Quantum Duality in Mathematical Finance

Mathematical finance explores the consistency relationships between the prices of securities imposed by elementary economic principles. Commonplace among these are replicability and the absence of arbitrage, both essentially algebraic constraints on the valuation map from a security to its price. The discussion is framed in terms of observables, the securities, and states, the linear and positive maps from security to price. Founded on the principles of replicability and the absence of arbitrage, mathematical finance then equates to the theory of positive linear maps and their numeraire invariances. This acknowledges the algebraic nature of the defining principles which, crucially, may be applied in the context of quantum probability as well as the more familiar classical setting. Quantum groups are here defined to be dual pairs of *-Hopf algebras, and the central claim of this thesis is that the model for the dynamics of information relies solely on the quantum group properties of observables and states, as demonstrated by the application to finance. This naturally leads to the study of models based on restrictions of the *-Hopf algebras, such as the Quadratic Gauss model, that retain much of the phenomenology of their parent within a more tractable domain, and extensions of the *-Hopf algebras, such as the Linear Dirac model, with novel features unattainable in the classical case.Comment: Presented as "From Quadratic Gaussian to Quantum Groups" at the Global Derivatives Trading and Risk Management Conference, Barcelona, May 201

An Analysis of Once-per-revolution Oscillating Aerodynamic Thrust Loads on Single-Rotation Propellers on Tractor Airplanes at Zero Yaw

A simplified procedure is shown for calculating the once-per-revolution oscillating aerodynamic thrust loads on propellers of tractor airplanes at zero yaw. The only flow field information required for the application of the procedure is a knowledge of the upflow angles at the horizontal center line of the propeller disk. Methods are presented whereby these angles may be computed without recourse to experimental survey of the flow field. The loads computed by the simplified procedure are compared with those computed by a more rigorous method and the procedure is applied to several airplane configurations which are believed typical of current designs. The results are generally satisfactory

Co-infection with Pansensitive and Multidrug-Resistant Strains of Mycobacterium tuberculosis

We report a case of a 23-year-old HIV-negative man with multidrug-resistant Mycobacterium tuberculosis that became evident while he was being treated for M. tuberculosis that was sensitive to all first-line drugs. This case should alert clinicians to consider co-infection as a possible cause of recrudescent disease

Linked randomised controlled trials of face-to-face and electronic brief intervention methods to prevent alcohol related harm in young people aged 14–17 years presenting to Emergency Departments (SIPS junior)

Background: Alcohol is a major global threat to public health. Although the main burden of chronic alcohol-related disease is in adults, its foundations often lie in adolescence. Alcohol consumption and related harm increase steeply from the age of 12 until 20 years. Several trials focusing upon young people have reported significant positive effects of brief interventions on a range of alcohol consumption outcomes. A recent review of reviews also suggests that electronic brief interventions (eBIs) using internet and smartphone technologies may markedly reduce alcohol consumption compared with minimal or no intervention controls. Interventions that target non-drinking youth are known to delay the onset of drinking behaviours. Web based alcohol interventions for adolescents also demonstrate significantly greater reductions in consumption and harm among ‘high-risk’ drinkers; however changes in risk status at follow-up for non-drinkers or low-risk drinkers have not been assessed in controlled trials of brief alcohol interventions

Standard smoking cessation services in sites participating in the SCIMITAR+ trial for people with severe mental ill health

Aims and method: SCIMITAR+ trial was commissioned to evaluate the effectiveness of a bespoke smoking cessation intervention for people with severe mental ill health compared to usual services. It is difficult to define what constitutes ‘usual care’ in stop smoking services. We aimed to define what this was during the trial. Twenty-two NHS healthcare providers participated in a bespoke survey asking about usual care in their area. Results: All sites offered smoking cessation support, however, service provider and service type varied substantially. In some cases services were not streamlined, meaning that people received smoking cessation counselling from one organisation and smoking cessation medication from another. Clinical implications: To better implement the NICE guideline PH48, clearer referral pathways need to be implemented and communicated to patients, staff and carers. People with SMI need to be able to access services that combine Nicotine Replacement Therapy and behavioural support in a streamlined manner

Transanal endoscopic microsurgery versus endoscopic mucosal resection for large rectal adenomas (TREND-study)

Background: Recent non-randomized studies suggest that extended endoscopic mucosal resection (EMR) is equally effective in removing large rectal adenomas as transanal endoscopic microsurgery (TEM). If equally effective, EMR might be a more cost-effective approach as this strategy does not require expensive equipment, general anesthesia and hospital admission. Furthermore, EMR appears to be associated with fewer complications. The aim of this study is to compare the cost-effectiveness and cost-utility of TEM and EMR for the resection of large rectal adenomas. Methods/design. Multicenter randomized trial among 15 hospitals in the Netherlands. Patients with a rectal adenoma 3 cm, located between 115 cm ab ano, will be randomized to a TEM- or EMR-treatment strategy. For TEM, patients will be treated under general anesthesia, adenomas will be dissected en-bloc by a full-thickness excision, and patients will be admitted to the hospital. For EMR, no or conscious sedation is used, lesions will be resected through the submucosal plane i

Expanding the diversity of mycobacteriophages: insights into genome architecture and evolution.

