Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.

Look before you leap : a confidence-based method for selecting species criticality while avoiding negative populations in τ-leaping

The stochastic simulation algorithm was introduced by Gillespie and in a different form by Kurtz. There have been many attempts at accelerating the algorithm without deviating from the behavior of the simulated system. The crux of the explicit τ-leaping procedure is the use of Poisson random variables to approximate the number of occurrences of each type of reaction event during a carefully selected time period, τ. This method is acceptable providing the leap condition, that no propensity function changes “significantly” during any time-step, is met. Using this method there is a possibility that species numbers can, artificially, become negative. Several recent papers have demonstrated methods that avoid this situation. One such method classifies, as critical, those reactions in danger of sending species populations negative. At most, one of these critical reactions is allowed to occur in the next time-step. We argue that the criticality of a reactant species and its dependent reaction channels should be related to the probability of the species number becoming negative. This way only reactions that, if fired, produce a high probability of driving a reactant population negative are labeled critical. The number of firings of more reaction channels can be approximated using Poisson random variables thus speeding up the simulation while maintaining the accuracy. In implementing this revised method of criticality selection we make use of the probability distribution from which the random variable describing the change in species number is drawn. We give several numerical examples to demonstrate the effectiveness of our new method.

Population genetic structure and patterns of dispersal in the Giant Long-Armed Prawn, Macrobrachium lar (Fabricius, 1798) (Decapoda : Palaemonidae)

The Giant Long-Armed Prawn, Macrobrachium lar is a freshwater species native to the Indo-Pacific. M. lar has a long-lived, passive, pelagic marine larval stage where larvae need to colonise freshwater within three months to complete their development. Dispersal is likely to be influenced by the extensive distances larvae must transit between small oceanic islands to find suitable freshwater habitat, and by prevailing east to west wind and ocean currents in the southern Pacific Ocean. Thus, both intrinsic and extrinsic factors are likely to influence wild population structure in this species. The present study sought to define the contemporary broad and fine-scale population genetic structure of Macrobrachium lar in the south-western Pacific Ocean. Three polymorphic microsatellite loci were used to assess patterns of genetic variation within and among 19 wild adult sample sites. Statistical procedures that partition variation implied that at both spatial scales, essentially all variation was present within sample sites and differentiation among sites was low. Any differentiation observed also was not correlated with geographical distance. Statistical approaches that measure genetic distance, at the broad-scale, showed that all south-western Pacific Islands were essentially homogeneous, with the exception of a well supported divergent Cook Islands group. These findings are likely the result of some combination of factors that may include the potential for allelic homoplasy, through to the effects of sampling regime. Based on the findings, there is most likely a divergent M. lar Cook Islands clade in the south-western Pacific Ocean, resulting from prevailing ocean currents. Confirmation of this pattern will require a more detailed analysis of nDNA variation using a larger number of loci and, where possible, use of larger population sizes.

Assessing population limits : a carrying capacity approach to planning

While purporting to enhance Australia’s sustainability, the federal government’s Population Strategy rejects the assessment of the limiting factors to future population growth, thus avoiding urgent threshold issues such as resource depletion and environmental destruction. A more forward-thinking and whole-system perspective would assess and incorporate critical biophysical limits into governance processes with suitable prioritisation. It would encourage communities to examine their individual and collective responsibilities in the context of these limits in order to most equitably optimise outcomes; and it would employ both a resource-based examination of minimum population requirements, and an impact-based assessment of maximum thresholds. This carrying capacity approach to planning could help guide society towards a more sustainable future.

A sequential Monte Carlo approach to design for population pharmacokinetics studies

Here we present a sequential Monte Carlo approach that can be used to find optimal designs. Our focus is on the design of phase III clinical trials where the derivation of sampling windows is required, along with the optimal sampling schedule. The search is conducted via a particle filter which traverses a sequence of target distributions artificially constructed via an annealed utility. The algorithm derives a catalogue of highly efficient designs which, not only contain the optimal, but can also be used to derive sampling windows. We demonstrate our approach by designing a hypothetical phase III clinical trial.

