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mu_i(epsilon), sometimes denoted P_i(epsilon), is the probability that element i is populated, normalized such that sum_(i=1)^Nmu_i(epsilon)=1.

Possessing a three equivalent modes.

Consider a broadcast scheme on a connected graph from an originator vertex v in a graph G consisting of a sequence of parallel calls starting from v. In each time step, every ...

A dimension also called the fractal dimension, Hausdorff dimension, and Hausdorff-Besicovitch dimension in which nonintegral values are permitted. Objects whose capacity ...

In machine learning theory and artificial intelligence, a concept c over a domain X is a Boolean function c:X->{0,1}. A collection of concepts is called a concept class. In ...

Define the correlation integral as C(epsilon)=lim_(N->infty)1/(N^2)sum_(i,j=1; i!=j)^inftyH(epsilon-|x_i-x_j|), (1) where H is the Heaviside step function. When the below ...

Let S be a nonempty set, then a filter on S is a nonempty collection F of subsets of S having the following properties: 1. emptyset not in F, 2. If A,B in F, then A ...

The term "fractal dimension" is sometimes used to refer to what is more commonly called the capacity dimension of a fractal (which is, roughly speaking, the exponent D in the ...

A global field is either a number field, a function field on an algebraic curve, or an extension of transcendence degree one over a finite field. From a modern point of view, ...

The study of number fields by embedding them in a local field is called local class field theory. Information about an equation in a local field may give information about ...