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3.3. Nonlinear methods 27−0.6−0.8log F(n)−1−1.2−1.4α 1α 2−1.6−1.80.6 0.8 1 1.2 1.4 1.6 1.8log nFigure 3.2: Detrended fluctuation analysis. A double log plot of the index F (n) as a functionof segment length n. α 1 and α 2 are the short term and long term fluctuation slopes,respectively.3.3.5 Correlation dimensionAnother method for measuring the complexity or strangeness of the time series is the correlationdimension which was proposed in [13]. The correlation dimension is expected to giveinformation on the minimum number of dynamic variables needed to model the underlyingsystem and it can be obtained as follows.Similarly as in the calculation of approximate and sample entropies, form length mvectors u ju j =(RR j , RR j+1 ,...,RR j+m−1 ), j =1, 2,...,N − m + 1 (3.17)and calculate the number of vectors u k for which d(u j ,u k ) ≤ r, thatisCj m (r) = nbr of { ∣u k d(uj ,u k ) ≤ r }N − m +1∀ k (3.18)where the distance function d(u j ,u k ) is now defined as∑d(u j ,u k )= √ m (u j (l) − u k (l)) 2 . (3.19)l=1Next, an average of the term C m j(r) istakenC m (r) =N−m+11 ∑N − m +1j=1C m j(r) (3.20)Kubios HRV Analysisversion 2.0 betaBiosignal Analysis and Medical Imaging GroupDepartment of PhysicsUniversity of Kuopio, FINLAND