Quantum stochastic convolution cocycles II

Schuermann's theory of quantum Levy processes, and more generally the theory of quantum stochastic convolution cocycles, is extended to the topological context of compact quantum groups and operator space coalgebras. Quantum stochastic convolution cocycles on a C*-hyperbialgebra, which are Markov-regular, completely positive and contractive, are shown to satisfy coalgebraic quantum stochastic differential equations with completely bounded coefficients, and the structure of their stochastic generators is obtained. Automatic complete boundedness of a class of derivations is established, leading to a characterisation of the stochastic generators of *-homomorphic convolution cocycles on a C*-bialgebra. Two tentative definitions of quantum Levy process on a compact quantum group are given and, with respect to both of these, it is shown that an equivalent process on Fock space may be reconstructed from the generator of the quantum Levy process. In the examples presented, connection to the algebraic theory is emphasised by a focus on full compact quantum groups.Comment: 32 pages, expanded introduction and updated references. The revised version will appear in Communications in Mathematical Physic

‘Changing it up’: the lived experiences of a wheelchair sport intervention amongst secondary school pupils aged 11-12 in Lincolnshire

Despite recent developments, related to adapted physical activity programs, much is still needed to enhance the contributions these programs make toward rearticulating conceptions of disability (Fitzgerald, 2005). Research often suggests that a superficial belief in traditional, ‘normalised’ physical education habiti is held within schools and is rarely questioned. Sport integration typically focuses on either the inclusion of disabled individuals within traditionally able-bodied sports, or the inclusion of disability sports as separate events within mainstream sport (Nixon, 2007). Based on this, a call to look beyond typical strategies of adaption and integration has been made, with an aim to identifying innovative methods to question dominant conceptions regarding disability and disability sport (Fitzgerald, 2005). The key aim of this study was to investigate changes in secondary school pupils’ perceptions of disability sport during a Lincolnshire County Sports Partnership intervention entitled ‘The LSP Wheelchair Sports Project.’ The intervention utilised a reverse-integration method of delivery, incorporating wheelchair basketball into pupils PE lessons for a 12 week period. Bourdieu’s theoretical standpoint was used to provide theoretical foundation for the study while Chris Shillings work (2003) provided context specific, theoretical foundation to explain potential perceptions of participants prior to the intervention. 50 pupils aged between 1 and 12 took part in this research. All pupils, regardless of physical status, took part in the intervention. Semi-embedded ethnographic observations were made over the 12 week intervention period at one school in the city of Lincoln. This highlighted key behaviour themes among pupils which were then discussed in guided group interviews. Guided group interviews with 40 of participants highlighted pupils perceptions of disability and disability sport prior to the intervention. They also provided pupils with an opportunity to discuss their experiences of the intervention and thus any potential perceptual changes

Quantum stochastic convolution cocycles III

Every Markov-regular quantum Levy process on a multiplier C*-bialgebra is shown to be equivalent to one governed by a quantum stochastic differential equation, and the generating functionals of norm-continuous convolution semigroups on a multiplier C*-bialgebra are then completely characterised. These results are achieved by extending the theory of quantum Levy processes on a compact quantum group, and more generally quantum stochastic convolution cocycles on a C*-bialgebra, to locally compact quantum groups and multiplier C*-bialgebras. Strict extension results obtained by Kustermans, together with automatic strictness properties developed here, are exploited to obtain existence and uniqueness for coalgebraic quantum stochastic differential equations in this setting. Then, working in the universal enveloping von Neumann bialgebra, we characterise the stochastic generators of Markov-regular, *-homomorphic (respectively completely positive and contractive), quantum stochastic convolution cocycles.Comment: 20 pages; v2 corrects some typos and no longer contains a section on quantum random walk approximations, which will now appear as a separate submission. The article will appear in the Mathematische Annale

Hannah Arendt, the problem of the absolute and the paradox of constitutionalism, or ‘How to restart time within an inexorable time continuum’

Contemporary theorists of constituent power recognise a tension in which the omnipotent novelty of constituent power is necessarily policed by constituted power. Beginning with Arendt’s claim that the categories of constitutional stability and political novelty should be thought together rather than treated as oppositional, this article presents an interpretation of her work that seeks to address this ‘paradox of constitutionalism’. Whilst commentators have come to assert that Arendt repudiates ‘absolutes’ in favour of an account of ‘relative beginnings’, this article demonstrates that Arendt’s argument involves a critical redescription of the absolute, rather than a repudiation. This is significant, for it illuminates the manner in which her account of founding seeks to dismantle the commonplace temporalisations we attribute to our political vocabulary. This is employed to argue that particular stylings of absolutes naturalise the appearance of the new only as temporal ruptures, allowing us to get a handle upon the paradox of constitutionalism, and to think tentatively beyond this paradigm

