Velocity-jump models with crowding effects

Velocity jump processes are discrete random walk models that have many applications including the study of biological and ecological collective motion. In particular, velocity jump models are often used to represent a type of persistent motion, known as a “run and tumble”, which is exhibited by some isolated bacteria cells. All previous velocity jump processes are non-interacting, which means that crowding effects and agent-to-agent interactions are neglected. By neglecting these agent-to-agent interactions, traditional velocity jump models are only applicable to very dilute systems. Our work is motivated by the fact that many applications in cell biology, such as wound healing, cancer invasion and development, often involve tissues that are densely packed with cells where cell-to-cell contact and crowding effects can be important. To describe these kinds of high cell density problems using a velocity jump process we introduce three different classes of crowding interactions into a one-dimensional model. Simulation data and averaging arguments lead to a suite of continuum descriptions of the interacting velocity jump processes. We show that the resulting systems of hyperbolic partial differential equations predict the mean behavior of the stochastic simulations very well.

Analysis of indirect message injection for MAC generation using stream ciphers

This paper presents a model for generating a MAC tag with a stream cipher using the input message indirectly. Several recent proposals represent instances of this model with slightly different options. We investigate the security of this model for different options, and identify cases which permit forgery attacks. Based on this, we present a new forgery attack on version 1.4 of 128-EIA3. Design recommendations to enhance the security of proposals following this general model are given.

Velocity jump processes with proliferation

Cell invasion involves a population of cells that migrate along a substrate and proliferate to a carrying capacity density. These two processes, combined, lead to invasion fronts that move into unoccupied tissues. Traditional modelling approaches based on reaction–diffusion equations cannot incorporate individual–level observations of cell velocity, as information propagates with infinite velocity according to these parabolic models. In contrast, velocity jump processes allow us to explicitly incorporate individual–level observations of cell velocity, thus providing an alternative framework for modelling cell invasion. Here, we introduce proliferation into a standard velocity–jump process and show that the standard model does not support invasion fronts. Instead, we find that crowding effects must be explicitly incorporated into a proliferative velocity–jump process before invasion fronts can be observed. Our observations are supported by numerical and analytical solutions of a novel coupled system of partial differential equations, including travelling wave solutions, and associated random walk simulations.

Marginal reversible jump Markov chain Monte Carlo with application to motor unit number estimation

Motor unit number estimation (MUNE) is a method which aims to provide a quantitative indicator of progression of diseases that lead to loss of motor units, such as motor neurone disease. However the development of a reliable, repeatable and fast real-time MUNE method has proved elusive hitherto. Ridall et al. (2007) implement a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to produce a posterior distribution for the number of motor units using a Bayesian hierarchical model that takes into account biological information about motor unit activation. However we find that the approach can be unreliable for some datasets since it can suffer from poor cross-dimensional mixing. Here we focus on improved inference by marginalising over latent variables to create the likelihood. In particular we explore how this can improve the RJMCMC mixing and investigate alternative approaches that utilise the likelihood (e.g. DIC (Spiegelhalter et al., 2002)). For this model the marginalisation is over latent variables which, for a larger number of motor units, is an intractable summation over all combinations of a set of latent binary variables whose joint sample space increases exponentially with the number of motor units. We provide a tractable and accurate approximation for this quantity and also investigate simulation approaches incorporated into RJMCMC using results of Andrieu and Roberts (2009).

Pinned fronts in heterogeneous media of jump type

In this paper, we analyse the impact of a (small) heterogeneity of jump type on the most simple localized solutions of a 3-component FitzHugh–Nagumo-type system. We show that the heterogeneity can pin a 1-front solution, which travels with constant (non-zero) speed in the homogeneous setting, to a fixed, explicitly determined, distance from the heterogeneity. Moreover, we establish the stability of this heterogeneous pinned 1-front solution. In addition, we analyse the pinning of 1-pulse, or 2-front, solutions. The paper is concluded with simulations in which we consider the dynamics and interactions of N-front patterns in domains with M heterogeneities of jump type (N = 3, 4, M ≥ 1).

