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.

Continuous non-destructive monitoring of cell health using impedance based interdigitated electrode structured sensors

This article examines some preliminary tests which were performed in order to evaluate the best electrode configuration (width and spacing) for cell culture analyses. Biochips packaged with indium tin oxide (ITO) interdigitated electrodes (IDEs) were used to perform impedance measurements on A549 cells cultured on the surface of the biochip. Several tests were carried out using a 10 mM solution of Sodium Chloride (NaCl), cell medium and the cell culture itself to characterize some of the configurations already fabricated in the facilities at Tyndall National Institute.

Impact of non-optimal grounding of the CC2420 RFIC on a 802.15.4 Tyndall sensor wireless mote

The performance of an RF output matching network is dependent on integrity of the ground connection. If this connection is compromised in anyway, additional parasitic elements may occur that can degrade performance and yield unreliable results. Traditionally, designers measure Constant Wave (CW) power to determine that the RF chain is performing optimally, the device is properly matched and by implication grounded. It is shown that there are situations where modulation quality can be compromised due to poor grounding that is not apparent using CW power measurements alone. The consequence of this is reduced throughput, range and reliability. Measurements are presented on a Tyndall Mote using a CC2420 RFIC todemonstrate how poor solder contact between the ground contacts and the ground layer of the PCB can lead tothe degradation of modulated performance. Detailed evaluation that required the development of a new measurement definition for 802.15.4 and analysis is presented to show how waveform quality is affected while the modulated output power remains within acceptable limits.

Use of oxygen sensors for the non destructive measurement of oxygen in packaged food and beverage products and its impact on product quality and shelf life

The principal objective of this thesis was to investigate the ability of reversible optical O2 sensors to be incorporated into food/beverage packaging systems to continuously monitor O2 levels in a non-destructive manner immediately postpackaging and over time. Residual levels of O2 present in packs can negatively affect product quality and subsequently, product shelf-life, especially for O2-sensitive foods/beverages. Therefore, the ability of O2 sensors to continuously monitor O2 levels present within food/beverage packages was considered commercially relevant in terms of identifying the consequences of residual O2 on product safety and quality over time. Research commenced with the development of a novel range of O2 sensors based on phosphorescent platinum and palladium octaethylporphyrin-ketones (OEPk) in nano-porous high density polyethylene (HDPE), polypropylene (PP) polytetrafluoroethylene (PTFE) polymer supports. Sensors were calibrated over a temperature range of -10°C to +40°C and deemed suitable for food and beverage packaging applications. This sensor technology was used and demonstrated itself effective in determining failures in packaging containment. This was clearly demonstrated in the packaging of cheese string products. The sensor technology was also assessed across a wide range of packaged products; beer, ready-to-eat salad products, bread and convenience-style, muscle-based processed food products. The O2 sensor technology performed extremely well within all packaging systems. The sensor technology adequately detected O2 levels in; beer bottles prior to and following pasteurisation, modified atmosphere (MA) packs of ready-to-eat salad packs as respiration progressed during product storage and MA packs of bread and convenience-style muscle-based products as mycological growth occurred in food packs over time in the presence and absence of ethanol emitters. The use of the technology, in conjunction with standard food quality assessment techniques, showed remarkable usefulness in determining the impact of actual levels of O2 on specific quality attributes. The O2 sensing probe was modified, miniaturised and automated to screen for the determination of total aerobic viable counts (TVC) in several fish species samples. The test showed good correlation with conventional TVC test (ISO:4833:2003), analytical performance and ruggedness with respect to variation of key assay parameters (probe concentration and pipetting volume). Overall, the respirometric fish TVC test was simple to use, possessed a dynamic microbial range (104-107 cfu/g sample), had an accuracy of +/- one log(cfu/g sample) and was rapid. Its ability to assess highly perishable products such as fish for total microbial growth in <12 hr demonstrates commercial potential.