19,846 research outputs found
Applications of BGP-reflection functors: isomorphisms of cluster algebras
Given a symmetrizable generalized Cartan matrix , for any index , one
can define an automorphism associated with of the field of rational functions of independent indeterminates It is an isomorphism between two cluster algebras associated to the
matrix (see section 4 for precise meaning). When is of finite type,
these isomorphisms behave nicely, they are compatible with the BGP-reflection
functors of cluster categories defined in [Z1, Z2] if we identify the
indecomposable objects in the categories with cluster variables of the
corresponding cluster algebras, and they are also compatible with the
"truncated simple reflections" defined in [FZ2, FZ3]. Using the construction of
preprojective or preinjective modules of hereditary algebras by Dlab-Ringel
[DR] and the Coxeter automorphisms (i.e., a product of these isomorphisms), we
construct infinitely many cluster variables for cluster algebras of infinite
type and all cluster variables for finite types.Comment: revised versio
Trions in a periodic potential
The group-theoretical classification of trion states is presented. It is
based on considerations of products of irreducible representations of the 2D
translation group. For a given BvK period N degeneracy of obtained states is
N^2. Trions consist of two identical particles so the symmetrization of states
with respect to particles transposition is considered. Completely antisymmetric
states can be constructed by introducing antisymmetric spin functions. Two
symmetry adapted bases are considered. The third possibility is postponed for
the further investigations.Comment: revtex, 5 p., sub. to Physica
On Combining Lensing Shear Information from Multiple Filters
We consider the possible gain in the measurement of lensing shear from
imaging data in multiple filters. Galaxy shapes may differ significantly across
filters, so that the same galaxy offers multiple samples of the shear. On the
other extreme, if galaxy shapes are identical in different filters, one can
combine them to improve the signal-to-noise and thus increase the effective
number density of faint, high redshift galaxies. We use the GOODS dataset to
test these scenarios by calculating the covariance matrix of galaxy
ellipticities in four visual filters (B,V,i,z). We find that galaxy shapes are
highly correlated, and estimate the gain in galaxy number density by combining
their shapes.Comment: 8 pages, no figures, submitted to JCA
The Evolution of Distorted Rotating Black Holes III: Initial Data
In this paper we study a new family of black hole initial data sets
corresponding to distorted ``Kerr'' black holes with moderate rotation
parameters, and distorted Schwarzschild black holes with even- and odd-parity
radiation. These data sets build on the earlier rotating black holes of Bowen
and York and the distorted Brill wave plus black hole data sets. We describe
the construction of this large family of rotating black holes. We present a
systematic study of important properties of these data sets, such as the size
and shape of their apparent horizons, and the maximum amount of radiation that
can leave the system during evolution. These data sets should be a very useful
starting point for studying the evolution of highly dynamical black holes and
can easily be extended to 3D.Comment: 16 page
CFH Y402H Confers similar risk of soft Drusen and both forms of advanced AMD
Journal ArticleBACKGROUND: Age-related macular degeneration (AMD) is the most common cause of irreversible visual impairment in the developed world. The two forms of advanced AMD, geographic atrophy and neovascular AMD, represent different pathological processes in the macula that lead to loss of central vision. Soft drusen, characterized by deposits in the macula without visual loss, are considered to be a precursor of advanced AMD. Recently, it has been proposed that a common missense variant, Y402H, in the Complement Factor H (CFH) gene increases the risk for advanced AMD. However, its impact on soft drusen, GA, or neovascular AMD--or the relationship between them--is unclear. METHODS AND FINDINGS: We genotyped 581 Icelandic patients with advanced AMD (278 neovascular AMD, 203 GA, and 100 with mixed neovascular AMD/GA), and 435 with early AMD (of whom 220 had soft drusen). A second cohort of 431 US patients from Utah, 322 with advanced AMD (244 neovascular AMD and 78 GA) and 109 early-AMD cases with soft drusen, were analyzed. We confirmed that the CFH Y402H variant shows significant association to advanced AMD, with odds ratio of 2.39 in Icelandic patients (p = 5.9 x 10(-12)) and odds ratio of 2.14 in US patients from Utah (p = 2.0 x 10(-9)) with advanced AMD. Furthermore, we show that the Y402H variant confers similar risk of soft drusen and both forms of advanced AMD (GA or neovascular AMD). CONCLUSION: Soft drusen occur prior to progression to advanced AMD and represent a histological feature shared by neovascular AMD and GA. Our results suggest that CFH is a major risk factor of soft drusen, and additional genetic factors and/or environmental factors may be required for progression to advanced AMD
SECOND-ORDER SYSTEMS WITH SINGULAR MASS MATRIX AND AN EXTENSION OF GUYAN REDUCTION
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57864/1/BhatBernsteinGuyanReductionSIMAX.pd
FINITE-TIME STABILITY OF CONTINUOUS AUTONOMOUS SYSTEMS
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57815/1/BhatFiniteTimeStabilitySIAM2000.pd
Tight-binding study of structure and vibrations of amorphous silicon
We present a tight-binding calculation that, for the first time, accurately
describes the structural, vibrational and elastic properties of amorphous
silicon. We compute the interatomic force constants and find an unphysical
feature of the Stillinger-Weber empirical potential that correlates with a much
noted error in the radial distribution function associated with that potential.
We also find that the intrinsic first peak of the radial distribution function
is asymmetric, contrary to usual assumptions made in the analysis of
diffraction data. We use our results for the normal mode frequencies and
polarization vectors to obtain the zero-point broadening effect on the radial
distribution function, enabling us to directly compare theory and a high
resolution x-ray diffraction experiment
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