Conformally invariant powers of the Laplacian, Q-curvature, and tractor calculus

We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS operators due to C.R. Graham et alia. These differential operators have leading part a power of the Laplacian. Conformal tractor calculus is the natural induced bundle calculus associated to the conformal Cartan connection. Applications discussed include standard formulae for these operators in terms of the Levi-Civita connection and its curvature and a direct definition and formula for T. Branson's so-called Q-curvature (which integrates to a global conformal invariant) as well as generalisations of the operators and the Q-curvature. Among examples, the operators of order 4, 6, and 8 and the related Q-curvatures are treated explicitly. The algorithm exploits the ambient metric construction of Fefferman and Graham and includes a procedure for converting the ambient curvature and its covariant derivatives into tractor calculus expressions. This is partly based on "Standard tractors and the conformal ambient metric construction" (A. Cap and A.R. Gover, math.DG/0207016), where the relationship of the normal standard tractor bundle to the ambient construction is described.Comment: 42 pages. No figures. Record of changes: V1, 15 January 2002: Original posting. V2, 17 January 2002: Changing comment fields. Leaving abstract and text of article unchanged. V3, 1 February 2003: Minor changes and typographical corrections throughout articl

Lose the plot: cost-effective survey of the Peak Range, central Queensland

The Peak Range (22˚ 28’ S; 147˚ 53’ E) is an archipelago of rocky peaks set in grassy basalt rolling-plains, east of Clermont in central Queensland. This report describes the flora and vegetation based on surveys of 26 peaks. The survey recorded all plant species encountered on traverses of distinct habitat zones, which included the ‘matrix’ adjacent to each peak. The method involved effort comparable to a general flora survey but provided sufficient information to also describe floristic association among peaks, broad habitat types, and contrast vegetation on the peaks with the surrounding landscape matrix. The flora of the Peak Range includes at least 507 native vascular plant species, representing 84 plant families. Exotic species are relatively few, with 36 species recorded, but can be quite prominent in some situations. The most abundant exotic plants are the grass Melinis repens and the forb Bidens bipinnata. Plant distribution patterns among peaks suggest three primary groups related to position within the range and geology. The Peak Range makes a substantial contribution to the botanical diversity of its region and harbours several endemic plants among a flora clearly distinct from that of the surrounding terrain. The distinctiveness of the range’s flora is due to two habitat components: dry rainforest patches reliant upon fire protection afforded by cliffs and scree, and; rocky summits and hillsides supporting xeric shrublands. Plants endemic to the Peak Range are mainly associated with the latter of these habitats

Surviving a Genome Collision: Genomic Signatures of Allopolyploidization in the Recent Crop Species

Polyploidization has played a major role in crop plant evolution, leading to advantageous traits that have been selected by humans. Here, we describe restructuring patterns in the genome of Brassica napus L., a recent allopolyploid species. Widespread segmental deletions, duplications, and homeologous chromosome exchanges were identified in diverse genome sequences from 32 natural and 20 synthetic accessions, indicating that homeologous exchanges are a major driver of postpolyploidization genome diversification. Breakpoints of genomic rearrangements are rich in microsatellite sequences that are known to interact with the meiotic recombination machinery. In both synthetic and natural B. napus, a subgenome bias was observed toward exchanges replacing larger chromosome segments from the C-subgenome by their smaller, homeologous A-subgenome segments, driving postpolyploidization genome size reduction. Selection in natural B. napus favored segmental deletions involving genes associated with immunity, reproduction, and adaptation. Deletions affecting mismatch repair system genes, which are assumed to control homeologous recombination, were also found to be under selection. Structural exchanges between homeologous subgenomes appear to be a major source of novel genetic diversity in de novo allopolyploids. Documenting the consequences of genomic collision by genomic resequencing gives insights into the adaptive processes accompanying allopolyploidization

SURVEYING FOR RANAVIRUS IN GREEN FROGS (LITHOBATES CLAMITANS) AT FIVE LOCATIONS IN INDIANA

Ranaviruses are an emerging pathogen within the United States that infects amphibians, reptiles, and fish. A Frog Virus 3-like (FV3) ranavirus has been detected at only two locations in Indiana; however, there have been few attempts to broadly sample for ranaviruses to determine their distribution across the state. This knowledge is necessary for the continued management and conservation of native amphibian populations. Our objective was to assess the occurrence of FV3-like ranaviruses in larval Green Frog (Lithobates clamitans) populations at five sites located in different regions of Indiana. Tissue samples were collected from 166 individuals and were assayed using both conventional and qPCR methods. We did not detect the presence of any FV3-like ranaviruses at any of the five sites with either PCR method, suggesting the possibility that at these sites, FV3-like ranaviruses may not be present. However, continued sampling should be carried out to monitor the status of the presence of ranaviruses in this portion of the Midwest

Optimal Modeling and Filtering of Stochastic Time Series for Geoscience Applications

Sequences of observations or measurements are often modeled as realizations of stochastic processes with some stationary properties in the first and second moments. However in practice, the noise biases and variances are likely to be different for different epochs in time or regions in space, and hence such stationarity assumptions are often questionable. In the case of strict stationarity with equally spaced data, the Wiener-Hopf equations can readily be solved with fast Fourier transforms (FFTs) with optimal computational efficiency. In more general contexts, covariance matrices can also be diagonalized using the Karhunen-Loève transforms (KLTs), or more generally using empirical orthogonal and biorthogonal expansions, which are unfortunately much more demanding in terms of computational efforts. In cases with increment stationarity, the mathematical modeling can be modified and generalized covariances can be used with some computational advantages. The general nonlinear solution methodology is also briefly overviewed with the practical limitations. These different formulations are discussed with special emphasis on the spectral properties of covariance matrices and illustrated with some numerical examples. General recommendations are included for practical geoscience applications