On the effect of topology on cellular automata rule spaces

This thesis presents an empirical study of the effects of topology on cellular automata rule spaces. The classical definition of a cellular automaton is restricted to that of a regular lattice, often with periodic boundary conditions. This definition is extended to allow for arbitrary topologies. The dynamics of cellular automata within the triangular tessellation were analysed when transformed to 2-manifolds of topological genus 0, genus 1 and genus 2. Cellular automata dynamics were analysed from a statistical mechanics perspective. The sample sizes required to obtain accurate entropy calculations were determined by an entropy error analysis which observed the error in the computed entropy against increasing sample sizes. Each cellular automata rule space was sampled repeatedly and the selected cellular automata were simulated over many thousands of trials for each topology. This resulted in an entropy distribution for each rule space. The computed entropy distributions are indicative of the cellular automata dynamical class distribution. Through the comparison of these dynamical class distributions using the E-statistic, it was identified that such topological changes cause these distributions to alter. This is a significant result which implies that both global structure and local dynamics play a important role in defining long term behaviour of cellular automata.

Biological monitoring and Biological Limit Values (BLV): the strategy of the European Union

Occupational standards concerning allowable concentrations of chemical compounds in the ambient air of workplaces have been established in several countries worldwide. With the integration of the European Union (EU), there has been a need of establishing harmonised Occupational Exposure Limits (OEL). The European Commission Directive 95/320/EC of 12 July 1995 has given the tasks to a Scientific Committee for Occupational Exposure Limits (SCOEL) to propose, based on scientific data and where appropriate, occupational limit values which may include the 8-h time-weighted average (TWA), short-term limits/excursion limits (STEL) and Biological Limit Values (BLVs). In 2000, the European Union issued a list of 62 chemical substances with Occupational Exposure Limits. Of these, 25 substances received a "skin" notation, indicating that toxicologically significant amounts may be taken up via the skin. For such substances, monitoring of concentrations in ambient air may not be sufficient, and biological monitoring strategies appear of potential importance in the medical surveillance of exposed workers. Recent progress has been made with respect to formulation of a strategy related to health-based BLVs.

Influence of polymorphisms of the human glutathione transferases and cytochrome P450 2E1 enzyme on the metabolism and toxicity of ethylene oxide and acrylonitrile

A cohort of 59 persons with industrial handling of low levels of acrylonitrile is being studied as part of a medical surveillance programme. Previously, an extended haemoglobin adduct monitoring (N-(cyanoethyl)valine and N-(hydroxyethyl)-valine) was performed regarding the glutathione transferases hGSTM1 and hGSTT1 polymorphisms but no influence of hGSTM1 or hGSTT1 polymorphisms on specific adduct levels was found. A compilation of case reports of human accidental poisonings had pointed to significant individual differences in human acrylonitrile metabolism and toxicity. Therefore, a re-evaluation of the industrial cohort included known polymorphisms of the glutathione transferases hGSTM3 and hGSTP1 as well as of the cytochrome P450 CYP2E1. A detailed statistical analysis revealed that exposed carriers of the allelic variants of hGSTP1, hGSTP1*B/hGSTP1*C, characterized by a single nucleotide polymorphism at nucleotide 313 which results in a change from Ile to Val at codon 104, had higher levels of the acrylonitrile-specific haemoglobin adduct N-(cyanoethyl)valine compared to the carriers of the codon 113 alleles hGSTP1*A and hGSTP1*D. The single nucleotide polymorphism at codon 113 of hGSTP1 (hGSTP1*A/hGSTP1*B versus hGSTP1*C/hGSTP1*D) did not show an effect, and also no influence was seen on specific haemoglobin adduct levels of the polymorphisms of hGSTM3 or CYP2E1. The data, therefore, point to a possible influence of a human enzyme polymorphism of the GSTP1 gene at codon 104 on the detoxication of acrylonitrile which calls for experimental toxicological investigation. The study also confirmed the impact of GSTT1 polymorphism on background N-(hydroxyethyl)-valine adduct levels in haemoglobin which are caused by endogenous ethylene oxide.

Possible impact of human CYP2E1 polymorphisms on the metabolism of acrylonitrile

Case reports of human accidental poisonings point to significant individual differences in human acrylonitrile metabolism and toxicity. A cohort of 59 persons with industrial handling of low levels of acrylonitrile has repetitively been studied from 1994 through 1999 as part of a medical surveillance programme. The analyses included adduct determinations of N-terminal N-(cyanoethyl)valine in haemoglobin and genotypings of the following cytochrome P-450 2E1 (CYP2E1) polymorphisms: G-1259C and C-1019T (two subjects heterozygous), A-316G (three subjects heterozygous), T-297A (15 subjects heterozygous), G-35T (eight subjects heterozygous), G4804A (two subjects heterozygous), T7668A (six subjects heterozygous). N-(Cyanoethyl)valine adduct levels were, if any, only slightly influenced by smoking and mainly determined by the external acrylonitrile exposures. The individual means and medians of N-(cyanoethyl)valine levels over the entire observation period were compared with the CYP2E1 variants (Wilcoxon rank sum test). No influences of the investigated CYP2E1 polymorphisms on the N-(cyanoethyl)valine levels appeared at the 5% level. However, there was a trend, at a level of P≃0.1, pointing to higher acrylonitrile-specific adduct levels in persons with the A-316G mutation. Higher adduct levels would be compatible with a slower CYP2E1-mediated metabolism of acrylonitrile and with lower extents of toxification to cyanide.