Early evidence for direct and indirect effects of the infant rotavirus vaccine program in Queensland

Objective: To assess the impact of introducing a publicly funded infant rotavirus vaccination program on disease notifications and on laboratory testing and results. Design and setting: Retrospective analysis of routinely collected data (rotavirus notifications [2006–2008] and laboratory rotavirus testing data from Queensland Health laboratories [2000–2008]) to monitor rotavirus trends before and after the introduction of a publicly funded infant rotavirus vaccination program in Queensland in July 2007. Main outcome measures: Age group-specific rotavirus notification trends; number of rotavirus tests performed and the proportion positive. Results: In the less than 2 years age group, rotavirus notifications declined by 53% (2007) and 65% (2008); the number of laboratory tests performed declined by 3% (2007) and 15% (2008); and the proportion of tests positive declined by 45% (2007) and 43% (2008) compared with data collected before introduction of the vaccination program. An indirect effect of infant vaccination was seen: notifications and the proportion of tests positive for rotavirus declined in older age groups as well. Conclusions: The publicly funded rotavirus vaccination program in Queensland is having an early impact, direct and indirect, on rotavirus disease as assessed using routinely collected data. Further observational studies are required to assess vaccine effectiveness. Parents and immunisation providers should ensure that all Australian children receive the recommended rotavirus vaccine doses in the required timeframe.

Bayesian algorithms with applications

Advances in algorithms for approximate sampling from a multivariable target function have led to solutions to challenging statistical inference problems that would otherwise not be considered by the applied scientist. Such sampling algorithms are particularly relevant to Bayesian statistics, since the target function is the posterior distribution of the unobservables given the observables. In this thesis we develop, adapt and apply Bayesian algorithms, whilst addressing substantive applied problems in biology and medicine as well as other applications. For an increasing number of high-impact research problems, the primary models of interest are often sufficiently complex that the likelihood function is computationally intractable. Rather than discard these models in favour of inferior alternatives, a class of Bayesian "likelihoodfree" techniques (often termed approximate Bayesian computation (ABC)) has emerged in the last few years, which avoids direct likelihood computation through repeated sampling of data from the model and comparing observed and simulated summary statistics. In Part I of this thesis we utilise sequential Monte Carlo (SMC) methodology to develop new algorithms for ABC that are more efficient in terms of the number of model simulations required and are almost black-box since very little algorithmic tuning is required. In addition, we address the issue of deriving appropriate summary statistics to use within ABC via a goodness-of-fit statistic and indirect inference. Another important problem in statistics is the design of experiments. That is, how one should select the values of the controllable variables in order to achieve some design goal. The presences of parameter and/or model uncertainty are computational obstacles when designing experiments but can lead to inefficient designs if not accounted for correctly. The Bayesian framework accommodates such uncertainties in a coherent way. If the amount of uncertainty is substantial, it can be of interest to perform adaptive designs in order to accrue information to make better decisions about future design points. This is of particular interest if the data can be collected sequentially. In a sense, the current posterior distribution becomes the new prior distribution for the next design decision. Part II of this thesis creates new algorithms for Bayesian sequential design to accommodate parameter and model uncertainty using SMC. The algorithms are substantially faster than previous approaches allowing the simulation properties of various design utilities to be investigated in a more timely manner. Furthermore the approach offers convenient estimation of Bayesian utilities and other quantities that are particularly relevant in the presence of model uncertainty. Finally, Part III of this thesis tackles a substantive medical problem. A neurological disorder known as motor neuron disease (MND) progressively causes motor neurons to no longer have the ability to innervate the muscle fibres, causing the muscles to eventually waste away. When this occurs the motor unit effectively ‘dies’. There is no cure for MND, and fatality often results from a lack of muscle strength to breathe. The prognosis for many forms of MND (particularly amyotrophic lateral sclerosis (ALS)) is particularly poor, with patients usually only surviving a small number of years after the initial onset of disease. Measuring the progress of diseases of the motor units, such as ALS, is a challenge for clinical neurologists. Motor unit number estimation (MUNE) is an attempt to directly assess underlying motor unit loss rather than indirect techniques such as muscle strength assessment, which generally is unable to detect progressions due to the body’s natural attempts at compensation. Part III of this thesis builds upon a previous Bayesian technique, which develops a sophisticated statistical model that takes into account physiological information about motor unit activation and various sources of uncertainties. More specifically, we develop a more reliable MUNE method by applying marginalisation over latent variables in order to improve the performance of a previously developed reversible jump Markov chain Monte Carlo sampler. We make other subtle changes to the model and algorithm to improve the robustness of the approach.

