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We review the step-by-step method of constructing finitely generated free modal algebras. First we discuss the global step-by-step method, which works well for rank one modal logics. Next we refine the global step-by-step method to obtain the local step-by-step method, which is applicable beyond rank one modal logics. In particular, we show that it works well for constructing the finitely generated free algebras for such well-known modal systems as T, K4 and S4. This yields the notions of one-step algebras and of one-step frames, as well as of universal one-step extensions of one-step algebras and of one-step frames. We show that finitely generated free algebras for T, K4 and S4 and their dual spaces can be obtained by iterating the universal one-step extensions of one-step algebras and of one-step frames. In the final part of the paper we compare our construction with recent literature, especially with [11] which has a very similar approach

Fixed-point elimination in the intuitionistic propositional calculus

It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras-that is, the algebraic models of the Intuitionistic Propositional Calculus-always exist, even when these algebras are not complete as lattices. The reason is that these extremal fixed-points are definable by formulas of the IPC. Consequently, the $\mu$-calculus based on intuitionistic logic is trivial, every $\mu$-formula being equivalent to a fixed-point free formula. We give in this paper an axiomatization of least and greatest fixed-points of formulas, and an algorithm to compute a fixed-point free formula equivalent to a given $\mu$-formula. The axiomatization of the greatest fixed-point is simple. The axiomatization of the least fixed-point is more complex, in particular every monotone formula converges to its least fixed-point by Kleene's iteration in a finite number of steps, but there is no uniform upper bound on the number of iterations. We extract, out of the algorithm, upper bounds for such n, depending on the size of the formula. For some formulas, we show that these upper bounds are polynomial and optimal

Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and thus the free algebras can be obtained by a direct limit process. Dually, the final coalgebras can be obtained by an inverse limit process. In order to explore the limits of this method we look at Heyting algebras which have mixed rank 0-1 axiomatizations. We will see that Heyting algebras are special in that they are almost rank 1 axiomatized and can be handled by a slight variant of the rank 1 coalgebraic methods

Admissible Bases Via Stable Canonical Rules

We establish the dichotomy property for stable canonical multi-conclusionrules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics

Global environmental changes: setting priorities for Latin American coastal habitats.

The definitive version is available at www.blackwell-synergy.comThe Intergovernmental Panel for Climate Change (IPCC) reports that Global Environmental Changes (GEC) are occurring quicker than at any other time over the last 25 million years and impacting upon marine environments (Bellard et al., 2012). There is overwhelming evidence showing that GEC are affecting both the quality and quantity of the goods and services provided by a wide range of marine ecosystems. In order to discuss regional preparedness for global environmental changes, a workshop was held in Ilhabela, Brazil (22- 26 April 2012) entitled "Evaluating the Sensitivity of Central and South American Benthic Communities to Global Environmental Changes" that drew together scientists from ten Latin American and three European countries. © 2013 Blackwell Publishing Ltd

Ultime novit\ue0 nello studio dei tessuti connettivi mutabili (MCTs) : un approccio biochimico e biomolecolare in Paracentrotus lividus

I tessuti connettivi collageni sono ubiquitari nel regno animale e svolgono funzioni di protezione, supporto, immagazzinamento dell'energia elastica e trasferimento di tensione. Gli echinodermi posseggono un peculiare tipo di tessuto connettivo mutabile (MCT), in grado di andare incontro a rapidi cambiamenti delle intrinseche propriet\ue0 meccaniche, mediati dal sistema nervoso, fenomeno noto come mutabilit\ue0. Date queste premesse, gli MCTs possono quindi rappresentare una fonte di ispirazione per biomateriali indirizzati ad esempio all'applicazione biomedica. Le principali componenti extracellulari degli MCTs sono rappresentate da: fibrille di collagene, fibrillina, proteoglicani e glicoproteine, in particolare stiparina e tensilina, che modulano l\u2019aggregazione delle fibrille collagene e le loro possibilit\ue0 di slittamento reciproco, stabilendo legami interfibrillari. Scopo del presente lavoro \ue8 stato mettere a punto un protocollo di estrazione biochimica del collagene dagli MCTs del riccio di mare Paracentrotus lividus, e di purificazione e quantificazione del collagene estratto. Inoltre, dati preliminari sono stati ottenuti con riferimento alla caratterizzazione biomolecolare della tensilina. Il fine ultimo sar\ue0 testare le propriet\ue0 di modulazione da parte della tensilina sullo stato di aggregazione sul collagene estratto a diversi gradi di purezza

Blocking the tropomyosin receptor kinase A (TrkA) receptor inhibits pain behaviour in two rat models of osteoarthritis

Objectives: Tropomyosin receptor kinase A (TrkA) mediates nociceptor sensitisation by nerve growth factor (NGF), but it is unknown whether selective TrkA inhibition will be an effective strategy for treating osteoarthritis (OA) pain. We determined the effects of a TrkA inhibitor (AR786) on pain behaviour, synovitis and joint pathology in two rat OA models. Methods: Knee OA was induced in rats by intraarticular monosodium-iodoacetate (MIA) injection or meniscal transection (MNX) and compared with saline injected or sham-operated controls. Pain behaviour was assessed as weight-bearing asymmetry and paw withdrawal threshold to punctate stimulation. Oral doses (30 mg/kg) of AR786 or vehicle were administered twice daily in either preventive (day −1 to –27) or treatment (day 14–28) protocols. Effect maintenance was evaluated for 2 weeks after treatment discontinuation. Alterations in knee structure (cartilage, subchondral bone and synovium) were examined by macroscopic visualisation of articular surfaces and histopathology. Results: Preventive AR786 treatment inhibited pain behaviour development and therapeutic treatment attenuated established pain behaviour. Weight-bearing asymmetry increased 1 week after treatment discontinuation, but remained less than in vehicle- treated arthritic rats, whereas paw withdrawal thresholds returned to levels of untreated rats within 5 days of treatment discontinuation. AR786 treatment reduced MIA-induced synovitis and did not significantly affect osteochondral pathology in either model. Conclusions: Blocking NGF activity by inhibiting TrkA reduced pain behaviour in two rat models of OA. Analgesia was observed both using preventive and treatment protocols, and was sustained after treatment discontinuation. Selective inhibitors of TrkA therefore hold potential for OA pain relief