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.

Numerical model of the human cornea based on stromal microstructure: identification of mechanical properties for two age groups

The optical quality of the human eye mainly depends on the refractive performance of the cornea. The shape of the cornea is a mechanical balance between intraocular pressure and tissue intrinsic stiffness. Several surgical procedures in ophthalmology alter the biomechanics of the cornea to provoke local or global curvature changes for vision correction. Legitimated by the large number of surgical interventions performed every day, the demand for a deeper understanding of corneal biomechanics is rising to improve the safety of procedures and medical devices. The aim of our work is to propose a numerical model of corneal biomechanics, based on the stromal microstructure. Our novel anisotropic constitutive material law features a probabilistic weighting approach to model collagen fiber distribution as observed on human cornea by Xray scattering analysis (Aghamohammadzadeh et. al., Structure, February 2004). Furthermore, collagen cross-linking was explicitly included in the strain energy function. Results showed that the proposed model is able to successfully reproduce both inflation and extensiometry experimental data (Elsheikh et. al., Curr Eye Res, 2007; Elsheikh et. al., Exp Eye Res, May 2008). In addition, the mechanical properties calculated for patients of different age groups (Group A: 65-79 years; Group B: 80-95 years) demonstrate an increased collagen cross-linking, and a decrease in collagen fiber elasticity from younger to older specimen. These findings correspond to what is known about maturing fibrous biological tissue. Since the presented model can handle different loading situations and includes the anisotropic distribution of collagen fibers, it has the potential to simulate clinical procedures involving nonsymmetrical tissue interventions. In the future, such mechanical model can be used to improve surgical planning and the design of next generation ophthalmic devices.

Gender, age and ethnic aspects of analgesia in acute abdominal pain: is analgesia even across the groups?

Numerous studies have shown differences in pain perception between men and women, which may affect pain management strategies.

Risk factors of mortality in different age groups after thoracic endovascular aortic repair

The aim of this study was to determine risk factors for mortality in different age groups after thoracic endovascular aortic repair (TEVAR).

A simple, economical, and effective portable paediatric mock circulatory system

Ventricular assist devices (VADs) and total artificial hearts have been in development for the last 50 years. Since their inception, simulators of the circulation with different degrees of complexity have been produced to test these devices in vitro. Currently, a new path has been taken with the extensive efforts to develop paediatric VADs, which require totally different design constraints. This paper presents the manufacturing details of an economical simulator of the systemic paediatric circulation. This simulator allows the insertion of a paediatric VAD, includes a pumping ventricle, and is adjustable within the paediatric range. Rather than focusing on complexity and physiological simulation, this simulator is designed to be simple and practical for rapid device testing. The simulator was instrumented with medical sensors and data were acquired under different conditions with and without the new PediaFlowTM paediatric VAD. The VAD was run at different impeller speeds while simulator settings such as vascular resistance and stroke volume were varied. The hydraulic performance of the VAD under pulsatile conditions could be characterized and the magnetic suspension could be tested via manipulations such as cannula clamping. This compact mock loop has proven to be valuable throughout the PediaFlow development process and has the advantage that it is uncomplicated and can be manufactured cheaply. It can be produced by several research groups and the results of different VADs can then be compared easily.

A Comparison of Psychosocial Risk Factors Between 3 Groups of Cardiovascular Disease Patients Referred for Outpatient Cardiac Rehabilitation

Few studies have examined psychosocial risk factors for cardiovascular disease (CVD) between diagnostic groups of CVD patients. We compared levels of depression, anxiety, hostility, exhaustion, positive affect, and social support, and the prevalence of type D personality between patient groups with a primary diagnosis of coronary heart disease (CHD), chronic heart failure (CHF), or peripheral arterial disease (PAD).