Dirichlet problem at infinity for p-harmonic functions on negatively curved spaces

The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.

Indigofera linnaei-a problem legume across northern pastures

Indigofera linnaei (or Birdsville Indigo) is a native legume with widespread abundance in pastures across northern Australian, and occurs in all northern regions of Australia from the tropical Kimberleys and arid central Australia to subhumid coastal Queensland (Figure 1). I. linnaei in central Australia has been linked to canine fatalities due to the toxin indospicine. Indospicine, an analog of arginine, is an unusual non-protein amino acid found only in a number of Indigofera species including I. linnaei. Dogs are particularly sensitive to the heptatoxicity of indospicine, and while they do not themselves consume the plant, dogs have been poisoned indirectly through the consumption of indospicine-contaminated meat from horses and camels grazing in regions where I. linnaei is common (Hegarty and Pound 1988, FitzGerald et al 2011). I. linnaei is observed to occur in various forms from strongly prostrate in south-east Queensland to an erect shrub-like form growing to more than 50cm in height in some northern regions. It mostly occurs as a minor proportion of native pasture but denser stands develop under certain circumstances. The indospicine content of I. linnaei has not previously been reported outside of central Australia, and in this study we investigate the indospicine content of plant samples collected across various regions, including both prostrate and upright forms. All samples were collected in March-July, dried, milled and analysed by UPLC-MS/MS in an adaption of our method (Tan et al 2014). Indospicine was determined in all I. linnaei plant samples regardless of region or growth form (Table 1). Measured levels were in the range 159.5 to 658.8 mg/kg DM and indicate that this plant may pose a similar problem in all areas dependent on local seasonal abundance.

On the orthogonality of suboptimum estimate in the combined estimation and control problem

By deriving the equations for an error analysis of modeling inaccuracies for the combined estimation and control problem, it is shown that the optimum estimation error is orthogonal to the actual suboptimum estimate.

Some Generalisations of the Time Minimising Assignment Problem

The time minimising assignment problem is the problem of finding an assignment of n jobs to n facilities, one to each, which minimises the total time for completing all the jobs. The usual assumption made in these problems is that all the jobs are commenced simultaneously. In this paper two generalisations of this assumption are considered, and algorithms are presented to solve these general problems. Numerical examples are worked out illustrating the algorithms.

Fate of pathogen indicators in a domestic blend of food waste and wastewater through a two-stage anaerobic digestion system

Anaerobic digestion is a viable on-site treatment technology for rich organic waste streams such as food waste and blackwater. In contrast to large-scale municipal wastewater treatment plants which are typically located away from the community, the effluent from any type of on-site system is a potential pathogenic hazard because of the intimacy of the system to the community. The native concentrations of the pathogen indicators Escherichia coli, Clostridium perfringens and somatic coliphage were tracked for 30 days under stable operation (organic loading rate (OLR) = 1.8 kgCOD m(-3) day(-1), methane yield = 52% on a chemical oxygen demand (COD) basis) of a two-stage laboratory-scale digester treating a mixture of food waste and blackwater. E. coli numbers were reduced by a factor of 10(6.4) in the thermophilic stage, from 10(7.5+/-0.3) to 10(1.1+/-0.1) cfu 100 mL(-1), but regenerated by a factor of 10(4) in the mesophilic stage. Neither the thermophilic nor mesophilic stages had any significant impact on C. perfringens concentrations. Coliphage concentrations were reduced by a factor of 10(1.4) across the two stages. The study shows that anaerobic digestion only reduces pathogen counts marginally but that counts in effluent samples could be readily reduced to below detection limits by filtration through a 0.22 microm membrane, to investigate membrane filtration as a possible sanitation technique.

Fate of key food-borne pathogens associated with intensive pig and poultry farming environments

