Generalized iterated wreath products of cyclic groups and rooted trees correspondence

Consider the generalized iterated wreath product $\mathbb{Z}_{r_1}\wr \mathbb{Z}_{r_2}\wr \ldots \wr \mathbb{Z}_{r_k}$ where $r_i \in \mathbb{N}$. We prove that the irreducible representations for this class of groups are indexed by a certain type of rooted trees. This provides a Bratteli diagram for the generalized iterated wreath product, a simple recursion formula for the number of irreducible representations, and a strategy to calculate the dimension of each irreducible representation. We calculate explicitly fast Fourier transforms (FFT) for this class of groups, giving literature's fastest FFT upper bound estimate.Comment: 15 pages, to appear in Advances in the Mathematical Science

Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence

Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv admin note: text overlap with arXiv:1409.060

The Symbolic and cancellation-free formulae for Schur elements

In this paper we give a symbolical formula and a cancellation-free formula for the Schur elements associated to the simple modules of the degenerate cyclotomic Hecke algebras. As some direct applications, we show that the Schur elements are symmetric with respect to the natural symmetric group action and are integral coefficients polynomials and we give a different proof of Ariki-Mathas-Rui's criterion on the semi-simplicity of degenerate cyclotomic Hecke algebras.Comment: To appear in Monatshefte fur Mathemati

Search for new phenomena in final states with an energetic jet and large missing transverse momentum in pp collisions at √ s = 8 TeV with the ATLAS detector

Results of a search for new phenomena in final states with an energetic jet and large missing transverse momentum are reported. The search uses 20.3 fb−1 of √ s = 8 TeV data collected in 2012 with the ATLAS detector at the LHC. Events are required to have at least one jet with pT > 120 GeV and no leptons. Nine signal regions are considered with increasing missing transverse momentum requirements between Emiss T > 150 GeV and Emiss T > 700 GeV. Good agreement is observed between the number of events in data and Standard Model expectations. The results are translated into exclusion limits on models with either large extra spatial dimensions, pair production of weakly interacting dark matter candidates, or production of very light gravitinos in a gauge-mediated supersymmetric model. In addition, limits on the production of an invisibly decaying Higgs-like boson leading to similar topologies in the final state are presente

A marine biogenic source of atmospheric ice nucleating particles

The amount of ice present in clouds can affect cloud lifetime, precipitation and radiative properties1,2. The formation of ice in clouds is facilitated by the presence of airborne ice nucleating particles1,2. Sea spray is one of the major global sources of atmospheric particles, but it is unclear to what extent these particles are capable of nucleating ice3-11. Sea spray aerosol contains large amounts of organic material that is ejected into the atmosphere during bubble bursting at the organically enriched sea-air interface or sea surface microlayer12-19. Here we show that organic material in the sea surface microlayer nucleates ice under conditions relevant for mixed-phase cloud and high-altitude ice cloud formation. The ice nucleating material is likely biogenic and less than ~0.2 μm in size. We find that exudates separated from cells of the marine diatom T. Pseudonana nucleate ice and propose that organic material associated with phytoplankton cell exudates is a likely candidate for the observed ice nucleating ability of the microlayer samples. Global model simulations of marine organic aerosol in combination with our measurements suggest that marine organic material may be an important source of ice nucleating particles in remote marine environments such as the Southern Ocean, North Pacific and North Atlantic

Tumor interactions with soluble factors and the nervous system

In the genomic era of cancer research, the development of metastases has been attributed to mutations in the tumor that enable the cells to migrate. However, gene analyses revealed that primary tumors and metastases were in some cases genetically identical and the question was raised whether metastasis formation might be an inherent feature of certain tumor cells. In contradiction to this view, the last decade of cancer research has brought to light, that tumor cell migration, similar to leukocyte and fibroblast migration, is a highly regulated process. The nervous system plays an important role in this regulation, at least in two respects: firstly, neurotransmitters are known to regulate the migratory activity of tumor cells, and secondly, nerve fibers are used as routes for perineural invasion. We also summarize here the current knowledge on the innervation of tumors. Such a process might establish a neuro-neoplastic synapse, with the close interaction of tumor cells and nerve cells supporting metastasis formation

Characterization in vitro and in vivo of a pandemic H1N1 influenza virus from a fatal case

Pandemic 2009 H1N1 (pH1N1) influenza viruses caused mild symptoms in most infected patients. However, a greater rate of severe disease was observed in healthy young adults and children without co-morbid conditions. Here we tested whether influenza strains displaying differential virulence could be present among circulating pH1N1 viruses. The biological properties and the genotype of viruses isolated from a patient showing mild disease (M) or from a fatal case (F), both without known co-morbid conditions were compared in vitro and in vivo. The F virus presented faster growth kinetics and stronger induction of cytokines than M virus in human alveolar lung epithelial cells. In the murine model in vivo, the F virus showed a stronger morbidity and mortality than M virus. Remarkably, a higher proportion of mice presenting infectious virus in the hearts, was found in F virus-infected animals. Altogether, the data indicate that strains of pH1N1 virus with enhanced pathogenicity circulated during the 2009 pandemic. In addition, examination of chemokine receptor 5 (CCR5) genotype, recently reported as involved in severe influenza virus disease, revealed that the F virus-infected patient was homozygous for the deleted form of CCR5 receptor (CCR5Δ32).Funding Statement: This work was supported by Instituto de Salud Carlos III (Programa especial de investigación sobre la gripe pándemica GR09/0023, GR09/0040, GR09/0039) and Ciber de Enfermedades Respiratorias. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.S