Persistent homology of groups

We introduce and investigate notions of persistent homology for p-groups and for coclass trees of p-groups. Using computer techniques we show that persistent homology provides fairly strong homological invariants for p-groups of order at most 81. The strength of these invariants, and some elementary theoretical properties, suggest that persistent homology may be a useful tool in the study of prime-power groups.Comment: 12 pages, 6 figure

Origins of the amphiploid species Brassica napus L. investigated by chloroplast and nuclear molecular markers

Background: The amphiploid species Brassica napus (oilseed rape, Canola) is a globally important oil crop yielding food, biofuels and industrial compounds such as lubricants and surfactants. Identification of the likely ancestors of each of the two genomes (designated A and C) found in B. napus would facilitate incorporation of novel alleles from the wider Brassica genepool in oilseed rape crop genetic improvement programmes. Knowledge of the closest extant relatives of the genotypes involved in the initial formation of B. napus would also allow further investigation of the genetic factors required for the formation of a stable amphiploid and permit the more efficient creation of fully fertile re-synthesised B. napus. We have used a combination of chloroplast and nuclear genetic markers to investigate the closest extant relatives of the original maternal progenitors of B. napus. This was based on a comprehensive sampling of the relevant genepools, including 83 accessions of A genome B. rapa L. (both wild and cultivated types), 94 accessions of B. napus and 181 accessions of C genome wild and cultivated B. oleracea L. and related species. Results: Three chloroplast haplotypes occurred in B. napus. The most prevalent haplotype (found in 79% of accessions) was not present within the C genome accessions but was found at low frequencies in B. rapa. Chloroplast haplotypes characteristic of B. napus were found in a small number of wild and weedy B. rapa populations, and also in two accessions of cultivated B. rapa 'brocoletto'. Whilst introgression of the B. napus chloroplast type in the wild and weedy B. rapa populations has been proposed by other studies, the presence of this haplotype within the two brocoletto accessions is unexplained. Conclusions: The distribution of chloroplast haplotypes eliminates any of the C genome species as being the maternal ancestor of the majority of the B. napus accessions. The presence of multiple chloroplast haplotypes in B. napus and B. rapa accessions was not correlated with nuclear genetic diversity as determined by AFLPs, indicating that such accessions do not represent recent hybrids. Whilst some chloroplast diversity observed within B. napus can be explained by introgression from inter-specific crosses made during crop improvement programmes, there is evidence that the original hybridisation event resulting in to B. napus occurred on more than one occasion, and involved different maternal genotypes

Investigating intra-host and intra-herd sequence diversity of foot-and-mouth disease virus

Due to the poor-fidelity of the enzymes involved in RNA genome replication, foot-and-mouth disease (FMD) virus samples comprise of unique polymorphic populations. In this study, deep sequencing was utilised to characterise the diversity of FMD virus (FMDV) populations in 6 infected cattle present on a single farm during the series of outbreaks in the UK in 2007. A novel RT–PCR method was developed to amplify a 7.6 kb nucleotide fragment encompassing the polyprotein coding region of the FMDV genome. Illumina sequencing of each sample identified the fine polymorphic structures at each nucleotide position, from consensus level changes to variants present at a 0.24% frequency. These data were used to investigate population dynamics of FMDV at both herd and host levels, evaluate the impact of host on the viral swarm structure and to identify transmission links with viruses recovered from other farms in the same series of outbreaks. In 7 samples, from 6 different animals, a total of 5 consensus level variants were identified, in addition to 104 sub-consensus variants of which 22 were shared between 2 or more animals. Further analysis revealed differences in swarm structures from samples derived from the same animal suggesting the presence of distinct viral populations evolving independently at different lesion sites within the same infected animal

SU(3) family symmetry and neutrino bi-tri-maximal mixing

The observed large mixing angles in the lepton sector may be the first signal for the presence of a non-Abelian family symmetry. However, to obtain the significant differences between the mixing of the neutrino and charged fermion sectors, the vacuum expectation values involved in the breaking of such a symmetry in the two sectors must be misaligned. We investigate how this can be achieved in models with an SU(3) family symmetry consistent with an underlying GUT. We show that such misalignment can be achieved naturally via the see-saw mechanism. We construct a specific example in which the vacuum (mis)alignment is guaranteed by additional symmetries. This model generates a fermion mass structure consistent with all quark and lepton masses and mixing angles. Neutrino mixing is close to bi-tri-maximal mixing.Comment: References added; typos correcte

Systems modelling and simulation in the product development process for automotive powertrains : executive summary