Mycobacteriophages are viruses that infect mycobacterial hosts such as Mycobacterium smegmatis and Mycobacterium tuberculosis. All mycobacteriophages characterized to date are dsDNA tailed phages, and have either siphoviral or myoviral morphotypes. However, their genetic diversity is considerable, and although sixty-two genomes have been sequenced and comparatively analyzed, these likely represent only a small portion of the diversity of the mycobacteriophage population at large. Here we report the isolation, sequencing and comparative genomic analysis of 18 new mycobacteriophages isolated from geographically distinct locations within the United States. Although no clear correlation between location and genome type can be discerned, these genomes expand our knowledge of mycobacteriophage diversity and enhance our understanding of the roles of mobile elements in viral evolution. Expansion of the number of mycobacteriophages grouped within Cluster A provides insights into the basis of immune specificity in these temperate phages, and we also describe a novel example of apparent immunity theft. The isolation and genomic analysis of bacteriophages by freshman college students provides an example of an authentic research experience for novice scientists

A bespoke smoking cessation service compared with treatment as usual for people with severe mental ill health: the SCIMITAR+ RCT

BackgroundThere is a high prevalence of smoking among people with severe mental ill health (SMI). Helping people with SMI to quit smoking could improve their health and longevity, and reduce health inequalities. However, those with SMI are less likely to access and engage with routine smoking cessation services than the general population.ObjectivesTo compare the clinical effectiveness and cost-effectiveness of a bespoke smoking cessation (BSC) intervention with usual stop smoking services for people with SMI.DesignA pragmatic, two-arm, individually randomised controlled trial.SettingPrimary care and secondary care mental health services in England.ParticipantsSmokers aged ≥ 18 years with SMI who would like to cut down on or quit smoking.InterventionsA BSC intervention delivered by mental health specialists trained to deliver evidence-supported smoking cessation interventions compared with usual care.Main outcome measuresThe primary outcome was self-reported, CO-verified smoking cessation at 12 months. Smoking-related secondary outcomes were self-reported smoking cessation, the number of cigarettes smoked per day, the Fagerström Test for Nicotine Dependence and the Motivation to Quit questionnaire. Other secondary outcomes were Patient Health Questionnaire-9 items, Generalised Anxiety Disorder Assessment-7 items and 12-Item Short-Form Health Survey, to assess mental health and body mass index measured at 6 and 12 months post randomisation.ResultsThe trial randomised 526 people (265 to the intervention group, 261 to the usual-care group) aged 19 to 72 years (mean 46 years). About 60% of participants were male. Participants smoked between 3 and 100 cigarettes per day (mean 25 cigarettes per day) at baseline. The intervention group had a higher rate of exhaled CO-verified smoking cessation at 6 and 12 months than the usual-care group [adjusted odds ratio (OR) 12 months: 1.6, 95% confidence interval (CI) 0.9 to 2.8; adjusted OR 6 months: 2.4, 95% CI 1.2 to 4.7]. This was not statistically significant at 12 months (p = 0.12) but was statistically significant at 6 months (p = 0.01). In total, 111 serious adverse events were reported (69 in the BSC group and 42 in the usual-care group); the majority were unplanned hospitalisations due to a deterioration in mental health (n = 98). The intervention is likely (57%) to be less costly but more effective than usual care; however, this result was not necessarily associated with participants’ smoking status.LimitationsFollow-up was not blind to treatment allocation. However, the primary outcome included a biochemically verified end point, less susceptible to observer biases. Some participants experienced difficulties in accessing nicotine replacement therapy because of changes in service provision. Efforts were made to help participants access nicotine replacement therapy, but this may have affected participants’ quit attempt.ConclusionsPeople with SMI who received the intervention were more likely to have stopped smoking at 6 months. Although more people who received the intervention had stopped smoking at 12 months, this was not statistically significant.Future workFurther research is needed to establish how quitting can be sustained among people with SMI.Trial registrationCurrent Controlled Trials ISRCTN72955454.FundingThis project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 23, No. 50. See the NIHR Journals Library website for further project information