Indirect message injection for MAC generation

This paper presents a model for the generation of a MAC tag using a stream cipher. The input message is used indirectly to control segments of the keystream that form the MAC tag. Several recent proposals can be considered as instances of this general model, as they all perform message accumulation in this way. However, they use slightly different processes in the message preparation and finalisation phases. We examine the security of this model for different options and against different types of attack, and conclude that the indirect injection model can be used to generate MAC tags securely for certain combinations of options. Careful consideration is required at the design stage to avoid combinations of options that result in susceptibility to forgery attacks. Additionally, some implementations may be vulnerable to side-channel attacks if used in Authenticated Encryption (AE) algorithms. We give design recommendations to provide resistance to these attacks for proposals following this model.

Automatic classification of human epithelial type 2 cell indirect immunofluorescence images using cell pyramid matching

This paper describes a novel system for automatic classification of images obtained from Anti-Nuclear Antibody (ANA) pathology tests on Human Epithelial type 2 (HEp-2) cells using the Indirect Immunofluorescence (IIF) protocol. The IIF protocol on HEp-2 cells has been the hallmark method to identify the presence of ANAs, due to its high sensitivity and the large range of antigens that can be detected. However, it suffers from numerous shortcomings, such as being subjective as well as time and labour intensive. Computer Aided Diagnostic (CAD) systems have been developed to address these problems, which automatically classify a HEp-2 cell image into one of its known patterns (eg. speckled, homogeneous). Most of the existing CAD systems use handpicked features to represent a HEp-2 cell image, which may only work in limited scenarios. We propose a novel automatic cell image classification method termed Cell Pyramid Matching (CPM), which is comprised of regional histograms of visual words coupled with the Multiple Kernel Learning framework. We present a study of several variations of generating histograms and show the efficacy of the system on two publicly available datasets: the ICPR HEp-2 cell classification contest dataset and the SNPHEp-2 dataset.

Wheat breeding nurseries, target environments, and indirect selection for grain yield

Use of appropriate nursery environments will maximize gain from selection for yield of wheat (Triticum aestivum L.) in the target population of environments of a breeding program. The objective of this study was to investigate how well-irrigated (low-stress) nursery environments predict yield of lines in target environments that varied in degree of water limitation. Fifteen lines were sampled from the preliminary yield evaluation stage of the Queensland wheat breeding program and tested in 26 trials under on-farm conditions (Target Environments) across nine years (1985 to 1993) and also in 27 trials conducted at three research stations (Nursery Environments) in three years (1987 to 1989). The nursery environments were structured to impose different levels of water and nitrogen (N) limitation, whereas the target environments represented a random sample of on-farm conditions from the target population of environments. Indirect selection and pattern analysis methods were used to investigate selection for yield in the nursery environments and gain from selection in the target environments. Yield under low-stress nursery conditions was an effective predictor of yield under similar low-stress target environments (r = 0.89, P < 0.01). However, the value of the low-stress nursery as a predictor of yield in the water-limited target environments decreased with increasing water stress (moderate stress r = 0.53, P < 0.05, to r = 0.38, P > 0.05; severe stress r = -0.08, P > 0.05). Yield in the stress nurseries was a poor predictor of yield in the target environments. Until there is a clear understanding of the physiological-genetic basis of variation for adaptation of wheat to the water-limited environments in Queensland, yield improvement can best be achieved by selection for a combination of yield potential in an irrigated low-stress nursery and yield in on-farm trials that sample the range of water-limited environments of the target population of environments.

