Lenses, fibrations and universal translations† MICHAEL JOHNSON‡, ROBERT ROSEBRUGH§ and R. J. WOOD¶ ‡School of Mathematics and Computing, Macquarie University, Sydney, New South Wales, Australia Email: [email protected] §Department of Mathematics and Computer Science, Mount Allison University, Sackville, New Brunswick, Canada Email: [email protected] ¶Department of Mathematics and Statis...

| ij ∩ i′j′ | =   1 if i = i′; 0 if i= i′, j = j′; n if i= i′, j= j′. Thus the lines are partitioned into k parallel classes { ij : 1≤ j≤n}, 1≤ i≤ k, and each line has n points. Note that an (n+1)-net is the same thing as an affine plane of order n. For any k-net N and any k′-subset of the parallel classes of N , we obtain a k′-subnet N ′ ⊆ N of order n, also with point set P. The descriptio...

The translation of information between heterogeneous representations is a long standing issue. With the large spreading of cooperative applications fostered by the advent of the Internet the problem has gained more and more attention but there are still few and partial solutions. In general, given an information source, different translations can be defined for the same target model. In this wo...

A translation lexicon is a mapping between two disjoint sets of symbols. Given some corpus sample over each set of symbols, one might induce the mapping by performing statistical analyses on the corpora to find correlations between the symbols (Hwa et al., 2006). The sets stand for the source and target languages, while the symbols most often refer to words. Simplistically, a translation lexico...