Developing analytical distributions for temperature indices for the purposes of pricing temperature-based weather derivatives

Temperature-based weather derivatives are written on an index which is normally defined to be a nonlinear function of average daily temperatures. Recent empirical work has demonstrated the usefulness of simple time-series models of temperature for estimating the payoffs to these instruments. This paper develops analytical distributions of temperature indices on which temperature derivatives are written. If deviations of daily temperature from its expected value is modelled as an Ornstein-Uhlenbeck process with time-varying variance, then the distributions of the temperature index on which the derivative is written is the sum of truncated, correlated Gaussian deviates. The key result of this paper is to provide an analytical approximation to the distribution of this sum, thus allowing the accurate computation of payoffs without the need for any simulation. A data set comprising average daily temperature spanning over a hundred years for four Australian cities is used to demonstrate the efficacy of this approach for estimating the payoffs to temperature derivatives. It is demonstrated that expected payoffs computed directly from historical records is a particulary poor approach to the problem when there are trends in underlying average daily temperature. It is shown that the proposed analytical approach is superior to historical pricing.Weather Derivatives, Temperature Models, Cooling Degree Days, Maximum Likelihood Estimation, Distribution for Correlated Variables

Quantum Feynman-Kac perturbations

We develop fully noncommutative Feynman-Kac formulae by employing quantum stochastic processes. To this end we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by multiplier cocycles. Multiplier cocycles are constructed via quantum stochastic differential equations whose coefficients are driven by the flow. The resulting class of cocycles is characterised under alternative assumptions of separability or Markov regularity. Our results generalise those obtained using classical Brownian motion on the one hand, and results for unitarily implemented flows on the other.Comment: 27 pages. Minor corrections to version 2. To appear in the Journal of the London Mathematical Societ

Estimating the Payoffs of Temperature-based Weather Derivatives

Temperature-based weather derivatives are written on an index which is normally defined to be a nonlinear function of average daily temperatures. Recent empirical work has demonstrated the usefulness of simple time-series models of temperature for estimating the payoffs to these instruments. This paper argues that a more direct and parsimonious approach is to model the time-series behaviour of the index itself, provided a sufficiently rich supply of historical data is available. A data set comprising average daily temperature spanning over a hundred years for four Australian cities is assembled. The data is then used to compare the actual payoffs of temperature-based European call options with the expected payoffs computed from historical temperature records and two time-series approaches. It is concluded that expected payoffs computed directly from historical records perform poorly by comparison with the expected payoffs generated by means of competing time-series models. It is also found that modeling the relevant temperature index directly is superior to modeling average daily temperatures.Temperature, Weather Derivatives, Cooling Degree Days, Time-series Models.

Effect of alcohol addition on the movement of petroleum hydrocarbon fuels in soil

Groundwater contamination by fuel spills from aboveground and underground storage tanks has been of growing concern in recent years. This problem has been magnified by the addition of oxygenates, such as ethanol and methyl-tertiary-butyl ether (MTBE) to fuels to reduce vehicular emissions to the atmosphere. These additives, although beneficial in reducing atmospheric pollution, may, however, increase groundwater contamination due to the co-solvency of petroleum hydrocarbons and by the provision of a preferential substrate for microbial utilisation. With the introduction of ethanol to diesel fuel imminent and the move away from MTBE use in many states of the USA, the environmental implications associated with ethanol additive fuels must be thoroughly investigated. Diesel fuel movement was followed in a 1-m soil column and the effect of ethanol addition to diesel fuel on this movement determined. The addition of 51% ethanol to diesel fuel was found to enhance the downward migration of the diesel fuel components, thus increasing the risk of groundwater contamination. A novel method using soil packcd HPLC columns allowed the influence of ethanol on individual aromatic hydrocarbon movement to be studied. The levels of ethanol addition investigated were at the current additive level (approx. 25%) for ethanol additive fuels in Brazil and values above (50%) and below (10%) this level. An aqueous ethanol concentration above 10% was required for any movement to occur. At 25% aqueous ethanol, the majority of hydrocarbons were mobilised and the retention behaviour of the soil column lessened. At 50% aqueous ethanol, all the hydrocarbons were found to move unimpeded through the columns. The retention behaviour of the soil was found to change significantly when both organic matter content and silt/clay content was reduced. Unexpectedly, sandy soil with low organic matter and low silt/clay was found to have a retentive behaviour similar to sandy subsoil with moderate silt/clay, but little organic matter. It was concluded that sand grains might have a more important role in the adsorption of petroleum hydrocarbons than first realised. This method has shown that soil packed HPLC columns can be used to provide a quick estimate of petroleum hydrocarbon, and possibly other organic contaminant, movement in a variety of different soil types