Novel solutions for a model of wound healing angiogenesis

We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al (2000 IMA J. Math. App. Med. 17 395–413) assuming two conjectures hold. In the previous work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime. We construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.

Canards in advection-reaction-diffusion systems in one spatial dimension

This thesis contains a mathematical investigation of the existence of travelling wave solutions to singularly perturbed advection-reaction-diffusion models of biological processes. An enhanced mathematical understanding of these solutions and models is gained via the identification of canards (special solutions of fast/slow dynamical systems) and their role in the existence of the most biologically relevant, shock-like solutions. The analysis focuses on two existing models. A new proof of existence of a whole family of travelling waves is provided for a model describing malignant tumour invasion, while new solutions are identified for a model describing wound healing angiogenesis.

When can a tenancy be terminated under s 129 of the Property Law Act 1974 (Qld)?

This article reviews the nature and purpose of s 129 of the Property Law Act 1974 (Qld) whose application has given rise to some confusion in the past, particularly where the lessee against whom it is being used is also in breach of the lease at the time of receiving the notice. The article explores the historical origins of the section, firstly in New South Wales where it was enacted in 1930, and attempts to outline modern circumstances where it may be applied or particularly applied in Queensland.

Butterfly catastrophe for fronts in a three-component reaction–diffusion system

We study the dynamics of front solutions in a three-component reaction–diffusion system via a combination of geometric singular perturbation theory, Evans function analysis, and center manifold reduction. The reduced system exhibits a surprisingly complicated bifurcation structure including a butterfly catastrophe. Our results shed light on numerically observed accelerations and oscillations and pave the way for the analysis of front interactions in a parameter regime where the essential spectrum of a single front approaches the imaginary axis asymptotically.

Establishing the impact of temporary tissue expanders on electron and photon beam dose distributions

Purpose: This study investigates the effects of temporary tissue expanders (TTEs) on the dose distributions in breast cancer radiotherapy treatments under a variety of conditions. Methods: Using EBT2 radiochromic film, both electron and photon beam dose distribution measurements were made for different phantoms, and beam geometries. This was done to establish a more comprehensive understanding of the implant’s perturbation effects under a wider variety of conditions. Results: The magnetic disk present in a tissue expander causes a dose reduction of approximately 20% in a photon tangent treatment and 56% in electron boost fields immediately downstream of the implant. The effects of the silicon elastomer are also much more apparent in an electron beam than a photon beam. Conclusions: Evidently, each component of the TTE attenuates the radiation beam to different degrees. This study has demonstrated that the accuracy of photon and electron treatments of post-mastectomy patients is influenced by the presence of a tissue expander for various beam orientations. The impact of TTEs on dose distributions establishes the importance of an accurately modelled high-density implant in the treatment planning system for post-mastectomy patients.

Model-based analysis and optimization of bioreactor for hematopoietic stem cell cultivation

One of the problems to be solved in attaining the full potentials of hematopoietic stem cell (HSC) applications is the limited availability of the cells. Growing HSCs in a bioreactor offers an alternative solution to this problem. Besides, it also offers the advantages of eliminating labour intensive process as well as the possible contamination involved in the periodic nutrient replenishments in the traditional T-flask stem cell cultivation. In spite of this, the optimization of HSC cultivation in a bioreactor has been barely explored. This manuscript discusses the development of a mathematical model to describe the dynamics in nutrient distribution and cell concentration of an ex vivo HSC cultivation in a microchannel perfusion bioreactor. The model was further used to optimize the cultivation by proposing three alternative feeding strategies in order to prevent the occurrence of nutrient limitation in the bioreactor. The evaluation of these strategies, the periodic step change increase in the inlet oxygen concentration, the periodic step change increase in the media inflow, and the feedback control of media inflow, shows that these strategies can successfully improve the cell yield of the bioreactor. In general, the developed model is useful for the design and optimization of bioreactor operation.

Further development of discrete computational techniques for calculation of restricted diffusion propagators in porous media

Magnetic resonance is a well-established tool for structural characterisation of porous media. Features of pore-space morphology can be inferred from NMR diffusion-diffraction plots or the time-dependence of the apparent diffusion coefficient. Diffusion NMR signal attenuation can be computed from the restricted diffusion propagator, which describes the distribution of diffusing particles for a given starting position and diffusion time. We present two techniques for efficient evaluation of restricted diffusion propagators for use in NMR porous-media characterisation. The first is the Lattice Path Count (LPC). Its physical essence is that the restricted diffusion propagator connecting points A and B in time t is proportional to the number of distinct length-t paths from A to B. By using a discrete lattice, the number of such paths can be counted exactly. The second technique is the Markov transition matrix (MTM). The matrix represents the probabilities of jumps between every pair of lattice nodes within a single timestep. The propagator for an arbitrary diffusion time can be calculated as the appropriate matrix power. For periodic geometries, the transition matrix needs to be defined only for a single unit cell. This makes MTM ideally suited for periodic systems. Both LPC and MTM are closely related to existing computational techniques: LPC, to combinatorial techniques; and MTM, to the Fokker-Planck master equation. The relationship between LPC, MTM and other computational techniques is briefly discussed in the paper. Both LPC and MTM perform favourably compared to Monte Carlo sampling, yielding highly accurate and almost noiseless restricted diffusion propagators. Initial tests indicate that their computational performance is comparable to that of finite element methods. Both LPC and MTM can be applied to complicated pore-space geometries with no analytic solution. We discuss the new methods in the context of diffusion propagator calculation in porous materials and model biological tissues.