Intensive pig and poultry farming in Australia can be a source of pathogens with implications for food-safety and/or human illness. Seven studies were undertaken with the following objectives: · Assess the types of zoonotic pathogens in waste · Assess the transfer of pathogens during re-use both within the shed and externally in the environment · The potential for movement of pathogens via aerosols In the first and second studies the extent of zoonotic pathogens was evaluated in both piggery effluent and chicken litter and Salmonella and Campylobacter were detected in both wastes. In the third study the dynamics of Salmonella during litter re-use was examined and results showed a trend for lower Salmonella levels and serovar diversity in re-used litter compared to new litter. Thus, re-use within the poultry farming system posed no increased risk. The fourth study addressed the direct risks of pathogens to farm workers due to reuse of piggery effluent within the pig shed. Based on air-borne Escherichia coli (E. coli) levels, re-using effluent did not pose a risk. In the fifth study high levels of Arcobacter spp. were detected in effluent ponds and freshly irrigated soils with potential food-safety risks during the irrigation of food-crops and pasture. The sixth and seventh studies addressed the risks from aerosols from mechanically ventilated sheds. Staphylococci were shown to have potential as markers, with airborne levels gradually dropping and reaching background levels at 400 m distance. Salmonella was detected (at low levels) both inside and outside the shed (at 10 m). Campylobacter was detected only once inside the shed during the 3-year period (at low levels). Results showed there was minimal risk to humans living adjacent to poultry farms This is the first comprehensive analysis studying key food-safety pathogens and potential public health risks associated with intensively farmed pigs and poultry in Australia.

Re-use of chicken litter across broiler cycles – managing the food-borne pathogen risk

Thus the objectives of this study can be broadly categorised as follows:-  Evaluate current practices adopted (e.g. litter pile-up) prior to re-use of litter for subsequent chicken cycles  To establish pathogen die-off that occurs during currently adopted methods of in-shed treatment of litter  To establish simple physical parameters to monitor this pathogen reduction and create an understanding of such reduction strategies to aid in-shed management of re-use litter  To carry out studies to assess the potential of the re-used litter (once spread) to support pathogens during a typical chicken production cycle.  To provide background data for the development of a simple code of practice for an in-shed litter pile-up process

Post-head-emergence frost in wheat and barley: defining the problem, assessing the damage, and identifying resistance

Radiant frost is a significant production constraint to wheat (Triticum aestivum) and barley (Hordeum vulgare), particularly in regions where spring-habit cereals are grown through winter, maturing in spring. However, damage to winter-habit cereals in reproductive stages is also reported. Crops are particularly susceptible to frost once awns or spikes emerge from the protection of the flag leaf sheath. Post-head-emergence frost (PHEF) is a problem distinct from other cold-mediated production constraints. To date, useful increased PHEF resistance in cereals has not been identified. Given the renewed interest in reproductive frost damage in cereals, it is timely to review the problem. Here we update the extent and impacts of PHEF and document current management options to combat this challenge. We clarify terminology useful for discussing PHEF in relation to chilling and other freezing stresses. We discuss problems characterizing radiant frost, the environmental conditions leading to PHEF damage, and the effects of frost at different growth stages. PHEF resistant cultivars would be highly desirable, to both reduce the incidence of direct frost damage and to allow the timing of crop maturity to be managed to maximize yield potential. A framework of potential adaptation mechanisms is outlined. Clarification of these critical issues will sharpen research focus, improving opportunities to identify genetic sources for improved PHEF resistance.

Post-head-emergence frost in wheat and barley: defining the problem, assessing the damage, and identifying resistance

Radiant frost is a significant production constraint to wheat (Triticum aestivum) and barley (Hordeum vulgare), particularly in regions where spring-habit cereals are grown through winter, maturing in spring. However, damage to winter-habit cereals in reproductive stages is also reported. Crops are particularly susceptible to frost once awns or spikes emerge from the protection of the flag leaf sheath. Post-head-emergence frost (PHEF) is a problem distinct from other cold-mediated production constraints. To date, useful increased PHEF resistance in cereals has not been identified. Given the renewed interest in reproductive frost damage in cereals, it is timely to review the problem. Here we update the extent and impacts of PHEF and document current management options to combat this challenge. We clarify terminology useful for discussing PHEF in relation to chilling and other freezing stresses. We discuss problems characterizing radiant frost, the environmental conditions leading to PHEF damage, and the effects of frost at different growth stages. PHEF resistant cultivars would be highly desirable, to both reduce the incidence of direct frost damage and to allow the timing of crop maturity to be managed to maximize yield potential. A framework of potential adaptation mechanisms is outlined. Clarification of these critical issues will sharpen research focus, improving opportunities to identify genetic sources for improved PHEF resistance.

