Two-point Rule Research Articles

Harnessing the parallax for better spatial awareness.

Despite easy access to imaging diagnostic procedures and an abundance of spatial data, most cardiac interventions are still performed under two-dimensional fluoroscopy. Incorporating anatomical data from scans into procedures plans has the potential to improve the swiftness and outcomes of percutaneous cardiac interventions. Therefore, procedure planning based on the specific anatomy is becoming a new standard of excellence in interventional cardiology. Still, we often tend to disregard specific spatial relations and the actual direction of catheter tip movement inside the body, relying on a try and error approach. The precise spatial orientation of instruments and prosthetic devices is crucial, especially during structural heart interventions. Here, we present how deliberate movements of objects under fluoroscopy can reveal the spatial orientation of catheters and other devices. We also propose a novel "two-point rule" for identifying three-dimensional relations between points in space. Understanding and applying this rule might substantially increase the spatial awareness of operators performing cardiovascular interventions. Although the concept is pretty simple, using it "live" during interventional cardiology procedures requires thorough understanding and practice. We propose the "two-point rule" as a crucial rule to develop expertise in spatial orientation under fluoroscopy and ensure high-quality outcomes.

When does risk outweigh reward? Identifying potential scoring strategies with netball's new two-point rule.

Changing rules to promote scoring through more 'high-risk' play has become common in team sports. Australia's national netball league (i.e. Suncorp Super Netball) has recently taken this approach-introducing a two-point shooting rule. Teams will be awarded two-points for shots made from an 'outer circle' 3.0m-4.9m from the goal in the final five minutes of quarters. We sought to answer a series of questions regarding the implementation and potential strategies surrounding the two-point rule in Suncorp Super Netball. We used video coded data from the 2018 Suncorp Super Netball season to identify the total number of made and missed shots from different distances across the season. We also used shooting statistics from recent Fast5 Netball World Series (a competition with a two-point shooting rule already in place) as a comparator. The reward of two-points is relatively well-aligned to the relative risk of missing shots from the proposed outer versus inner circle (2.22 [1.98, 2.48 95% CIs]) based on existing shooting data from Suncorp Super Netball teams. We found that the relative risk of missing shots from 'long-' (i.e. 3.5m-4.0m) versus 'mid-range' (i.e. 3.0-3.5m) was only slightly elevated (1.52 [1.21, 1.86 95% CIs])-suggesting teams should favour long- over mid-range shots when the two-point shot is available. Based on the typical number of shots a team receives in a five-minute period, we found that teams may be able to score ~3.51 extra points per quarter when taking all versus no-shots from the two-point outer circle. Analysis of the Fast5 versus Suncorp Super Netball data did, however, reveal that shooting accuracy from long-range may decrease when a two-point shot is available. Teams may need to consider situational factors (e.g. altered opposition defensive strategies) when developing their shooting strategy for taking advantage of the two-point shot.

Implementation of Two-point Quadrature Gauss-Legendre Method on 2D Gravity Anomaly Modeling in Basins with Density Distribution Varied Polynomially as a Function of Depth

Study of basin geometry basin is important in geosciences and geophysical exploration. Gravity method can be used to address this issue by measuring gravity anomalies on the surface caused by density contrast between the bedrock and the sediment that fills the basin, geometry of the basin and surface topography. Numerically, gravity anomaly modeling can be conducted using two-point rule Gauss-Legendre Quadrature method, for a case where density contrast varies with depth exponentially. Within the scope of this study, gravity anomalies on the surface are significantly affected by the geometry of the curvature of the bedrock as well as the topographic elevation of the surface and the selected density contrast, and are not significantly affected by the undulation of the bedrock curvature.

A One-Step Method for the Numerical Integration of the Differential Equation y'' = f(x)y + g(x)

1. The numerical integration of ordinary differential equations by the use of Gaussian quadrature methods was introduced into the literature by Hammer and Hollingsworth (1955), for subsequent developments, see Morrison and Stoller (1958), Korganoff (1958), Kuntzmann (1961), Henrici (1962). In this paper we develop a one-step method for the numerical integration of the ordinary differential equation y = f(x)y + g{x), y(o) — .Vo> y(*o) — yo based on the Gauss two-point rule (see Hildebrand, 1956). Theoretical and computational comparison of the new method with other methods is given.