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Many problems in applied mathematics require the evaluation of the sum of N Gaussians at M points in space. The work required for direct evaluation grows like NM as N and M increase; this makes it very expensive to carry out such calculations on a large scale. In this paper, an algorithm is presented which evaluates the sum of N Gaussians at M arbitrarily(More)
We present a numerical method which computes the motion of complex solid/liquid boundaries in crystal growth. The model we solve includes physical effects such as crystalline anisotropy, surface tension, molecular kinetics and undercooling. The method is based on two ideas. First, the equations of motion are recast as a single history-dependent boundary(More)
BACKGROUND Although many case reports describe manifestations of autosomal-dominant polycystic kidney disease (ADPKD) in children, no longitudinal studies have examined the natural progression or risk factors for more rapid progression in a large number of children from ADPKD families. METHODS Since 1985, we have studied 312 children from 131 families(More)
Level set methods for moving interface problems require efficient techniques for transforming an interface to a globally defined function whose zero set is the interface, such as the signed distance to the interface. This paper presents efficient algorithms for this “redistancing” problem. The algorithms use quadtrees and triangulation to compute global(More)
A new piecewise-polynomial interface method (PIM) for discretizing elliptic problems with complex interfaces between high-contrast materials is derived, analyzed and tested. A Krylov-accelerated interface multigrid approach (IMG) solves the discretization efficiently. Stability and convergence are proved in one dimension, while an extensive array of(More)
BACKGROUND Rib fractures have a strong association with nonaccidental trauma (NAT) and severe trauma. The purposes of this study were to evaluate rib fractures in children to determine (1) the positive predictive value of a rib fracture in defining NAT and (2) the frequency of rib fractures as the only skeletal manifestation of NAT. METHODS We reviewed(More)
To determine the utility of ultrasonography (US) in diagnosing autosomal dominant polycystic kidney disease (ADPKD) in children, this study examined 106 children who were at 50% risk for the disease. The children underwent a history, physical examination, abdominal US, and gene linkage analysis (GLA) with tightly linked markers for ADPKD1 and ADPKD2 genes.(More)
BACKGROUND AND OBJECTIVES In autosomal dominant polycystic kidney disease (ADPKD), progressive kidney cyst formation commonly leads to ESRD. Because important manifestations of ADPKD may be evident in childhood, early intervention may have the largest effect on long-term outcome. Statins are known to slow progressive nephropathy in animal models of ADPKD.(More)