The Forcing Weak Edge Detour Number of a Graph

The forcing weak edge detour numbers of certain classes of graphs are determined

Biodeterioration of wooden boats: a major problem facing marine fisheries

In India, the fishing industry alone incurs an annual loss of over 120 million rupees on account of biodeterioration of wooden fishing craft. None of the timber species, currently in demand for boat-building, possesses an natural bioresistance and will be completely destroyed within 6 to 12 months. Preventive measures against biodeterioration range from application of several indigenous formulations to metallic sheathings and pressure impregnation of wood with preservative chemicals. These methods do not provide lasting protection, as each has its own short-comings and inadequacies. The need for long-term research in the field of marine biodeterioration for improving the efficiency of currently known control measures, with emphasis on application of non-polluting biological methods, is stressed

UNIQUE ECCENTRIC CLIQUE GRAPHS

Let $G$ be a connected graph and $\zeta$ the set of all cliques in $G$. In this paper we introduce the concepts of unique $(\zeta, \zeta)$-eccentric clique graphs and self $(\zeta, \zeta)$-centered graphs. Certain standard classes of graphs are shown to be self $(\zeta, \zeta)$-centered, and we characterize unique $(\zeta, \zeta)$-eccentric clique graphs which are self $(\zeta, \zeta)$-centered

Monophonic Distance in Graphs

For any two vertices u and v in a connected graph G, a u − v path is a monophonic path if it contains no chords, and the monophonic distance dm(u, v) is the length of a longest u − v monophonic path in G. For any vertex v in G, the monophonic eccentricity of v is em(v) = max {dm(u, v) : u ∈ V}. The subgraph induced by the vertices of G having minimum monophonic eccentricity is the monophonic center of G, and it is proved that every graph is the monophonic center of some graph. Also it is proved that the monophonic center of every connected graph G lies in some block of G. With regard to convexity, this monophonic distance is the basis of some detour monophonic parameters such as detour monophonic number, upper detour monophonic number, forcing detour monophonic number, etc. The concept of detour monophonic sets and detour monophonic numbers by fixing a vertex of a graph would be introduced and discussed. Various interesting results based on these parameters are also discussed in this chapter

Statistical implications of centralised care for estimating neonatal unit mortality rates

Monitoring clinical outcomes across healthcare providers is increasingly important in the UK National Health Service. Neonatal care is no exception, but care is centralised, so is delivered via co-ordinated networks of neonatal units (NNUs), with sicker infants treated in larger centres. This results in frequent transfers, but it is unclear how to attribute outcomes of transferred infants. Hierarchical regression is recommended for assessing performance of healthcare providers, but existing studies have either excluded transferred patients or assigned them to a single provider. In this thesis, hierarchical Bayesian multiple membership (MM) models are used to evaluate NNU mortality of very preterm infants, attributing outcomes to all NNUs providing care. Data for all singleton infants born 2011-2013 below 32 weeks gestation and admitted to neonatal care in England are obtained from the National Neonatal Research Database. Using established methods, a series of Bayesian hierarchical models with two (infants within NNUs) and three levels (infants within NNUs within networks) are developed for non-transferred infants. This approach is extended to include transferred infants using MM models. A variety of weightings, some specified using Beta distributions, are used to allocate outcomes of transferred infants. In contrast to other applications of MM models, results differ across weightings due to transfer patterns. The recommendation is that transferred patients are allocated equally to all providers, regardless of duration or intensity of care, accompanied by sensitivity analyses using alternative weights. Methodologically, this thesis demonstrates a statistically principled way of accounting for transfers when evaluating provider-specific outcomes, and presents a new application of MM models with novel weightings. Clinically, the variation attributable to providers is low, and for each NNU an estimate of risk-adjusted mortality compared with similar NNUs is obtained. Practical implications extend beyond neonatal medicine as centralisation and electronic patient data become integral to improving healthcare.Open Acces

A stochastic model for sero conversion times of HIV transmission

This paper focuses on the study of a Stochastic Model for predicting the seroconversion time of HIV transmission. As the immune capacities of an individual vary and also have its own resistance, the antigenic diversity threshold is different for different person. We propose a stochastic model to study the damage process acting on the immune system that is non- linear. The mean of seroconversion time of HIV and its variance are derived. A numerical example is given to illustrate the seroconversion times of HIV transmission