Energy and population policies in Australia

The Australian Government is about to release Australia’s first sustainable population policy. Sustainable population growth, among other things, implies sustainable energy demand. Current modelling of future energy demand both in Australia and by agencies such as the International Energy Agency sees population growth as one of the key drivers of energy demand. Simply increasing the demand for energy in response to population policy is sustainable only if there is a radical restructuring of the energy system away from energy sources associated with environmental degradation towards one more reliant on renewable fuels and less reliant on fossil fuels. Energy policy can also address the present nexus between energy consumption per person and population growth through an aggressive energy efficiency policy. The paper considers the link between population policies and energy policies and considers how the overall goal of sustainability can be achieved. The methods applied in this analysis draw on the literature of sustainable development to develop elements of an energy planning framework to support a sustainable population policy. Rather than simply accept that energy demand is a function of population increase moderated by an assumed rate of energy efficiency improvement, the focus is on considering what rate of energy efficiency improvement is necessary to significantly reduce the standard connections between population growth and growth in energy demand and what policies are necessary to achieve this situation. Energy efficiency policies can only moderate unsustainable aspects of energy demand and other policies are essential to restructure existing energy systems into on-going sustainable forms. Policies to achieve these objectives are considered. This analysis shows that energy policy, population policy and sustainable development policies are closely integrated. Present policy and planning agencies do not reflect this integration and energy and population policies in Australia have largely developed independently and whether the outcome is sustainable is largely a matter of chance. A genuinely sustainable population policy recognises the inter-dependence between population and energy policies and it is essential that this is reflected in integrated policy and planning agencies

Energy and population policies in Australia

The Australian Government is about to release Australia’s first sustainable population policy. Sustainable population growth, among other things, implies sustainable energy demand. Current modelling of future energy demand both in Australia and by agencies such as the International Energy Agency sees population growth as one of the key drivers of energy demand. Simply increasing the demand for energy in response to population policy is sustainable only if there is a radical restructuring of the energy system away from energy sources associated with environmental degradation towards one more reliant on renewable fuels and less reliant on fossil fuels. Energy policy can also address the present nexus between energy consumption per person and population growth through an aggressive energy efficiency policy. The paper considers the link between population policies and energy policies and considers how the overall goal of sustainability can be achieved. The methods applied in this analysis draw on the literature of sustainable development to develop elements of an energy planning framework to support a sustainable population policy. Rather than simply accept that energy demand is a function of population increase moderated by an assumed rate of energy efficiency improvement, the focus is on considering what rate of energy efficiency improvement is necessary to significantly reduce the standard connections between population growth and growth in energy demand and what policies are necessary to achieve this situation. Energy efficiency policies can only moderate unsustainable aspects of energy demand and other policies are essential to restructure existing energy systems into on-going sustainable forms. Policies to achieve these objectives are considered. This analysis shows that energy policy, population policy and sustainable development policies are closely integrated. Present policy and planning agencies do not reflect this integration and energy and population policies in Australia have largely developed independently and whether the outcome is sustainable is largely a matter of chance. A genuinely sustainable population policy recognises the inter-dependence between population and energy policies and it is essential that this is reflected in integrated policy and planning agencies

The relationship between abdominal obesity and depression in the general population : a systematic review and meta-analysis

Obesity has been widely regarded as a public health concern because of its adverse impact on individuals’ health. Systematic reviews have been published in examining the effect of obesity on depression, but with major emphasis on general obesity as measured by the body mass index. Despite a stronger effect of abdominal obesity on individuals’ physical health outcomes, to our best knowledge, no systematic review was undertaken with regard to the relationship between abdominal obesity and depression. This paper reports the results of a systematic review and meta-analysis of cross-sectional studies examining the relationship between abdominal obesity and depression in a general population. Multiple electronic databases were searched until the end of September 2009. 15 articles were systematically reviewed and meta-analyzed. The analysis showed that the odds ratio of having depression for individuals with abdominal obesity was 1.38 (95% CI, 1.22–1.57) as compared to those who are not obese. Furthermore, it was found that this relationship did not vary with potential confounders including gender, age, measurement of depression and abdominal obesity, and study quality.

Attachment Security and Alexithymia in a Heavy Drinking Population

Attachment difficulties have been proposed as a key risk factor for the development of alexithymia, a multifaceted personality trait characterised by difficulties identifying and describing feelings, a lack of imagination and an externally oriented thinking style. The present study investigated the relationship between attachment and alexithymia in an alcohol dependent population. Participants were 210 outpatients in a Cognitive Behavioural Treatment Program assessed on the Toronto Alexithymia Scale (TAS-20) and the Revised Adult Attachment Scale (RAAS). Significant relationships between anxious attachment and alexithymia factors were confirmed. Furthermore, alexithymic alcoholics reported significantly higher levels of anxious attachment and significantly lower levels of closeness (secure attachment) compared to non-alexithymic alcoholics. These findings highlight the importance of assessing and targeting anxious attachment among alexithymic alcoholics in order to improve alcohol treatment outcomes. Keywords: Attachment, alexithymia, alcohol dependence.

Predictive compensation for variable network delays and packet losses in networked control systems

Networked control systems (NCSs) offer many advantages over conventional control; however, they also demonstrate challenging problems such as network-induced delay and packet losses. This paper proposes an approach of predictive compensation for simultaneous network-induced delays and packet losses. Different from the majority of existing NCS control methods, the proposed approach addresses co-design of both network and controller. It also alleviates the requirements of precise process models and full understanding of NCS network dynamics. For a series of possible sensor-to-actuator delays, the controller computes a series of corresponding redundant control values. Then, it sends out those control values in a single packet to the actuator. Once receiving the control packet, the actuator measures the actual sensor-to-actuator delay and computes the control signals from the control packet. When packet dropout occurs, the actuator utilizes past control packets to generate an appropriate control signal. The effectiveness of the approach is demonstrated through examples.

