Quadratic Word Equations with Length Constraints, Counter Systems, and Presburger Arithmetic with Divisibility

Word equations are a crucial element in the theoretical foundation of constraint solving over strings, which have received a lot of attention in recent years. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant strings that equate the left and right hand sides of the equation. While the problem of solving word equations is decidable, the decidability of the problem of solving a word equation with a length constraint (i.e., a constraint relating the lengths of words in the word equation) has remained a long-standing open problem. In this paper, we focus on the subclass of quadratic word equations, i.e., in which each variable occurs at most twice. We first show that the length abstractions of solutions to quadratic word equations are in general not Presburger-definable. We then describe a class of counter systems with Presburger transition relations which capture the length abstraction of a quadratic word equation with regular constraints. We provide an encoding of the effect of a simple loop of the counter systems in the theory of existential Presburger Arithmetic with divisibility (PAD). Since PAD is decidable, we get a decision procedure for quadratic words equations with length constraints for which the associated counter system is \emph{flat} (i.e., all nodes belong to at most one cycle). We show a decidability result (in fact, also an NP algorithm with a PAD oracle) for a recently proposed NP-complete fragment of word equations called regular-oriented word equations, together with length constraints. Decidability holds when the constraints are additionally extended with regular constraints with a 1-weak control structure.Comment: 18 page

Minor troponin T elevation and mortality in patients with atrial fibrillation presenting to the emergency department

Background There are limited data on the association of minor troponin elevation in unselected patients with atrial fibrillation (AF) presenting to the emergency department (ED) with adverse events. In this study, we sought to assess the early and mid-term mortality of these patients. Methods In this observational study, 2911 patients with AF were admitted to the ED. They were divided into 3 groups based on peak high-sensitivity troponin (TnT) levels: normal ( Results All-cause mortality was 6.7% (n = 196) at 30 days and 22.2% (n = 646) at 1 year. Mortality rate increased along with increasing levels of TnT irrespective of baseline covariates, primary discharge diagnosis and type of AF. A significant association between TnT levels and all-cause mortality was observed. The adjusted hazard ratio (HR) at 30 days was 6.02 (95% CI 2.62-13.83) for TnT 15-50 ng/L and 11.28 (95% CI 4.87-26.12) for TnT 51-100 ng/L (P Conclusions Among patients with AF admitted to the ED, increased TnT levels were associated with increased early and mid-term all-cause mortality irrespective of baseline covariates and type of AF.Peer reviewe

Outcome of patients undergoing open heart surgery at the Uganda heart institute, Mulago hospital complex

Background: Heart disease is a disabling condition and necessary surgical intervention is often lacking in many developing countries. Training of the superspecialties abroad is largely limited to observation with little or no opportunity for hands on experience. An approach in which open heart surgeries are conducted locally by visiting teams enabling skills transfer to the local team and helps build to build capacity has been adopted at the Uganda Heart Institute (UHI).Objectives: We reviewed the progress of open heart surgery at the UHI and evaluated the postoperative outcomes and challenges faced in conducting open heart surgery in a developing country.Methods: Medical records of patients undergoing open heart surgery at the UHI from October 2007 to June 2012 were reviewed.Results: A total of 124 patients underwent open heart surgery during the study period. The commonest conditions were: venticular septal defects (VSDs) 34.7% (43/124), Atrial septal defects (ASDs) 34.7% (43/124) and tetralogy of fallot (TOF) in 10.5% (13/124). Non governmental organizations (NGOs) funded 96.8% (120/124) of the operations, and in only 4 patients (3.2%) families paid for the surgeries. There was increasing complexity in cases operated upon from predominantly ASDs and VSDs at the beginning to more complex cases like TOFs and TAPVR. The local team independently operated 19 patients (15.3%). Postoperative morbidity was low with arrhythmias, left ventricular dysfunction and re-operations being the commonest seen. Post operative sepsis occurred in only 2 cases (1.6%). The overall mortality rate was 3.2 %Conclusion: Open heart surgery though expensive is feasible in a developing country. With increased direct funding from governments and local charities to support open heart surgeries, more cardiac patients access surgical treatment locally.Keywords: Open heart surgery, Uganda Heart Institut

Regionalism and changing regional order in the Pacific Islands

Institutional developments in Pacific Islands regionalism have been dramatic in recent years. These include the changing role of the Parties to the Nauru Agreement, a grouping of eight ‘tuna-rich’ Pacific Island states that is transforming the dynamics of regional fisheries; the emergence of a more activist Melanesian Spearhead Group, which comprises the four largest economies of the Pacific Islands and is leading the process of regional economic integration; and the establishment of the Pacific Islands Development Forum, which promises a more inclusive ‘regionalism through partnerships’ approach in addressing climate change and sustainable development issues. This new dynamism is driven by the discontent of a growing number of island states with the established regional order,defined by prevailing institutions, power and ideas, and by a desire to assert greater control over their own futures. Against the backdrop of an increasingly dynamic geopolitical and geoeconomic landscape, Pacific Island states are using alternative regional frameworks to develop new approaches to the challenges facing them

Effects of serum proteins on corrosion behavior of ISO 5832–9 alloy modified by titania coatings

Stainless steel ISO 5832–9 type is often used to perform implants which operate in protein-containing physiological environments. The interaction between proteins and surface of the implant may affect its corrosive properties. The aim of this work was to study the effect of selected serum proteins (albumin and γ-globulins) on the corrosion of ISO 5832–9 alloy (trade name M30NW) which surface was modified by titania coatings. These coatings were obtained by sol– gel method and heated at temperatures of 400 and 800 °C. To evaluate the effect of the proteins, the corrosion tests were performed with and without the addition of proteins with concentration of 1 g L−1 to the physiological saline solution (0.9 % NaCl, pH 7.4) at 37 °C. The tests were carried out within 7 days. The following electrochemical methods were used: open circuit potential, linear polarization resistance, and electrochemical impedance spectroscopy. In addition, surface analysis by optical microscopy and X-ray photoelectron spectroscopy (XPS) method was done at the end of weekly corrosion tests. The results of corrosion tests showed that M30NW alloy both uncoated and modified with titania coatings exhibits a very good corrosion resistance during weekly exposition to corrosion medium. The best corrosion resistance in 0.9 % NaCl solution is shown by alloy samples modified by titania coating annealed at 400 °C. The serumproteins have no significant effect onto corrosion of investigated biomedical steel. The XPS results confirmed the presence of proteins on the alloy surface after 7 days of immersion in proteincontaining solutions.The investigations were supported by the National Science Centre project No. N N507 501339. The authors gratefully acknowledge Dr. Janusz Sobczak and Dr. hab. Wojciech Lisowski from Institute of Physical Chemistry of PAS for XPS surface analyses