Positive Semidefiniteness and Positive Definiteness of a Linear Parametric Interval Matrix

We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters, the matrix is positive definite (or positive semidefinite). We state a characterization in the form of equivalent conditions, and also propose some computationally cheap sufficient\,/\,necessary conditions. Our results extend the classical results on positive (semi-)definiteness of interval matrices. They may be useful for checking convexity or non-convexity in global optimization methods based on branch and bound framework and using interval techniques

Antibodies to Serine Proteases in the Antiphospholipid Syndrome

It is generally accepted that the major autoantigen for antiphospholipid antibodies (aPL) in the antiphospholipid syndrome (APS) is β2-glycoprotein I (β2GPI). However, a recent study has revealed that some aPL bind to certain conformational epitope(s) on β2GPI shared by the homologous enzymatic domains of several serine proteases involved in hemostasis and fibrinolysis. Importantly, some serine protease–reactive aPL correspondingly hinder anticoagulant regulation and resolution of clots. These results extend several early findings of aPL binding to other coagulation factors and provide a new perspective about some aPL in terms of binding specificities and related functional properties in promoting thrombosis. Moreover, a recent immunological and pathological study of a panel of human IgG monoclonal aPL showed that aPL with strong binding to thrombin promote in vivo venous thrombosis and leukocyte adherence, suggesting that aPL reactivity with thrombin may be a good predictor for pathogenic potentials of aPL