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

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

Magnetization Plateaux in Bethe Ansatz Solvable Spin-S Ladders

We examine the properties of the Bethe Ansatz solvable two- and three-leg spin-$S$ ladders. These models include Heisenberg rung interactions of arbitrary strength and thus capture the physics of the spin-$S$ Heisenberg ladders for strong rung coupling. The discrete values derived for the magnetization plateaux are seen to fit with the general prediction based on the Lieb-Schultz- Mattis theorem. We examine the magnetic phase diagram of the spin-1 ladder in detail and find an extended magnetization plateau at the fractional value $= {1/2}$ in agreement with the experimental observation for the spin-1 ladder compound BIP-TENO.Comment: 11 pages, 1 figur

Comparison of phenomics and cfDNA in a large breast screening population: the Breast Screening and Monitoring Study (BSMS)

To assess their roles in breast cancer diagnostics, we aimed to compare plasma cell-free DNA (cfDNA) levels with the circulating metabolome in a large breast screening cohort of women recalled for mammography, including healthy women and women with mammographically detected breast diseases, ductal carcinoma in situ and invasive breast cancer: the Breast Screening and Monitoring Study (BSMS). In 999 women, plasma was analyzed by nuclear magnetic resonance (NMR) and Ultra-Performance Liquid Chromatography-Mass Spectrometry (UPLC-MS) and then processed to isolate and quantify total cfDNA. NMR and UPLC-MS results were compared with data for 186 healthy women derived from the AIRWAVE cohort. Results showed no significant differences between groups for all metabolites, whereas invasive cancers had significantly higher plasma cfDNA levels than all other groups. When stratified the supervised OPLS-DA analysis and total cfDNA concentration showed high discrimination accuracy between invasive cancers and the disease/medication-free subjects. Furthermore, comparison of OPLS-DA data for invasive breast cancers with the AIRWAVE cohort showed similar discrimination between breast cancers and healthy controls. This is the first report of agreement between metabolomics and plasma cfDNA levels for discriminating breast cancer from healthy subjects in a true screening population. It also emphasizes the importance of sample standardization. Follow on studies will involve analysis of candidate features in a larger validation series as well as comparing results with serial plasma samples taken at the next routine screening mammography appointment. The findings here help establish the role of plasma analysis in the diagnosis of breast cancer in a large real-world cohort

Note on the thermodynamic Bethe Ansatz approach to the quantum phase diagram of the strong coupling ladder compounds

We investigate the low-temperature phase diagram of the exactly solved su(4) two-leg spin ladder as a function of the rung coupling $J_{\perp}$ and magnetic field $H$ by means of the thermodynamic Bethe Ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases, while in the presence of a strong magnetic field there is no singlet ground state for ferromagnetic rung coupling. For antiferromagnetic rung coupling, there is a gapped phase in the regime H H_{c2} and a Luttinger liquid magnetic phase in the regime H_{c1} < H < H_{c2}. The critical behaviour derived using the TBA is consistent with the existing experimental, numerical and perturbative results for the strong coupling ladder compounds. This includes the spin excitation gap and the critical fields H_{c1} and H_{c2}, which are in excellent agreement with the experimental values for the known strong coupling ladder compounds (5IAP)_2CuBr_4 2H_2 O, Cu_2(C_5 H_{12} N_2)_2 Cl_4 and (C_5 H_{12} N)_2 CuBr_4. In addition we predict the spin gap $\Delta \approx J_{\perp}-{1/2}J_{\parallel}$ for the weak coupling compounds with $J_{\perp} \sim J_{\parallel}$, such as (VO)_2 P_2 O_7, and also show that the gap opens for arbitrary $J_{\perp}/ J_{\parallel}$.Comment: 10 pages, 3 figure

Ensembl Genomes 2013: scaling up access to genome-wide data

Ensembl Genomes (http://www.ensemblgenomes.org) is an integrating resource for genome-scale data from non-vertebrate species. The project exploits and extends technologies for genome annotation, analysis and dissemination, developed in the context of the vertebrate-focused Ensembl project, and provides a complementary set of resources for non-vertebrate species through a consistent set of programmatic and interactive interfaces. These provide access to data including reference sequence, gene models, transcriptional data, polymorphisms and comparative analysis. This article provides an update to the previous publications about the resource, with a focus on recent developments. These include the addition of important new genomes (and related data sets) including crop plants, vectors of human disease and eukaryotic pathogens. In addition, the resource has scaled up its representation of bacterial genomes, and now includes the genomes of over 9000 bacteria. Specific extensions to the web and programmatic interfaces have been developed to support users in navigating these large data sets. Looking forward, analytic tools to allow targeted selection of data for visualization and download are likely to become increasingly important in future as the number of available genomes increases within all domains of life, and some of the challenges faced in representing bacterial data are likely to become commonplace for eukaryotes in future

Drug-resistant genotypes and multi-clonality in Plasmodium falciparum analysed by direct genome sequencing from peripheral blood of malaria patients.

