Algebras with Operator and Campbell--Hausdorff Formula

We introduce some new classes of algebras and estabilish in these algebras Campbell--Hausdorff like formula. We describe the application of these constructions to the problem of the connectivity of the Feynman graphs corresponding to the Green functions in Quantum Fields Theory.Comment: 12 page

Effective Symmetries of the Minimal Supermultiplet of N = 8 Extended Worldline Supersymmetry

A minimal representation of the N = 8 extended worldline supersymmetry, known as the `ultra-multiplet', is closely related to a family of supermultiplets with the same, E(8) chromotopology. We catalogue their effective symmetries and find a Spin(4) x Z(2) subgroup common to them all, which explains the particular basis used in the original construction. We specify a constrained superfield representation of the supermultiplets in the ultra-multiplet family, and show that such a superfield representation in fact exists for all adinkraic supermultiplets. We also exhibit the correspondences between these supermultiplets, their Adinkras and the E(8) root lattice bases. Finally, we construct quadratic Lagrangians that provide the standard kinetic terms and afford a mixing of an even number of such supermultiplets controlled by a coupling to an external 2-form of fluxes.Comment: 13 Figure

Stein structures: existence and flexibility

This survey on the topology of Stein manifolds is an extract from our recent joint book. It is compiled from two short lecture series given by the first author in 2012 at the Institute for Advanced Study, Princeton, and the Alfred Renyi Institute of Mathematics, Budapest.Comment: 29 pages, 11 figure

Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory

We study D-branes and Ramond-Ramond fields on global orbifolds of Type II string theory with vanishing H-flux using methods of equivariant K-theory and K-homology. We illustrate how Bredon equivariant cohomology naturally realizes stringy orbifold cohomology. We emphasize its role as the correct cohomological tool which captures known features of the low-energy effective field theory, and which provides new consistency conditions for fractional D-branes and Ramond-Ramond fields on orbifolds. We use an equivariant Chern character from equivariant K-theory to Bredon cohomology to define new Ramond-Ramond couplings of D-branes which generalize previous examples. We propose a definition for groups of differential characters associated to equivariant K-theory. We derive a Dirac quantization rule for Ramond-Ramond fluxes, and study flat Ramond-Ramond potentials on orbifolds.Comment: 46 pages; v2: typos correcte

Capture of complete ciliate chromosomes in single sequencing reads reveals widespread chromosome isoforms

Background Whole-genome shotgun sequencing, which stitches together millions of short sequencing reads into a single genome, ushered in the era of modern genomics and led to a rapid expansion of the number of genome sequences available. Nevertheless, assembly of short reads remains difficult, resulting in fragmented genome sequences. Ultimately, only a sequencing technology capable of capturing complete chromosomes in a single run could resolve all ambiguities. Even “third generation” sequencing technologies produce reads far shorter than most eukaryotic chromosomes. However, the ciliate Oxytricha trifallax has a somatic genome with thousands of chromosomes averaging only 3.2 kbp, making it an ideal candidate for exploring the benefits of sequencing whole chromosomes without assembly. Results We used single-molecule real-time sequencing to capture thousands of complete chromosomes in single reads and to update the published Oxytricha trifallax JRB310 genome assembly. In this version, over 50% of the completed chromosomes with two telomeres derive from single reads. The improved assembly includes over 12,000 new chromosome isoforms, and demonstrates that somatic chromosomes derive from variable rearrangements between somatic segments encoded up to 191,000 base pairs away. However, while long reads reduce the need for assembly, a hybrid approach that supplements long-read sequencing with short reads for error correction produced the most complete and accurate assembly, overall. Conclusions This assembly provides the first example of complete eukaryotic chromosomes captured by single sequencing reads and demonstrates that traditional approaches to genome assembly can mask considerable structural variation

