MacNeille completion and profinite completion can coincide on finitely generated modal algebras

Following Bezhanishvili & Vosmaer, we confirm a conjecture of Yde Venema by piecing together results from various authors. Specifically, we show that if $\mathbb{A}$ is a residually finite, finitely generated modal algebra such that $\operatorname{HSP}(\mathbb{A})$ has equationally definable principal congruences, then the profinite completion of $\mathbb{A}$ is isomorphic to its MacNeille completion, and $\Diamond$ is smooth. Specific examples of such modal algebras are the free $\mathbf{K4}$-algebra and the free $\mathbf{PDL}$-algebra.Comment: 5 page

Canonical extension and canonicity via DCPO presentations

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 \emph{selected} directed joins. Secondly, we show that the general techniques for dcpo presentations of dcpo algebras used in the second stage of the construction immediately give us the well-known canonicity result for bounded lattices with operators.Comment: 17 pages. Definition 5 was revised slightly, without changing any of the result

Generalised powerlocales via relation lifting

This paper introduces an endofunctor VT on the category of frames that is parametrised by an endofunctor T on the category Set that satisfies certain constraints. This generalises Johnstone's construction of the Vietoris powerlocale in the sense that his construction is obtained by taking for T the finite covariant power set functor. Our construction of the T-powerlocale VT out of a frame is based on ideas from coalgebraic logic and makes explicit the connection between the Vietoris construction and Moss's coalgebraic cover modality.We show how to extend certain natural transformations between set functors to natural transformations between T-powerlocale functors. Finally, we prove that the operation VT preserves some properties of frames, such as regularity, zero-dimensionality and the combination of zero-dimensionality and compactness.</jats:p

Skeletal immaturity, rostral sparing, and disparate hip morphologies as biomechanical causes for Legg-Calvé-Perthes’ disease

Legg-Calvé-Perthes' (Perthes') disease is a developmental disease of the hip joint that may result in numerous short and long term problems. The etiology of the disease remains largely unknown, but the mechanism is believed to be vascular and/or biomechanical in nature. There are several anatomical characteristics that tend to be prevalent in children with Perthes' disease, namely: skeletal immaturity, reduced height, and rostral sparing. We present an overview of the literature, summarizing the current understanding of the pathogenesis, particularly related to how the formation of the vasculature to the femoral epiphysis places children aged 5–8 at a higher risk for Perthes' disease, how skeletal immaturity and rostral sparing could increase the probability of developing Perthes' disease, and how animal models have aided our understanding of the disease. In doing so, we also explore why Perthes' disease is correlated to latitude, with populations at higher latitudes having higher incidence rates than populations closer to the Equator. Finally, we present five hypotheses detailing how Perthes' disease could have a biomechanical cause. Clin. Anat. 29:759–772, 2016. © 2016 Wiley Periodicals, Inc

The History of Makassan Trepang Fishing and Trade

The Malayan term trepang describes a variety of edible holothurians commonly known as sea cucumbers. Although found in temperate and tropical marine waters all over the world, the centre of species diversity and abundance are the shallow coastal waters of Island Southeast Asia. For at least 300 years, trepang has been a highly priced commodity in the Chinese market. Originally, its fishing and trade was a specialized business, centred on the town of Makassar in South Sulawesi (Indonesia). The rise of trepang fishing in the 17th century added valuable export merchandize to the rich shallow seas surrounding the islands of Southeast Asia. This enabled local communities to become part of large trading networks and greatly supported their economic development. In this article, we follow Makassan trepang fishing and trading from its beginning until the industrialization of the fishery and worldwide depletion of sea cucumbers in the 20th century. Thereby, we identify a number of characteristics which trepang fishing shares with the exploitation of other marine resources, including (1) a strong influence of international markets, (2) the role of patron-client relationships which heavily influence the resource selection, and (3) the roving-bandit-syndrome, where fishermen exploit local stocks of valuable resources until they are depleted, and then move to another area. We suggest that understanding the similarities and differences between historical and recent exploitation of marine resources is an important step towards effective management solutions