The canonical extension of a lattice is in an essential way a two-sided completion. Domain theory, on the contrary, is primarily concerned with one-sided completeness. In this paper, we show two things. Firstly, that the canonical extension of a lattice can be given an asymmetric description in two stages: a free co-directed meet completion, followed by a completion by selected directed joins. ...

Kraft's inequality [9] is essential for the classical theory of noiseless coding [1, 8]. In algorithmic information theory [5, 7, 2] one needs an extension of Kraft's condition from nite sets to (in nite) recursively enumerable sets. This extension, known as Kraft-Chaitin Theorem, was obtained by Chaitin in his seminal paper [4] (see also, [3, 2]). The aim of this note is to o er a simpler proo...

Weight constraints represent an extension of logic programs under the answer set semantics that is essential for many applications to knowledge representation. The relation of this extension to the original semantics is an important topic. It has been proved that there exists a modular algorithm for eliminating weight constraints that is guaranteed to terminate in polynomial time under the assu...

We report 4 cases of olfactory neuroblastoma with anterior cranial fossa extension treated by craniofacial surgery. Three patients have been alive and well for 4 years, 1 year and 11 months after the initial treatment without major surgical complications but one patient died of local recurrence 11 months after treatment. Multidisciplinary surgery for olfactory neuroblastoma with intracranial ex...

The canonical extension of a lattice is in an essential way a two-sided completion. Domain theory, on the contrary, is primarily concerned with one-sided completeness. In this paper, we show two things. Firstly, that the canonical extension of a lattice can be given an asymmetric description in two stages: a free co-directed meet completion, followed by a completion by selected directed joins. ...

Recent developments in subjectivity, composition technology and novel prototype-based languages demonstrate that dynamic object extension is an essential feature in modern object-orientation. The total absence of static type systems for dynamic object extension is a major obstacle for its adoption. We describe a static type system using specialisation interfaces with a trade-off between possibl...

We show that a bounded domain in Euclidean space is W1,1-extension if and only it strong BV-extension domain. In the planar case, domains are shown to be exactly those for which set ∂Ω∖⋃iΩ‾i purely 1-unrectifiable, where Ωi open connected components of R2∖Ω‾.

Learning abstract relationships is an essential capability in human intelligence. Christie & Gentner (2010) argued that comparison plays a crucial role in such learning. Structural alignment highlights the shared relational structure between compared examples, thereby making it more salient and accessible for subsequent use. They showed that 3-4 year old children who compared examples in a word...

Deep brain stimulation (DBS) is a common surgical procedure used for the treatment of Parkinson's disease (PD) and essential tremor. A potential complication of this procedure is hardware failure. The authors report a case of DBS hardware failure in which repeated fractures of the extension wire were caused by abnormal rotational movements of the IPG placed in the loose subclavicular tissue of ...

In Boolean logic, a Karnaugh map may be regarded either as a pictorial form of a trugh table, or as an extension of the Venn diagram. However, when fuzzy logic is concerned another minimization method is required, and therefore an extension of a Karnaugh map is investigated. In this paper a new minimization algorithm is developed in order to remove the existing disadvantage of simplifying fuzzy...