Local Asymmetry and the Inner Radius of Nodal Domains

Let M be a closed Riemannian manifold of dimension n. Let f be an eigenfunction of the Laplace-Beltrami operator corresponding to an eigenvalue \lambda. We show that the volume of {f>0} inside any ball B whose center lies on {f=0} is > C|B|/\lambda^n. We apply this result to prove that each nodal domain contains a ball of radius > C/\lambda^n.Comment: 12 pages, 1 figure; minor corrections; to appear in Comm. PDE

Lower bounds for nodal sets of eigenfunctions

We prove lower bounds for the Hausdorff measure of nodal sets of eigenfunctions.Comment: To appear in Communications in Mathematical Physics; revised to include two additional references and update bibliographic informatio

Lower bounds for nodal sets of Dirichlet and Neumann eigenfunctions

Let \phi\ be a Dirichlet or Neumann eigenfunction of the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We prove lower bounds for the size of the nodal set {\phi=0}.Comment: 7 page

Enhancing the surgeons reality : Smart visualization of bolus time of arrival and blood flow anomalies from time lapse series for safety and speed of

A noise adaptive Cusum-based algorithm for determining the arrival times of contrast at each spatial location in a 2D time sequence of angiographic images is presented. We employ a new group-wise registration algorithm to remove the effect of patient motions during the acquisition process. By using the registered image the proposed arrival time provides accurate results without relying on a priori knowledge of the shape of the time series at each location or even on the time series at each location having the same shape under translation.Charles Stark Draper Laborator

Spatio-Temporal Data Fusion for 3D+T Image Reconstruction in Cerebral Angiography

This paper provides a framework for generating high resolution time sequences of 3D images that show the dynamics of cerebral blood flow. These sequences have the potential to allow image feedback during medical procedures that facilitate the detection and observation of pathological abnormalities such as stenoses, aneurysms, and blood clots. The 3D time series is constructed by fusing a single static 3D model with two time sequences of 2D projections of the same imaged region. The fusion process utilizes a variational approach that constrains the volumes to have both smoothly varying regions separated by edges and sparse regions of nonzero support. The variational problem is solved using a modified version of the Gauss-Seidel algorithm that exploits the spatio-temporal structure of the angiography problem. The 3D time series results are visualized using time series of isosurfaces, synthetic X-rays from arbitrary perspectives or poses, and 3D surfaces that show arrival times of the contrasted blood front using color coding. The derived visualizations provide physicians with a previously unavailable wealth of information that can lead to safer procedures, including quicker localization of flow altering abnormalities such as blood clots, and lower procedural X-ray exposure. Quantitative SNR and other performance analysis of the algorithm on computational phantom data are also presented.National Institutes of Health (U.S.)Charles Stark Draper Laboratory (Internal Research and Development funds)Cam Neely Foundation for Cancer CareNational Institute of Biomedical Imaging and Bioengineering (U.S.) (Grant 1 R01 EB006161-01A2)National Institute of Biomedical Imaging and Bioengineering (U.S.) (Grant 1 R21 HL102685-01