Derivations of the Lie Algebras of Differential Operators

This paper encloses a complete and explicit description of the derivations of the Lie algebra D(M) of all linear differential operators of a smooth manifold M, of its Lie subalgebra D^1(M) of all linear first-order differential operators of M, and of the Poisson algebra S(M)=Pol(T*M) of all polynomial functions on T*M, the symbols of the operators in D(M). It turns out that, in terms of the Chevalley cohomology, H^1(D(M),D(M))=H^1_{DR}(M), H^1(D^1(M),D^1(M))=H^1_{DR}(M)\oplus\R^2, and H^1(S(M),S(M))=H^1_{DR}(M)\oplus\R. The problem of distinguishing those derivations that generate one-parameter groups of automorphisms and describing these one-parameter groups is also solved.Comment: LaTeX, 15 page

Examining the efficacy of a genotyping-by-sequencing technique for population genetic analysis of the mushroom Laccaria bicolor and evaluating whether a reference genome is necessary to assess homology

Given the diversity and ecological importance of Fungi, there is a lack of population genetic research on these organisms. The reason for this can be explained in part by their cryptic nature and difficulty in identifying genets. In addition the difficulty (relative to plants and animals) in developing molecular markers for fungal population genetics contributes to the lack of research in this area. This study examines the ability of restriction-site associated DNA (RAD) sequencing to generate SNPs in Laccaria bicolor. Eighteen samples of morphologically identified L. bicolor from the United States and Europe were selected for this project. The RAD sequencing method produced anywhere from 290 000 to more than 3 000 000 reads. Mapping these reads to the genome of L. bicolor resulted in 84 000-940 000 unique reads from individual samples. Results indicate that incorporation of non-L. bicolor taxa into the analysis resulted in a precipitous drop in shared loci among samples, suggests the potential of these methods to identify cryptic species. F-statistics were easily calculated, although an observable "noise" was detected when using the "All Loci" treatment versus filtering loci to those present in at least 50% of the individuals. The data were analyzed with tests of Hardy-Weinburg equilibrium, population genetic statistics (FIS and FST), and population structure analysis using the program Structure. The results provide encouraging feedback regarding the potential utility of these methods and their data for population genetic analysis. We were unable to draw conclusions of life history of L. bicolor populations from this dataset, given the small sample size. The results of this study indicate the potential of these methods to address population genetics and general life history questions in the Agaricales. Further research is necessary to explore the specific application of these methods in the Agaricales or other fungal groups

Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains

In this contribution we briefly review recent developments in the theory of long-range integrable spin chains. These spin chains constitute a natural generalisation of the well-studied integrable nearest-neighbour chains and are of particular relevance to the integrability in the AdS/CFT correspondence since the dilatation operator in the asymptotic region is conjectured to be a Hamiltonian of an integrable long-range psu spin chain.Comment: 17 pages, see also overview article arXiv:1012.3982, v2: references to other chapters updated, v3: minor typos corrected, references adde

Interplane magnetic coupling effects in the multilattice compound Y_2Ba_4Cu_7O_{15}

We investigate the interplane magnetic coupling of the multilattice compound Y_2Ba_4Cu_7O_{15} by means of a bilayer Hubbard model with inequivalent planes. We evaluate the spin response, effective interaction and the intra- and interplane spin-spin relaxation times within the fluctuation exchange approximation. We show that strong in-plane antiferromagnetic fluctuations are responsible for a magnetic coupling between the planes, which in turns leads to a tendency of the fluctuation in the two planes to equalize. This equalization effect grows whit increasing in-plane antiferromagnetic fluctuations, i. e., with decreasing temperature and decreasing doping, while it is completely absent when the in-layer correlation length becomes of the order of one lattice spacing. Our results provide a good qualitative description of NMR and NQR experiments in Y_2Ba_4Cu_7O_{15}.Comment: Final version, to appear. in Phys. Rev. B (Rapid Communications), sched. Jan. 9

FÖRSTER TRANSFER CALCULATIONS BASED ON CRYSTAL STRUCTURE DATA FROM Agmenellum quadruplicatum C-PHYCOCYANIN

Excitation energy transfer in C-phycocyanin is modeled using the Forster inductive resonance mechanism. Detailed calculations are carried out using coordinates and orientations of the chromophores derived from X-ray crystallographic studies of C-phycocyanin from two different species (Schirmer et al, J. Mol. Biol. 184, 257–277 (1985) and ibid., 188, 651-677 (1986)). Spectral overlap integrals are estimated from absorption and fluorescence spectra of C-phycocyanin of Mastigocladus laminosus and its separated subunits. Calculations are carried out for the β-subunit, αβ-monomer, (αβ)3-trimer and (αβ)0-hexamer species with the following chromophore assignments: β155 = 's’(sensitizer), β84 =‘f (fluorescer) and α84 =‘m’(intermediate):]:. The calculations show that excitation transfer relaxation occurs to 3=98% within 200 ps in nearly every case; however, the rates increase as much as 10-fold for the higher aggregates. Comparison with experimental data on fluorescence decay and depolarization kinetics from the literature shows qualitative agreement with these calculations. We conclude that Forster transfer is sufficient to account for all of the observed fluorescence properties of C-phycocyanin in aggregation states up to the hexamer and in the absence of linker polypeptides

Higher Charges in Dynamical Spin Chains for SYM Theory

We construct, to the first two non-trivial orders, the next conserved charge in the su(2|3) sector of N=4 Super Yang-Mills theory. This represents a test of integrability in a sector where the interactions change the number of sites of the chain. The expression for the charge is completely determined by the algebra and can be written in a diagrammatic form in terms of the interactions already present in the Hamiltonian. It appears likely that this diagrammatic expression remains valid in the full theory and can be generalized to higher loops and higher charges thus helping in establishing complete integrability for these dynamical chains.Comment: 14 pages; V2: Appendix added with diagrammatic expression for H_{3,2