This paper explores open source as a metaphor for e-learning. It builds the case that e-learning and open source movement are rooted in the constructivist movement and the constructivist movement is itself rooted in the pragmatism and instrumentalism that pervades John Dewey’s theories of understanding as applied to learning. As a result, it is recommended that the use of open source as metapho...

An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. An asteroidal quadruple is a stable set of four vertices such that any three of them is an asteroidal triple. Two non adjacent vertices are linked by a special connection if either they have a common neighbor or they are the endpoints of two vertex-dis...

We present an approach for programming with graph transformation rules in which programs can be as efficient as programs in imperative languages. The basic idea is to equip rules and host graphs with distinguished nodes, so-called roots, and to match roots in rules with roots in host graphs. This enables graph transformation rules to be matched in constant time, provided that host graphs have a...

In this paper, we consider an arbitrary class H of rooted graphs such that each biconnected component is given by a representation with reflectional symmetry, which allows a rooted graph to have several different representations, called embeddings. We give a general framework to design algorithms for enumerating embeddings of all graphs in H without repetition. The framework yields an efficient...

A stationary random graph is a random rooted graph whose distribution is invariant under re-rooting along the simple random walk. We adapt the entropy technique developed for Cayley graphs and show in particular that stationary random graphs of subexponential growth are almost surely Liouville, that is, admit no non constant bounded harmonic functions. Applications include the uniform infinite ...

Objectives: To determine the prevalence of three-rooted mandibular molars in a Brazilian population using cone beam computed tomography (CBCT) and to analyze the anatomy of mandibular first molars with three roots through micro-CT. Material and Methods: CBCT images of 116 patients were reviewed to determine the prevalence of three-rooted first mandibular molars in a Brazilian subpopulation. F...

Intuitively, a tangle of large order in a graph is a highly-connected part of the graph, and it is known that if a graph has a tangle of large order then it has a large grid minor. Here we show that for any k, if G has a tangle of large order and Z is a set of vertices of cardinality k that cannot be separated from the tangle by any separation of order less than k, then G has a large grid minor...

This thesis investigates a pragmatic approach to typing, static analysis and static optimization of Web query languages, in special the Web query language Xcerpt[43]. The approach is pragmatic in the sense, that no restriction on the types are made for decidability or efficiency reasons, instead precision is given up if necessary. Pragmatics on the dynamic side means to use types not only to en...

We introduce “rooted valuation products” and use them to construct universal Abelian lattice-ordered groups (with prescribed set of components) [CHH] from the more classical theory of [Ha]. The Wreath product construction of [H] and [HMc] generalised the Abelian (lattice-ordered) group ideas to a permutation group setting to respectively give universals for transitive (`-) permutation groups wi...