Gauge Poisson representations for birth/death master equations

Poisson representation techniques provide a powerful method for mapping master equations for birth/death processes -- found in many fields of physics, chemistry and biology -- into more tractable stochastic differential equations. However, the usual expansion is not exact in the presence of boundary terms, which commonly occur when the differential equations are nonlinear. In this paper, a gauge Poisson technique is introduced that eliminates boundary terms, to give an exact representation as a weighted rate equation with stochastic terms. These methods provide novel techniques for calculating and understanding the effects of number correlations in systems that have a master equation description. As examples, correlations induced by strong mutations in genetics, and the astrophysical problem of molecule formation on microscopic grain surfaces are analyzed. Exact analytic results are obtained that can be compared with numerical simulations, demonstrating that stochastic gauge techniques can give exact results where standard Poisson expansions are not able to.

Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros

Count data with excess zeros relative to a Poisson distribution are common in many biomedical applications. A popular approach to the analysis of such data is to use a zero-inflated Poisson (ZIP) regression model. Often, because of the hierarchical Study design or the data collection procedure, zero-inflation and lack of independence may occur simultaneously, which tender the standard ZIP model inadequate. To account for the preponderance of zero counts and the inherent correlation of observations, a class of multi-level ZIP regression model with random effects is presented. Model fitting is facilitated using an expectation-maximization algorithm, whereas variance components are estimated via residual maximum likelihood estimating equations. A score test for zero-inflation is also presented. The multi-level ZIP model is then generalized to cope with a more complex correlation structure. Application to the analysis of correlated count data from a longitudinal infant feeding study illustrates the usefulness of the approach.

Dimensionless spray flux in wet granulation: Monte-Carlo simulations and experimental validation

Dimensionless spray flux Ψa is a dimensionless group that characterises the three most important variables in liquid dispersion: flowrate, drop size and powder flux through the spray zone. In this paper, the Poisson distribution was used to generate analytical solutions for the proportion of nuclei formed from single drops (fsingle) and the fraction of the powder surface covered by drops (fcovered) as a function of Ψa. Monte-Carlo simulations were performed to simulate the spray zone and investigate how Ψa, fsingle and fcovered are related. The Monte-Carlo data was an excellent match with analytical solutions of fcovered and fsingle as a function of Ψa. At low Ψa, the proportion of the surface covered by drops (fcovered) was equal to Ψa. As Ψa increases, drop overlap becomes more dominant and the powder surface coverage levels off. The proportion of nuclei formed from single drops (fsingle) falls exponentially with increasing Ψa. In the ranges covered, these results were independent of drop size, number of drops, drop size distribution (mono-sized, bimodal and trimodal distributions), and the uniformity of the spray. Experimental data of nuclei size distributions as a function of spray flux were fitted to the analytical solution for fsingle by defining a cutsize for single drop nuclei. The fitted cutsizes followed the spray drop sizes suggesting that the method is robust and that the cutsize does indicate the transition size between single drop and agglomerate nuclei. This demonstrates that the nuclei distribution is determined by the dimensionless spray flux and the fraction of drop controlled nuclei can be calculated analytically in advance.

Tourism as a contributor to development in Sri Lanka: An overview and a case study

General background is provided on the potential of tourism growth to contribute to economic development, paying particular attention to the experience of Sri Lanka. An overview of trends in inbound tourism to Sri Lanka is presented with particular consideration being given to its number of inbound tourist arrivals. Sri Lanka’s comparative position in international tourism markets, the composition of its tourist arrivals by area of origin, the extent of foreign earnings by the Sri Lankan tourism industry and variations in the amount of these earnings, and the extent of employment generation by this industry are examined. Regional aspects of the tourism industry in Sri Lanka are given special consideration, and this is followed by a report on the regional economic impact of tourism of Pinnawala Elephant Orphanage. This major tourist attraction near the edge of the Western Highlands of Sri Lanka is shown to make a significant contribution to economic decentralisation. A general discussion follows of tourism development in the Sri Lankan context. The main factors that have hindered tourism growth in Sri Lanka and its decentralisation are considered. Indications are that major impediment posed by civil disturbance and terrorism is at an end in Sri Lanka.

Classical and quantum noise in electronic systems

We review the description of noise in electronic circuits in terms of electron transport. The Poisson process is used as a unifying principle. In recent years, much attention has been given to current noise in light-emitting diodes and laser diodes. In these devices, random events associated with electron transport are correlated with photon emission times, thus modifying both the current statistics and the statistics of the emitted light. We give a review of experiments in this area with special emphasis on the ability of such devices to produce subshot-noise currents and light beams. Finally we consider the noise properties of a class of mesoscopic devices based on the quantum tunnelling of an electron into and out of a bound state. We present a simple quantum model of this process which confirms that the current noise in such a device should be subshot-noise.

