Reduction rules for reset/inhibitor nets

Reset/inhibitor nets are Petri nets extended with reset arcs and inhibitor arcs. These extensions can be used to model cancellation and blocking. A reset arc allows a transition to remove all tokens from a certain place when the transition fires. An inhibitor arc can stop a transition from being enabled if the place contains one or more tokens. While reset/inhibitor nets increase the expressive power of Petri nets, they also result in increased complexity of analysis techniques. One way of speeding up Petri net analysis is to apply reduction rules. Unfortunately, many of the rules defined for classical Petri nets do not hold in the presence of reset and/or inhibitor arcs. Moreover, new rules can be added. This is the first paper systematically presenting a comprehensive set of reduction rules for reset/inhibitor nets. These rules are liveness and boundedness preserving and are able to dramatically reduce models and their state spaces. It can be observed that most of the modeling languages used in practice have features related to cancellation and blocking. Therefore, this work is highly relevant for all kinds of application areas where analysis is currently intractable.

Access and Quality of Heart Failure Management Programs in Australia

Background/aim In response to the high burden of disease associated with chronic heart failure (CHF), in particular the high rates of hospital admissions, dedicated CHF management programs (CHF-MP) have been developed. Over the past five years there has been a rapid growth of CHF-MPs in Australia. Given the apparent mismatch between the demand for, and availability of CHF-MPs, this paper has been designed to discuss the accessibility to and quality of current CHF-MPs in Australia. Methods The data presented in this report has been combined from the research of the co-authors, in particular a review of the inequities in access to chronic heart failure which utilised geographical information systems (GIS) and the survey of heterogeneity in quality and service provision in Australian. Results Of the 62 CHF-MPs surveyed in this study 93% (58) centres had been located areas that are rated as Highly Accessible. This result indicated that most of the CHF-MPs have been located in capital cities or large regional cities. Six percent (4 CHF-MPs) had been located in Accessible areas which were country towns or cities. No CHF-MPs had been established outside of cities to service the estimated 72,000 individuals with CHF living in rural and remote areas. 16% of programs recruited NYHA Class I patients and of these 20% lacked confirmation (echocardiogram) of their diagnosis. Conclusion Overall, these data highlight the urgent need to provide equitable access to CHF-MP's. When establishing CHF-MPs consideration of current evidence based models to ensure quality in practice.

Getting to know a stranger-rural nurses' experiences of mentoring : a grounded theory

Background: Mentoring is often proposed as a solution to the problem of successfully recruiting and retaining nursing staff. The aim of this constructivist grounded theory study was to explore Australian rural nurses' experiences of mentoring. Design: The research design used was reflexive in nature resulting in a substantive, constructivist grounded theory study. Participants: A national advertising campaign and snowball sampling were used to recruit nine participants from across Australia. Participants were rural nurses who had experience in mentoring others. Methods: Standard grounded theory methods of theoretical sampling, concurrent data collection and analysis using open, axial and theoretical coding and a story line technique to develop the core category and category saturation were used. To cultivate the reflexivity required of a constructivist study, we also incorporated reflective memoing, situational analysis mapping techniques and frame analysis. Data was generated through eleven interviews, email dialogue and shared situational mapping. Results: Cultivating and growing new or novice rural nurses using supportive relationships such as mentoring was found to be an existing, integral part of experienced rural nurses' practice, motivated by living and working in the same communities. Getting to know a stranger is the first part of the process of cultivating and growing another. New or novice rural nurses gain the attention of experienced rural nurses through showing potential or experiencing a critical incidence. Conclusions: The problem of retaining nurses is a global issue. Experienced nurses engaged in clinical practice have the potential to cultivate and grow new or novice nurses-many already do so. Recognising this role and providing opportunities for development will help grow a positive, supportive work environment that nurtures the experienced nurses of tomorrow.

