Cartesian Bicategories II

The notion of cartesian bicategory, introduced by Carboni and Walters for locally ordered bicategories, is extended to general bicategories. It is shown that a cartesian bicategory is a symmetric monoidal bicategory

Deriving Bisimulation Congruences: 2-categories vs precategories

G-relative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner’s approach to deriving labelled bisimulation congruences from reduction systems. This paper develops the theory of GRPOs further, arguing that they provide a simple and powerful basis towards a comprehensive solution. As an example, we construct GRPOs in a category of ‘bunches and wirings.’ We then examine the approach based on Milner’s precategories and Leifer’s functorial reactive systems, and show that it can be recast in a much simpler way into the 2-categorical theory of GRPOs

Video thoracoscopic surgery used to manage tuberculosis in thoracic surgery

Background: The aim of this study was to evaluate the indications and results of video-assisted thoracic surgery (VATS) for the management of tuberculosis in 10 patients with unusual clinical and radiologic presentation for the disease. Methods: From March 2000 to March 2002, 96 diagnostic VATS operations for unclear thoracic lesions were performed at the authors' institution. Their final diagnosis for 10 (10.4%) of these patients was tuberculosis. The suspected preoperative diagnoses were pancoast tumour (n = 1), pericardial effusion (n = 1), pleural mesothelioma (n = 1), pleural empyema (n = 2), mediastinal lymphoma (n = l), and lung cancer (n = 4). Results: For all the patients, the diagnosis of tuberculosis was achieved by VATS. The duration of drainage was 2.5 days. There have been neither morbidity nor mortality since surgery. The hospital stay was 3 to 5 days. Conclusion: Thoracoscopy is a safe and effective procedure for the management of tuberculosis. Tuberculosis should be kept in mind during the differential diagnosis of unknown thoracic lesions, and also for patients who live in economically well developed countries and are not immune compromise

Higher Order Containers

Abstract. Containers are a semantic way to talk about strictly positive types. In previous work it was shown that containers are closed under various constructions including products, coproducts, initial algebras and terminal coalgebras. In the present paper we show that, surprisingly, the category of containers is cartesian closed, giving rise to a full cartesian closed subcategory of endofunctors. The result has interesting applications syntax. We also show that while the category of containers has finite limits, it is not locally cartesian closed.

Calculating Colimits Compositionally

We show how finite limits and colimits can be calculated compositionally using the algebras of spans and cospans, and give as an application a proof of the Kleene Theorem on regular languages

Picturing classical and quantum Bayesian inference

We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators rather than probability distributions as representative of degrees of belief. The diagrammatic framework is stated in the graphical language of symmetric monoidal categories and of compact structures and Frobenius structures therein, in which Bayesian inversion boils down to transposition with respect to an appropriate compact structure. We characterize classical Bayesian inference in terms of a graphical property and demonstrate that our approach eliminates some purely conventional elements that appear in common representations thereof, such as whether degrees of belief are represented by probabilities or entropic quantities. We also introduce a quantum-like calculus wherein the Frobenius structure is noncommutative and show that it can accommodate Leifer's calculus of `conditional density operators'. The notion of conditional independence is also generalized to our graphical setting and we make some preliminary connections to the theory of Bayesian networks. Finally, we demonstrate how to construct a graphical Bayesian calculus within any dagger compact category.Comment: 38 pages, lots of picture