The application of Bowen’s family system theory (BFST) to the Malay population in Malaysia

The rapid economic development and social changes in Malaysia recently have led to many psychosocial problems in young people, such as drug addiction, child sexual abuse and mental illness. The Malaysian government is beginning to focus more attention on its social welfare and human service needs in order to alleviate these psychosocial problems. Although counselling is accepted and widespread in Malaysia, the practice of family therapy is not as accepted as it is still a widely held belief that family problems need to be kept within the family. However, changes are imminent and thus the theoretical basis of family therapy needs to be culturally relevant. Bowen‟s Family Systems Theory (BFST) is already one of the major theories taught to tertiary counselling students in Malaysian universities. The main tenet of Bowen‟s theory is that the family as a system may be unstable unless each member of the family is well differentiated. High differentiation levels in the family allow a person to both leave the family‟s boundaries in search of uniqueness and to continually return to the family fold in order to establish a more mature sense of belonging. The difficulty, however, is that while Bowen has claimed that his theory is universal nearly all of the research confirming the theory has been conducted in the United States of America. The only known study outside America, however, did show that Bowen‟s theory applied to a Filipino population but, one of the theory‟s propositions that differentiation is intergenerational was not supported in this non-American sample. The American sample that was compared to the Malay sample was taken from Skowron and Friedlander‟s (1998) study. One hundred and twenty-seven faculty staff in an American university completed the Differentiation of Self Inventory (DSI) to measure level of differentiation of self. This thesis therefore, set out to determine whether Bowen‟s theory applied to another non-American sample, the Malaysian community. The research also investigated if the intergenerational effect was present in the Malaysian sample as well as explored the role of socio-economic status on Bowen‟s theory of differentiation and gender effect. Three hundred and seventy-four families completed four measures to examine these research questions: the Differentiation of Self Inventory (DSI), the Family Inventory of Life Event (FILE), the Depression Anxiety and Stress Scale (DASS) and the Connor-Davidson Resilience Scale (CD-RISC). The results of the study showed that differentiation of self is a valid construct for the Malay population. However, all four subscales of the Differentiation of Self Inventory (DSI); emotional reactivity (ER), emotional cut-off (EC), fusion with other (FO) and I position (IP), showed significant differences compared to the American sample from Skowron and Friedlander‟s (1998) study. The Malay sample scored higher in emotional reaction (ER), fusion with other (FO), but lower on emotional cut-off (EC) and I position (IP) than the American sample. The intergenerational effect was found in the Malay population as the parent‟s level of differentiation correlated with their children‟s level of differentiation. It was found that stress as measured by the Family Inventory of Life Event (FILE) and as measured by the Depression Anxiety and Stress Scale (DASS) were not correlated with the level of differentiation of self in parents. However, gender had a significant effect in predicting the level of differentiation among parents in Malay population with females scores higher on emotional reactivity (ER) and fusion with other (FO) than males. An additional finding was that resilience can be predicted from the level of differentiation of self in children in the Malay sample. There was also a positive correlation between the level of differentiation of self in parents and resilience in their children. Findings from this study indicate that the concept of differentiation of self is applicable to a Malay sample; however, the implementation of the theory should be applied with cultural sensitivity.

Can the Cardiac ARIA Index Improve Cardiac Care for Australia's Indigenous Population?

Background: Timely access to appropriate cardiac care is critical for optimising outcomes. Our aim was to derive an objective, comparable, geographic measure reflecting access to cardiac services for Australia's 20,387 population locations. Methods: An expert panel defined a single patient care pathway. Using geographic information systems (GIS) the numeric/alpha index was modelled in two phases. The acute phase index (numeric) ranged from 1 (access to tertiary centre with PCI ≤1 h) to 8 (no ambulance service, >3 h to medical facility, air transport required). The aftercare index was modelled into 5 alphabetic categories; A (Access to general practitioner, pharmacy, cardiac rehabilitation, pathology ≤1 h) to E (no services available within 1 h). Results: Approximately 70% or 13.9 million people lived within a CardiacARIAindex category 1A location. Disparity continues in access to category 1A cardiac services for 5.8 million (30%) of all Australians, 60% of Aboriginal and Torres Strait Islander people and 32% of people over 65 years of age. In a cardiac emergency only 40% of the Indigenous population reside within one hour of category 1 hospital. Approximately 30% (81,491 Indigenous persons) are more than one to three hours from basic cardiac services. Conclusion: Geographically, the majority of Australian's have timely access for survival of a cardiac event. The CardiacARIAindex objectively demonstrates that the healthcare system may not be providing for the needs of 60% of Indigenous people residing outside the 1A geographic radius. Innovative clinical practice maybe required to address these disparities.

