Peanut Allergen Threshold Study (PATS): validation of eliciting doses using a novel single-dose challenge protocol

Background: The eliciting dose (ED) for a peanut allergic reaction in 5% of the peanut allergic population, the ED05, is 1.5 mg of peanut protein. This ED05 was derived from oral food challenges (OFC) that use graded, incremental doses administered at fixed time intervals. Individual patients’ threshold doses were used to generate population dose-distribution curves using probability distributions from which the ED05 was then determined. It is important to clinically validate that this dose is predictive of the allergenic response in a further unselected group of peanut-allergic individuals. Methods/Aims: This is a multi-centre study involving three national level referral and teaching centres. (Cork University Hospital, Ireland, Royal Children’s Hospital Melbourne, Australia and Massachusetts General Hospital, Boston, U.S.A.) The study is now in process and will continue to run until all centres have recruited 125 participates in each respective centre. A total of 375 participants, aged 1–18 years will be recruited during routine Allergy appointments in the centres. The aim is to assess the precision of the predicted ED05 using a single dose (6 mg peanut = 1.5 mg of peanut protein) in the form of a cookie. Validated Food Allergy related Quality of Life Questionnaires-(FAQLQ) will be self-administered prior to OFC and 1 month after challenge to assess the impact of a single dose OFC on FAQL. Serological and cell based in vitro studies will be performed. Conclusion: The validation of the ED05 threshold for allergic reactions in peanut allergic subjects has potential value for public health measures. The single dose OFC, based upon the statistical dose-distribution analysis of past challenge trials, promises an efficient approach to identify the most highly sensitive patients within any given food-allergic population.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

An investigation on the use of SNR distributions for the optimisation of coarse-fine spectrum sensing for cognitive radio

This thesis investigates the optimisation of Coarse-Fine (CF) spectrum sensing architectures under a distribution of SNRs for Dynamic Spectrum Access (DSA). Three different detector architectures are investigated: the Coarse-Sorting Fine Detector (CSFD), the Coarse-Deciding Fine Detector (CDFD) and the Hybrid Coarse-Fine Detector (HCFD). To date, the majority of the work on coarse-fine spectrum sensing for cognitive radio has focused on a single value for the SNR. This approach overlooks the key advantage that CF sensing has to offer, namely that high powered signals can be easily detected without extra signal processing. By considering a range of SNR values, the detector can be optimised more effectively and greater performance gains realised. This work considers the optimisation of CF spectrum sensing schemes where the security and performance are treated separately. Instead of optimising system performance at a single, constant, low SNR value, the system instead is optimised for the average operating conditions. The security is still provided such that at the low SNR values the safety specifications are met. By decoupling the security and performance, the system’s average performance increases whilst maintaining the protection of licensed users from harmful interference. The different architectures considered in this thesis are investigated in theory, simulation and physical implementation to provide a complete overview of the performance of each system. This thesis provides a method for estimating SNR distributions which is quick, accurate and relatively low cost. The CSFD is modelled and the characteristic equations are found for the CDFD scheme. The HCFD is introduced and optimisation schemes for all three architectures are proposed. Finally, using the Implementing Radio In Software (IRIS) test-bed to confirm simulation results, CF spectrum sensing is shown to be significantly quicker than naive methods, whilst still meeting the required interference probability rates and not requiring substantial receiver complexity increases.