An explicit criterion for finite-time stability of linear nonautonomous systems with delays

In this paper, the problem of finite-time stability of linear nonautonomous systems with time-varying delays is considered. Using a novel approach based on some techniques developed for linear positive systems, we derive new explicit conditions in terms of matrix inequalities ensuring that the state trajectories of the system do not exceed a certain threshold over a pre-specified finite time interval. These conditions are shown to be relaxed for the Lyapunov asymptotic stability. A numerical example is given to illustrate the effectiveness of the obtained result.

Robust Controller Design of Networked Control Systems with Nonlinear Uncertainties

We address robust stabilization problem for networked control systems with nonlinear uncertainties and packet losses by modelling such systems as a class of uncertain switched systems. Based on theories on switched Lyapunov functions, we derive the robustly stabilizing conditions for state feedback stabilization and design packet-loss dependent controllers by solving some matrix inequalities. A numerical example and some simulations are worked out to demonstrate the effectiveness of the proposed design method.

Increasing socio-economic inequalities in drug-induced deaths in Australia : 1981-2002

Introduction and Aims: Since the 1990s illicit drug use death rates in Australia have increased markedly. There is a notable gap in knowledge about changing socio-economic inequalities in drug use death rates. Some limited Australian and overseas data point to higher rates of drug death in the lowest socio-economic groups, but the paucity of available studies and their sometimes conflicting findings need to be addressed. Design and Methods: This paper uses data obtained from the Australian Bureau of Statistics (ABS) to examine changes in age-standardised drug-induced mortality rates for Australian males over the period 1981 – 2002. Socio-economic status was categorised as manual or non-manual work status. Results: With the rapid increase in drug-induced mortality rates in the 1990s, there was a parallel increase in socio-economic inequalities in drug-induced deaths. The decline in drug death rates from 2000 onwards was associated with a decline in socio-economic inequalities. By 2002, manual workers had drug death rates well over twice the rate of non-manual workers. Discussion: Three factors are identified which contribute to these socio-economic inequalities in mortality. First, there has been an age shift in deaths evident only for manual workers. Secondly, there has been an increase in availability until 1999 and a relative decline in the cost of the drug, which most often leads to drug death (heroin). Thirdly, there has been a shift to amphetamine use which may lead to significant levels of morbidity, but few deaths. [Najman JM, Toloo G, Williams GM. Increasing socio-economic inequalities in drug-induced deaths in Australia: 1981–2002.

Social inequalities and parent involvement in children’s education in the early years of school

Strengthening cooperation between schools and parents is critical to improving learning outcomes for children. The chapter focuses on parental engagement in their children’s education in the early years of school. It considers issues of social and cultural capital as important to whether, or not, parents are involved in their children’s schooling. Analyses of data from a national representative sample of children and their families who participate in Growing up in Australia: The Longitudinal Study of Australian Children are presented. Results indicated that higher family socio-economic position was associated with higher levels of parental involvement and higher expectations about children’s future level of education.

New Approach on Robust Delay-Dependent H∞ Control for Uncertain T-S Fuzzy Systems With Interval Time-Varying Delay

This paper investigates the robust H∞ control for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, delay-dependent stability criteria are derived for the control problem. Because neither any model transformation nor free weighting matrices are employed in our theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions. Also, the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

Socioeconomic differences in takeaway food consumption and their contribution to inequalities in dietary intakes

