64,721 research outputs found
From counting to construction of BPS states in N=4 SYM
We describe a universal element in the group algebra of symmetric groups,
whose characters provides the counting of quarter and eighth BPS states at weak
coupling in N=4 SYM, refined according to representations of the global
symmetry group. A related projector acting on the Hilbert space of the free
theory is used to construct the matrix of two-point functions of the states
annihilated by the one-loop dilatation operator, at finite N or in the large N
limit. The matrix is given simply in terms of Clebsch-Gordan coefficients of
symmetric groups and dimensions of U(N) representations. It is expected, by
non-renormalization theorems, to contain observables at strong coupling. Using
the stringy exclusion principle, we interpret a class of its eigenvalues and
eigenvectors in terms of giant gravitons. We also give a formula for the action
of the one-loop dilatation operator on the orthogonal basis of the free theory,
which is manifestly covariant under the global symmetry.Comment: 41 pages + Appendices, 4 figures; v2 - refs and acknowledgments adde
Orientifolds and the Refined Topological String
We study refined topological string theory in the presence of orientifolds by
counting second-quantized BPS states in M-theory. This leads us to propose a
new integrality condition for both refined and unrefined topological strings
when orientifolds are present. We define the SO(2N) refined Chern-Simons theory
which computes refined open string amplitudes for branes wrapping Seifert
three-manifolds. We use the SO(2N) refined Chern-Simons theory to compute new
invariants of torus knots that generalize the Kauffman polynomials. At large N,
the SO(2N) refined Chern-Simons theory on the three-sphere is dual to refined
topological strings on an orientifold of the resolved conifold, generalizing
the Gopakumar-Sinha-Vafa duality. Finally, we use the (2,0) theory to define
and solve refined Chern-Simons theory for all ADE gauge groups
Topological Quantum Field Theory for Calabi-Yau threefolds and G_2 manifolds
We introduce a homology theory whose Euler characteristics counts ASD bundles
over four dimensional co-associative submanifolds in (almost) G_2 manifolds.
As a TQFT, in relative situations, we have the Fukaya-Floer category of
Lagrangians intersection in the moduli space of special Lagrangian submanifolds
in CY threefolds.Comment: 14 pages. To appear in Adv. Theor. Math. Phy
Mapping Crop Cycles in China Using MODIS-EVI Time Series
As the Earth’s population continues to grow and demand for food increases, the need for improved and timely information related to the properties and dynamics of global agricultural systems is becoming increasingly important. Global land cover maps derived from satellite data provide indispensable information regarding the geographic distribution and areal extent of global croplands. However, land use information, such as cropping intensity (defined here as the number of cropping cycles per year), is not routinely available over large areas because mapping this information from remote sensing is challenging. In this study, we present a simple but efficient algorithm for automated mapping of cropping intensity based on data from NASA’s (NASA: The National Aeronautics and Space Administration) MODerate Resolution Imaging Spectroradiometer (MODIS). The proposed algorithm first applies an adaptive Savitzky-Golay filter to smooth Enhanced Vegetation Index (EVI) time series derived from MODIS surface reflectance data. It then uses an iterative moving-window methodology to identify cropping cycles from the smoothed EVI time series. Comparison of results from our algorithm with national survey data at both the provincial and prefectural level in China show that the algorithm provides estimates of gross sown area that agree well with inventory data. Accuracy assessment comparing visually interpreted time series with algorithm results for a random sample of agricultural areas in China indicates an overall accuracy of 91.0% for three classes defined based on the number of cycles observed in EVI time series. The algorithm therefore appears to provide a straightforward and efficient method for mapping cropping intensity from MODIS time series data
Tilings of quadriculated annuli
Tilings of a quadriculated annulus A are counted according to volume (in the
formal variable q) and flux (in p). We consider algebraic properties of the
resulting generating function Phi_A(p,q). For q = -1, the non-zero roots in p
must be roots of unity and for q > 0, real negative.Comment: 33 pages, 12 figures; Minor changes were made to make some passages
cleare
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