Distribution and characterization of Poleroviruses affecting food legumes in Central/West Asia and North Africa (CWANA) region and Australia

During the past 15 years, surveys to identify virus diseases affecting cool-season food legume crops in Australia and 11 CWANA countries (Algeria, China, Egypt, Ethiopia, Lebanon, Morocco, Sudan, Syria, Tunisia, Uzbekistan and Yemen) were conducted. More than 20,000 samples were collected and tested for the presence of 14 legume viruses by the tissue-blot immunoassay (TBIA) using a battery of antibodies, including the following Luteovirus monoclonal antibodies (McAbs): a broad-spectrum legume Luteovirus (5G4), BLRV, BWYV, SbDV and CpCSV. A total of 195 Luteovirus samples were selected for further testing by RT-PCR using 7 primers (one is degenerate, and can detect a wide range of Luteoviridae virus species and the other six are species-specific primers) at the Virology Laboratory, QDAF, Australia, during 2014. A total of 145 DNA fragments (represented 105 isolates) were sequenced. The following viruses were characterized based on molecular analysis: BLRV from Lebanon, Morocco, Tunisia and Uzbekistan; SbDV from Australia, Syria and Uzbekistan; BWYV from Algeria, China, Ethiopia, Lebanon, Morocco, Sudan, Tunisia and Uzbekistan; CABYV from Algeria, Lebanon, Syria, Sudan and Uzbekistan; CpCSV from Algeria, Ethiopia, Lebanon, Morocco, Syria and Tunisia, and unknown Luteoviridae species from Algeria, Ethiopia, Morocco, Sudan, Uzbekistan and Yemen. This study has clearly shown that there are a number of Polerovirus species, in addition to BWYV, all can produce yellowing/stunting symptoms in pulses (e.g. CABYV, CpCSV, and other unknown Polerovirus species). Based on our knowledge this is the first report of CABYV affecting food legumes. Moreover, there was about 95% agreement between results obtained from serological analysis (TBIA) and molecular analysis for the detection of BLRV and SbDV. Whereas, TBIA results were not accurate when using CpCSV and BWYV McAbs . It seems that the McAbs for CpCSV and BWYV used in this study and those available worldwide, are not virus species specific. Both antibodies, reacted with other Polerovirus species (e.g. CABYV, and unknown Polerovirus). This highlights the need for more accurate characterization of existing antibodies and where necessary the development of better, virus-specific antibodies to enable their use for accurate diagnosis of Poleroviruses.

First detection of extended-spectrum cephalosporin- and fluoroquinolone-resistant Escherichia coli in Australian food-producing animals

This study aimed to define the frequency of resistance to critically important antimicrobials (CIAs) [i.e. extended-spectrum cephalosporins (ESCs), fluoroquinolones (FQs) and carbapenems] among Escherichia coli isolates causing clinical disease in Australian food-producing animals. Clinical E. coli isolates (n = 324) from Australian food-producing animals [cattle (n = 169), porcine (n = 114), poultry (n = 32) and sheep (n = 9)] were compiled from all veterinary diagnostic laboratories across Australia over a 1-year period. Isolates underwent antimicrobial susceptibility testing to 18 antimicrobials using the Clinical and Laboratory Standards Institute disc diffusion method. Isolates resistant to CIAs underwent minimum inhibitory concentration determination, multilocus sequence typing (MLST), phylogenetic analysis, plasmid replicon typing, plasmid identification, and virulence and antimicrobial resistance gene typing. The 324 E. coli isolates from different sources exhibited a variable frequency of resistance to tetracycline (29.0–88.6%), ampicillin (9.4–71.1%), trimethoprim/sulfamethoxazole (11.1–67.5%) and streptomycin (21.9–69.3%), whereas none were resistant to imipenem or amikacin. Resistance was detected, albeit at low frequency, to ESCs (bovine isolates, 1%; porcine isolates, 3%) and FQs (porcine isolates, 1%). Most ESC- and FQ-resistant isolates represented globally disseminated E. coli lineages (ST117, ST744, ST10 and ST1). Only a single porcine E. coli isolate (ST100) was identified as a classic porcine enterotoxigenic E. coli strain (non-zoonotic animal pathogen) that exhibited ESC resistance via acquisition of blaCMY-2. This study uniquely establishes the presence of resistance to CIAs among clinical E. coli isolates from Australian food-producing animals, largely attributed to globally disseminated FQ- and ESC-resistant E. coli lineages.