Optimal Bayesian experimental design for models with intractable likelihoods using indirect inference applied to biological process models

This paper addresses the problem of determining optimal designs for biological process models with intractable likelihoods, with the goal of parameter inference. The Bayesian approach is to choose a design that maximises the mean of a utility, and the utility is a function of the posterior distribution. Therefore, its estimation requires likelihood evaluations. However, many problems in experimental design involve models with intractable likelihoods, that is, likelihoods that are neither analytic nor can be computed in a reasonable amount of time. We propose a novel solution using indirect inference (II), a well established method in the literature, and the Markov chain Monte Carlo (MCMC) algorithm of Müller et al. (2004). Indirect inference employs an auxiliary model with a tractable likelihood in conjunction with the generative model, the assumed true model of interest, which has an intractable likelihood. Our approach is to estimate a map between the parameters of the generative and auxiliary models, using simulations from the generative model. An II posterior distribution is formed to expedite utility estimation. We also present a modification to the utility that allows the Müller algorithm to sample from a substantially sharpened utility surface, with little computational effort. Unlike competing methods, the II approach can handle complex design problems for models with intractable likelihoods on a continuous design space, with possible extension to many observations. The methodology is demonstrated using two stochastic models; a simple tractable death process used to validate the approach, and a motivating stochastic model for the population evolution of macroparasites.

Effectiveness of a puppet show on iodine knowledge, attitudes and behaviour of elementary students and the indirect effects on their parents and households in Ho Chi Minh City : a pilot study

Deficiencies in iodine levels have been shown to seriously affect a child’s intellectual development and learning capacity.1 In South-East Asia, iodine deficiency remains a major public health concern. Approximately 30% of the region’s population of 503.6 million have insufficient iodine intake, and only 61% of households have access to iodized salt.1 For this reason, it is necessary to initiate effective, community-based health promotion activities that are targeted toward populations of various ages. A puppet show is one imaginative and entertaining method of health education that has been advocated for use in communicating positive health behaviours to children.2e5 The authors undertook a literature review and found no studies assessing the effectiveness of a puppet show to teach an iodine education programme...

Indirect effects of phytochemicals on offspring performance of Queensland fruit fly, Bactrocera tryoni (Diptera: Tephritidae)

Phytochemical lures such as methyl eugenol (ME) and cue-lure are used in the management of Bactrocera fruit flies for monitoring and control. These lures are not just attractants, but also trigger physiological changes in males that lead to enhanced mating success. Additionally, in the cue-lure-responsive Bactrocera tryoni, females mated with lure-fed males exhibit changes in fecundity, remating receptivity and longevity. While the lures show current generation effects, no research has been carried out on possible multigenerational effects, although such effects have been hypothesized within a ‘sexy-son’ sexual selection model. In this study, we test for indirect, cross-generational effects of lure exposure in F1offspring of B. tryoni females mated with cue-lure-fed, zingerone-fed and lure-unfed (=control) males. The F1 attributes we recorded were immature development time, immature survival, adult survival and adult male lure foraging. No significant differences were found between treatments for any of the three life-history measurements, except that the offspring sired by zingerone-fed males had a longer egg development time than cue-lure and control offspring. However, indirect exposure to lures significantly enhanced the lure-foraging ability of F1 adult males. More offspring of cue-lure-fed males arrived at a lure source in both large flight cages and small laboratory cages over a 2-h period than did control males. The offspring of zingerone-fed males were generally intermediate between cue-lure and control offspring. This study provides the first evidence of a next generation effect of fruit fly male lures. While the results of this study support a ‘sexy-son’ sexual selection mechanism for the evolution of lure response in Bactrocera fruit flies, our discussion urges caution in interpreting our results in this way.