Tangled closure algebras

The tangled closure of a collection of subsets of a topological space is the largest subset in which each member of the collection is dense. This operation models a logical ‘tangle modality’ connective, of significance in finite model theory. Here we study an abstract equational algebraic formulation of the operation which generalises the McKinsey-Tarski theory of closure algebras. We show that any dissectable tangled closure algebra, such as the algebra of subsets of any metric space without isolated points, contains copies of every finite tangled closure algebra. We then exhibit an example of a tangled closure algebra that cannot be embedded into any complete tangled closure algebra, so it has no MacNeille completion and no spatial representation

Spatial logic of tangled closure operators and modal mu-calculus

There has been renewed interest in recent years in McKinsey and Tarski’s interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric space. Here we extend this work to the modal mu-calculus and to a logic of tangled closure operators that was developed by Fernández-Duque after these two languages had been shown by Dawar and Otto to have the same expressive power over finite transitive Kripke models. We prove that this equivalence remains true over topological spaces. We extend the McKinsey–Tarski topological ‘dissection lemma’. We also take advantage of the fact (proved by us elsewhere) that various tangled closure logics with and without the universal modality ∀ have the finite model property in Kripke semantics. These results are used to construct a representation map (also called a d-p-morphism) from any dense-in-itself metric space X onto any finite connected locally connected serial transitive Kripke frame. This yields completeness theorems over X for a number of languages: (i) the modal mucalculus with the closure operator ; (ii) and the tangled closure operators (in fact can express ); (iii) , ∀; (iv) , ∀, ; (v) the derivative operator ; (vi) and the associated tangled closure operators ; (vii) , ∀; (viii) , ∀,. Soundness also holds, if: (a) for languages with ∀, X is connected; (b) for languages with , X validates the well-known axiom G1. For countable languages without ∀, we prove strong completeness. We also show that in the presence of ∀, strong completeness fails if X is compact and locally connecte

Chronic fibrosing osteomyelitis of the jaws: an important cause of recalcitrant facial pain. A clinicopathologic study of 331 cases in 227 patients

Objective This was a retrospective and follow-up analysis of 331 cases of chronic fibrosing osteomyelitis of the jaws (CFOJ) in 227 patients. Study Design Demographic, clinical, surgical, and microscopic characteristics were tabulated for all patients. A follow-up mail survey was used to determine the degree of symptom relief experienced after surgery. Results The female to male ratio approached 7:1, and mean age of patients was 53 years. The most common sites were the mandibular posterior region, followed by the maxillary posterior region. Consistent clinical findings included intractable jaw pain mimicking that of odontogenic origin but unresponsive to usual therapies, minimal or undetectable radiographic abnormalities on plain films but dramatic radiolucencies detected on cone beam computed tomography, and large cavities that were either empty or filled with blood mixed with lipid globules encountered at surgery. The most common histomorphologic findings were vital lamellar bone, prominent resting and reversal lines, microshards and splaying of trabeculae, rounded trabeculae, marrow fibrosis, and pools of erythrocytes and lipid globules, often together. Moderate to complete relief of symptoms for periods up to 108 months after surgery were reported by 83% of the 70 patients who returned the survey. Conclusions On the basis of the findings of this study, CFOJ can be considered a unique entity with consistent clinicopathologic features. Its features suggest a pathogenesis based on bone marrow ischemia. CFOJ can be treated on a rational basis with a justifiable expectation of success and probable cure

Design of a framework for the deployment of collaborative independent rare disease-centric registries: Gaucher disease registry model

Orphan drug clinical trials often are adversely affected by a lack of high quality treatment efficacy data that can be reliably compared across large patient cohorts derived from multiple governmental and country jurisdictions. It is critical that these patient data be captured with limited corporate involvement. For some time, there have been calls to develop collaborative, non-proprietary, patient-centric registries for post-market surveillance of aspects related to orphan drug efficacy. There is an urgent need for the development and sustainable deployment of these ‘independent’ registries that can capture comprehensive clinical, genetic and therapeutic information on patients with rare diseases. We therefore extended an open-source registry platform, the Rare Disease Registry Framework (RDRF) to establish an Independent Rare Disease Registry (IRDR). We engaged with an established rare disease community for Gaucher disease to determine system requirements, methods of data capture, consent, and reporting. A non-proprietary IRDR model is presented that can serve as autonomous data repository, but more importantly ensures that the relevant data can be made available to appropriate stakeholders in a secure, timely and efficient manner to improve clinical decision-making and the lives of those with a rare diseas

Design of a framework for the deployment of collaborative independent rare disease-centric registries: Gaucher disease registry model