Remote monitoring of underwater objects

A system for monitoring conditions in a remote environment. The system comprising a data transmission network including a plurality of data sensing nodes. Each data sensing node includes an environment sensing means for periodically sensing the environment around node, a transmission means for periodic wireless transmission of sensed data to adjacent data sensing nodes. These adjacent data sensing nodes combining their sensed data with the received data from other data sensing nodes and on transmit the combined data.

Saffman-Taylor fingers with kinetic undercooling

The mathematical model of a steadily propagating Saffman-Taylor finger in a Hele-Shaw channel has applications to two-dimensional interacting streamer discharges which are aligned in a periodic array. In the streamer context, the relevant regularisation on the interface is not provided by surface tension, but instead has been postulated to involve a mechanism equivalent to kinetic undercooling, which acts to penalise high velocities and prevent blow-up of the unregularised solution. Previous asymptotic results for the Hele-Shaw finger problem with kinetic undercooling suggest that for a given value of the kinetic undercooling parameter, there is a discrete set of possible finger shapes, each analytic at the nose and occupying a different fraction of the channel width. In the limit in which the kinetic undercooling parameter vanishes, the fraction for each family approaches 1/2, suggesting that this selection of 1/2 by kinetic undercooling is qualitatively similar to the well-known analogue with surface tension. We treat the numerical problem of computing these Saffman-Taylor fingers with kinetic undercooling, which turns out to be more subtle than the analogue with surface tension, since kinetic undercooling permits finger shapes which are corner-free but not analytic. We provide numerical evidence for the selection mechanism by setting up a problem with both kinetic undercooling and surface tension, and numerically taking the limit that the surface tension vanishes.

Accounting for management costs in sensitivity analyses of matrix population models

Traditional sensitivity and elasticity analyses of matrix population models have been used to inform management decisions, but they ignore the economic costs of manipulating vital rates. For example, the growth rate of a population is often most sensitive to changes in adult survival rate, but this does not mean that increasing that rate is the best option for managing the population because it may be much more expensive than other options. To explore how managers should optimize their manipulation of vital rates, we incorporated the cost of changing those rates into matrix population models. We derived analytic expressions for locations in parameter space where managers should shift between management of fecundity and survival, for the balance between fecundity and survival management at those boundaries, and for the allocation of management resources to sustain that optimal balance. For simple matrices, the optimal budget allocation can often be expressed as simple functions of vital rates and the relative costs of changing them. We applied our method to management of the Helmeted Honeyeater (Lichenostomus melanops cassidix; an endangered Australian bird) and the koala (Phascolarctos cinereus) as examples. Our method showed that cost-efficient management of the Helmeted Honeyeater should focus on increasing fecundity via nest protection, whereas optimal koala management should focus on manipulating both fecundity and survival simultaneously. These findings are contrary to the cost-negligent recommendations of elasticity analysis, which would suggest focusing on managing survival in both cases. A further investigation of Helmeted Honeyeater management options, based on an individual-based model incorporating density dependence, spatial structure, and environmental stochasticity, confirmed that fecundity management was the most cost-effective strategy. Our results demonstrate that decisions that ignore economic factors will reduce management efficiency. ©2006 Society for Conservation Biology.

Managing moose harvests by the seat of your pants

Moose populations are managed for sustainable yield balanced against costs caused by damage to forestry or agriculture and collisions with vehicles. Optimal harvests can be calculated based on a structured population model driven by data on abundance and the composition of bulls, cows, and calves obtained by aerial-survey monitoring during winter. Quotas are established by the respective government agency and licenses are issued to hunters to harvest an animal of specified age or sex during the following autumn. Because the cost of aerial monitoring is high, we use a Management Strategy Evaluation to evaluate the costs and benefits of periodic aerial surveys in the context of moose management. Our on-the-fly "seat of your pants" alternative to independent monitoring is management based solely on the kill of moose by hunters, which is usually sufficient to alert the manager to declines in moose abundance that warrant adjustments to harvest strategies. Harvests are relatively cheap to monitor; therefore, data can be obtained each year facilitating annual adjustments to quotas. Other sources of "cheap" monitoring data such as records of the number of moose seen by hunters while hunting also might be obtained, and may provide further useful insight into population abundance, structure and health. Because conservation dollars are usually limited, the high cost of aerial surveys is difficult to justify when alternative methods exist. © 2012 Elsevier Inc.