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Exact(5)
Here H stands for Shannon entropy, and I for mutual information (see, e.g., ([24], Eq. (2.35)–(2.35)).
Below denotes mutual information (see, e.g., [29]); for notational convenience, we suppress the dependence of the mutual information on the joint distribution.
Second order phase transitions are indicated by peaks in mutual information and whereas first order phase transitions are indicated by discontinuities in the entropy, rather than the mutual information, see (Solé et al.1996) for a brief discussion of the general differences in such systems.
Here, we supplement our previous analysis of the bigrams and trigrams with information theoretic measures such as the entropy, mutual information (see Materials and Methods for details) and perplexity.
So mutual information (see Equation 3) expresses how much we learn about the output (or input) of a channel when we receive information about the input (or output).
Similar(54)
If a given primary transmission fails and the primary receiver requests a retransmission, then it is very likely that after a second transmission from the primary, the accumulated mutual information seen at the primary receiver is above the attempted primary rate, so that there may be an 'excess of mutual information' in the primary link[10].
Thus, a possible explanation for the high mutual information seen between these residues is that the C-terminus of the CydX protein may interact with the Q-loop, potentially stabilizing the interaction of CydX with the Cyd complex.
For each concentration distribution {[p27], [Skp2]} (Both ranges for Skp2 and phosphorylated p27 were discretized into 100 values each) the mutual information is calculated (see Methods), producing a matrix of information values.
The multivariate approach to mutual information [ 11, 12] (see Methods) makes it possible to analyse the different components that define the information flow in this quaternary complex.
To quantify how much each of the GroEL paralogs has diverged not only functionally at particular sites but also in their evolutionary paths from GroEL1, we applied mutual information based coevolution analyses (see methods for details) between GroEL1 and GroEL2 and GroEL1 and GroEL3.
One can see that mutual information fails to reflect the spatial structure of a single realisation of an environment.
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