Orphan drug clinical trials often are adversely affected by a lack of high quality treatment efficacy data that can be reliably compared across large patient cohorts derived from multiple governmental and country jurisdictions. It is critical that these patient data be captured with limited corporate involvement. For some time, there have been calls to develop collaborative, non-proprietary, patient-centric registries for post-market surveillance of aspects related to orphan drug efficacy. There is an urgent need for the development and sustainable deployment of these ‘independent’ registries that can capture comprehensive clinical, genetic and therapeutic information on patients with rare diseases. We therefore extended an open-source registry platform, the Rare Disease Registry Framework (RDRF) to establish an Independent Rare Disease Registry (IRDR). We engaged with an established rare disease community for Gaucher disease to determine system requirements, methods of data capture, consent, and reporting. A non-proprietary IRDR model is presented that can serve as autonomous data repository, but more importantly ensures that the relevant data can be made available to appropriate stakeholders in a secure, timely and efficient manner to improve clinical decision-making and the lives of those with a rare disease

Immunogenicity and safety of a booster dose of the 13-valent pneumococcal conjugate vaccine in children primed with the 10-valent or 13-valent pneumococcal conjugate vaccine in the Czech Republic and Slovakia

Background: Although both the 13-valent pneumococcal conjugate vaccine (PCV13) and the 10-valent pneumococcal non-typeable Haemophilus influenzae protein D-conjugate vaccine (PHiD-CV) are widely used, it is unclear how interchangeable they are in terms of immunogenicity. Methods: Two phase 3, open-label, multicenter studies were conducted to assess the immunogenicity and safety of a booster dose of PCV13 in children primed with PHiD-CV or PCV13. In the Czech Republic, 12–15-month-old children received a PCV13 booster after 3-dose priming with either PHiD-CV or PCV13. In Slovakia, 11–12-month-old children received PCV13 following 2-dose priming with either PHiD-CV or PCV13. Serum IgG concentrations were assessed by enzyme-linked immunosorbent assay and functional antibodies were assessed by opsonophagocytic assay (OPA) before the booster and at 1 and 12 months afterward. The primary objective of these studies was to assess non-inferiority of OPA titers for serotype 19A in PHiD-CV-primed subjects compared to those in PCV13-primed children 1 month post-booster. Results: A total of 98 subjects in the Czech Republic and 89 subjects in Slovakia were included. One month after the PCV13 booster dose, the IgG and OPA immune responses to serotype 19A in subjects primed with 2 or 3 doses of PHiD-CV were non-inferior to those in subjects primed with PCV13. Non-inferior and persistent immune responses to most other vaccine serotypes were also observed after the PCV13 booster in PHiD-CV-primed subjects. No safety issues were raised in either study. Conclusions: Overall, robust IgG and OPA immunological responses were observed after booster vaccination with PCV13 in children primed with 2 or 3 doses of PHiD-CV or PCV13, including for serotypes not included in PHiD-CV. These results suggest that these vaccines are interchangeable in terms of safety and immunogenicity and that PCV13 can be used as a booster in the context of mixed schedules. (EudraCT numbers: 2012-005366-35 and 2012-005367-27)

"It All Ended in an Unsporting Way": Serbian Football and the Disintegration of Yugoslavia, 1989-2006

Part of a wider examination into football during the collapse of Eastern European Communism between 1989 and 1991, this article studies the interplay between Serbian football and politics during the period of Yugoslavia's demise. Research utilizing interviews with individuals directly involved in the Serbian game, in conjunction with contemporary Yugoslav media sources, indicates that football played an important proactive role in the revival of Serbian nationalism. At the same time the Yugoslav conflict, twinned with a complex transition to a market economy, had disastrous consequences for football throughout the territories of the former Yugoslavia. In the years following the hostilities the Serbian game has suffered decline, major financial hardship and continuing terrace violence, resulting in widespread nostalgia for the pre-conflict era

Bohrification of operator algebras and quantum logic

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families of projections indexed by a partially ordered set C(A) of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that C(A) consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Heyting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n-by-n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski-Mulvey) of the "Bohrification" of A, which is a commutative Rickart C*-algebra in the topos of functors from C(A) to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns-Lakser completions. Finally, we establish a connection between probability measure on the lattice of projections on a Hilbert space H and probability valuations on the internal Gelfand spectrum of A for A = B(H).Comment: 31 page

The Seroepidemiology of Haemophilus influenzae Type B Prior to Introduction of an Immunization Programme in Kathmandu, Nepal.

Haemophilus influenzae type b (Hib) is now recognized as an important pathogen in Asia. To evaluate disease susceptibility, and as a marker of Hib transmission before routine immunization was introduced in Kathmandu, 71 participants aged 7 months-77 years were recruited and 15 cord blood samples were collected for analysis of anti-polyribosylribitol phosphate antibody levels by enzyme-linked immunosorbent assay. Only 20% of children under 5 years old had levels considered protective (>0.15 µg/ml), rising to 83% of 15-54 year-olds. Prior to introduction of Hib vaccine in Kathmandu, the majority of young children were susceptible to disease