Quantum Algorithms: Entanglement Enhanced Information Processing

We discuss the fundamental role of entanglement as the essential nonclassical feature providing the computational speed-up in the known quantum algorithms. We review the construction of the Fourier transform on an Abelian group and the principles underlying the fast Fourier transform algorithm. We describe the implementation of the FFT algorithm for the group of integers modulo 2^n in the quantum context, showing how the group-theoretic formalism leads to the standard quantum network and identifying the property of entanglement that gives rise to the exponential speedup (compared to the classical FFT). Finally we outline the use of the Fourier transform in extracting periodicities, which underlies its utility in the known quantum algorithms.Comment: 17 pages latex, no figures. To appear in Phil. Trans. Roy. Soc. (Lond.) 1998, Proceedings of Royal Society Discussion Meeting ``Quantum Computation: Theory and Experiment'', held in November 199

Nematode distribution and damage to yam in central and eastern Uganda

Yams (Dioscorea spp.) are food crops of growing significance in sub Saharan Africa. Unfortunately, nematodes are major pests to their production. A study was undertaken in major yam growing areas of Uganda to investigate the association of plant parasitic nematodes with damage symptoms. Nematodes were assessed from tubers, roots and surrounding soil for seven cultivars belonging to Dioscorea alata, D. bulbisiana, D. burkilliana and D. cayenensis at harvest. Pratylenchus sudanensis was found in the greatest density and was followed byMeloidogyne spp. Higher densities of both nematodes were observed in the tubers rather than roots. Although symptoms of cracking and galling were relatively low, P. sudanensis incidence was strongly associated with cracking and Meloidogyne spp. with galling. Pratylenchus sudanensis and Meloidogyne spp. incidence their associated damage were, however, negatively correlated, suggesting inter-species competition. Principal components analysis of data suggested that differences in susceptibility to P. sudanensis occur between yam cultivars and species

Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to $J$, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform.Comment: 26 latex pages. Final version published in J. Fourier Anal. App

Stable carbon isotopic compositions of individual aromatic hydrocarbons as source and age indicators in oils from western Australian basins

The present study aims to establish the factors controlling the stable carbon isotopic compositions (d13C) of individual aromatic hydrocarbons analysed by compound specific isotope analysis (CSIA) in crude oils from western Australian petroleum basins of varying age and facies type. This paper reports d13C values of individual aromatic hydrocarbons, like alkylbenzenes, alkylnaphthalenes, alkylphenanthrenes and methylated biphenyls. The main aims are to confirm the origin (source) and age of these oils based on CSIA of selected aromatic compounds and to understand why the Sofer plot is ineffective in establishing the source of western Australian petroleum systems. The bulk d13C of saturated and aromatic hydrocarbon fractions of crude oils have been previously used to differentiate sources, however, many Australian crude oils are not classified correctly using this method. The oils were classified as marine by the d13C values of individual aromatic compounds and as terrigenous based on the bulk d13C data (Sofer plot). The oils where the d13C values of 1,6-DMN and 1,2,5-TMN isomers are most negative are indicative of a marine source, whereas oils with a less negative values for the 1,6-DMN and 1,2,5-TMN isomers are derived from marine source rocks that contain a significant terrigenous component. Similarly, oils with the least negative d13C values for the 1-MP and 1,9-DMP isomers reflect varying inputs of terrigenous organic matter to the their marine source rocks. Plots of P/DBT and Pr/Ph concentration ratios versus d13C values of DMP, 1,6-DMN, 1,2,5-TMN, 1-MP and 1,9-MP are constructed to establish the relative amount of terrigenous organic matter contributing to the source rock of a series of marine oils. The ratios of P/DBT and Pr/Ph plotted against the d13C values of the aromatic isomers (such as 1,6-DMN, 1,2,5-TMN, 1-MP and 1,9-MP) provide a novel and convenient way to discriminate crude oils derived from different source rocks that contain varying amounts of marine and terrigenous organic matter

A Wide Bandwidth Model for the Electrical Impedance of Magnetic BearingS

Magnetic bearings are often designed using magnetic circuit theory. When these bearings are built, however, effects not included in the usual circuit theory formulation have a significant influence on bearing performance. Two significant sources of error in the circuit theory approach are the neglect of leakage and fringing effects and the neglect of eddy current effects. This work formulates an augmented circuit model in which eddy current and flux leakage and fringing effects are included. Through the use of this model, eddy current power losses and actuator bandwidth can be derived. Electrical impedance predictions from the model are found to be in good agreement with experimental data from a typical magnetic bearing

Optimizing Illumina next-generation sequencing library preparation for extremely AT-biased genomes.

