embedding

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Related to Embedding dimension: Correlation dimension

embedding

[em′bed·iŋ]
(mathematics)
An injective homomorphism between two algebraic systems of the same type.

embedding

(mathematics)
One instance of some mathematical object contained with in another instance, e.g. a group which is a subgroup.

embedding

(theory)
(domain theory) A complete partial order F in [X -> Y] is an embedding if

(1) For all x1, x2 in X, x1 <= x2 <=> F x1 <= F x2 and

(2) For all y in Y, x | F x <= y is directed.

("<=" is written in LaTeX as \sqsubseteq).
References in periodicals archive ?
nearly linear sections of each integral plots) of the calculated correlation integrals, the correlation exponents were calculated with the least squares estimation method and each calculated correlation exponent was plotted against its embedding dimension as seen in Figure 4b.
The necessary parameters for this method are the delay time, the embedding dimension and the nearest neighbor number.
Determine the best delay time and the embedding dimension m;
Use the best delay time and the embedding dimension to carry out the phase-space reconstruction of the original time series to obtain the new phase-space vector:
There is a general rise in the Ka statistic as one increases the embedding dimension.
BDS statistics for four embedding dimensions and [epsilon] = 0.
Construct the n-histories of the filtered data to obtain the embedding dimension.
As the CD is estimated for increasingly larger values of the embedding dimension, if chaos is present the CD estimates will stabilize at some value.
Brock, Hsieh and LeBaron (1993) examine the finite sample distribution of the BDS statistic and find the asymptotic distribution will approximate the distribution of the statistic when the sample is n > 500; the embedding dimension is selected to be 5 or lower; and [epsilon] is selected to be between 0.
Linear artifacts and noise are less sensitive to the effects of higher embedding dimensions.
Similarly, the point estimates of the GP correlation dimensions for the Baa bond portfolio series stays well below 3, even as the number of embedding dimensions rises to thirty.