Search results

Known as a branch of Discrete Mathematics (DM), Graph Theory (GT) describes and solves problems of discrete nature through nodes (i.e., vertices) and arcs (i.e., edges). In this regard, a prominent problem is to find the Eulerian circuits. This paper indicates that the problem can be analyzed through operations research methods. In more general terms, finding the Eulerian circuits could be considered a pathfinding problem. Hence, this paper proposes a pure binary mathematical model to describe the relationship between the variables employed to find the Eulerian circuits. All the analyses in this paper were performed in MATLAB. The proposed model can be solved by many optimization software applications. Finally, several numerical examples are presented and solved through the proposed method. All the analyses in this paper were performed in MATLAB. This paper indicated that the problem(Eulerian Circuits in Complete Graphs) could be studied and solved from the perspective of operations research.

Background: This study evaluates the dementia care system in a local area and aimed to include all specialised services designed to provide health and social services to people with dementia or age-related cognitive impairment, as well as general services with a high or very high proportion of clients with dementia. Methods: The study used an internationally standardised service classification instrument called Description and Evaluation of Services and DirectoriEs for Long Term Care (DESDE-LTC) to identify and describe all services providing care to people with dementia in the Australian Capital Territory (ACT). Results: A total of 47 service providers were eligible for inclusion. Basic information about the services was collected from their websites, and further information was obtained through interviews with the service providers. Of the 107 services offered by the 47 eligible providers, 27% (n = 29) were specialised services and 73% (n = 78) were general services. Most of the services were residential or outpatient, with a target population mostly of people aged 65 or older, and 50 years or older in the case of Aboriginal and Torres Strait Islander Australians. There were government supports available for most types of care through various programmes. Conclusions: Dementia care in the ACT relies heavily on general services. More widespread use of standardised methods of service classification in dementia will facilitate comparison with other local areas, allow for monitoring of changes over time, permit comparison with services provided for other health conditions and support evidence-informed local planning.