Extensions and block decompositions for finite-dimensional representations of equivariant map algebras

Suppose a finite group acts on a scheme $X$ and a finite-dimensional Lie algebra $\mathfrak{g}$. The associated equivariant map algebra is the Lie algebra of equivariant regular maps from $X$ to $\mathfrak{g}$. The irreducible finite-dimensional representations of these algebras were classified in previous work with P. Senesi, where it was shown that they are all tensor products of evaluation representations and one-dimensional representations. In the current paper, we describe the extensions between irreducible finite-dimensional representations of an equivariant map algebra in the case that $X$ is an affine scheme of finite type and $\mathfrak{g}$ is reductive. This allows us to also describe explicitly the blocks of the category of finite-dimensional representations in terms of spectral characters, whose definition we extend to this general setting. Applying our results to the case of generalized current algebras (the case where the group acting is trivial), we recover known results but with very different proofs. For (twisted) loop algebras, we recover known results on block decompositions (again with very different proofs) and new explicit formulas for extensions. Finally, specializing our results to the case of (twisted) multiloop algebras and generalized Onsager algebras yields previously unknown results on both extensions and block decompositions.Comment: 41 pages; v2: minor corrections, formatting changed to match published versio

What Makes Educational Campaings Succeed?

PDF pages:

Ozone Depletion from Nearby Supernovae

Estimates made in the 1970's indicated that a supernova occurring within tens of parsecs of Earth could have significant effects on the ozone layer. Since that time, improved tools for detailed modeling of atmospheric chemistry have been developed to calculate ozone depletion, and advances have been made in theoretical modeling of supernovae and of the resultant gamma-ray spectra. In addition, one now has better knowledge of the occurrence rate of supernovae in the galaxy, and of the spatial distribution of progenitors to core-collapse supernovae. We report here the results of two-dimensional atmospheric model calculations that take as input the spectral energy distribution of a supernova, adopting various distances from Earth and various latitude impact angles. In separate simulations we calculate the ozone depletion due to both gamma-rays and cosmic rays. We find that for the combined ozone depletion roughly to double the ``biologically active'' UV flux received at the surface of the Earth, the supernova must occur at <8 pc. Based on the latest data, the time-averaged galactic rate of core-collapse supernovae occurring within 8 pc is ~1.5/Gyr. In comparing our calculated ozone depletions with those of previous studies, we find them to be significantly less severe than found by Ruderman (1974), and consistent with Whitten et al. (1976). In summary, given the amplitude of the effect, the rate of nearby supernovae, and the ~Gyr time scale for multicellular organisms on Earth, this particular pathway for mass extinctions may be less important than previously thought.Comment: 24 pages, 4 Postscript figures, to appear in The Astrophysical Journal, 2003 March 10, vol. 58

Kinetic Accessibility of Buried DNA Sites in Nucleosomes

Using a theoretical model for spontaneous partial DNA unwrapping from histones, we study the transient exposure of protein-binding DNA sites within nucleosomes. We focus on the functional dependence of the rates for site exposure and reburial on the site position, which is measurable experimentally and pertinent to gene regulation. We find the dependence to be roughly described by a random walker model. Close inspection reveals a surprising physical effect of flexibility-assisted barrier crossing, which we characterize within a toy model, the "semiflexible Brownian rotor."Comment: final version as published in Phys. Rev. Let

Reduced tillage, but not organic matter input, increased nematode diversity and food web stability in European long‐term field experiments

Soil nematode communities and food web indices can inform about the complexity, nutrient flows and decomposition pathways of soil food webs, reflecting soil quality. Relative abundance of nematode feeding and life‐history groups are used for calculating food web indices, i.e., maturity index (MI), enrichment index (EI), structure index (SI) and channel index (CI). Molecular methods to study nematode communities potentially offer advantages compared to traditional methods in terms of resolution, throughput, cost and time. In spite of such advantages, molecular data have not often been adopted so far to assess the effects of soil management on nematode communities and to calculate these food web indices. Here, we used high‐throughput amplicon sequencing to investigate the effects of tillage (conventional vs. reduced) and organic matter addition (low vs. high) on nematode communities and food web indices in 10 European long‐term field experiments and we assessed the relationship between nematode communities and soil parameters. We found that nematode communities were more strongly affected by tillage than by organic matter addition. Compared to conventional tillage, reduced tillage increased nematode diversity (23% higher Shannon diversity index), nematode community stability (12% higher MI), structure (24% higher SI), and the fungal decomposition channel (59% higher CI), and also the number of herbivorous nematodes (70% higher). Total and labile organic carbon, available K and microbial parameters explained nematode community structure. Our findings show that nematode communities are sensitive indicators of soil quality and that molecular profiling of nematode communities has the potential to reveal the effects of soil management on soil quality

Molecular analysis of Ku redox regulation

<p>Abstract</p> <p>Background</p> <p>DNA double-strand breaks (DSBs) can occur in response to ionizing radiation (IR), radiomimetic agents and from endogenous DNA-damaging reactive oxygen metabolites. Unrepaired or improperly repaired DSBs are potentially the most lethal form of DNA damage and can result in chromosomal translocations and contribute to the development of cancer. The principal mechanism for the repair of DSBs in humans is non-homologous end-joining (NHEJ). Ku is a key member of the NHEJ pathway and plays an important role in the recognition step when it binds to free DNA termini. Ku then stimulates the assembly and activation of other NHEJ components. DNA binding of Ku is regulated by redox conditions and evidence from our laboratory has demonstrated that Ku undergoes structural changes when oxidized that results in a reduction in DNA binding activity. The C-terminal domain and cysteine 493 of Ku80 were investigated for their contribution to redox regulation of Ku.</p> <p>Results</p> <p>We effectively removed the C-terminal domain of Ku80 generating a truncation mutant and co-expressed this variant with wild type Ku70 in an insect cell system to create a Ku70/80ΔC heterodimer. We also generated two single amino acid variants of Cys493, replacing this amino acid with either an alanine (C493A) or a serine (C493S), and over-expressed the variant proteins in SF9 insect cells in complex with wild type Ku70. Neither the truncation nor the amino acid substitutions alters protein expression or stability as determined by SDS-PAGE and Western blot analysis. We show that the C493 mutations do not alter the ability of Ku to bind duplex DNA in vitro under reduced conditions while truncation of the Ku80 C-terminus slightly reduced DNA binding affinity. Diamide oxidation of cysteines was shown to inhibit DNA binding similarly for both the wild-type and all variant proteins. Interestingly, differential DNA binding activity following re-reduction was observed for the Ku70/80ΔC truncation mutant.</p> <p>Conclusion</p> <p>Together, these results suggest that the C-terminal domain and C493 of Ku80 play at most a minor role in the redox regulation of Ku, and that other cysteines are likely involved, either alone or in conjunction with these regions of Ku80.</p