Defines the H_α family of balance indices for phylogenetic networks, establishes structural properties including a grafting property, and analyzes minima, maxima, and distributions under random models such as Yule and PDA.
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2 Pith papers cite this work. Polarity classification is still indexing.
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Proves E[max_j | (1/n) sum_i ε_ij |] ≥ min{255/256, (1/sqrt(2 log 2)) sqrt(log(2p)/n)} with equality for (n,p)=(2,1) and (2,8).
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A parameterized family of balance indices for phylogenetic networks
Defines the H_α family of balance indices for phylogenetic networks, establishes structural properties including a grafting property, and analyzes minima, maxima, and distributions under random models such as Yule and PDA.
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Notes on constants for maxima of Rademacher averages
Proves E[max_j | (1/n) sum_i ε_ij |] ≥ min{255/256, (1/sqrt(2 log 2)) sqrt(log(2p)/n)} with equality for (n,p)=(2,1) and (2,8).