BAckground: Massively parallel sequencing technology is revolutionizing approaches to genomic and genetic research. Since its advent, the scale and efficiency of Next-Generation Sequencing (NGS) has rapidly improved. In spite of this success, sequencing genomes or genomic regions with extremely biased base composition is still a great challenge to the currently available NGS platforms. The genomes of some important pathogenic organisms like Plasmodium falciparum (high AT content) and Mycobacterium tuberculosis (high GC content) display extremes of base composition. The standard library preparation procedures that employ PCR amplification have been shown to cause uneven read coverage particularly across AT and GC rich regions, leading to problems in genome assembly and variation analyses. Alternative library-preparation approaches that omit PCR amplification require large quantities of starting material and hence are not suitable for small amounts of DNA/RNA such as those from clinical isolates. We have developed and optimized library-preparation procedures suitable for low quantity starting material and tolerant to extremely high AT content sequences. Results: We have used our optimized conditions in parallel with standard methods to prepare Illumina sequencing libraries from a non-clinical and a clinical isolate (containing ~53% host contamination). By analyzing and comparing the quality of sequence data generated, we show that our optimized conditions that involve a PCR additive (TMAC), produces amplified libraries with improved coverage of extremely AT-rich regions and reduced bias toward GC neutral templates. Conclusion: We have developed a robust and optimized Next-Generation Sequencing library amplification method suitable for extremely AT-rich genomes. The new amplification conditions significantly reduce bias and retain the complexity of either extremes of base composition. This development will greatly benefit sequencing clinical samples that often require amplification due to low mass of DNA starting material

Molecular basis of APC/C regulation by the spindle assembly checkpoint.

In the dividing eukaryotic cell, the spindle assembly checkpoint (SAC) ensures that each daughter cell inherits an identical set of chromosomes. The SAC coordinates the correct attachment of sister chromatid kinetochores to the mitotic spindle with activation of the anaphase-promoting complex (APC/C), the E3 ubiquitin ligase responsible for initiating chromosome separation. In response to unattached kinetochores, the SAC generates the mitotic checkpoint complex (MCC), which inhibits the APC/C and delays chromosome segregation. By cryo-electron microscopy, here we determine the near-atomic resolution structure of a human APC/C–MCC complex (APC/C(MCC)). Degron-like sequences of the MCC subunit BubR1 block degron recognition sites on Cdc20, the APC/C coactivator subunit responsible for substrate interactions. BubR1 also obstructs binding of the initiating E2 enzyme UbcH10 to repress APC/C ubiquitination activity. Conformational variability of the complex enables UbcH10 association, and structural analysis shows how the Cdc20 subunit intrinsic to the MCC (Cdc20(MCC)) is ubiquitinated, a process that results in APC/C reactivation when the SAC is silenced

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

Molecular mechanism of APC/C activation by mitotic phosphorylation.

In eukaryotes, the anaphase-promoting complex (APC/C, also known as the cyclosome) regulates the ubiquitin-dependent proteolysis of specific cell-cycle proteins to coordinate chromosome segregation in mitosis and entry into the G1 phase. The catalytic activity of the APC/C and its ability to specify the destruction of particular proteins at different phases of the cell cycle are controlled by its interaction with two structurally related coactivator subunits, Cdc20 and Cdh1. Coactivators recognize substrate degrons, and enhance the affinity of the APC/C for its cognate E2 (refs 4-6). During mitosis, cyclin-dependent kinase (Cdk) and polo-like kinase (Plk) control Cdc20- and Cdh1-mediated activation of the APC/C. Hyperphosphorylation of APC/C subunits, notably Apc1 and Apc3, is required for Cdc20 to activate the APC/C, whereas phosphorylation of Cdh1 prevents its association with the APC/C. Since both coactivators associate with the APC/C through their common C-box and Ile-Arg tail motifs, the mechanism underlying this differential regulation is unclear, as is the role of specific APC/C phosphorylation sites. Here, using cryo-electron microscopy and biochemical analysis, we define the molecular basis of how phosphorylation of human APC/C allows for its control by Cdc20. An auto-inhibitory segment of Apc1 acts as a molecular switch that in apo unphosphorylated APC/C interacts with the C-box binding site and obstructs engagement of Cdc20. Phosphorylation of the auto-inhibitory segment displaces it from the C-box-binding site. Efficient phosphorylation of the auto-inhibitory segment, and thus relief of auto-inhibition, requires the recruitment of Cdk-cyclin in complex with a Cdk regulatory subunit (Cks) to a hyperphosphorylated loop of Apc3. We also find that the small-molecule inhibitor, tosyl-l-arginine methyl ester, preferentially suppresses APC/C(Cdc20) rather than APC/C(Cdh1), and interacts with the binding sites of both the C-box and Ile-Arg tail motifs. Our results reveal the mechanism for the regulation of mitotic APC/C by phosphorylation and provide a rationale for the development of selective inhibitors of this state

High Performance Magnetic Bearings for Aero Applications

Several previous annual reports were written and numerous papers published on the topics for this grant. That work is not repeated here in this final report. Only the work completed in the final year of the grant is presented in this final report. This final year effort concentrated on power loss measurements in magnetic bearing rotors. The effect of rotor power losses in magnetic bearings are very important for many applications. In some cases, these losses must be minimized to maximize the length of time the rotating machine can operate on a fixed energy or power supply. Examples include aircraft gas turbine engines, space devices, or energy storage flywheels. In other applications, the heating caused by the magnetic bearing must be removed. Excessive heating can be a significant problem in machines as diverse as large compressors, electric motors, textile spindles, and artificial heart pumps