Basic topological constructions of manifold stratified spaces and stratified approximate fibrations are studied. These include products of manifold stratified spaces, products and compositions of stratified approximate fibrations and Euclidean stabilization of stratified approximate fibrations. The main result shows that the adjunction of two manifold stratified spaces via a manifold stratified...

A 2-stratified graph G is a graph whose vertex set has been partitioned into two subsets, called the strata or color classes of G. Two 2-stratified graphs G and H are isomorphic if there exists a color-preserving isomorphism φ from G to H. A 2-stratified graph G is said to be homogeneously embedded in a 2-stratified graph H if for every vertex x of G and every vertex y of H, where x and y are c...

Suppose that the conditional density of a response variable given a vector of explanatory variables is parametrically modelled, and that data are collected by a two-phase sampling design. First, a simple random sample is drawn from the population. The stratum membership in a finite number of strata of the response and explanatory variables is recorded for each unit. Second, a subsample is drawn...

We investigate the relationship between three-valued Kripke/Kleene semantics and stratified semantics for stratifiable logic programs. We first show these are compatible, in the sense that if the three-valued semantics assigns a classical truth value, the stratified approach will assign the same value. Next, the familiar fixed point semantics for pure Horn clause programs gives both smallest an...

Prentice & Pyke (1979) established that the maximum likelihood estimate of an odds ratio in a case-control study is the same as would be found by fitting a logistic regression; in other words, for this specific target the incorrect prospective model is inferentially equivalent to the correct retrospective model. Similar results have been obtained for other models, and conditions have also been ...

Surveys are frequently required to produce estimates for subpopulations, sometimes for a single subpopulation and sometimes for several subpopulations in addition to the total population. When membership of a rare subpopulation (or domain) can be determined from the sampling frame, selecting the required domain sample size is relatively straightforward. In this case the main issue is the extent...