Twisted modules and co-invariants for commutative vertex algebras of jet schemes

Let Z⊂k be an affine scheme over \C and \J Z its jet scheme. It is well-known that \mathbb{C}[\J Z], the coordinate ring of \J Z, has the structure of a commutative vertex algebra. This paper develops the orbifold theory for \mathbb{C}[\J Z]. A finite-order linear automorphism g of Z acts by vertex algebra automorphisms on \mathbb{C}[\J Z]. We show that \mathbb{C}[\J^g Z], where \J^g Z is the scheme of g--twisted jets has the structure of a g-twisted \mathbb{C}[\J Z] module. We consider spaces of orbifold coinvariants valued in the modules \mathbb{C}[\J^g Z] on orbicurves [Y/G], with Y a smooth projective curve and G a finite group, and show that these are isomorphic to ℂ[ZG]

Hopf algebras for matroids over hyperfields

Recently, M.~Baker and N.~Bowler introduced the notion of matroids over hyperfields as a unifying theory of various generalizations of matroids. In this paper we generalize the notion of minors and direct sums from ordinary matroids to matroids over hyperfields. Using this we generalize the classical construction of matroid-minor Hopf algebras to the case of matroids over hyperfields

The Hopf algebra of skew shapes, torsion sheaves on A^n/F_1, and ideals in Hall algebras of monoid representations

We study ideals in Hall algebras of monoid representations on pointed sets corresponding to certain conditions on the representations. These conditions include the property that the monoid act via partial permutations, that the representation possess a compatible grading, and conditions on the support of the module. Quotients by these ideals lead to combinatorial Hopf algebras which can be interpreted as Hall algebras of certain sub-categories of modules. In the case of the free commutative monoid on n generators, we obtain a co-commutative Hopf algebra structure on n-dimensional skew shapes, whose underlying associative product amounts to a "stacking" operation on the skew shapes. The primitive elements of this Hopf algebra correspond to connected skew shapes, and form a graded Lie algebra by anti-symmetrizing the associative product. We interpret this Hopf algebra as the Hall algebra of a certain category of coherent torsion sheaves on _n/_1 supported at the origin, where _1 denotes the field of one element. This Hopf algebra may be viewed as an n-dimensional generalization of the Hopf algebra of symmetric functions, which corresponds to the case n=1

Third Harmonic Cavity Modal Analysis

Third harmonic cavities have been designed and fabricated by FNAL to be used at the FLASH/XFEL facility at DESY to minimise the energy spread along the bunches. Modes in these cavities are analysed and the sensitivity to frequency errors are assessed. A circuit model is employed to model the monopole bands. The monopole circuit model is enhanced to include successive cell coupling, in addition to the usual nearest neighbour coupling. A mode matching code is used to facilitate rapid simulations, incorporating fabrication errors. Curves surfaces are approximated by a series of abrupt transitions and the validity of this approach is examinedComment: Proceedings of 14th International Conference on RF Superconductivity (SRF 2009), 2009, Berlin, German

When does cyclic dominance lead to stable spiral waves?

Species diversity in ecosystems is often accompanied by characteristic spatio-temporal patterns. Here, we consider a generic two-dimensional population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species, mutation, pair-exchange and individual hopping. The dynamics is characterized by nonlinear mobility and a Hopf bifurcation around which the system's four-phase state diagram is inferred from a complex Ginzburg-Landau equation derived using a perturbative multiscale expansion. While the dynamics is generally characterized by spiraling patterns, we show that spiral waves are stable in only one of the four phases. Furthermore, we characterize a phase where nonlinearity leads to the annihilation of spirals and to the spatially uniform dominance of each species in turn. Away from the Hopf bifurcation, when the coexistence fixed point is unstable, the spiraling patterns are also affected by the nonlinear diffusion

