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Like approximate entropy (ApEn), Sample entropy (SampEn) is a measure of complexity. [1] But it does not include self-similar patterns as ApEn does. For a given embedding dimension, tolerance and number of data points, SampEn is the negative natural logarithm of the probability that if two sets of simultaneous data points of length have distance < then two sets of simultaneous data points of ...
Here x ≥ 0 means that each component of the vector x should be non-negative, and ‖·‖ 2 denotes the Euclidean norm. Non-negative least squares problems turn up as subproblems in matrix decomposition, e.g. in algorithms for PARAFAC [2] and non-negative matrix/tensor factorization. [3] [4] The latter can be considered a generalization of ...
In early 2005, NumPy developer Travis Oliphant wanted to unify the community around a single array package and ported Numarray's features to Numeric, releasing the result as NumPy 1.0 in 2006. [9] This new project was part of SciPy. To avoid installing the large SciPy package just to get an array object, this new package was separated and ...
where n is the number of sample points used. The x i are the roots of the physicists' version of the Hermite polynomial H n ( x ) ( i = 1,2,..., n ), and the associated weights w i are given by [ 1 ]
Its particular values can be expressed in closed form for integer and half-integer arguments, but no simple expressions are known for the values at rational points in general. Other fractional arguments can be approximated through efficient infinite products, infinite series, and recurrence relations.
Throughout this article, boldfaced unsubscripted and are used to refer to random vectors, and Roman subscripted and are used to refer to scalar random variables.. If the entries in the column vector = (,, …,) are random variables, each with finite variance and expected value, then the covariance matrix is the matrix whose (,) entry is the covariance [1]: 177 ...
y = x 4 – x has a 2nd derivative of zero at point (0,0), but it is not an inflection point because the fourth derivative is the first higher order non-zero derivative (the third derivative is zero as well). Points of inflection can also be categorized according to whether f ' (x) is zero or nonzero. if f ' (x) is zero, the point is a ...
The index can be easily defined in the setting of complex analysis: Let f(z) be a holomorphic mapping on the complex plane, and let z 0 be a fixed point of f. Then the function f(z) − z is holomorphic, and has an isolated zero at z 0. We define the fixed-point index of f at z 0, denoted i(f, z 0), to be the multiplicity of the zero of the ...