Automatic stellar spectra parameterisation in the IR CaII triplet region

(Abridged) Galactic archaeology aims to determine the evolution of the Galaxy from the chemical and kinematical properties of its stars. The analysis of current large spectroscopic surveys (thousands of stars) and future ones (millions of stars) require automated analysis techniques to obtain robust estimates of the stellar parameters. Several on-going and planned spectroscopic surveys have selected their wavelength region to contain the IR CaII triplet and this paper focuses on the automatic analysis of such spectra. We investigated two algorithms, MATISSE and DEGAS, both of which compare the observed spectrum to a grid of synthetic spectra, but each uses a different mathematical approach for finding the optimum match and hence the best stellar parameters. We identified degeneracies in different regions of the HR diagram: hot dwarfs and giants share the same spectral signatures. Furthermore, the surface gravity of cooler dwarfs is difficult to determine accurately. These effects are intensified when the information decreases (e.g. metal-poor stars or low SNR spectra). Our results show that the local projection method MATISSE is preferred for high SNR spectra, whereas the decision-tree method DEGAS is preferred for noisier spectra. We therefore propose a hybrid approach of both methods and show that sufficiently accurate results for the purposes of galactic archaeology are retrieved down to SNR~20 for typical thin or thick disc stars, and down to SNR~50 for the more metal-poor halo giants. If unappreciated, degeneracies in stellar parameters can introduce biases in derived quantities for target stars such as distances and full space motions. These biases can be minimised using the knowledge gained by thorough testing of the proposed algorithm, which in turn lead to robust automated methods for the coming extensive stellar spectroscopic surveys in the Local Group.Comment: 17 pages, 11 figures, accepted for publication in A&

Two-Dimensional Twisted Sigma Models, the Mirror Chiral de Rham Complex, and Twisted Generalised Mirror Symmetry

In this paper, we study the perturbative aspects of a "B-twisted" two-dimensional $(0,2)$ heterotic sigma model on a holomorphic gauge bundle $\mathcal E$ over a complex, hermitian manifold $X$. We show that the model can be naturally described in terms of the mathematical theory of ``Chiral Differential Operators". In particular, the physical anomalies of the sigma model can be reinterpreted as an obstruction to a global definition of the associated sheaf of vertex superalgebras derived from the free conformal field theory describing the model locally on $X$. In addition, one can also obtain a novel understanding of the sigma model one-loop beta function solely in terms of holomorphic data. At the $(2,2)$ locus, one can describe the resulting half-twisted variant of the topological B-model in terms of a $\it{mirror}$ "Chiral de Rham complex" (or CDR) defined by Malikov et al. in \cite{GMS1}. Via mirror symmetry, one can also derive various conjectural expressions relating the sheaf cohomology of the mirror CDR to that of the original CDR on pairs of Calabi-Yau mirror manifolds. An analysis of the half-twisted model on a non-K\"ahler group manifold with torsion also allows one to draw conclusions about the corresponding sheaves of CDR (and its mirror) that are consistent with mathematically established results by Ben-Bassat in \cite{ben} on the mirror symmetry of generalised complex manifolds. These conclusions therefore suggest an interesting relevance of the sheaf of CDR in the recent study of generalised mirror symmetry.Comment: 97 pages. Companion paper to hep-th/0604179. Published versio

The Physarum polycephalum Genome Reveals Extensive Use of Prokaryotic Two-Component and Metazoan-Type Tyrosine Kinase Signaling

Physarum polycephalum is a well-studied microbial eukaryote with unique experimental attributes relative to other experimental model organisms. It has a sophisticated life cycle with several distinct stages including amoebal, flagellated, and plasmodial cells. It is unusual in switching between open and closed mitosis according to specific life-cycle stages. Here we present the analysis of the genome of this enigmatic and important model organism and compare it with closely related species. The genome is littered with simple and complex repeats and the coding regions are frequently interrupted by introns with a mean size of 100 bases. Complemented with extensive transcriptome data, we define approximately 31,000 gene loci, providing unexpected insights into earlyeukaryoteevolution.Wedescribeextensiveuseofhistidinekinase-basedtwo-componentsystemsandtyrosinekinasesignaling, the presence of bacterial and plant type photoreceptors (phytochromes, cryptochrome, and phototropin) and of plant-type pentatricopeptide repeat proteins, as well as metabolic pathways, and a cell cycle control system typically found in more complex eukaryotes. Our analysis characterizes P. polycephalum as a prototypical eukaryote with features attributed to the last common ancestor of Amorphea, that is, the Amoebozoa and Opisthokonts. Specifically, the presence of tyrosine kinases inAcanthamoeba and Physarum as representatives of two distantly related subdivisions ofAmoebozoa argues against the later emergence of tyrosine kinase signaling in the opisthokont lineage and also against the acquisition by horizontal gene transfe