H. pylori-infection and antibody immune response in a rural Tanzanian population

Abstract Background: Helicobacter pylori (H. pylori) infection is ubiquitous in sub-Saharan Africa, but paradoxically gastric cancer is rare. Methods: Sera collected during a household-based survey in rural Tanzania in 1985 were tested for anti-H. pylori IgG and IgG subclass antibodies by enzyme immunoassay. Odds ratios (OR) and confidence intervals (CI) of association of seropositivity with demographic variables were computed by logistic regression models. Results: Of 788 participants, 513 were aged ≤17 years. H. pylori seropositivity increased from 76% at 0–4 years to 99% by ≥18 years of age. Seropositivity was associated with age (OR 11.5, 95% CI 4.2–31.4 for 10–17 vs. 0–4 years), higher birth-order (11.1; 3.6–34.1 for ≥3rd vs. 1st born), and having a seropositive next-older sibling (2.7; 0.9–8.3). Median values of IgG subclass were 7.2 for IgG1 and 2.0 for IgG2. The median IgG1/IgG2 ratio was 3.1 (IQR: 1.7–5.6), consistent with a Th2- dominant immune profile. Th2-dominant response was more frequent in children than adults (OR 2.4, 95% CI 1.3–4.4). Conclusion: H. pylori seropositivity was highly prevalent in Tanzania and the immunological response was Th2-dominant. Th2-dominant immune response, possibly caused by concurrent bacterial or parasitic infections, could explain, in part, the lower risk of H. pylori-associated gastric cancer in Africa.

The economics of happiness : a lifetime perspective

The three studies in this thesis focus on happiness and age and seek to contribute to our understanding of happiness change over the lifetime. The first study contributes by offering an explanation for what was evolving to a ‘stylised fact’ in the economics literature, the U-shape of happiness in age. No U-shape is evident if one makes a visual inspection of the age happiness relationship in the German socio-economic panel data, and, it seems counter-intuitive that we just have to wait until we get old to be happy. Eliminating the very young, the very old, and the first timers from the analysis did not explain away regression results supporting the U-shape of happiness in age, but fixed effect analysis did. Analysis revealed found that reverse causality arising from time-invariant individual traits explained the U-shape of happiness in age in the German population, and the results were robust across six econometric methods. Robustness was added to the German fixed effect finding by replicating it with the Australian and the British socio-economic panel data sets. During analysis of the German data an unexpected finding emerged, an exceedingly large negative linear effect of age on happiness in fixed-effect regressions. There is a large self-reported happiness decline by those who remain in the German panel. A similar decline over time was not evident in the Australian or the British data. After testing away age, time and cohort effects, a time-in-panel effect was found. Germans who remain in the panel for longer progressively report lower levels of happiness. Because time-in-panel effects have not been included in happiness regression specifications, our estimates may be biased; perhaps some economics of the happiness studies, that used German panel data, need revisiting. The second study builds upon the fixed-effect finding of the first study and extends our view of lifetime happiness to a cohort little visited by economists, children. Initial analysis extends our view of lifetime happiness beyond adulthood and revealed a happiness decline in adolescent (15 to 23 year-old) Australians that is twice the size of the happiness decline we see in older Australians (75 to 86 yearolds), who we expect to be unhappy due to declining income, failing health and the onset of death. To resolve a difference of opinion in the literature as to whether childhood happiness decreases, increases, or remains flat in age; survey instruments and an Internet-based survey were developed and used to collect data from four hundred 9 to 14 year-old Australian children. Applying the data to a Model of Childhood Happiness revealed that the natural environment life-satisfaction domain factor did not have a significant effect on childhood happiness. However, the children’s school environment and interactions with friends life-satisfaction domain factors explained over half a steep decline in childhood happiness that is three times larger than what we see in older Australians. Adding personality to the model revealed what we expect to see with adults, extraverted children are happier, but unexpectedly, so are conscientious children. With the steep decline in the happiness of young Australians revealed and explanations offered, the third study builds on the time-invariant individual trait finding from the first study by applying the Australian panel data to an Aggregate Model of Average Happiness over the lifetime. The model’s independent variable is the stress that arises from the interaction between personality and the life event shocks that affect individuals and peers throughout their lives. Interestingly, a graphic depiction of the stress in age relationship reveals an inverse U-shape; an inverse U-shape that looks like the opposite of the U-shape of happiness in age we saw in the first study. The stress arising from life event shocks is found to explain much of the change in average happiness over a lifetime. With the policy recommendations of economists potentially invoking unexpected changes in our lives, the ensuing stress and resulting (un)happiness warrant consideration before economists make policy recommendations.

Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.