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We develop a method for solving mathematical models of messenger RNA (mRNA) translation based on the totally asymmetric simple exclusion process (TASEP). Our main goal is to demonstrate that the method is versatile and applicable to realistic models of translation. To this end we consider the TASEP with codon-dependent elongation rates, premature termination due to ribosome drop-off and translation reinitiation due to circularisation of the mRNA. We apply the method to the model organism {\it Saccharomyces cerevisiae} under physiological conditions and find excellent agreements with the results of stochastic simulations. Our findings suggest that the common view on translation as being rate-limited by initiation is oversimplistic. Instead we find theoretical evidence for ribosome interference and also theoretical support for the ramp hypothesis which argues that codons at the beginning of genes have slower elongation rates in order to reduce ribosome density and jamming., Comment: 13 pages, 10 figures

The Ray-Singer analytic torsion is the zeta-function trace of a certain sum of logarithm operators on the de Rham complex. In this note we examine the residue analytic torsion, defined using the residue-trace instead of the spectral zeta function quasi-trace., Comment: Final (published) version

Generalised characteristic classes are constructed for bordism cohomologies which allow a natural extension of classical genera to these bordism cohomology rings taking values in singular cohomology., Comment: Minor improvements, typos corrected

Based on Guillemin's work on gauged Lagrangian distributions, we will introduce the notion of a poly-$\log$-homogeneous distribution as an approach to $\zeta$-functions for a class of Fourier Integral Operators which includes cases of amplitudes with asymptotic expansion $\sum_{k\in\mathbb{N}}a_{m_k}$ where each $a_{m_k}$ is $\log$-homogeneous with degree of homogeneity $m_k$ but violating $\Re(m_k)\to-\infty$. We will calculate the Laurent expansion for the $\zeta$-function and give formulae for the coefficients in terms of the phase function and amplitude as well as investigate generalizations to the Kontsevich-Vishik quasi-trace. Using stationary phase approximation, series representations for the Laurent coefficients and values of $\zeta$-functions will be stated explicitly. Additionally, we will introduce an approximation method (mollification) for $\zeta$-functions of Fourier Integral Operators whose symbols have singularities at zero by $\zeta$-functions of Fourier Integral Operators with regular symbols., Comment: 45 pages

To tackle the challenge of providing higher data rates within limited spectral resources we consider the case of multiple operators sharing a common pool of radio resources. Four algorithms are proposed to address co-primary multi-operator radio resource sharing under heterogeneous traffic in both centralized and distributed scenarios. The performance of these algorithms is assessed through extensive system-level simulations for two indoor small cell layouts. It is assumed that the spectral allocations of the small cells are orthogonal to the macro network layer and thus, only the small cell traffic is modeled. The main performance metrics are user throughput and the relative amount of shared spectral resources. The numerical results demonstrate the importance of coordination among co-primary operators for an optimal resource sharing. Also, maximizing the spectrum sharing percentage generally improves the achievable throughput gains over non-sharing.

The Graphics Processing Unit (GPU) has become an integral part of astronomical instrumentation, enabling high-performance online data reduction and accelerated online signal processing. In this paper, we describe a wide-band reconfigurable spectrometer built using an off-the-shelf GPU card. This spectrometer, when configured as a polyphase filter bank (PFB), supports a dual-polarization bandwidth of up to 1.1 GHz (or a single-polarization bandwidth of up to 2.2 GHz) on the latest generation of GPUs. On the other hand, when configured as a direct FFT, the spectrometer supports a dual-polarization bandwidth of up to 1.4 GHz (or a single-polarization bandwidth of up to 2.8 GHz)., Comment: 5 pages, 3 figures, Accepted for publication in PASA

Logarithmic representations of the bordism category are considered as a framework for capturing a class of additive invariants characterising Reidemeister torsions., Comment: Minor edits, 32 pages

