Asymptotics of Relativistic Spin Networks

The stationary phase technique is used to calculate asymptotic formulae for SO(4) Relativistic Spin Networks. For the tetrahedral spin network this gives the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j symbol. For the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical calculations of the Spin Network evaluation. Finally we discuss the asymptotics of the SO(3,1) 10j-symbol.Comment: 31 pages, latex. v3: minor clarification

Temperature dependent nonlinear metal matrix laminae behavior

An analytical method is described for computing the nonlinear thermal and mechanical response of laminated plates. The material model focuses upon the behavior of metal matrix materials by relating the nonlinear composite response to plasticity effects in the matrix. The foundation of the analysis is the unidirectional material model which is used to compute the instantaneous properties of the lamina based upon the properties of the fibers and matrix. The unidirectional model assumes that the fibers properties are constant with temperature and assumes that the matrix can be modelled as a temperature dependent, bilinear, kinematically hardening material. An incremental approach is used to compute average stresses in the fibers and matrix caused by arbitrary mechanical and thermal loads. The layer model is incorporated in an incremental laminated plate theory to compute the nonlinear response of laminated metal matrix composites of general orientation and stacking sequence. The report includes comparisons of the method with other analytical approaches and compares theoretical calculations with measured experimental material behavior. A section is included which describes the limitations of the material model

A superconducting cavity bus for single Nitrogen Vacancy defect centres in diamond

Circuit-QED has demonstrated very strong coupling between individual microwave photons trapped in a superconducting coplanar resonator and nearby superconducting qubits. In this work we show how, by designing a novel interconnect, one can strongly connect the superconducting resonator, via a magnetic interaction, to a small number (perhaps single), of electronic spins. By choosing the electronic spin to be within a Nitrogen Vacancy centre in diamond one can perform optical readout, polarization and control of this electron spin using microwave and radio frequency irradiation. More importantly, by utilising Nitrogen Vacancy centres with nearby 13C nuclei, using this interconnect, one has the potential build a quantum device where the nuclear spin qubits are connected over centimeter distances via the Nitrogen Vacancy electronic spins interacting through the superconducting bus.Comment: 4 pages, 6 figure

The MEROPS Database

Many proteins undergo important post-translational proteolytic processing to remove targeting signals and activation peptides, and most proteins undergo proteolytic inactivation and catabolism. The enzymes that hydrolyse the peptide bonds in proteins and peptides are known as peptidases, proteases or proteolytic enzymes. The MEROPS database ("http://merops.sanger.ac.uk":http://merops.sanger.ac.uk) presents the classification and nomenclature of peptidases, their inhibitors and substrates. In 1993 we proposed the scheme for the classification of peptidases that has been internationally accepted, and in 1996 we established the MEROPS database. Protein inhibitors have been included in the database since 2004. About 2% of the genes in a genome encode peptidase homologues, and a further 1% encode protein inhibitors. For example, the human genome has 1037 genes encoding peptidase homologues (of which 643 are known or predicted to be active peptidases) and 433 protein inhibitor genes (of which 144 have been biochemically characterized as inhibitors). 

The MEROPS classification is hierarchical. Sequences are grouped into a peptidase species (each of which is given a unique identifier, for example C01.060 for cathepsin B); peptidase species are grouped into a family (for example C1); and families grouped into a clan (for example CA). To be included in the same protein species, sequences must be derived from the same node on a dendrogram derived from the family sequence alignment and known (or predicted) to share similar specificity. To be included in the same family sequences must be homologous over the sequence domain that contains the active site residues (peptidases) or reactive site (inhibitors). To be included in the same clan, the proteins must share similar tertiary structures (or the same linear arrangement of active site residues if the structure is unknown). Over 117,000 peptidase homologues are classified into 3114 protein species, 205 families and 52 clans, and 12,104 protein inhibitors are classified into 663 protein species, 64 families and 33 clans.

The database includes manually curated summaries for each clan, family and protein species. There are also sequence alignments and manually curated bibliographies (with over 41,000 references) at every level. In addition to protein inhibitors we also include 158 manually curated summaries for synthetic and naturally occurring small molecule inhibitors. There is also a summary page for each organism listing all known homologues and an analysis highlighting significant presences, absences or gene family expansions for organisms with a completely sequenced genome. 

The MEROPS database includes known peptidase substrates: naturally occurring peptides and proteins, and synthetic substrates. Currently there are 4091 cleavages of synthetic substrates and 95,413 cleavages of proteins (of which 74,740 are physiological). Cleavages in proteins are mapped to UniProt entries. An alignment of very close homologues of each substrate sequence is shown, highlighting residues around each cleavage site indicating whether the peptidase is known to accept the amino acid at that position or not. Cleavage sites that are conserved are likely to be physiological; cleavage sites that are not conserved may be pathological for the species in which they occur or coincidental.

The MEROPS data is freely available to download from our FTP site ("http://ftp.sanger.ac.uk/pub/MEROPS":http://ftp.sanger.ac.uk/pub/MEROPS) and via our Distributed Annotation System (DAS) server ("http://das.sanger.ac.uk/das/merops":http://das.sanger.ac.uk/das/merops).
&#xa

Holonomy observables in Ponzano-Regge type state sum models

We study observables on group elements in the Ponzano-Regge model. We show that these observables have a natural interpretation in terms of Feynman diagrams on a sphere and contrast them to the well studied observables on the spin labels. We elucidate this interpretation by showing how they arise from the no-gravity limit of the Turaev-Viro model and Chern-Simons theory.Comment: 15 pages, 2 figure

Finiteness and Dual Variables for Lorentzian Spin Foam Models

We describe here some new results concerning the Lorentzian Barrett-Crane model, a well-known spin foam formulation of quantum gravity. Generalizing an existing finiteness result, we provide a concise proof of finiteness of the partition function associated to all non-degenerate triangulations of 4-manifolds and for a class of degenerate triangulations not previously shown. This is accomplished by a suitable re-factoring and re-ordering of integration, through which a large set of variables can be eliminated. The resulting formulation can be interpreted as a ``dual variables'' model that uses hyperboloid variables associated to spin foam edges in place of representation variables associated to faces. We outline how this method may also be useful for numerical computations, which have so far proven to be very challenging for Lorentzian spin foam models.Comment: 15 pages, 1 figur