Suicide in urban New South Wales, Australia 1985-1994: Socio-economic and migrant interactions

Variation of suicide with socio-economic status (SES) in urban NSW (Australia) during 1985-1994, by sex and country or region of birth, was examined using Poisson regression analysis of vital statistics and population data (age greater than or similar to 15 yr). Quintiles of SES were defined by municipality of residence and comparisons of suicide by SES were adjusted for age and country (or region) of birth (COB), and examined by COB. Risk of suicide in females was 28% that of males for all adults and 21% for youth (age 15-24 yr). Suicide risk was lower in males from southern Europe, Middle East and Asia, and higher in northern and eastern European males, compared to the Australian-born. Risks for suicide increased significantly with decreasing SES in males, but not in females. The relationship of male suicide and SES was stronger when controlled for COB. For males, the relative risk of suicide, adjusted for age and COB, was 66% higher in the lowest SES quintile compared to the highest quintile, and 39% higher for youth (age 15-24 yr). For male suicide, the population attributable fraction for SES (less than the highest quintile) was 27%. Analysis of SES differentials in male suicide according to COB indicated a significant inverse suicide gradient in relation to SES for the Australian-born and those burn in New Zealand and the United Kingdom or fire. but not in non-English speaking COB groups, except for Asia. For Australian-born males, suicide risk was 71% higher in the lowest SES group (compared to the highest), adjusted for age. These findings indicate that SES plays an important role in male suicide rates among the Australian-born and migrants from English-speaking countries and Asia, and among youth; but not in female suicide, nor suicide in most non-English speaking migrant groups. Reduction in SES differentials through economic and social policies may reduce male suicide in lower SES groups and should be seen to be at least as important as individual level interventions. (C) 1998 Elsevier Science Ltd. All rights reserved.

Hysterectomy fractions in New South Wales, 1971-2006

Hysterectomy fractions by age group for particular periods are of interest for: estimating proper population denominators for calculation of disease and procedure rates affecting the cervix and uterus; estimating the target population for Pap test programs, and response rates; and as a way of displaying the cumulative consequences of hysterectomies in a population. Hysterectomy fractions for populations can be determined by direct inquiry via a representative sample survey, or, as in this study, from prior hysterectomy rates of the cohorts of women which compose each age bracket. Hysterectomy data 1979-93 were obtained from the hospital In-patients Statistics Collection (ISC) which covers both public and private hospitals in NSW. Annual population denominators of women were obtained from Census data. Data were modelled by Poisson regression, using five.-year age group (15-greater than or equal to 85 years), annual period, and five-year birth cohort (APC model). Forward- and back-projection of the period effects were undertaken. The resultant NSW hysterectomy fractions by age and period are consistent with fractions obtained from modelled hysterectomy rates for Western Australia (1980-84), and fractions from national representative sample surveys (1989/90 and 1995) for younger women, but not for women aged greater than or equal to 70 years in 1995, which revealed higher hysterectomy fractions than modelled hysterectomy data would suggest. Hysterectomy fractions for NSW women by five-year age group for quinquennia centred on 1971 to 2006 are provided.

Socio-economic, migrant and geographic differentials in coronary heart disease occurrence in New South Wales

Objective: This study examines the variation in coronary heart disease (CHD) mortality and acute myocardial infarction (AMI) by socio-economic status (SES), country of birth (COB) and geography (urban/rural) in the total population of New South Wales (Australia) in 1991-95. Method: CHD deaths and AMI are from complete enumerations of deaths and hospital admissions, respectively; and population denominators are from census information. Data are examined separately by sex, and comparisons of SES groups (based on municipalities), COB and region are analysed using Poisson regression, after adjustment for age. Results: The study identified higher risk for AMI admissions and CHD mortality in lower SES populations with significant linear trends, for both sexes, adjusted for age, region and COB. According to the population attributable fractions (PAF), 23-41% of the risk of CHD occurrence is due to SES lower than the highest quartile. The higher age-adjusted risk for CHD occurrence in rural and remote populations for both sexes, compared with urban communities, was lessened by adjustment for COB, and all but abolished when also adjusted for SES. COB analysis indicated significantly lower age-adjusted AMI admissions and CHD mortality compared with the Australian-born, Conclusions: Higher risks for CHD in rural populations compared with the capital city (Sydney) are due, in part, to lower SES, lesser migrant composition. Implications: Strategies for reducing CHD differentials should consider demographic factors and the fundamental need to reduce socio-economic inequalities, as well as targeting appropriate prevention measures.