This submission is a summary of the ten submissions that form the Engineering Doctorate Portfolio. The aim of the portfolio is to demonstrate the benefit of applying systems modelling and simulation in a modified powertrain product development process. A description is given of the competitive pressures that are faced by motor manufacturers in the global automotive business environment. Competitive pressures include a requirement for reduced time to market, exacting product quality standards, manufacturing over-capacity that increases fixed costs and compromises profit margins, and legislation that is increasingly difficult to meet. High-level strategic responses that are being made by manufacturers to these pressures are presented. Each strategic response requires organisational changes and improved approaches to the way in which day-to-day business is conducted. Computer Aided Engineering (CAE) is presented as an approach that can help to improve the competitiveness of motor manufacturers by reducing product development time and the level of hardware prototyping that is required. An investigation in five engineering companies yielded a number of observations about the use of CAE and its integration into product development. Best practice in the implementation of CAE in the product development process is defined. The use of CAE by a leading motor manufacturer in powertrain development is compared with the best practice model, and it is identified that there is a lack of coherence in the application of CAE. It is used to tackle specific problems but the use of CAE is not integrated into the product development process. More importantly, it was found that there is limited application of systems modelling and simulation, which is a critical technique for the effective integration of vehicle systems and the development of on-board vehicle control systems. Before systems modelling and simulation can be applied III powertrain development, an appropriate set of tools and associated modelling architecture must be determined. An appraisal of a range of different tools is undertaken, each tool being appraised against a set of criteria. A combination of DymolaIModelica and MATLAB/Simulink tools is recommended as the optimum solution. DymolaIModelica models of the vehicle plant should be embedded into Simulink models that also contain controller and driver models. MATLAB should be used as the numerical engine and for the creation of user environments. Transmission calibration is selected as a suitable pilot example for applying systems modelling and simulation in powertrain development. Best practice in CAE implementation and the systems modelling and simulation architecture are validated using this example. Simulation models of vehicles equipped with CVT and discrete ratio automatic transmissions are presented. A full description of the operation of the transmission system, of the simulation model itself, and of the validation of the model is presented in each case. The potential benefit of the CVT model in transmission calibration is demonstrated. A Transmission Calibration Simulation Tool (TCST) is described within which the discrete ratio simulation model is encapsulated. The TCST includes a user environment in which the simulation model can be parameterised, a variety of simulation runs can be specified, and simulation results are processed. Development of the TCST requires an objective measure of driveability effects that are influenced by the transmission shift schedule. A method for objective assessment of driveability is developed, correlated, and implemented as an integral part of the TCST. This element of the TCST allows trade-off exercises to be conducted between fuel economy and driveability. The development of a transmission calibration based on experimental testing is compared with a similar exercise based on simulation testing. This study shows that, if the TCST is properly integrated into the transmission calibration process, the vehicle test time taken to optimise the calibration for fuel economy could be reduced by six weeks, and a week of calibrator time could be saved. Thus, the aim of the submission is fulfilled, since the benefit of applying systems modelling and simulation in the powertrain development process has been demonstrated. It is concluded that a consistent approach is required for effectively integrating systems modelling and simulation into the product development process. A model is proposed that clarifies how this can be achieved at a local level. It is proposed that in the future, the model is applied whenever systems modelling and simulation is introduced into a powertrain department

Standardized gene nomenclature for the Brassica genus

The genus Brassica (Brassicaceae, Brassiceae) is closely related to the model plant Arabidopsis, and includes several important crop plants. Against the background of ongoing genome sequencing, and in line with efforts to standardize and simplify description of genetic entities, we propose a standard systematic gene nomenclature system for the Brassica genus. This is based upon concatenating abbreviated categories, where these are listed in descending order of significance from left to right (i.e. genus – species – genome – gene name – locus – allele). Indicative examples are provided, and the considerations and recommendations for use are discussed, including outlining the relationship with functionally well-characterized Arabidopsis orthologues. A Brassica Gene Registry has been established under the auspices of the Multinational Brassica Genome Project that will enable management of gene names within the research community, and includes provisional allocation of standard names to genes previously described in the literature or in sequence repositories. The proposed standardization of Brassica gene nomenclature has been distributed to editors of plant and genetics journals and curators of sequence repositories, so that it can be adopted universally

Implementing quadratic supergravity inflation

We study inflation driven by a slow-rolling inflaton field, characterised by a quadratic potential, and incorporating radiative corrections within the context of supergravity. In this model the energy scale of inflation is not overly constrained by the requirement of generating the observed level of density fluctuations and can have a physically interesting value, e.g. the supersymmetry breaking scale of $10^{10}$ GeV or the electroweak scale of $10^3$ GeV. In this mass range the inflaton is light enough to be confined at the origin by thermal effects, naturally generating the initial conditions for a (last) stage of inflation of the new inflationary type.Comment: 8 pages, 1 figur