Decomposition algebras and axial algebras

We introduce decomposition algebras as a natural generalization of axial algebras, Majorana algebras and the Griess algebra. They remedy three limitations of axial algebras: (1) They separate fusion laws from specific values in a field, thereby allowing repetition of eigenvalues; (2) They allow for decompositions that do not arise from multiplication by idempotents; (3) They admit a natural notion of homomorphisms, making them into a nice category. We exploit these facts to strengthen the connection between axial algebras and groups. In particular, we provide a definition of a universal Miyamoto group which makes this connection functorial under some mild assumptions. We illustrate our theory by explaining how representation theory and association schemes can help to build a decomposition algebra for a given (permutation) group. This construction leads to a large number of examples. We also take the opportunity to fix some terminology in this rapidly expanding subject.Comment: 23 page

Signatures of hybridization in <i>Trypanosoma brucei</i>

Genetic exchange among disease-causing micro-organisms can generate progeny that combine different pathogenic traits. Though sexual reproduction has been described in trypanosomes, its impact on the epidemiology of Human African Trypanosomiasis (HAT) remains controversial. However, human infective and non-human infective strains of Trypanosoma brucei circulate in the same transmission cycles in HAT endemic areas in subsaharan Africa, providing the opportunity for mating during the developmental cycle in the tsetse fly vector. Here we investigated inheritance among progeny from a laboratory cross of T. brucei and then applied these insights to genomic analysis of field-collected isolates to identify signatures of past genetic exchange. Genomes of two parental and four hybrid progeny clones with a range of DNA contents were assembled and analysed by k-mer and single nucleotide polymorphism (SNP) frequencies to determine heterozygosity and chromosomal inheritance. Variant surface glycoprotein (VSG) genes and kinetoplast (mitochondrial) DNA maxi- and minicircles were extracted from each genome to examine how each of these components was inherited in the hybrid progeny. The same bioinformatic approaches were applied to an additional 37 genomes representing the diversity of T. brucei in subsaharan Africa and T. evansi. SNP analysis provided evidence of crossover events affecting all 11 pairs of megabase chromosomes and demonstrated that polyploid hybrids were formed post-meiotically and not by fusion of the parental diploid cells. VSGs and kinetoplast DNA minicircles were inherited biparentally, with approximately equal numbers from each parent, whereas maxicircles were inherited uniparentally. Extrapolation of these findings to field isolates allowed us to distinguish clonal descent from hybridization by comparing maxicircle genotype to VSG and minicircle repertoires. Discordance between maxicircle genotype and VSG and minicircle repertoires indicated inter-lineage hybridization. Significantly, some of the hybridization events we identified involved human infective and non-human infective trypanosomes circulating in the same geographic areas

Radio Foregrounds for the 21cm Tomography of the Neutral Intergalactic Medium at High Redshifts

Absorption or emission against the cosmic microwave background radiation (CMB) may be observed in the redshifted 21cm line if the spin temperature of the neutral intergalactic medium prior to reionization differs from the CMB temperature. This so-called 21cm tomography should reveal important information on the physical state of the intergalactic medium at high redshifts. The fluctuations in the redshifted 21 cm, due to gas density inhomogeneities at early times, should be observed at meter wavelengths by the next generation radio telescopes such as the proposed {\it Square Kilometer Array (SKA)}. Here we show that the extra-galactic radio sources provide a serious contamination to the brightness temperature fluctuations expected in the redshifted 21 cm emission from the IGM at high redshifts. Unless the radio source population cuts off at flux levels above the planned sensitivity of SKA, its clustering noise component will dominate the angular fluctuations in the 21 cm signal. The integrated foreground signal is smooth in frequency space and it should nonetheless be possible to identify the sharp spectral feature arising from the non-uniformities in the neutral hydrogen density during the epoch when the first UV sources reionize the intergalactic medium.Comment: 5 pages emulateapj with 1 figure, accepted to Ap

Imperfect Homoclinic Bifurcations

Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an explicit mathematical model of the system.Comment: 8 pages, 11 figures, submitted to PR

Investigation of a Cluster of Sequence Type 22 Methicillin-Resistant Staphylococcus aureus Transmission in a Community Setting.

