A {em Roman dominating function} on a graph $G$ is a function $f:V(G)rightarrow {0,1,2}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. A {em total Roman dominating function} is a Roman dominating function with the additional property that the subgraph of $G$ induced by the set of all vertices of positive weight has n...

We deene the notion of total algorithms for networks of processes. A total algorithm enforces that a \decision" is taken by a subset of the processes, and that participation of all processes is required to reach this decision. Total algorithms are an important building block in the design of distributed algorithms. For some important network control problems it can be shown that an algorithm so...

7,000 plant species for food but today around 20 species provide 90 per cent of the global human diet. Of the 7,100 varieties of apple recorded in America a century ago, 6,800 have now been lost. And there are worries, for example, that the maize staple in southern Africa may be under increasing challenge from climate change. Svalbard provides " the last line in the defence against the extincti...

In this paper, we analyse a concept of total knowledge based on the idea that an agent’s total knowledge is the strongest proposition the agent knows. We propose semantics for propositional and first-order languages with a modal operator TK representing total knowledge, and establish a result showing that total knowledge is ‘epistemically categorical’, in the sense that it determines the agent’...