Background Takeaway consumption has been increasing and may contribute to socioeconomic inequalities in overweight/obesity and chronic disease. This study examined socioeconomic differences in takeaway consumption patterns, and their contributions to dietary intake inequalities. Method Cross-sectional dietary intake data from adults aged between 25 and 64 years from the Australian National Nutrition Survey (n= 7319, 61% response rate). Twenty-four hour dietary recalls ascertained intakes of takeaway food, nutrients and fruit and vegetables. Education was used as socioeconomic indicator. Data were analysed using logistic regression and general linear models. Results Thirty-two percent (n = 2327) consumed takeaway foods in the 24 hour period. Lower-educated participants were less likely than their higher-educated counterparts to have consumed total takeaway foods (OR 0.64; 95% CI 0.52, 0.80). Of those consuming takeaway foods, the lowest-educated group was more likely to have consumed “less healthy” takeaway choices (OR 2.55; 95% CI 1.73, 3.77), and less likely to have consumed “healthy” choices (OR 0.52; 95% CI 0.36, 0.75). Takeaway foods made a greater contribution to energy, total fat, saturated fat, and fibre intakes among lower than higher-educated groups. Lower likelihood of fruit and vegetable intakes were observed among “less healthy” takeaway consumers, whereas a greater likelihood of their consumption was found among “healthy” takeaway consumers. Conclusions Total and the types of takeaway foods consumed may contribute to socioeconomic inequalities in intakes of energy, total and saturated fats. However, takeaway consumption is unlikely to be a factor contributing to the lower fruit and vegetable intakes among socioeconomically-disadvantaged groups.

Inequalities in cardiovascular disease mortality : the role of behavioural, physiological and social risk factors

Background: While the relationship between socioeconomic disadvantage and cardiovascular disease (CVD) is well established, the role that traditional cardiovascular risk factors play in this association remains unclear. We examined the association between education attainment and CVD mortality and the extent to which behavioural, social and physiological factors explained this relationship. Methods: Adults (n=38 355) aged 40-69 years living in Melbourne, Australia were recruited in 1990-1994. Subjects with baseline CVD risk factor data ascertained through questionnaire and physical measurement were followed for an average of 9.4 years with CVD deaths verified by review of medical records and autopsy reports. Results: CVD mortality was higher for those with primary education only compared to those who had completed tertiary education, with a hazard ratio (HR) of 1.66 (95% confidence interval [CI] 1.11-2.49) after adjustment for age, country of birth and gender. Those from the lowest educated group had a more adverse cardiovascular risk factor profile compared to the highest educated group, and adjustment for these risk factors reduced the HR to 1.18 (95% CI 0.78-1.77). In analysis of individual risk factors, smoking and waist circumference explained most of the difference in CVD mortality between the highest and lowest education groups. Conclusions: Most of the excess CVD mortality in lower socioeconomic groups can be explained by known risk factors, particularly smoking and overweight. While targeting cardiovascular risk factors should not divert efforts from addressing the underlying determinants of health inequalities, it is essential that known risk factors are addressed effectively among lower socioeconomic groups.

Diagnostic and treatment pathways for men with prostate cancer in Queensland : investigating spatial and demographic inequalities

Background: Patterns of diagnosis and management for men diagnosed with prostate cancer in Queensland, Australia, have not yet been systematically documented and so assumptions of equity are untested. This longitudinal study investigates the association between prostate cancer diagnostic and treatment outcomes and key area-level characteristics and individual-level demographic, clinical and psychosocial factors.---------- Methods/Design: A total of 1064 men diagnosed with prostate cancer between February 2005 and July 2007 were recruited through hospital-based urology outpatient clinics and private practices in the centres of Brisbane, Townsville and Mackay (82% of those referred). Additional clinical and diagnostic information for all 6609 men diagnosed with prostate cancer in Queensland during the study period was obtained via the population-based Queensland Cancer Registry. Respondent data are collected using telephone and self-administered questionnaires at pre-treatment and at 2 months, 6 months, 12 months, 24 months, 36 months, 48 months and 60 months post-treatment. Assessments include demographics, medical history, patterns of care, disease and treatment characteristics together with outcomes associated with prostate cancer, as well as information about quality of life and psychological adjustment. Complementary detailed treatment information is abstracted from participants’ medical records held in hospitals and private treatment facilities and collated with health service utilisation data obtained from Medicare Australia. Information about the characteristics of geographical areas is being obtained from data custodians such as the Australian Bureau of Statistics. Geo-coding and spatial technology will be used to calculate road travel distances from patients’ residences to treatment centres. Analyses will be conducted using standard statistical methods along with multilevel regression models including individual and area-level components.---------- Conclusions: Information about the diagnostic and treatment patterns of men diagnosed with prostate cancer is crucial for rational planning and development of health delivery and supportive care services to ensure equitable access to health services, regardless of geographical location and individual characteristics. This study is a secondary outcome of the randomised controlled trial registered with the Australian New Zealand Clinical Trials Registry (ACTRN12607000233426)

