Amalgamation and interpolation in ordered algebras

The first part of this paper provides a comprehensive and self-contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations. In particular, proofs are given of known equivalences between the amalgamation property and the Robinson property, the congruence extension property and the extension property, and the flat amalgamation property and the deductive interpolation property, as well as various dependencies between these properties. These relationships are then exploited in the second part of the paper in order to provide new proofs of amalgamation and deductive interpolation for the varieties of lattice-ordered abelian groups and MV-algebras, and to determine important subvarieties of residuated lattices where these properties hold or fail. In particular, a full description is given of all subvarieties of commutative GMV-algebras possessing the amalgamation property.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

Nitric oxide and metalloproteinases in canine articular ligaments: a comparison between the cranial cruciate, the medial genual collateral and the femoral head ligament

Osteoarthritis due to cranial cruciate ligament (CCL) rupture or hip dysplasia is one of the most important causes of chronic lameness in dogs. This study aimed at comparing nitric oxide (NO) production by the CCL with that of the femoral head ligament (FHL) and the medial collateral ligament (MCL), and investigating the pathway of NO production and the concomitant metalloproteinase (MMP) activity in the presence or absence of an inflammatory stimulus. Ligaments of normal dogs were subjected to different stimuli, and NO and MMP activity from explant culture supernatants were compared. The results showed that in explant cultures of the canine CCL more NO was produced than in those of the other two ligaments. A higher level of NO was produced when CCLs were exposed to the inducible nitric oxide synthase (iNOS)-inducing cocktail TNF/IL-1/LPS, and NO synthesis could be inhibited by both l-NMMA, a general nitric oxide synthase (NOS) inhibitor and l-NIL, a specific iNOS inhibitor. However, a correlation between NO synthesis and iNOS expression levels as determined by immunohistochemistry was not observed. In contrast to CCL, no evidence for iNOS-dependent NO synthesis was observed for MCL and FHL. The CCL produced less MMP than MCL and FHL, and no correlation between MMP and NO could be demonstrated. MMP activity in the CCL increased significantly after 48 h of incubation with the inflammatory stimulus. The results suggest that in canine osteoarthritis NO synthesized by canine CCL plays a more important role in the pathogenesis of osteoarthritis of the stifle than that synthesized by FHL and MCL.

Therapy of basilar artery occlusion: a systematic analysis comparing intra-arterial and intravenous thrombolysis

BACKGROUND AND PURPOSE: Basilar artery occlusion (BAO) is an infrequent form of acute stroke, which invariably leads to death or long-term disability if not recanalized. A traditional recanalization approach based on historical controls and pathophysiological consideration is local intra-arterial thrombolysis (IAT) in eligible patients. This necessitates diagnostic evaluation and treatment in stroke centers equipped with an interventional neuroradiological service on a 24-hour basis, but its superiority to the technically simple intravenous thrombolysis (IVT) remains unproven. METHODS: We analyzed systematically published case series of substantial size reporting the outcome of BAO after IAT or IVT. RESULTS: In 420 BAO patients treated with IVT (76) and IAT (344), death or dependency were equally common: 78% (59 of 76) and 76% (260 of 344), respectively (P=0.82). Recanalization was achieved more frequently with IAT (225 of 344; 65%) than with IVT (40 of 76; 53%; P=0.05), but survival rates after IVT (38 of 76; 50%) and IAT (154 of 344; 45%) were equal (P=0.48). A total of 24% of patients treated with IAT and 22% treated with IVT reached good outcomes (P=0.82). Without recanalization, the likelihood of good outcome was close to nil (2%). CONCLUSIONS: Recanalization occurs in more than half of BAO patients treated with IAT or IVT, and 45% to 55% of survivors regain functional independence. Although improved therapy forms for BAO are necessary, hospitals not equipped for IAT may set up IVT protocols. The effect of IVT is probably not much different from the effect of IAT. IVT represents probably the best treatment that can be offered to victims of acute BAO in such hospitals.