Reliability control of GNSS carrier-phase integer ambiguity resolution

This research investigates how to obtain accurate and reliable positioning results with global navigation satellite systems (GNSS). The work provides a theoretical framework for reliability control in GNSS carrier phase ambiguity resolution, which is the key technique for precise GNSS positioning in centimetre levels. The proposed approach includes identification and exclusion procedures of unreliable solutions and hypothesis tests, allowing the reliability of solutions to be controlled in the aspects of mathematical models, integer estimation and ambiguity acceptance tests. Extensive experimental results with both simulation and observed data sets effectively demonstrate the reliability performance characteristics based on the proposed theoretical framework and procedures.

Light history-dependent respiration explains the hysteresis in the daily ecosystem metabolism of seagrass

Oxygen flux between aquatic ecosystems and the water column is a measure of ecosystem metabolism. However, the oxygen flux varies during the day in a “hysteretic” pattern: there is higher net oxygen production at a given irradiance in the morning than in the afternoon. In this study, we investigated the mechanism responsible for the hysteresis in oxygen flux by measuring the daily pattern of oxygen flux, light, and temperature in a seagrass ecosystem (Zostera muelleri in Swansea Shoals, Australia) at three depths. We hypothesised that the oxygen flux pattern could be due to diel variations in either gross primary production or respiration in response to light history or temperature. Hysteresis in oxygen flux was clearly observed at all three depths. We compared this data to mathematical models, and found that the modification of ecosystem respiration by light history is the best explanation for the hysteresis in oxygen flux. Light history-dependent respiration might be due to diel variations in seagrass respiration or the dependence of bacterial production on dissolved organic carbon exudates. Our results indicate that the daily variation in respiration rate may be as important as the daily changes of photosynthetic characteristics in determining the metabolic status of aquatic ecosystems.

Exact solutions of coupled multispecies linear reaction–diffusion equations on a uniformly growing domain

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

ANZIAM 2015

The 51st ANZIAM Conference was held on 1–5 February 2015 in the Outrigger Hotel, Surfers Paradise, Australia. A total of 229 people registered for the conference, with nine plenary presentations, 78 student presentations and 107 non-student presentations. Highlights of the conference included the plenary talks, presentations by the 2014 Michell and ANZIAM Medalists, the Women in Mathematics Lunch and the Conference Dinner and Awards Ceremony. The main conference was followed by a one-day workshop entitled ‘Discrete mathematical models in the life sciences’, held at Queensland University of Technology, Brisbane, on February 6, 2015.

Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0

Modelling the movement of interacting cell populations: A moment dynamics approach

Mathematical models describing the movement of multiple interacting subpopulations are relevant to many biological and ecological processes. Standard mean-field partial differential equation descriptions of these processes suffer from the limitation that they implicitly neglect to incorporate the impact of spatial correlations and clustering. To overcome this, we derive a moment dynamics description of a discrete stochastic process which describes the spreading of distinct interacting subpopulations. In particular, we motivate our model by mimicking the geometry of two typical cell biology experiments. Comparing the performance of the moment dynamics model with a traditional mean-field model confirms that the moment dynamics approach always outperforms the traditional mean-field approach. To provide more general insight we summarise the performance of the moment dynamics model and the traditional mean-field model over a wide range of parameter regimes. These results help distinguish between those situations where spatial correlation effects are sufficiently strong, such that a moment dynamics model is required, from other situations where spatial correlation effects are sufficiently weak, such that a traditional mean-field model is adequate.

Influences of Allee effects in the spreading of malignant tumours

A recent study by Korolev et al. [Nat. Rev. Cancer, 14:371–379, 2014] evidences that the Allee effect—in its strong form, the requirement of a minimum density for cell growth—is important in the spreading of cancerous tumours. We present one of the first mathematical models of tumour invasion that incorporates the Allee effect. Based on analysis of the existence of travelling wave solutions to this model, we argue that it is an improvement on previous models of its kind. We show that, with the strong Allee effect, the model admits biologically relevant travelling wave solutions, with well-defined edges. Furthermore, we uncover an experimentally observed biphasic relationship between the invasion speed of the tumour and the background extracellular matrix density.

Build-up of toxic metals on the impervious surfaces of a commercial seaport

In the context of increasing threats to the sensitive marine ecosystem by toxic metals, this study investigated the metal build-up on impervious surfaces specific to commercial seaports. The knowledge generated in this study will contribute to managing toxic metal pollution of the marine ecosystem. The study found that inter-modal operations and main access roadway had the highest loads followed by container storage and vehicle marshalling sites, while the quay line and short term storage areas had the lowest. Additionally, it was found that Cr, Al, Pb, Cu and Zn were predominantly attached to solids, while significant amount of Cu, Pb and Zn were found as nutrient complexes. As such, treatment options based on solids retention can be effective for some metal species, while ineffective for other species. Furthermore, Cu and Zn are more likely to become bioavailable in seawater due to their strong association with nutrients. Mathematical models to replicate the metal build-up process were also developed using experimental design approach and partial least square regression. The models for Cr and Pb were found to be reliable, while those for Al, Zn and Cu were relatively less reliable, but could be employed for preliminary investigations.

Assessing uncertainty in pollutant build-up and wash-off processes

Assessing build-up and wash-off process uncertainty is important for accurate interpretation of model outcomes to facilitate informed decision making for developing effective stormwater pollution mitigation strategies. Uncertainty inherent to pollutant build-up and wash-off processes influences the variations in pollutant loads entrained in stormwater runoff from urban catchments. However, build-up and wash-off predictions from stormwater quality models do not adequately represent such variations due to poor characterisation of the variability of these processes in mathematical models. The changes to the mathematical form of current models with the incorporation of process variability, facilitates accounting for process uncertainty without significantly affecting the model prediction performance. Moreover, the investigation of uncertainty propagation from build-up to wash-off confirmed that uncertainty in build-up process significantly influences wash-off process uncertainty. Specifically, the behaviour of particles <150µm during build-up primarily influences uncertainty propagation, resulting in appreciable variations in the pollutant load and composition during a wash-off event.