1. What have the authors contributed in "Quantifying high-order interdependencies via multivariate extensions of the mutual information" ?
Fernando E. Rosas, Pedro A. M. Mediano, Michael Gastpar,4 and Henrik J. Jensen this paper
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2. What is the common approach to address high-order interactions in the statistical physics literature?
OF HIGH-ORDER EFFECTSA popular approach to address high-order interactions in the statistical physics literature is via Hamiltonians that include interaction terms with three or more variables [12].
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3. What can be done to avoid the need to compute the PID of the whole system?
the local O-information can be employed to identify subsystems with interesting highorder properties, which can guide the application of PID analyses while avoiding the need of computing the PID of the whole system.
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4. What is the weight of the edge joining 1 and 2?
If the edge joining π1 and π2 has a weight v(π1, π2) associated, then the corresponding path weight of p = (π1, . . . , πL ) is merely the summation of all edge weights along p:W (p; v) := L−1∑ k=1 v(πk, πk+1).
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![FIG. 1. The total information that can be stored in the system X n ( ∑n j=1 log |X j |) is decomposed by a given state of knowledge (i.e., a probability distribution) into two parts: what is determined by the constraints [the negentropy, N (X n)] and what is not instantiated until an actual measurement takes place [the entropy, H (X n)]. Both terms can be further decomposed into their individual and collective components, yielding different perspectives on interdependency seen as either collective constraints [measured by the total correlation TC(X n)] or shared randomness [corresponding to the dual total correlation DTC(X n)].](/figures/fig-1-the-total-information-that-can-be-stored-in-the-system-1l00a4mr.webp)