Naturally acquired blood-stage infections of the malaria parasite Plasmodium falciparum typically harbour multiple haploid clones. The apparent number of clones observed in any single infection depends on the diversity of the polymorphic markers used for the analysis, and the relative abundance of rare clones, which frequently fail to be detected among PCR products derived from numerically dominant clones. However, minority clones are of clinical interest as they may harbour genes conferring drug resistance, leading to enhanced survival after treatment and the possibility of subsequent therapeutic failure. We deployed new generation sequencing to derive genome data for five non-propagated parasite isolates taken directly from 4 different patients treated for clinical malaria in a UK hospital. Analysis of depth of coverage and length of sequence intervals between paired reads identified both previously described and novel gene deletions and amplifications. Full-length sequence data was extracted for 6 loci considered to be under selection by antimalarial drugs, and both known and previously unknown amino acid substitutions were identified. Full mitochondrial genomes were extracted from the sequencing data for each isolate, and these are compared against a panel of polymorphic sites derived from published or unpublished but publicly available data. Finally, genome-wide analysis of clone multiplicity was performed, and the number of infecting parasite clones estimated for each isolate. Each patient harboured at least 3 clones of P. falciparum by this analysis, consistent with results obtained with conventional PCR analysis of polymorphic merozoite antigen loci. We conclude that genome sequencing of peripheral blood P. falciparum taken directly from malaria patients provides high quality data useful for drug resistance studies, genomic structural analyses and population genetics, and also robustly represents clonal multiplicity

Celebrating Cercignani's conjecture for the Boltzmann equation

Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s.Comment: This paper is dedicated to the memory of the late Carlo Cercignani, powerful mind and great scientist, one of the founders of the modern theory of the Boltzmann equation. 24 pages. V2: correction of some typos and one ref. adde

InterPro: the integrative protein signature database

The InterPro database (http://www.ebi.ac.uk/interpro/) integrates together predictive models or ‘signatures' representing protein domains, families and functional sites from multiple, diverse source databases: Gene3D, PANTHER, Pfam, PIRSF, PRINTS, ProDom, PROSITE, SMART, SUPERFAMILY and TIGRFAMs. Integration is performed manually and approximately half of the total ∼58 000 signatures available in the source databases belong to an InterPro entry. Recently, we have started to also display the remaining un-integrated signatures via our web interface. Other developments include the provision of non-signature data, such as structural data, in new XML files on our FTP site, as well as the inclusion of matchless UniProtKB proteins in the existing match XML files. The web interface has been extended and now links out to the ADAN predicted protein-protein interaction database and the SPICE and Dasty viewers. The latest public release (v18.0) covers 79.8% of UniProtKB (v14.1) and consists of 16 549 entries. InterPro data may be accessed either via the web address above, via web services, by downloading files by anonymous FTP or by using the InterProScan search software (http://www.ebi.ac.uk/Tools/InterProScan/

Advancing vector biology research: a community survey for future directions, research applications and infrastructure requirements

Vector-borne pathogens impact public health, animal production, and animal welfare. Research on arthropod vectors such as mosquitoes, ticks, sandflies, and midges which transmit pathogens to humans and economically important animals is crucial for development of new control measures that target transmission by the vector. While insecticides are an important part of this arsenal, appearance of resistance mechanisms is increasingly common. Novel tools for genetic manipulation of vectors, use of Wolbachia endosymbiotic bacteria, and other biological control mechanisms to prevent pathogen transmission have led to promising new intervention strategies, adding to strong interest in vector biology and genetics as well as vector-pathogen interactions. Vector research is therefore at a crucial juncture, and strategic decisions on future research directions and research infrastructure investment should be informed by the research community. A survey initiated by the European Horizon 2020 INFRAVEC-2 consortium set out to canvass priorities in the vector biology research community and to determine key activities that are needed for researchers to efficiently study vectors, vector-pathogen interactions, as well as access the structures and services that allow such activities to be carried out. We summarize the most important findings of the survey which in particular reflect the priorities of researchers in European countries, and which will be of use to stakeholders that include researchers, government, and research organizations