Urban and rural suicide differentials in migrants and the Australian-born, New South Wales, Australia 1985-1994

We estimated risk of suicide in adults in New South Wales (NSW) by sex, country of birth and rural/urban residence, after adjusting for age; we also examined youth suicide (age 15-24 years). The study population was the entire population of NSW, Australia, aged greater than or equal to 15 years during the period 1985-1994. Poisson regression was used to examine the relationship between predictor variables and the risk of suicide, with the focus on migrant status and area of residence. A significantly higher risk of suicide was found in male migrants from Northern Europe and Eastern Europe/former USSR, compared to Australian-born males; a significantly lower suicide risk occurred in males from Southern Europe, the Middle East and Asia. In female migrants, those from UK/Eire, Northern Europe, Eastern Europe/former USSR and New Zealand exhibited a significantly higher risk of suicide compared to Australian-born females. A significantly lower risk of suicide occurred in females from the Middle East. Male migrants overall were at significantly lower risk of suicide than the Australian-born, while female migrants overall had a significantly higher risk of suicide than Australian-born females. Among migrant males overall, the rural-urban suicide risk differential was significantly higher for those living in non-metropolitan areas (RR = 1.9; 95% CI: 1.7-2.1). Suicide risk was significantly higher in non-metropolitan male immigrants from the UK/Eire (RR = 1.4; 95% CI: 1.1-1.7), Southern Europe (RR = 1.7; 95% CI: 1.2-2.4), Northern/Western Europe (1.5; 95% CI: 1.2-1.9), the Middle East (RR = 3.8; 95% CI: 1.9-7.8), New :Zealand (RR = 1.4; 95% CI: 1.0-1.8) and 'other' (RR = 2.6; 95% CI: 1.9-3.5), when compared to their urban counterparts. There was no statistically significant difference in suicide risk between rural and urban Australian-born males. For female suicide, significantly lower risk was found in female immigrants living in non-metropolitan areas who were from Northern/Western Europe (RR = 0.7; 95% CI: 0.4-0.96), as well as the Australian-born (RR = 0.7; 95% CI: 0.6-0.8), when compared to their urban counterparts. The non-metropolitan/metropolitan relative risk for suicide in female migrants overall was not significantly different from one. Among male youth there was a significantly higher suicide risk in non-metropolitan areas, with a relative risk estimate of 1.4 for Australian-born youth (95% CI: 1.2-1.5) and 1.7 for migrant youth (95% CI: 1.2-2.4), when compared with metropolitan counterparts. We conclude that suicide among migrant males living in non-metropolitan areas accounts for most of the excess of male suicide in rural NSW, and the significantly lower risk of suicide for non-metropolitan Australian-born women does not apply to migrant women. (C) 1999 Published by Elsevier Science Ltd. All rights reserved.

Trends in the incidence, severity, and short-term outcome of stroke in Perth, Western Australia

Background and Purpose-This report describes trends in the key indices of cerebrovascular disease over 6 years from the end of the 1980s in a geographically defined segment of the city of Perth, Western Australia. Methods-Identical methods were used to find and assess all cases of suspected stroke in a population of approximately 134 000 residents in a triangular area of the northern suburbs of Perth. Case fatality was measured as vital status at 28 days after the onset of symptoms. Data for first-ever strokes and for all strokes for equivalent periods of 12 months in 1989-1990 and 1995-1996 were compared by age-standardized rates and proportions and Poisson regression. Results-There were 355 strokes in 328 patients and 251 first-ever strokes (71%) for 1989-1990 and 290 events in 281 patients and 213 first-ever strokes (73%) for 1995-1996. In Poisson models including age and period, overall trends in the incidence of both first-ever strokes (rate ratio = 0.75; 95% confidence limits, 0.63, 0.90) and all strokes (rate ratio = 0.73; 95% confidence limits, 0.62, 0.85) were obviously significant, but only the changes in men were independently significant. Case fatality did not change, and the balance between hemorrhagic and occlusive strokes in 1995-1996 was almost indistinguishable from that observed in 1989-1990. Conclusions-Our results, which are the only longitudinal population-based data available for Australia for key indices of stroke, suggest that it is a change in the frequency of stroke, rather than its outcome, that is chiefly responsible nationally for the fall in mortality from cerebrovascular disease.