Hadamard Type Asymptotics for Eigenvalues of the Neumann Problem for Elliptic Operators

This paper considers how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain. The proximity of two domains is measured in terms of the norm of the difference between the two resolvents corresponding to the reference domain and the perturbed domain, and the size of eigenfunctions outside the intersection of the two domains. This construction enables the possibility of comparing both nonsmooth domains and domains with different topology. An abstract framework is presented, where the main result is an asymptotic formula where the remainder is expressed in terms of the proximity quantity described above when this is relatively small. We consider two applications: the Laplacian in both $C^{1,\alpha}$ and Lipschitz domains. For the $C^{1,\alpha}$ case, an asymptotic result for the eigenvalues is given together with estimates for the remainder, and we also provide an example which demonstrates the sharpness of our obtained result. For the Lipschitz case, the proximity of eigenvalues is estimated

Spatial orientation of cross-sectional images of coronary arteries: point of view in intracoronary imaging

<p>Abstract</p> <p>Background</p> <p>In studies where cross-sectional images of coronary arteries obtained with different imaging modalities are compared, the importance of correct co-localization and matching of images along the coronary artery longitudinal axis is obvious. However, it appears neglected that correct spatial orientation of the cross-sectional plane may not be obtainable just by rotating the images to ensure co-localization of identifiable landmarks such as sidebranches. A cross-section has two sides, one facing proximally and the other distally, and pairs of images reconstructed corresponding to these opposite points of view are mirror images of each other and not superimposable. This may be difficult if not impossible to recognize and unrecognized it will give rise to flawed results in the development and validation of imaging technologies aimed at plaque characterization (tissue mapping). We determined the imagined point of view for three commercially available intracoronary imaging systems used by invasive cardiologists and illustrate its importance in imaging modality validation.</p> <p>Methods and Results</p> <p>We made an asymmetric phantom and investigated it with two different intravascular ultrasound (IVUS) systems and one optical coherence tomography (OCT) system. The asymmetry of the phantom allowed determination of the spatial orientation of the cross-sectional images. On all tested systems, an observer should imagine herself/himself standing proximal to the cross-section when looking at the intravascular images.</p> <p>Conclusions</p> <p>The tested intracoronary imaging modalities displayed cross-sectional images with a spatial orientation corresponding to a proximal point of view. Knowledge of the spatial orientation is mandatory when comparing and validating different imaging modalities aimed at plaque characterization.</p

Self-Stabilizing Supervised Publish-Subscribe Systems

In this paper we present two major results: First, we introduce the first self-stabilizing version of a supervised overlay network by presenting a self-stabilizing supervised skip ring. Secondly, we show how to use the self-stabilizing supervised skip ring to construct an efficient self-stabilizing publish-subscribe system. That is, in addition to stabilizing the overlay network, every subscriber of a topic will eventually know all of the publications that have been issued so far for that topic. The communication work needed to processes a subscribe or unsubscribe operation is just a constant in a legitimate state, and the communication work of checking whether the system is still in a legitimate state is just a constant on expectation for the supervisor as well as any process in the system