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The MI values that were significantly larger than those of the random surrogate set of sequences were selected to construct the MI graph.
Lempel-Ziv complexity can also be normalized by comparisons with random surrogate symbol strings provided that the complexity of the surrogate is also determined with the Lempel-Ziv algorithm.
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Replacing random surrogates by other kinds of networks, e.g., lattices, will yield equivalent normalization problems.
We here used the algorithm described by Maslov and Sneppen [46] to generate these types of random networks and repeated all simulations but found little to no difference between these and plain random surrogates (see Figure 3).
To avoid answering this question one can generate random surrogates that do not only match the original network's N and k but also have the same degree distribution [7], [13], [26], [30], [33] [35].
Put differently, histograms ('frequency spectra') of motifs are compared with those of random surrogates by which the probability for the presence of a certain motif can be estimated including a corresponding significance value.
Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index.
The normalization with equi-probable random surrogates was also implemented with Lempel-Ziv complexity.
Comparison of complexity values against values obtained from equiprobable random surrogates established the presence of a nonrandom structure in patient-therapist dialog (P =.002).
In one long, stable complex time series (day 100), we used the technique of random surrogates (see Materials and Methods) to show that the recurrence of this complex activity was highly significant (P<0.001).
During last 4 s, the random permutation surrogate of the period between 4 s and 8 s was included.
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