We prove the equality of doubly refined enumerations of Alternating Sign Matrices and of Totally Symmetric Self-Complementary Plane Partitions using integral formulae originating from certain solutions of quantum Knizhnik-Zamolodchikov equation.

Key PointsQuestionIs transcatheter aortic valve implantation (TAVI) noninferior to surgical aortic valve replacement (surgery) in patients aged 70 years or older with severe, symptomatic aortic stenosis and moderately increased operative risk?FindingsIn this randomized clinical trial that included 913 patients at moderately increased operative risk due to age or comorbidity, all-cause mortality at 1 year was 4.6% with TAVI vs 6.6% with surgery, a difference that met the prespecified noninferiority margin of 5%.MeaningAmong patients aged 70 years or older with severe, symptomatic aortic stenosis and moderately increased operative risk, treatment with TAVI was noninferior to surgery with respect to all-cause mortality at 1 year.

BackgroundChronic obstructive pulmonary disease (COPD) is a progressive and irreversible disease responsible for the deaths of 3 million people worldwide in 2005, and predicted to be the third leading cause of death worldwide by 2030. Many COPD models developed to date have followed a Markov structure, in which patients or populations can move between defined health states over successive time periods or cycles. In COPD, health states are typically based on disease severity defined solely by lung function, as described by the Global Initiative for Chronic Obstructive Lung Disease (GOLD) guidelines. These current modelling methods may restrict the ability to reflect the disease progression/clinical pathway or clinical practice.ObjectivesGiven these limitations in previous COPD models, the authors aimed to develop a more flexible model that could improve on the description of the clinical disease pathway. The overall objective of this model was to inform the development of policies, guidelines or cost-effectiveness analyses. A second objective was to validate the model in relation to existing epidemiology studies of COPD.MethodsA patient simulation model was developed in Microsoft Excel™. The predictability of the model was tested by populating it with data from natural history of disease studies as well as with clinical trial data. Each patient moves through the model with demographic characteristics randomly generated from a set distribution. These characteristics determine the risk of clinical events occurring in the model.ResultsThe validation with these studies found the model to have generally good predictive ability, yielding in this way a good degree of external validity.ConclusionsThe micro-simulation model is a flexible approach for modelling COPD that allows consideration of complex COPD treatment pathways. The model was found to be generally robust in terms of predicting clinical outcomes of published studies when tested against other studies. It has significant potential as a tool for supporting future COPD treatment positioning decisions as well as to inform the development of policies, guidelines or cost-effectiveness analyses.

We address a number of conjectures about the ground state O(1) loop model, computing in particular two infinite series of partial sums of its entries and relating them to the enumeration of plane partitions. Our main tool is the use of integral formulae for a polynomial solution of the quantum Knizhnik-Zamolodchikov equation.