Locally Polynomially Bounded Structures

We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally definable in a fixed o-minimal and polynomially bounded reduct. As an application we show that in certain o-minimal structures definable functions are piecewise implicitly defined over the basic functions in the language.Comment: Change of titl

A Strategy for the Design of Flame Retardants: Cross-linking Processes

Cross-linking is identified as an effective means for flame retardation of polymers and schemes for the cross-linking of poly(ethylene terephthalate) and poly(methyl methacrylate) are presented. For poly(ethylene terephthalate) the scheme involves polymerization of the initially produced vinyl ester. This is followed by chain-stripping, producing a polyene, and cyclization of this polyene. For poly(methyl methacrylate) the scheme entails the formation of anhydride linkages between adjacent polymer strands. Evidence is presented to show the efficacy of these processes and information is produced to aid in the identification of new flame retardants

Exact norm-conserving stochastic time-dependent Hartree-Fock

We derive an exact single-body decomposition of the time-dependent Schroedinger equation for N pairwise-interacting fermions. Each fermion obeys a stochastic time-dependent norm-preserving wave equation. As a first test of the method we calculate the low energy spectrum of Helium. An extension of the method to bosons is outlined.Comment: 21 pages, 3 figures, LaTeX fil

On Recurrent Reachability for Continuous Linear Dynamical Systems

The continuous evolution of a wide variety of systems, including continuous-time Markov chains and linear hybrid automata, can be described in terms of linear differential equations. In this paper we study the decision problem of whether the solution $\boldsymbol{x}(t)$ of a system of linear differential equations $d\boldsymbol{x}/dt=A\boldsymbol{x}$ reaches a target halfspace infinitely often. This recurrent reachability problem can equivalently be formulated as the following Infinite Zeros Problem: does a real-valued function $f:\mathbb{R}_{\geq 0}\rightarrow\mathbb{R}$ satisfying a given linear differential equation have infinitely many zeros? Our main decidability result is that if the differential equation has order at most $7$, then the Infinite Zeros Problem is decidable. On the other hand, we show that a decision procedure for the Infinite Zeros Problem at order $9$ (and above) would entail a major breakthrough in Diophantine Approximation, specifically an algorithm for computing the Lagrange constants of arbitrary real algebraic numbers to arbitrary precision.Comment: Full version of paper at LICS'1

Suppression of decoherence via strong intra-environmental coupling

We examine the effects of intra-environmental coupling on decoherence by constructing a low temperature spin--spin-bath model of an atomic impurity in a Debye crystal. The impurity interacts with phonons of the crystal through anti-ferromagnetic spin-spin interactions. The reduced density matrix of the central spin representing the impurity is calculated by dynamically integrating the full Schroedinger equation for the spin--spin-bath model for different thermally weighted eigenstates of the spin-bath. Exact numerical results show that increasing the intra-environmental coupling results in suppression of decoherence. This effect could play an important role in the construction of solid state quantum devices such as quantum computers.Comment: 4 pages, 3 figures, Revtex fil

Bioinformatics tools for analysing viral genomic data

The field of viral genomics and bioinformatics is experiencing a strong resurgence due to high-throughput sequencing (HTS) technology, which enables the rapid and cost-effective sequencing and subsequent assembly of large numbers of viral genomes. In addition, the unprecedented power of HTS technologies has enabled the analysis of intra-host viral diversity and quasispecies dynamics in relation to important biological questions on viral transmission, vaccine resistance and host jumping. HTS also enables the rapid identification of both known and potentially new viruses from field and clinical samples, thus adding new tools to the fields of viral discovery and metagenomics. Bioinformatics has been central to the rise of HTS applications because new algorithms and software tools are continually needed to process and analyse the large, complex datasets generated in this rapidly evolving area. In this paper, the authors give a brief overview of the main bioinformatics tools available for viral genomic research, with a particular emphasis on HTS technologies and their main applications. They summarise the major steps in various HTS analyses, starting with quality control of raw reads and encompassing activities ranging from consensus and de novo genome assembly to variant calling and metagenomics, as well as RNA sequencing

A Schanuel property for exponentially transcendental powers

We prove the analogue of Schanuel's conjecture for raising to the power of an exponentially transcendental real number. All but countably many real numbers are exponentially transcendental. We also give a more general result for several powers in a context which encompasses the complex case.Comment: 5 page

When is Quantum Decoherence Dynamics Classical?

A direct classical analog of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum mechanically and classically are exposed via a second-order perturbative treatment and via a strong decoherence theory, showing a strong dependence on the nature of the system-environment coupling. For example, for the traditionally assumed linear coupling, the classical and quantum results are shown to be in exact agreement.Comment: 5 pages, no figures, to appear in Physical Review Letter