Thinking culturally about place

This paper explains the bases for an alternative approach to place branding and marketing, based on the disciplines of Cultural Mapping and Cultural Planning. After an introduction of key cultural mapping and planning concepts and issues, the paper discusses some innovative practical examples of culturally sensitive place branding and marketing from Sweden and the UK, and concludes by outlining some components of a possible future agenda for action

Free Heyting algebra endomorphisms: Ruitenburg’s Theorem and beyond

Ruitenburg\u2019s Theorem says that every endomorphism f of a finitely generated free Heyting algebra is ulti- mately periodic if f fixes all the generators but one. More precisely, there is N 65 0 such that f^N+2 = f^N , thus the period equals 2. We give a semantic proof of this theorem, using duality techniques and bounded bisimulation ranks. By the same techniques, we tackle investigation of arbitrary endomorphisms of free algebras. We show that they are not, in general, ultimately periodic. Yet, when they are (e.g. in the case of locally finite subvarieties), the period can be explicitly bounded as function of the cardinality of the set of generators

EXISTENTIALLY CLOSED BROUWERIAN SEMILATTICES

The variety of Brouwerian semilattices is amalgamable and locally finite, hence by well-known results, it has a model completion (whose models are the existen- tially closed structures). In this paper, we supply a finite and rather simple axiomatization of the model completio

Admissibility of Π₂-inference rules: Interpolation, model completion, and contact algebras

We devise three strategies for recognizing admissibility of non-standard inference rules via interpolation, uniform interpolation, and model completions. We apply our machinery to the case of symmetric implication calculus S2IC, where we also supply a finite axiomatization of the model completion of its algebraic counterpart, via the equivalent theory of contact algebras. Using this result we obtain a finite basis for admissible Π2-rules

Quantifier-Free Interpolation of a Theory of Arrays

The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the impossibility of deriving quantifier- free interpolants in general. In this paper, we show that it is possible to obtain quantifier-free interpolants for a Skolemized version of the extensional theory of arrays. We prove this in two ways: (1) non-constructively, by using the model theoretic notion of amalgamation, which is known to be equivalent to admit quantifier-free interpolation for universal theories; and (2) constructively, by designing an interpolating procedure, based on solving equations between array updates. (Interestingly, rewriting techniques are used in the key steps of the solver and its proof of correctness.) To the best of our knowledge, this is the first successful attempt of computing quantifier- free interpolants for a variant of the theory of arrays with extensionality

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

hungry bone syndrome after parathyroidectomy for primary hyperthyroidism

Parathyroidectomy is the treatment of choice in patients with primary hyperparathyroidism (PHPT). This disease affects calcium metabolism at the level of bone tissue and renal tubules, resulting in hypercalcaemia, often asymptomatic, associated with hypophosphataemia and hypomagnesaemia. Sudden suppression of parathyroid hormone (PTH), caused by successful parathyroidectomy, in patients with preoperative high levels of PTH and hypercalcaemia from enhanced bone turnover, may induce severe postoperative hypocalcaemia that may lead to symptoms of tetany. This relatively uncommon condition is known as "hungry bone syndrome" (HBS), because it is believed to be due mainly to enhanced bone formation. Several risk factors have been advocated for HBS, and the syndrome is reported to be more likely to rise in subjects with severe preoperative bone disease. Other modifiable risk factors are preoperative vitamin D deficiency and high PTH and calcium levels. Treatment of HBS is basically the administration of high amounts of calcium immediately after the onset of postoperative hypocalcaemia. Supplements of active metabolites of vitamin D, as well as magnesium in depleted subjects are complementary in supporting bone remineralization. Oral supplementation may be requested for months after parathyroidectomy. Prevention is poorly documented, but it is reasonable to propose the correction of vitamin D deficit and the use of bisphosphonates aimed to lower PTH levels and bone resorption before parathyroidectomy

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