Mitral valve disease is a frequent cause of heart failure and death. Emerging evidence indicates that the mitral valve is not a passive structure, but—even in adult life—remains dynamic and accessible for treatment. This concept motivates efforts to reduce the clinical progression of mitral valve disease through early detection and modification of underlying mechanisms. Discoveries of genetic mutations causing mitral valve elongation and prolapse have revealed that growth factor signalling and cell migration pathways are regulated by structural molecules in ways that can be modified to limit progression from developmental defects to valve degeneration with clinical complications. Mitral valve enlargement can determine left ventricular outflow tract obstruction in hypertrophic cardiomyopathy, and might be stimulated by potentially modifiable biological valvular–ventricular interactions. Mitral valve plasticity also allows adaptive growth in response to ventricular remodelling. However, adverse cellular and mechanobiological processes create relative leaflet deficiency in the ischaemic setting, leading to mitral regurgitation with increased heart failure and mortality. Our approach, which bridges clinicians and basic scientists, enables the correlation of observed disease with cellular and molecular mechanisms, leading to the discovery of new opportunities for improving the natural history of mitral valve disease.
Abstract. We describe the C * -algebra of an E-unitary or strongly 0-E-unitary inverse semigroup as the partial crossed product of a commutative C * -algebra by the maximal group image of the inverse semigroup. We give a similar result for the C * -algebra of the tight groupoid of an inverse semigroup. We also study conditions on a groupoid C * -algebra to be Morita equivalent to a full crossed product of a commutative C * -algebra with an inverse semigroup, generalizing results of Khoshkam and Skandalis for crossed products with groups.
We show Exel's tight representation of an inverse semigroup can be described in terms of joins and covers in the natural partial order. Using this, we show that the C * -algebra of a finitely aligned category of paths, developed by Spielberg, is the tight C * -algebra of a natural inverse semigroup. This includes as a special case finitely aligned higher-rank graphs: that is, for such a higher-rank graph Λ, the tight C * -algebra of the inverse semigroup associated to Λ is the same as the C * -algebra of Λ.2010 Mathematics subject classification: primary 46L05; secondary 20M18, 47D03.
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