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In machine learning theory, the Vapnik-Chervonenkis dimension or VC-dimension of a concept class C is the cardinality of the largest set S which can be shattered by C. If ...

A continuous-time stochastic process W(t) for t>=0 with W(0)=0 and such that the increment W(t)-W(s) is Gaussian with mean 0 and variance t-s for any 0<=s<t, and increments ...

Numerical integration is the approximate computation of an integral using numerical techniques. The numerical computation of an integral is sometimes called quadrature. ...

The subset B of the Euclidean plane formed by the union of the interval [0,1] of the x-axis and all line segments of unit length passing through the origin which form an ...

The computation of points or values between ones that are known or tabulated using the surrounding points or values. In particular, given a univariate function f=f(x), ...

Legendre's conjecture asserts that for every n there exists a prime p between n^2 and (n+1)^2 (Hardy and Wright 1979, p. 415; Ribenboim 1996, pp. 397-398). It is one of ...

Define q=e^(2piitau) (cf. the usual nome), where tau is in the upper half-plane. Then the modular discriminant is defined by ...

A space-filling function which maps a one-dimensional interval into a two-dimensional area. Plane-filling functions were thought to be impossible until Hilbert discovered the ...

The Riemann integral is the definite integral normally encountered in calculus texts and used by physicists and engineers. Other types of integrals exist (e.g., the Lebesgue ...

There are at least two distinct notions of when a point process is stationary. The most commonly utilized terminology is as follows: Intuitively, a point process X defined on ...