolution of the shock waves and amplification of
magnetic field by Rayleigh-Taylor convective flows and by shocks propagating in
a turbulent medium; (2) We reproduce rather complex morphological structure for
-rays, suggesting intrinsic variations of the source morphology not
related to the structure of the progenitor and environment; (3)The observed
radial profile of several remnants are well reproduced with an ambient medium
density of cm. An even lower ambient density leads to a sharper
drop of the TeV brightness with radius than what is observed near the outer
edge of these remnants. Conclusions. In a turbulent background medium, we can
reproduce the observed characteristics of several shell-type TeV SNRs with
reasonable parameters except for a higher ambient density than that inferred
from X-ray observations.Comment: 7pages,12figures,Accepted for publication in A&A. arXiv admin note:
text overlap with arXiv:1306.439
Inverse Projection Representation and Category Contribution Rate for Robust Tumor Recognition
Sparse representation based classification (SRC) methods have achieved
remarkable results. SRC, however, still suffer from requiring enough training
samples, insufficient use of test samples and instability of representation. In
this paper, a stable inverse projection representation based classification
(IPRC) is presented to tackle these problems by effectively using test samples.
An IPR is firstly proposed and its feasibility and stability are analyzed. A
classification criterion named category contribution rate is constructed to
match the IPR and complete classification. Moreover, a statistical measure is
introduced to quantify the stability of representation-based classification
methods. Based on the IPRC technique, a robust tumor recognition framework is
presented by interpreting microarray gene expression data, where a two-stage
hybrid gene selection method is introduced to select informative genes.
Finally, the functional analysis of candidate's pathogenicity-related genes is
given. Extensive experiments on six public tumor microarray gene expression
datasets demonstrate the proposed technique is competitive with
state-of-the-art methods.Comment: 14 pages, 19 figures, 10 table
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