Error bounds on complex floating-point multiplication

Given floating-point arithmetic with t-digit base-β significands in which all arithmetic operations are performed as if calculated to infinite precision and rounded to a nearest representable value, we prove that the product of complex values z0 and z1 can be computed with maximum absolute error |z0||z1|1/2β 1-t√5. In particular, this provides relative error bounds of 2-24√5 and 2-53√5. for IEEE 754 single and double precision arithmetic respectively, provided that overflow, underflow, and denormals do not occur. We also provide the numerical worst cases for IEEE 754 single and double precision arithmetic

Image transfer protocol in progressively increasing resolution

A method of transferring digital image data over a communication link transforms and orders the data so that, as data is received by a receiving station, a low detail version of the image is immediately generated with later transmissions of data providing progressively greater detail in this image. User instructions are accepted, limiting the ultimate resolution of the image or suspending enhancement of the image except in certain user defined regions. When a low detail image is requested followed by a request for a high detailed version of the same image, the originally transmitted data of the low resolution image is not discarded or retransmitted but used with later data to improve the originally transmitted image. Only a single copy of the transformed image need be retained by the transmitting device in order to satisfy requests for different amounts of image detail

Projecting the impacts of illness on labour force participation: An application of Health&WealthMOD

Health&WealthMOD is the first Australian microsimulation model designed to determine the economic impacts of disease on older workers, aged 45 to 65 years. Chronic health conditions are known to be associated with early retirement. This paper describes an application of Health&WealthMOD to estimate the impact of this association on projected labour force participation to 2020 given the ageing population and long-term trend in chronic conditions. Due to ageing and disease trends, the number of people with chronic conditions in the 45-64 years age group was expected to rise to about 4.8 million by 2020, an increase of 82% from the 2003 population of the same age group. About 904,000 persons in the 45-64 age group were projected to be out of the labour force due to ill health in 2020, when only the ageing and population growth were considered. When trends in illness were captured, the figure was increased to about 1.2 million persons. This demonstrates that health is a major driver of labour force participation and retirement and that economic policies alone, with no consideration of health interventions to treat or prevent chronic illness, will only have a limited impact on labour force participation. Thus, it is important that the government focuses on both health policies and economic policies in order to make sure that there will be an adequate supply of labour force in future.impacts of illness, labour force, participation, Health&WealthMOD

Case Studies - Health&WealthMOD: a microsimulation model of the economic impacts of diseases on older workers

The Australian Government is seeking to encourage older workers to remain in the labour force longer to overcome future labour shortages and ensure adequate taxation revenue to fund the needs of an ageing population. Longer labour force participation also has benefits to individuals in terms of available income and capacity to save for a better standard of living in retirement. While the Government recognises that not all older workers are able to participate in the labour force, there is little information on what health conditions keep people from working, or what the costs are to the government or the individual. This case study outlines how a new micro simulation model, Health&WealthMOD, is being designed to fill this information gap by estimating the economic impacts of illness. The general approach adopted is outlined, following which two early applications of the model are presented. The model is used to explore the determinants of the duration spent in retirement and to generate projections of retirement due to illness to 2020.health; disability; wealth; retirement period

The Economic Impacts of Illness in Older Workers: Quantifying the impact of illness on income, tax revenue and government spending

Background: Long term illness has far reaching impacts on individuals, and also places a large burden upon government. This paper quantifies the indirect economic impacts of illness related early retirement on individuals and government in Australia in 2009.\ud \ud Methods: The output data from a microsimulation model, Health&WealthMOD, was analysed. Health&WealthMOD is representative of the 45 to 64 year old Australian population in 2009. The average weekly total income, total government support payments, and total taxation revenue paid, for individuals who are employment full-time, employed part-time and not in the labour force due to ill health was quantified.\ud \ud Results: It was found that persons out of the labour force due to illness had significantly lower incomes ($218 per week as opposed to$1167 per week for those employed full-time), received significantly higher transfer payments, and paid significantly less tax than those employed full-time or part-time. This results in an annual national loss of income of over $17 billion, an annual national increase of$1.5 billion in spending on government support payments, and an annual loss of $2.1 billion in taxation revenue.\ud \ud Conclusions: Illness related early retirement has significant economic impacts on both the individual and on governments as a result of lost income, lost taxation revenue and increased government support payments. This paper has quantified the extent of these impacts for Australia

The Personal and National Costs of Lost Labour Force Participation Due to Arthritis: An Economic Study

Background: The costs of arthritis to the individuals and the state are considerable.\ud \ud Methods: Cross-sectional analysis of the base population of Health&WealthMOD, a microsimulation model of 45 to 64 year old Australians built on data from the Australian Bureau of Statistics' Survey of Disability, Ageing and Carers and STINMOD, an income and savings microsimulation model.\ud \ud Results: Individuals aged 45 to 64 years who had retired early due to arthritis had a median value of AU$260 in total weekly income whereas those who were employed full time were likely to average more than five times this. The large national aggregate impact of early retirement due to arthritis includes AU$9.4 billion in lost GDP, attributable to arthritis through its impact on labour force participation.\ud \ud When looking at the ongoing impact of being out of the labour force those who retired from the labour force early due to arthritis were estimated to have a median value of total savings by the time they are 65 of as little as $300 (for males aged 45–54). This is far lower than the median value of savings for those males aged 45–54 who remained in the labour force full time, who would have an estimated$339 100 of savings at age 65.\ud \ud Conclusions: The costs of arthritis to the individuals and the state are considerable. The impacts on the state include loss of productivity from reduced workforce participation, lost income taxation revenue, and increased government support payments – in addition to direct health care costs. Individuals bear the economic costs of lost income and the reduction of their savings over the long term

Error Bounds on Complex Floating-Point Multiplication

International audienceGiven floating-point arithmetic with $t$-digit base-$\beta$ significands in which all arithmetic operations are performed as if calculated to infinite precision and rounded to a nearest representable value, we prove that the product of complex values $z_0$ and $z_1$ can be computed with maximum absolute error \abs{z_0} \abs{z_1} \frac{1}{2} \beta^{1 - t} \sqrt{5}. In particular, this provides relative error bounds of $2^{-24} \sqrt{5}$ and $2^{-53} \sqrt{5}$ for {IEEE 754} single and double precision arithmetic respectively, provided that overflow, underflow, and denormals do not occur. We also provide the numerical worst cases for {IEEE 754} single and double precision arithmetic