Fisher’s Microscope and Haldane’s Ellipse

Fisher's microscope and Haldane's ellipse.

Fisher's geometrical model was introduced to study the phenotypic size of mutations contributing to adaptation. However, as pointed out by Haldane, the model involves a simplified picture of the action of natural selection, and this calls into question its generality. In particular, Fisher's model assumes that each trait contributes independently to fitness. Here, we show that Haldane's concern...

Commentary: Haldanes and trends in phenotypic change in humans.

no. 347. Hyattsville, MD: National Center for Health Statistics, 2004. http://www.cdc.gov/nchs/data/ad/ad347. pdf (8 September 2012, date last accessed). 43 Ogden CL, Carroll MD. Prevalence of overweight, obesity, and extreme obesity among adults: United States, trends 1960–1962 through 2007–2008; NHANES Health E-Stat, 2010. http://www.cdc.gov/nchs/data/hestat/obesity_adult_ 07_08/obesity_adult...

Ellipse Fitting with Hyperaccuracy

For fitting an ellipse to a point sequence, ML (maximum likelihood) has been regarded as having the highest accuracy. In this paper, we demonstrate the existence of a “hyperaccurate” method which outperforms ML. This is made possible by error analysis of ML followed by subtraction of high-order bias terms. Since ML nearly achieves the theoretical accuracy bound (the KCR lower bound), the result...

Calculating ellipse overlap areas

We present an approach for finding the overlap area between two ellipses that does not rely on proxy curves. The Gauss-Green formula is used to determine a segment area between two points on an ellipse. Overlap between two ellipses is calculated by combining the areas of appropriate segments and polygons in each ellipse. For four of the ten possible orientations of two ellipses, the method requ...

Intersection of Rectangle and Ellipse