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A function I_n(x) which is one of the solutions to the modified Bessel differential equation and is closely related to the Bessel function of the first kind J_n(x). The above ...

A direct search method of optimization that works moderately well for stochastic problems. It is based on evaluating a function at the vertices of a simplex, then iteratively ...

A pair of elements (p_i,p_j) is called an inversion in a permutation p if i>j and p_i<p_j (Skiena 1990, p. 27; Pemmaraju and Skiena 2003, p. 69). For example, in the ...

The illusion that the two ends of a straight line segment passing behind an obscuring rectangle are offset when, in fact, they are aligned. The Poggendorff illusion was ...

A sequence of n-tuples that fills n-space more uniformly than uncorrelated random points, sometimes also called a low-discrepancy sequence. Although the ordinary uniform ...

In the above illustration, black dots appear to form and vanish at the intersections of the gray horizontal and vertical lines. When focusing attention on a single white dot, ...

If a matrix A has a matrix of eigenvectors P that is not invertible (for example, the matrix [1 1; 0 1] has the noninvertible system of eigenvectors [1 0; 0 0]), then A does ...

The Spearman rank correlation coefficient, also known as Spearman's rho, is a nonparametric (distribution-free) rank statistic proposed by Spearman in 1904 as a measure of ...

A piecewise polynomial function that can have a locally very simple form, yet at the same time be globally flexible and smooth. Splines are very useful for modeling arbitrary ...

The median of a statistical distribution with distribution function D(x) is the value x such D(x)=1/2. For a symmetric distribution, it is therefore equal to the mean. Given ...