Critical Percolation in High Dimensions

We present Monte Carlo estimates for site and bond percolation thresholds in simple hypercubic lattices with 4 to 13 dimensions. For d<6 they are preliminary, for d >= 6 they are between 20 to 10^4 times more precise than the best previous estimates. This was achieved by three ingredients: (i) simple and fast hashing which allowed us to simulate clusters of millions of sites on computers with less than 500 MB memory; (ii) a histogram method which allowed us to obtain information for several p values from a single simulation; and (iii) a new variance reduction technique which is especially efficient at high dimensions where it reduces error bars by a factor up to approximately 30 and more. Based on these data we propose a new scaling law for finite cluster size corrections.Comment: 5 pages including figures, RevTe

Genetic characterization of human coxsackievirus A6 variants associated with atypical hand, foot and mouth disease: a potential role of recombination in emergence and pathogenicity

Human coxsackievirus A6 (CVA6) is an enterically transmitted enterovirus. Until recently, CVA6 infections were considered as being of minor clinical significance, and only rarely aetiologically linked with hand, foot and mouth disease (HFMD) associated with other species A enteroviruses (particularly EV71 and CVA16). From 2008 onwards, however, CVA6 infections have been associated with several outbreaks worldwide of atypical HFMD (aHFMD) accompanied by a varicelliform rash. We recently reported CVA6-associated eczema herpeticum occurring predominantly in children and young adults in Edinburgh in January and February 2014. To investigate genetic determinants of novel clinical phenotypes of CVA6, we genetically characterized and analysed CVA6 variants associated with eczema herpeticum in Edinburgh in 2014 and those with aHFMD in CAV isolates collected from 2008. A total of eight recombinant forms (RFs) have circulated worldwide over the past 10 years, with the particularly recent appearance of RF-H associated with eczema herpeticum cases in Edinburgh in 2014. Comparison of phylogenies and divergence of complete genome sequences of CVA6 identified recombination breakpoints in 2A-2C, within VP3, and between 5' untranslated region and VP1. A Bayesian temporal reconstruction of CVA6 evolution since 2004 provided estimates of dates and the actual recombination events that generated more recently appearing recombination groups (RF-E, -F, -G and -H). Associations were observed between recombination groups and clinical presentations of herpangina, aHFMD and eczema herpeticum, but not with VP1 or other structural genes. These observations provided evidence that NS gene regions may potentially contribute to clinical phenotypes and outcomes of CVA6 infection

Mechanistic Insights into the Palladium-Catalyzed Aziridination of Aliphatic Amines by C-H Activation.

Detailed kinetic studies and computational investigations have been performed to elucidate the mechanism of a palladium-catalyzed C-H activation aziridination. A theoretical rate law has been derived that matches with experimental observations and has led to an improvement in the reaction conditions. Acetic acid was found to be beneficial in controlling the formation of an off-cycle intermediate, allowing a decrease in catalyst loading and improved yields. Density functional theory (DFT) studies were performed to examine the selectivities observed in the reaction. Evidence for electronic-controlled regioselectivity for the cyclopalladation step was obtained by a distortion-interaction analysis, whereas the aziridination product was justified through dissociation of acetic acid from the palladium(IV) intermediate preceding the product-forming reductive elimination step. The understanding of this reaction mechanism under the synthesis conditions should provide valuable assistance in the comprehension and design of palladium-catalyzed reactions on similar systems.We are grateful to the EPSRC and Pfizer (A.P.S.) for a studentship and the ERC and EPSRC for fellowships (M.J.G.). We are also grateful to Dr Alex Thom and Dr David Pryde (Pfizer) for helpful discussions. The computational work was performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/), provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and funding from the Science and Technology Facilities Council. Mass spectrometry data were acquired at the EPSRC UK National Mass Spectrometry Facility at Swansea University.This is the accepted manuscript. The final version is available at http://pubs.acs.org/doi/abs/10.1021/jacs.5b05529

Microscopic analysis of multipole susceptibility of actinide dioxides: A scenario of multipole ordering in AmO2_2

By evaluating multipole susceptibility of a seven-orbital impurity Anderson model with the use of a numerical renormalization group method, we discuss possible multipole states of actinide dioxides at low temperatures. In particular, here we point out a possible scenario for multipole ordering in americium dioxide. For Am$^{4+}$ ion with five $5f$ electrons, it is considered that the ground state is $\Gamma_7^{-}$ doublet and the first excited state is $\Gamma_8^{-}$ quartet, but we remark that the $f^5$ ground state is easily converted due to the competition between spin-orbit coupling and Coulomb interactions. Then, we find that the $\Gamma_8^-$ quartet can be the ground state of AmO$_2$ even for the same crystalline electric field potential. In the case of $\Gamma_8^-$ quartet ground state, the numerical results suggest that high-order multipoles such as quadrupole and octupole can be relevant to AmO$_2$.Comment: 8 pages, 4 figures. To appear in Phys. Rev.