BACKGROUND: Whole-genome sequencing (WGS) has typically been used to confirm or refute hospital/ward outbreaks of methicillin-resistant Staphylococcus aureus (MRSA) identified through routine practice. However, appropriately targeted WGS strategies that identify routinely "undetectable" transmission remain the ultimate aim. METHODS: WGS of MRSA isolates sent to a regional microbiological laboratory was performed as part of a 12-month prospective observational study. Phylogenetic analyses identified a genetically related cluster of E-MRSA15 isolated from patients registered to the same general practice (GP) surgery. This led to an investigation to identify epidemiological links, find additional cases, and determine potential for ongoing transmission. RESULTS: We identified 15 MRSA-positive individuals with 27 highly related MRSA isolates who were linked to the GP surgery, 2 of whom died with MRSA bacteremia. Of the 13 cases that were further investigated, 11 had attended a leg ulcer/podiatry clinic. Cases lacked epidemiological links to hospitals, suggesting that transmission occurred elsewhere. Environmental and staff screening at the GP surgery did not identify an ongoing source of infection. CONCLUSIONS: Surveillance in the United Kingdom shows that the proportion of MRSA bacteremias apportioned to hospitals is decreasing, suggesting the need for greater focus on the detection of MRSA outbreaks and transmission in the community. This case study confirms that the typically nosocomial lineage (E-MRSA15) can transmit within community settings. Our study exemplifies the continued importance of WGS in detecting outbreaks, including those which may be missed by routine practice, and suggests that universal WGS of bacteremia isolates may help detect outbreaks in low-surveillance settings

A Precise Cluster Mass Profile Averaged from the Highest-Quality Lensing Data

We outline our methods for obtaining high precision mass profiles, combining independent weak-lensing distortion, magnification, and strong-lensing measurements. For massive clusters the strong and weak lensing regimes contribute equal logarithmic coverage of the radial profile. The utility of high-quality data is limited by the cosmic noise from large scale structure along the line of sight. This noise is overcome when stacking clusters, as too are the effects of cluster asphericity and substructure, permitting a stringent test of theoretical models. We derive a mean radial mass profile of four similar mass clusters of high-quality HST and Subaru images, in the range R=40kpc/h to 2800kpc/h, where the inner radial boundary is sufficiently large to avoid smoothing from miscentering effects. The stacked mass profile is detected at 58-sigma significance over the entire radial range, with the contribution from the cosmic noise included. We show that the projected mass profile has a continuously steepening gradient out to beyond the virial radius, in remarkably good agreement with the standard Navarro-Frenk-White form predicted for the family of CDM-dominated halos in gravitational equilibrium. The central slope is constrained to lie in the range, -dln{\rho}/dln{r}=0.89^{+0.27}_{-0.39}. The mean concentration is c_{vir}=7.68^{+0.42}_{-0.40} (at a mean virial mass 1.54^{+0.11}_{-0.10}\times 10^{15} M_{sun}/h), which is high for relaxed, high-mass clusters, but consistent with LCDM when a sizable projection bias estimated from N-body simulations is considered. This possible tension will be more definitively explored with new cluster surveys, such as CLASH, LoCuSS, Subaru HSC, and XXM-XXL, to construct the c-M relation over a wider mass range.Comment: Accepted by ApJ, minor text changes (10 pages, 3 figures

Final report on project SP1210: Lowland peatland systems in England and Wales – evaluating greenhouse gas fluxes and carbon balances

Lowland peatlands represent one of the most carbon-rich ecosystems in the UK. As a result of widespread habitat modification and drainage to support agriculture and peat extraction, they have been converted from natural carbon sinks into major carbon sources, and are now amongst the largest sources of greenhouse gas (GHG) emissions from the UK land-use sector. Despite this, they have previously received relatively little policy attention, and measures to reduce GHG emissions either through re-wetting and restoration or improved management of agricultural land remain at a relatively early stage. In part, this has stemmed from a lack of reliable measurements on the carbon and GHG balance of UK lowland peatlands. This project aimed to address this evidence gap via an unprecedented programme of consistent, multi year field measurements at a total of 15 lowland peatland sites in England and Wales, ranging from conservation managed ‘near-natural’ ecosystems to intensively managed agricultural and extraction sites. The use of standardised measurement and data analysis protocols allowed the magnitude of GHG emissions and removals by peatlands to be quantified across this heterogeneous data set, and for controlling factors to be identified. The network of seven flux towers established during the project is believed to be unique on peatlands globally, and has provided new insights into the processes the control GHG fluxes in lowland peatlands. The work undertaken is intended to support the future development and implementation of agricultural management and restoration measures aimed at reducing the contribution of these important ecosystems to UK GHG emissions