A new spectrometer for the Green Bank Telescope (GBT) is being built jointly by the NRAO and the CASPER, University of California, Berkeley. The spectrometer uses 8 bit ADCs and will be capable of processing up to 1.25 GHz bandwidth from 8 dual polarized beams. This mode will be used to process data from focal plane arrays. The spectrometer supports observing mode with 8 tunable digital sub-bands within the 1.25 GHz bandwidth. The spectrometer can also be configured to process a bandwidth of up to 10 GHz with 64 tunable sub-bands from a dual polarized beam. The vastly enhanced backend capabilities will support several new science projects with the GBT., Comment: To appear in the Proceedings of the XXXth URSI General Assembly in Istanbul, August 2011, 4 pages; 3 figures

We provide evidence for the conjecture that the Wodzicki-Chern classes vanish for all bundles with the group Z of invertible zeroth order pseudodifferential operators as structure group. In particular, we prove this vanishing if the structure group reduces to pseudodifferential operators with leading order symbol the identity. The leading order Chern classes are nonzero in general, and they detect elements of the de Rham cohomology groups of the classifying space BZ., Comment: Second version contains improved exposition and results. To appear in Contemporary Mathematics

We show that there is a canonical construction of a zeta (Bismut-Quillen) connection on the determinant line bundle of a family of APS elliptic boundary problems and that it has curvature equal to the 2-form part of a relative eta form., Comment: Minor technical clarifications

For a holomorphic family of classical pseudodifferential operators on a closed manifold we give exact formulae for all coefficients in the Laurent expansion of its Kontsevich-Vishik canonical trace. This generalizes a known result identifying the Wodzicki residue with the pole at zero to all higher order terms., Comment: Expanded explanations and applications

We study the zeta determinant of global boundary problems of APS-type through a general theory for relative spectral invariants. In particular, we compute the zeta determinant for Dirac-Laplacian boundary problems in terms of a scattering Fredholm determinant over the boundary., Comment: 62 pages

For a smooth family F of admissible elliptic pseudodifferential operators with differential form coefficients associated to a geometric fibration of manifolds M--> B we show that there is a natural zeta-form z(F,s) and zeta-determinant- form det(F) in the de-Rham algebra of smooth differential forms, generalizing the classical single operator spectral zeta function and determinant. In the case where F is the curvature of a superconnection the zeta form is exact, extending to families the Atiyah-Bott-Seeley zeta function formula for the pointwise index, and equivalent to the transgression formula for the graded Chern character. The zeta-determinant form leads to the definition of the graded zeta-Chern class form. For a family of compatible Dirac operators D with index bundle Ind(D) we prove a transgression formula leading to a local density representing the Chern class c(Ind(D))in terms of the A-hat genus and twisted Chern character. Globally the meromorphically continued zeta form and zeta determinant form exist only at the level of K-theory as characteristic class maps K(B)->H*(B)., Comment: 34 pages

The purpose of this paper is to present the construction of a canonical determinant functional on elliptic pseudodifferential operators associated to the Guillemin-Wodzicki residue trace. The resulting functional is multiplicative, a local invariant, and not defined by a regularization procedure. The residue determinant is consequently a quite different object to the zeta function (quasi-) determinant, which is non-local and non-multiplicative.

We compute the relative zeta-function metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we prove a general formula relating the zeta-determinant to a Fredholm determinant over the boundary for a class of higher-order elliptic boundary value problems., Comment: 11 pages

Using properties of the determinant line bundle for a family of elliptic boundary value problems, we explain how the Fock space functor defines an axiomatic quantum field theory which formally models the Fermionic path integral. The 'sewing axiom' of the theory arises as an algebraic pasting law for the determinant of the Dirac operator. We show how representations of the boundary gauge group fit into this description and that this leads to a Fock functor description of certain gauge anomalies., Comment: 40 pages (latex)

It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with contributions from the families of Dirac operators over the two halves. This curvature form is the natural differential representative which satisifies the same splitting principle as the Chern class of the determinant line bundle., Comment: To appear in Proc. Am. Math. Soc