Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

New methods for determining quasi-stationary distributions for Markov chains

We shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a mu-invariant measure m for Q to be mu-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.

Impact of increasing the re-supply interval on the seasonality of subsidised prescription use in Australia

Objective: To evaluate the impact of increasing the minimum resupply period for prescriptions on the Pharmaceutical Benefits Scheme (PBS) in November 1994. The intervention was designed to reduce the stockpiling of medicines used for chronic medical conditions under the PBS safety net. Methods: Interrupted times series regression analyses were performed on 114 months of PBS drug utilisation data from January 1991 to June 2000. These analyses assessed whether there had been a significant interaction between the onset of the intervention in November 1994 and the extreme levels of drug utilisation in the months of December (peak utilisation) and January (lowest utilisation) respectively. Both serial and 12-month lag autocorrelations were controlled for. Results: The onset of the intervention was associated with a significant reduction in the December peak in drug utilisation; after the introduction of the policy there were 1,150,196 fewer proscriptions on average or that month (95% Cl 708,333-1,592,059). There was, however, no significant change in the low level of utilisation in January. The effect of the policy appears to be decreasing across successive postintervention years. though the odds of a prescription being dispensed in December remained significantly lower in 1999 compared to each of the pre-intervention years (11% vs. 14%) Conclusion: Analysis of the impact of increasing the re-supply period for PBS prescriptions showed that the magnitude of peak utilisation in December had been markedly reduced by the policy, though this effect appears to be decreasing over time. Continued monitoring and policy review is warranted in order to ensure that the initial effect of the intervention be maintained.

Jordan-Wigner fermionization of the one-dimensional Bariev model of three coupled XY chains

The Jordan-Wigner fermionization for the one-dimensional Bariev model of three coupled XY chains is formulated. The L-matrix in terms of fermion operators and the R-matrix are presented explicitly. Furthermore, the graded reflection equations and their solutions are discussed.

Identification of river sections for domestic water supply along the Yangtze River in Jiangsu Province, China

This paper presents major findings from a recent study aiming to systematically determine suitable river sections for local domestic water supply along the Yangtze River in Jiangsu Province, China. On the basis of analysis on the current riverbank utilization and bank stability, accessible and stable river sections in the region were selected. The water quality in these river sections was then studied using a two-dimensional unsteady flow and pollutant transport/transformation model, RBFVM-2D. The model was calibrated and verified against the hydrodynamic data, water quality data and remote sensing data collected from the river. The investigation on the pollution sources along the river identified 56 main pollution point sources. The pollution zones downstream of these point sources are the main threat for the water quality in the river. The model was used to compute the pollution zones. In particular, simulations were conducted to establish the relationship between the extent of the pollution zone and the wastewater discharge rate of the associated point source. These water quality simulation results were combined with the riverbank stability analysis to determine suitable river sections for local domestic water supply.

Dietary trends: Estimates from food supply and survey data

Objective: To illustrate methodological issues involved in estimating dietary trends in populations using data obtained from various sources in Australia in the 1980s and 1990s. Methods: Estimates of absolute and relative change in consumption of selected food items were calculated using national data published annually on the national food supply for 1982-83 to 1992-93 and responses to food frequency questions in two population based risk factor surveys in 1983 and 1994 in the Hunter Region of New South Wales, Australia. The validity of estimated food quantities obtained from these inexpensive sources at the beginning of the period was assessed by comparison with data from a national dietary survey conducted in 1983 using 24 h recall. Results: Trend estimates from the food supply data and risk factor survey data were in good agreement for increases in consumption of fresh fruit, vegetables and breakfast food and decreases in butter, margarine, sugar and alcohol. Estimates for trends in milk, eggs and bread consumption, however, were inconsistent. Conclusions: Both data sources can be used for monitoring progress towards national nutrition goals based on selected food items provided that some limitations are recognized. While data collection methods should be consistent over time they also need to allow for changes in the food supply (for example the introduction of new varieties such as low-fat dairy products). From time to time the trends derived from these inexpensive data sources should be compared with data derived from more detailed and quantitative estimates of dietary intake.

On the construction of integrable closed chains with quantum supersymmetry

We present a general prescription for the construction of integrable one-dimensional systems with closed boundary conditions and quantum supersymmetry.