Multi-user resource-sharing problem for the Internet

In this thesis we study a series of multi-user resource-sharing problems for the Internet, which involve distribution of a common resource among participants of multi-user systems (servers or networks). We study concurrently accessible resources, which for end-users may be exclusively accessible or non-exclusively. For all kinds we suggest a separate algorithm or a modification of common reputation scheme. Every algorithm or method is studied from different perspectives: optimality of protocols, selfishness of end users, fairness of the protocol for end users. On the one hand the multifaceted analysis allows us to select the most suited protocols among a set of various available ones based on trade-offs of optima criteria. On the other hand, the future Internet predictions dictate new rules for the optimality we should take into account and new properties of the networks that cannot be neglected anymore. In this thesis we have studied new protocols for such resource-sharing problems as the backoff protocol, defense mechanisms against Denial-of-Service, fairness and confidentiality for users in overlay networks. For backoff protocol we present analysis of a general backoff scheme, where an optimization is applied to a general-view backoff function. It leads to an optimality condition for backoff protocols in both slot times and continuous time models. Additionally we present an extension for the backoff scheme in order to achieve fairness for the participants in an unfair environment, such as wireless signal strengths. Finally, for the backoff algorithm we suggest a reputation scheme that deals with misbehaving nodes. For the next problem -- denial-of-service attacks, we suggest two schemes that deal with the malicious behavior for two conditions: forged identities and unspoofed identities. For the first one we suggest a novel most-knocked-first-served algorithm, while for the latter we apply a reputation mechanism in order to restrict resource access for misbehaving nodes. Finally, we study the reputation scheme for the overlays and peer-to-peer networks, where resource is not placed on a common station, but spread across the network. The theoretical analysis suggests what behavior will be selected by the end station under such a reputation mechanism.

What do prisoners eat? Nutrient intakes and food practices in a high secure prison

There are limited studies on the adequacy of prisoner diet and food practices, yet understanding these are important to inform food provision and assure duty of care for this group. The aim of this research was to assess the dietary intakes of prisoners to inform food and nutrition policy in this setting. This research used a cross-sectional design with convenience sampling in a 945 bed male high secure prison. Multiple methods were used to assess food available at the group level, including verification of food portion, quality, and practices. A pictorial tool supported the diet history method. Of 276 eligible prisoners, 120 dietary interviews were conducted and verified against prison records, with 106 deemed plausible. The results showed the planned food to be nutritionally adequate, with the exception of vitamin D for older males and long chain fatty acids, with sodium above Upper Limits. The Australian Dietary Targets for chronic disease risk were not achieved. High energy intakes were reported with median 13.8MJ (SE 0.3MJ). Probability estimates of inadequate intake varied with age groups: magnesium 8% (>30 years), 2.9% (<30 years); calcium 6.0% (>70 years), 1.5% (<70 years); folate 3.5%; zinc and iodine 2.7%; and vitamin A 2.3%. Nutrient intakes were greatly impacted by self-funded snacks. Results suggest nutrient intakes nutritionally favourable when compared to males in the community. This study highlights the complexity of food provision in the prison environment, and also poses questions for population level dietary guidance in delivering appropriate nutrients within energy limits.

A probabilistic approach to the problem of electron localization in disordered systems and sharpness of the mobility edge

By applying the theory of the asymptotic distribution of extremes and a certain stability criterion to the question of the domain of convergence in the probability sense, of the renormalized perturbation expansion (RPE) for the site self-energy in a cellularly disordered system, an expression has been obtained in closed form for the probability of nonconvergence of the RPE on the real-energy axis. Hence, the intrinsic mobility mu (E) as a function of the carrier energy E is deduced to be given by mu (E)= mu 0exp(-exp( mod E mod -Ec) Delta ), where Ec is a nominal 'mobility edge' and Delta is the width of the random site-energy distribution. Thus mobility falls off sharply but continuously for mod E mod >Ec, in contradistinction with the notion of an abrupt 'mobility edge' proposed by Cohen et al. and Mott. Also, the calculated electrical conductivity shows a temperature dependence in qualitative agreement with experiments on disordered semiconductors.

An inhomogeneity problem in couple stress theory

Using Hilbert theory and Mindlin's couple stress theory, the problem of two-dimensional circular inhomogeneity (when the inserted material is of different size than the size of the cavity and having different elastic constants) is studiedin this paper. Stress could be bounded at infinity. The formulation is valid also for regions other then the circular ones when the matrix is finite has also been tackled. Numerical results are in conformity with the fact that the effect of couple stresses is negligible when the ratio of the smallest dimension of the body to the cahracteristic length is large.