Universal Formulae for Percolation Thresholds

A power law is postulated for both site and bond percolation thresholds. The formula writes $p_c=p_0[(d-1)(q-1)]^{-a}d^{\ b}$, where $d$ is the space dimension and $q$ the coordination number. All thresholds up to $d\rightarrow \infty$ are found to belong to only three universality classes. For first two classes $b=0$ for site dilution while $b=a$ for bond dilution. The last one associated to high dimensions is characterized by $b=2a-1$ for both sites and bonds. Classes are defined by a set of value for $\{p_0; \ a\}$. Deviations from available numerical estimates at $d \leq 7$ are within $\pm 0.008$ and $\pm 0.0004$ for high dimensional hypercubic expansions at $d \geq 8$. The formula is found to be also valid for Ising critical temperatures.Comment: 11 pages, latex, 3 figures not include

Counting Lattice Animals in High Dimensions

We present an implementation of Redelemeier's algorithm for the enumeration of lattice animals in high dimensional lattices. The implementation is lean and fast enough to allow us to extend the existing tables of animal counts, perimeter polynomials and series expansion coefficients in $d$-dimensional hypercubic lattices for $3 \leq d\leq 10$. From the data we compute formulas for perimeter polynomials for lattice animals of size $n\leq 11$ in arbitrary dimension $d$. When amended by combinatorial arguments, the new data suffices to yield explicit formulas for the number of lattice animals of size $n\leq 14$ and arbitrary $d$. We also use the enumeration data to compute numerical estimates for growth rates and exponents in high dimensions that agree very well with Monte Carlo simulations and recent predictions from field theory.Comment: 18 pages, 7 figures, 6 tables; journal versio

Towards micro-imaging with dissolution dynamic nuclear polarisation

Nuclear magnetic resonance (NMR) of small samples and nuclei with a low gyromagnetic ratio is intrinsically insensitive due to the received signal dependence on Boltzmann's statistics. This insensitivity can be partially overcome through the application of hyper polarisation techniques such as Dissolution Dynamic Nuclear Polarisation (D-DNP). It is hoped that the hyper polarised 13C signal received from labelled small molecules could facilitate imaging of metabolic and transporter processes in biological systems. In order to realise this, appropriate molecules and experimental hardware must be used. A detailed description of the experimental set-up used for carrying out DDNP is given and the system is characterised. the advantageous use of a dual iso-centre magnet system is elucidated with optimisation of acquisition of fast relaxing molecules. such a system allows for interrogation of processes with short relaxation times, not possible with traditional, stand-alone polarisers. To acquire the maximum amount of hyper-polarised 13C signal in an imaging experiment, parallel acquisition techniques have been implemented and the hardware designed with such goals in mind. Multiple coils have been used to allow accelerated image acquisition. As such this work has validated the SENSE algorithm for artefact free, image reconstruction on the micro-scale. These techniques require an array of coils which add to the complexity of the design of the probehead. Decoupling methods and array coil construction must be considered the methods used to ensure well isolated coils, such as geometric decoupling, are presented. The novel fabrication and implementation of micro-coils for imaging and spectroscopy of nL scale samples is presented this will help facilitate the acquisition of images showing metabolic processes in active transport in cells. By placing the coils close to the sample it is possible to gain sensitivity relative to the mass of the sample in question. To achieve signal detection on the order of nL a novel, exible micro-coil array has been fabricated and the results of NMR experiments carried out on both protons and 13C are shown. This is the final stage before integrating the coils with the D-DNP system. The acquisition of 13C signal with the micro-coils displays optimal electronic characteristics when compared with other detectors presented in the literature. The final goal of the work is to produce a system that is capable of micro imaging in small biological samples such as the Xenopus Oocyte with a view to monitoring metabolic processes and transportation without the need for the use of the large fluorescing proteins (GFP's) that have been used in previous work (1). The need for GFP's attached to metabolites results in the measured data being non-physical as the fluorescing protein is often much larger than the molecule being transported. It is hoped that the use of hyperpolarised small molecules (such as pyruvic acid) may be able to remove this need for GFP's in the study of metabolite transportation