Household food expenditure and its contribution to socioeconomic inequalities in purchasing foods consistent with Australian dietary guideline recommendations

Aim: To examine the amount of money spent on food by household income, and to ascertain whether food expenditure mediates the relationship between household income and the purchase of staple foods consistent with Australian dietary guideline recommendations. ----- ----- Methods: In face-to-face interviews (n = 1003, 66.4% response rate), households in Brisbane, Australia were asked about their purchasing choices for a range of staple foods, including grocery items, fruits and vegetables. For each participant, information was obtained about their total weekly household food expenditure, along with their sociodemographic and household characteristics. ----- ----- Results: Household income was significantly associated with food expenditure; participants residing in higher-income households spent more money on food per household member than those from lower-income households. Lower income households were less likely to make food purchasing choices of dietary staples that were consistent with recommendations. However, food expenditure did not attenuate the relationship between household income and the purchase of staple foods consistent with dietary guideline recommendations. ----- ----- Conclusions: The findings suggest that food expenditure may not contribute to income inequalities in purchasing staple foods consistent with dietary guideline recommendations: instead, other material or psychosocial factors not considered in the current study may be more important determinants of these inequalities. Further research should examine whether expenditure on non-staple items and takeaway foods is a larger contributor to socioeconomic inequalities in dietary behavior.

A systematic review of studies on socioeconomic inequalities in dietary intakes associated with weight gain and overweight/obesity conducted among European adults

This Review examined socioeconomic inequalities in intakes of dietary factors associated with weight gain, overweight/obesity among adults in Europe. Literature searches of studies published between 1990 and 2007 examining socioeconomic position (SEP) and the consumption of energy, fat, fibre, fruit, vegetables, energy-rich drinks and meal patterns were conducted. Forty-seven articles met the inclusion criteria. The direction of associations between SEP and energy intakes were inconsistent. Approximately half the associations examined between SEP and fat intakes showed higher total fat intakes among socioeconomically disadvantaged groups. There was some evidence that these groups consume a diet lower in fibre. The most consistent evidence of dietary inequalities was for fruit and vegetable consumption; lower socioeconomic groups were less likely to consume fruit and vegetables. Differences in energy, fat and fibre intakes (when found) were small-to-moderate in magnitude; however, differences were moderate-to-large for fruit and vegetable intakes. Socioeconomic inequalities in the consumption of energy-rich drinks and meal patterns were relatively under-studied compared with other dietary factors. There were no regional or gender differences in the direction and magnitude of the inequalities in the dietary factors examined. The findings suggest that dietary behaviours may contribute to socioeconomic inequalities in overweight/obesity in Europe. However, there is only consistent evidence that fruit and vegetables may make an important contribution to inequalities in weight status across European regions.

Fast rates for estimation error and oracle inequalities for model section

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many cases, however, where complexity penalties like this give loose upper bounds on the estimation error. In particular, if we choose a function from a suitably simple convex function class with a strictly convex loss function, then the estimation error (the difference between the risk of the empirical risk minimizer and the minimal risk in the class) approaches zero at a faster rate than the maximal deviation between empirical and true risks. In this paper, we address the question of whether it is possible to design a complexity penalized model selection method for these situations. We show that, provided the sequence of models is ordered by inclusion, in these cases we can use tight upper bounds on estimation error as a complexity penalty. Surprisingly, this is the case even in situations when the difference between the empirical risk and true risk (and indeed the error of any estimate of the approximation error) decreases much more slowly than the complexity penalty. We give an oracle inequality showing that the resulting model selection method chooses a function with risk no more than the approximation error plus a constant times the complexity penalty.