Feynman graphs, rooted trees, and Ringel-Hall algebras

We construct symmetric monoidal categories \LRF, \FD of rooted forests and Feynman graphs. These categories closely resemble finitary abelian categories, and in particular, the notion of Ringel-Hall algebra applies. The Ringel-Hall Hopf algebras of \LRF, \FD, \HH_{\LRF}, \HH_{\FD} are dual to the corresponding Connes-Kreimer Hopf algebras on rooted trees and Feynman graphs. We thus obtain an interpretation of the Connes-Kreimer Lie algebras on rooted trees and Feynman graphs as Ringel-Hall Lie algebras

Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level

We introduce the infinite-dimensional Lie superalgebra ${\mathcal A}$ and construct a family of mappings from certain category of ${\mathcal A}$-modules to the category of A_1^(1)-modules of critical level. Using this approach, we prove the irreducibility of a family of A_1^(1)-modules at the critical level. As a consequence, we present a new proof of irreducibility of certain Wakimoto modules. We also give a natural realizations of irreducible quotients of relaxed Verma modules and calculate characters of these representations.Comment: 21 pages, Late

Redox-Polymer-Wired [NiFeSe] Hydrogenase Variants with Enhanced O2 Stability for Triple-Protected High-Current-Density H2-Oxidation Bioanodes

Variants of the highly active [NiFeSe] hydrogenase from D. vulgaris Hildenborough that exhibit enhanced O2 tolerance were used as H2-oxidation catalysts in H2/O2 biofuel cells. Two [NiFeSe] variants were electrically wired by means of low-potential viologen-modified redox polymers and evaluated with respect to H2-oxidation and stability against O2 in the immobilized state. The two variants showed maximum current densities of (450±84) μA cm−2 for G491A and (476±172) μA cm−2 for variant G941S on glassy carbon electrodes and a higher O2 tolerance than the wild type. In addition, the polymer protected the enzyme from O2 damage and high-potential inactivation, establishing a triple protection for the bioanode. The use of gas-diffusion bioanodes provided current densities for H2-oxidation of up to 6.3 mA cm−2. Combination of the gas-diffusion bioanode with a bilirubin oxidase-based gas-diffusion O2-reducing biocathode in a membrane-free biofuel cell under anode-limiting conditions showed unprecedented benchmark power densities of 4.4 mW cm−2 at 0.7 V and an open-circuit voltage of 1.14 V even at moderate catalyst loadings, outperforming the previously reported system obtained with the [NiFeSe] wild type and the [NiFe] hydrogenase from D. vulgaris Miyazaki F.inpres

Hox-controlled reorganisation of intrasegmental patterning cues underlies Drosophila posterior spiracle organogenesis

10 páginas, 8 figuras. Material complementario del artículo esta disponible en http://dev.biologists.org/cgi/content/full/132/13/3093/DC1Hox proteins provide axial positional information and control segment morphology in development and evolution. Yet how they specify morphological traits that confer segment identity and how axial positional information interferes with intrasegmental patterning cues during organogenesis remain poorly understood. We have investigated the control of Drosophila posterior spiracle morphogenesis, a segment-specific structure that forms under Abdominal-B (AbdB) Hox control in the eighth abdominal segment (A8). We show that the Hedgehog (Hh), Wingless (Wg) and Epidermal Growth Factor Receptor (Egfr) pathways provide specific inputs for posterior spiracle morphogenesis and act in a genetic network made of multiple and rapidly evolving Hox/signalling interplays. A major function of AbdB during posterior spiracle organogenesis is to reset A8 intrasegmental patterning cues, first by reshaping wg and rhomboid expression patterns, then by reallocating the Hh signal and later by initiating de novo expression of the posterior compartment gene engrailed in anterior compartment cells. These changes in expression patterns confer axial specificity to otherwise reiteratively used segmental patterning cues, linking intrasegmental polarity and acquisition of segment identity.This work was supported by the `Centre National de la Recherche Scientifique' (CNRS), grants from `la Ligue Nationale Contre Le Cancer (équipe labellisée La Ligue)', `l'Association pour la Recherche contre le Cancer' (ARC), The Royal Society, The Welcome Trust, the `Minesterio de education y ciencia (BFU 2004 0 96) and ARC and EMBO long term fellowships to S. Merabet.Peer reviewe