Business cycle dynamics with duration dependence and leading indicators

Durland and McCurdy [Durland, J.M., McCurdy, T.H., 1994. Duration-dependent transitions in a Markov model of US GNP growth. Journal of Business and Economic Statistics 12, 279–288] investigated the issue of duration dependence in US business cycle phases using a Markov regime-switching approach, introduced by Hamilton [Hamilton, J., 1989. A new approach to the analysis of time series and the business cycle. Econometrica 57, 357–384] and extended to the case of variable transition parameters by Filardo [Filardo, A.J., 1994. Business cycle phases and their transitional dynamics. Journal of Business and Economic Statistics 12, 299–308]. In Durland and McCurdy’s model duration alone was used as an explanatory variable of the transition probabilities. They found that recessions were duration dependent whilst expansions were not. In this paper, we explicitly incorporate the widely-accepted US business cycle phase change dates as determined by the NBER, and use a state-dependent multinomial Logit modelling framework. The model incorporates both duration and movements in two leading indexes – one designed to have a short lead (SLI) and the other designed to have a longer lead (LLI) – as potential explanatory variables. We find that doing so suggests that current duration is not only a significant determinant of transition out of recessions, but that there is some evidence that it is also weakly significant in the case of expansions. Furthermore, we find that SLI has more informational content for the termination of recessions whilst LLI does so for expansions.

Propagation of low power low divergence Gaussian fields in unbiased self-defocusing photorefractive media and their interactions

Many optical networks are limited in speed and processing capability due to the necessity for the optical signal to be converted to an electrical signal and back again. In addition, electronically manipulated interconnects in an otherwise optical network lead to overly complicated systems. Optical spatial solitons are optical beams that propagate without spatial divergence. They are capable of phase dependent interactions, and have therefore been extensively researched as suitable all optical interconnects for over 20 years. However, they require additional external components, initially high voltage power sources were required, several years later, high power background illumination had replaced the high voltage. However, these additional components have always remained as the greatest hurdle in realising the applications of the interactions of spatial optical solitons as all optical interconnects. Recently however, self-focusing was observed in an otherwise self-defocusing photorefractive crystal. This observation raises the possibility of the formation of soliton-like fields in unbiased self-defocusing media, without the need for an applied electrical field or background illumination. This thesis will present an examination of the possibility of the formation of soliton-like low divergence fields in unbiased self-defocusing photorefractive media. The optimal incident beam and photorefractive media parameters for the formation of these fields will be presented, together with an analytical and numerical study of the effect of these parameters. In addition, preliminary examination of the interactions of two of these fields will be presented. In order to complete an analytical examination of the field propagating through the photorefractive medium, the spatial profile of the beam after propagation through the medium was determined. For a low power solution, it was found that an incident Gaussian field maintains its Gaussian profile as it propagates. This allowed the beam at all times to be described by an individual complex beam parameter, while also allowing simple analytical solutions to the appropriate wave equation. An analytical model was developed to describe the effect of the photorefractive medium on the Gaussian beam. Using this model, expressions for the required intensity dependent change in both the real and imaginary components of the refractive index were found. Numerical investigation showed that under certain conditions, a low powered Gaussian field could propagate in self-defocusing photorefractive media with divergence of approximately 0.1 % per metre. An investigation into the parameters of a Ce:BaTiO3 crystal showed that the intensity dependent absorption is wavelength dependent, and can in fact transition to intensity dependent transparency. Thus, with careful wavelength selection, the required intensity dependent change in both the real and imaginary components of the refractive index for the formation of a low divergence Gaussian field are physically realisable. A theoretical model incorporating the dependence of the change in real and imaginary components of the refractive index on propagation distance was developed. Analytical and numerical results from this model are congruent with the results from the previous model, showing low divergence fields with divergence less than 0.003 % over the propagation length of the photorefractive medium. In addition, this approach also confirmed the previously mentioned self-focusing effect of the self-defocusing media, and provided an analogy to a negative index GRIN lens with an intensity dependent focal length. Experimental results supported the findings of the numerical analysis. Two low divergence fields were found to possess the ability to interact in a Ce:BaTiO3 crystal in a soliton-like fashion. The strength of these interactions was found to be dependent on the degree of divergence of the individual beams. This research found that low-divergence fields are possible in unbiased self-defocusing photorefractive media, and that soliton-like interactions between two of these fields are possible. However, in order for these types of fields to be used in future all optical interconnects, the manipulation of these interactions, together with the ability for these fields to guide a second beam at a different wavelength, must be investigated.