|
|
| Line 1: |
Line 1: |
| {{Context|date=October 2009}}{{One source|date=November 2007}}
| | Hi there, I am Alyson Boon although it is not the title on my beginning certification. One of the extremely very best psychic readings ([http://cspl.postech.ac.kr/zboard/Membersonly/144571 cspl.postech.ac.kr]) things in the globe for him is doing ballet and he'll be beginning some thing else along with it. He functions as a bookkeeper. Mississippi is exactly where her house is but her husband wants them to transfer. |
| | |
| In [[chaos theory]], the '''correlation sum''' is the estimator of the [[correlation integral]], which reflects the mean probability that the states at two different times are close:
| |
| | |
| :<math>C(\varepsilon) = \frac{1}{N^2} \sum_{\stackrel{i,j=1}{i \neq j}}^N \Theta(\varepsilon - || \vec{x}(i) - \vec{x}(j)||), \quad \vec{x}(i) \in \Bbb{R}^m,</math> | |
| | |
| where <math>N</math> is the number of considered states <math>\vec{x}(i)</math>, <math>\varepsilon</math> is a threshold distance, <math>|| \cdot ||</math> a norm (e.g. [[Euclidean norm]]) and <math>\Theta( \cdot )</math> the [[Heaviside step function]]. If only a [[time series]] is available, the phase space can be reconstructed by using a time delay embedding (see [[Takens' theorem]]):
| |
| | |
| :<math>\vec{x}(i) = (u(i), u(i+\tau), \ldots, u(i+\tau(m-1)),</math>
| |
| | |
| where <math>u(i)</math> is the time series, <math>m</math> the embedding dimension and <math>\tau</math> the time delay. | |
| | |
| The correlation sum is used to estimate the [[correlation dimension]].
| |
| | |
| ==See also==
| |
| *[[Correlation integral]]
| |
| *[[Correlation dimension]]
| |
| *[[Recurrence quantification analysis]]
| |
| | |
| ==References==
| |
| * {{cite journal | author=P. Grassberger and I. Procaccia | title=Measuring the strangeness of strange attractors | journal=Physica | year=1983 | volume=9D| pages=189–208 | doi=10.1016/0167-2789(83)90298-1|bibcode = 1983PhyD....9..189G }}
| |
| | |
| [[Category:Chaos theory]]
| |
| [[Category:Dynamical systems]]
| |
| [[Category:Dimension theory]]
| |
Hi there, I am Alyson Boon although it is not the title on my beginning certification. One of the extremely very best psychic readings (cspl.postech.ac.kr) things in the globe for him is doing ballet and he'll be beginning some thing else along with it. He functions as a bookkeeper. Mississippi is exactly where her house is but her husband wants them to transfer.