Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)

The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible $gl(m|n)$ modules. In particular, we give matrix element formulae for all gl(m|n) generators, including the non-elementary generators, together with their phases on finite dimensional type 2 unitary irreducible representations. Remarkably, we find that the type 2 unitary matrix element equations coincide with the type 1 unitary matrix element equations for non-vanishing matrix elements up to a phase.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1311.424

Reduced Wigner coefficients for Lie superalgebra gl(m|n) corresponding to unitary representations and beyond

In this paper fundamental Wigner coefficients are determined algebraically by considering the eigenvalues of certain generalized Casimir invariants. Here this method is applied in the context of both type 1 and type 2 unitary representations of the Lie superalgebra gl(mjn). Extensions to the non-unitary case are investigated. A symmetry relation between two classes of Wigner coefficients is given in terms of a ratio of dimensions.Comment: 17 page

An Assessment of Alternative State Space Models for Count Time Series

This paper compares two alternative models for autocorrelated count time series. The first model can be viewed as a 'single source of error' discrete state space model, in which a time-varying parameter is specified as a function of lagged counts, with no additional source of error introduced. The second model is the more conventional 'dual source of error' discrete state space model, in which the time-varying parameter is driven by a random autocorrelated process. Using the nomenclature of the literature, the two representations can be viewed as observation-driven and parameter-driven respectively, with the distinction between the two models mimicking that between analogous models for other non-Gaussian data such as financial returns and trade durations. The paper demonstrates that when adopting a conditional Poisson specification, the two models have vastly different dispersion/correlation properties, with the dual source model having properties that are a much closer match to the empirical properties of observed count series than are those of the single source model. Simulation experiments are used to measure the finite sample performance of maximum likelihood (ML) estimators of the parameters of each model, and ML-based predictors, with ML estimation implemented for the dual source model via a deterministic hidden Markov chain approach. Most notably, the numerical results indicate that despite the very different properties of the two models, predictive accuracy is reasonably robust to misspecification of the state space form.Discrete state-space model; single source of error model; hidden Markov

Cellular mRNAs access second ORFs using a novel amino acid sequence-dependent coupled translation termination-reinitiation mechanism

Polycistronic transcripts are considered rare in the human genome. Initiation of translation of internal ORFs of eukaryotic genes has been shown to use either leaky scanning or highly structured IRES regions to access initiation codons. Studies on mammalian viruses identified a mechanism of coupled translation termination-reinitiation that allows translation of an additional ORF. Here, the ribosome terminating translation of ORF-1 translocates upstream to reinitiate translation of ORF-2. We have devised an algorithm to identify mRNAs in the human transcriptome in which the major ORF-1 overlaps a second ORF capable of encoding a product of at least 50 aa in length. This identified 4368 transcripts representing 2214 genes. We investigated 24 transcripts, 22 of which were shown to express a protein from ORF-2 highlighting that 3' UTRs contain protein-coding potential more frequently than previously suspected. Five transcripts accessed ORF-2 using a process of coupled translation termination-reinitiation. Analysis of one transcript, encoding the CASQ2 protein, showed that the mechanism by which the coupling process of the cellular mRNAs was achieved was novel. This process was not directed by the mRNA sequence but required an aspartate-rich repeat region at the carboxyl terminus of the terminating ORF-1 protein. Introduction of wobble mutations for the aspartate codon had no effect, whereas replacing aspartate for glutamate repeats eliminated translational coupling. This is the first description of a coordinated expression of two proteins from cellular mRNAs using a coupled translation termination-reinitiation process and is the first example of such a process being determined at the amino acid level

Momentum transfer to atoms by absorption and emission of radiation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1986.MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCEIncludes bibliographies.by Phillip Lloyd Gould.Ph.D

Casimir Invariants from Quasi-Hopf (Super)algebras

We show how to construct, starting from a quasi-Hopf (super)algebra, central elements or Casimir invariants. We show that these central elements are invariant under quasi-Hopf twistings. As a consequence, the elliptic quantum (super)groups, which arise from twisting the normal quantum (super)groups, have the same Casimir invariants as the corresponding quantum (super)groups.Comment: 24 pages, Latex fil