Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

Monte Carlo verification of gel dosimetry measurements for stereotactic radiotherapy

The quality assurance of stereotactic radiotherapy and radiosurgery treatments requires the use of small-field dose measurements that can be experimentally challenging. This study used Monte Carlo simulations to establish that PAGAT dosimetry gel can be used to provide accurate, high resolution, three-dimensional dose measurements of stereotactic radiotherapy fields. A small cylindrical container (4 cm height, 4.2 cm diameter) was filled with PAGAT gel, placed in the parietal region inside a CIRS head phantom, and irradiated with a 12 field stereotactic radiotherapy plan. The resulting three-dimensional dose measurement was read out using an optical CT scanner and compared with the treatment planning prediction of the dose delivered to the gel during the treatment. A BEAMnrc DOSXYZnrc simulation of this treatment was completed, to provide a standard against which the accuracy of the gel measurement could be gauged. The three dimensional dose distributions obtained from Monte Carlo and from the gel measurement were found to be in better agreement with each other than with the dose distribution provided by the treatment planning system's pencil beam calculation. Both sets of data showed close agreement with the treatment planning system's dose distribution through the centre of the irradiated volume and substantial disagreement with the treatment planning system at the penumbrae. The Monte Carlo calculations and gel measurements both indicated that the treated volume was up to 3 mm narrower, with steeper penumbrae and more variable out-of-field dose, than predicted by the treatment planning system. The Monte Carlo simulations allowed the accuracy of the PAGAT gel dosimeter to be verified in this case, allowing PAGAT gel to be utilised in the measurement of dose from stereotactic and other radiotherapy treatments, with greater confidence in the future.

The Remnant Emergency Artlab

The REMNANT/EMERGENCY Artlab was funded by the Australia Council InterArts ArtLab Program in 2010 and involves 22 months of rigorous research and experimentation in several countries. The process will be developed between a core transdisciplinary team of practicing media artists, designers and engineers where possible working in consultation and collaboration with local creatives at each venue. Our team asserts that today’s environmental crisis is underpinned by a deep cultural crisis - and so to get our ‘house in order’ we urgently need to create better and more powerful ‘images’ of what a ‘citizen-led’, sustainable world might be. This ArtLab’s core aim is therefore to begin to understand how to develop and create such ‘powerful images’.

Understanding evaluation of learning support in mathematics and statistics

With rapid and continuing growth of learning support initiatives in mathematics and statistics found in many parts of the world, and with the likelihood that this trend will continue, there is a need to ensure that robust and coherent measures are in place to evaluate the effectiveness of these initiatives. The nature of learning support brings challenges for measurement and analysis of its effects. After briefly reviewing the purpose, rationale for, and extent of current provision, this article provides a framework for those working in learning support to think about how their efforts can be evaluated. It provides references and specific examples of how workers in this field are collecting, analysing and reporting their findings. The framework is used to structure evaluation in terms of usage of facilities, resources and services provided, and also in terms of improvements in performance of the students and staff who engage with them. Very recent developments have started to address the effects of learning support on the development of deeper approaches to learning, the affective domain and the development of communities of practice of both learners and teachers. This article intends to be a stimulus to those who work in mathematics and statistics support to gather even richer, more valuable, forms of data. It provides a 'toolkit' for those interested in evaluation of learning support and closes by referring to an on-line resource being developed to archive the growing body of evidence. © 2011 Taylor & Francis.

Bribie Island groundwater resources : challenges in development of conceptual and numerical models

Groundwater is a major resource on Bribie Island and its sustainable management is essential to maintain the natural and modified eco-systems, as well as the human population and the integrity of the island as a sand mass. An effective numerical model is essential to enable predictions, and to test various water use and rainfall/climate scenarios. Such a numerical model must, however, be based on a representative conceptual hydrogeological model to allow incorporation of realistic controls and processes. Here we discuss the various hydrogeological models and parameters, and hydrological properties of the materials forming the island. We discuss the hydrological processes and how they can be incorporated into these models, in an integrated manner. Processes include recharge, discharge to wetlands and along the coastline, abstraction, evapotranspiration and potential seawater intrusion. The types and distributions of groundwater bores and monitoring are considered, as are scenarios for groundwater supply abstraction. Different types of numerical models and their applicability are also considered

Neoproterozoic glacial deposits of the Kimberly Region and northwestern Northern Territory, Australia

Neoproterozoic glacigenic formations are preserved in the Kimberley region and northwestern Northern Territory of northern Australia. They are distributed in the west Kimberley adjacent to the northern margins of the King Leopold Orogen, the Mt Ramsay area at the junction of the King Leopold and Halls Creek Orogens, and the east Kimberley, adjacent to the eastern margin of the Halls Creek Orogen. Small outlier glacigenic deposits are preserved in the Litchfield Province, Northern Territory (Uniya Formation) and Georgina Basin, western Queensland (Little Burke Formation). Glacigenic strata comprise diamictite, conglomerate, sandstone and pebbly mudstone and characterize the Walsh, Landrigan and Fargoo/Moonlight Valley formations. Thin units of laminated dolomite sit conformably at the top of the Walsh, Landrigan and Moonlight Valley formations. Glacigenic units are also interbedded with the carbonate platform deposits of the Egan Formation and Boonall Dolomite. δ13C data are available for all carbonate units. There is no direct chronological constraint on these successions. Dispute over regional correlation of the Neoproterozoic succession has been largely resolved through biostratigraphic, chemostratigraphic and lithostratigraphic analysis. However, palaeomagnetic results from the Walsh Formation are inconsistent with sedimentologically based correlations. Two stratigraphically defined glaciations are preserved in northwestern Australia: the ‘Landrigan Glaciation’, characterized by southwest-directed continental ice-sheet movement and correlated with late Cryogenian glaciation elsewhere in Australia and the world; and, the ‘Egan Glaciation’, a more localized glaciation of the Ediacaran Period. Future research focus should include chronology, palaeomagnetic constraint and tectonostratigraphic controls on deposition.