Converting three-space matrices to equivalent six-space matrices for Delone scalars in S6.

The transformations from the primitive cells of the centered Bravais lattices to the corresponding centered cells have conventionally been listed as three-by-three matrices that transform three-space lattice vectors. Using those three-by-three matrices when working in the six-dimensional space of lattices represented as Selling scalars as used in Delone (Delaunay) reduction, one could transform to the three-space representation, apply the three-by-three matrices and then back-transform to the six-space representation, but it is much simpler to have the equivalent six-by-six matrices and apply them directly. The general form of the transformation from the three-space matrix to the corresponding matrix operating on Selling scalars (expressed in space S6) is derived, and the particular S6matrices for the centered Delone types are listed. (Note: in his later publications, Boris Delaunay used the Russian version of his surname, Delone.)

Modelling the hepatitis B vaccination programme in prisons

A vaccination programme offering hepatitis B (HBV) vaccine at reception into prison has been introduced into selected prisons in England and Wales. Over the coming years it is anticipated this vaccination programme will be extended. A model has been developed to assess the potential impact of the programme on the vaccination coverage of prisoners, ex-prisoners, and injecting drug users (IDUs). Under a range of coverage scenarios, the model predicts the change over time in the vaccination status of new entrants to prison, current prisoners and IDUs in the community. The model predicts that at baseline in 2012 57% of the IDU population will be vaccinated with up to 72% being vaccinated depending on the vaccination scenario implemented. These results are sensitive to the size of the IDU population in England and Wales and the average time served by an IDU during each prison visit. IDUs that do not receive HBV vaccine in the community are at increased risk from HBV infection. The HBV vaccination programme in prisons is an effective way of vaccinating this hard-to-reach population although vaccination coverage on prison reception must be increased to achieve this

The hydrodynamic evolution of binary black holes embedded within the vertically stratified disks of active galactic nuclei

Stellar-mass black holes can become embedded within the gaseous disks of active galactic nuclei (AGNs). Afterwards, their interactions are mediated by their gaseous surroundings. In this work, we study the evolution of stellar-mass binary black holes (BBHs) embedded within AGN disks using a combination of three-dimensional hydrodynamic simulations and analytic methods, focusing on environments in which the AGN disk scale height $H$ is $\gtrsim$ the BBH sphere of influence. We model the local surroundings of the embedded BBHs using a wind tunnel formalism and characterize different accretion regimes based on the local properties of the disk, which range from wind-dominated to quasi-spherical. We use our simulations to develop prescriptions for mass accretion and drag for embedded BBHs. We use these prescriptions, along with AGN disk models that can represent the Toomre-unstable outer regions of AGN disks, to study the long-term evolution of the BBHs as they migrate through the disk. We find that BBHs typically merge within $\lesssim 5-30\,{\rm Myr}$, increasing their mass significantly in the process, allowing BBHs to enter (or cross) the pair-instability supernova mass gap. The rate at which gas is supplied to these BBHs often exceeds the Eddington limit, sometimes by several orders of magnitude. We conclude that most embedded BBHs will merge before migrating significantly in the disk. Depending on the conditions of the ambient gas and the distance to the system, LISA can detect the transition between the gas-dominated and gravitational wave dominated regime for inspiraling BBHs that are formed sufficiently close to the AGN ($\lesssim$ 0.1 pc). We also discuss possible electromagnetic signatures during and following the inspiral, finding that it is generally unlikely but not inconceivable for the bolometric luminosity of the BBH to exceed that of the host AGN.Comment: 19 pages, 8 figures, submitted to Ap

Identification of a Core Amino Acid Motif within the α Subunit of GABAARs that Promotes Inhibitory Synaptogenesis and Resilience to Seizures

The fidelity of inhibitory neurotransmission is dependent on the accumulation of γ-aminobutyric acid type A receptors (GABAARs) at the appropriate synaptic sites. Synaptic GABAARs are constructed from α(1-3), β(1-3), and γ2 subunits, and neurons can target these subtypes to specific synapses. Here, we identify a 15-amino acid inhibitory synapse targeting motif (ISTM) within the α2 subunit that promotes the association between GABAARs and the inhibitory scaffold proteins collybistin and gephyrin. Using mice in which the ISTM has been introduced into the α1 subunit (Gabra1-2 mice), we show that the ISTM is critical for axo-axonic synapse formation, the efficacy of GABAergic neurotransmission, and seizure sensitivity. The Gabra1-2 mutation rescues seizure-induced lethality in Gabra2-1 mice, which lack axo-axonic synapses due to the deletion of the ISTM from the α2 subunit. Taken together, our data demonstrate that the ISTM plays a critical role in promoting inhibitory synapse formation, both in the axonic and somatodendritic compartments

The Genomics of Streptococcus Pneumoniae Carriage Isolates from UK Children and Their Household Contacts, Pre-PCV7 to Post-PCV13.

We used whole genome sequencing (WGS) analysis to investigate the population structure of 877 Streptococcus pneumoniae isolates from five carriage studies from 2002 (N = 346), 2010 (N = 127), 2013 (N = 153), 2016 (N = 187) and 2018 (N = 64) in UK households which covers the period pre-PCV7 to post-PCV13 implementation. The genomic lineages seen in the population were determined using multi-locus sequence typing (MLST) and PopPUNK (Population Partitioning Using Nucleotide K-mers) which was used for local and global comparisons. A Roary core genome alignment of all the carriage genomes was used to investigate phylogenetic relationships between the lineages. The results showed an influx of previously undetected sequence types after vaccination associated with non-vaccine serotypes. A small number of lineages persisted throughout, associated with both non-vaccine and vaccine types (such as ST199), or that could be an example of serotype switching from vaccine to non-vaccine types (ST177). Serotype 3 persisted throughout the study years, represented by ST180 and Global Pneumococcal Sequencing Cluster (GPSC) 12; the local PopPUNK analysis and core genome maximum likelihood phylogeny separated them into two clades, one of which is only seen in later study years. The genomic data showed that serotype replacement in the carriage studies was mostly due to a change in genotype as well as serotype, but that some important genetic lineages, previously associated with vaccine types, persisted

Exact S-matrices for supersymmetric sigma models and the Potts model

We study the algebraic formulation of exact factorizable S-matrices for integrable two-dimensional field theories. We show that different formulations of the S-matrices for the Potts field theory are essentially equivalent, in the sense that they can be expressed in the same way as elements of the Temperley-Lieb algebra, in various representations. This enables us to construct the S-matrices for certain nonlinear sigma models that are invariant under the Lie ``supersymmetry'' algebras sl(m+n|n) (m=1,2; n>0), both for the bulk and for the boundary, simply by using another representation of the same algebra. These S-matrices represent the perturbation of the conformal theory at theta=pi by a small change in the topological angle theta. The m=1, n=1 theory has applications to the spin quantum Hall transition in disordered fermion systems. We also find S-matrices describing the flow from weak to strong coupling, both for theta=0 and theta=pi, in certain other supersymmetric sigma models.Comment: 32 pages, 8 figure