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1. Notes on Growing a Tree in a Graph

   Devroye, L.; Dujmović, V.; Frieze, A.; Mehrabian, A.; Morin, P.; Reed, B. (January 2019, Random structures algorithms)

   We study the height of a spanning tree $$T$$ of a graph $$G$$ obtained by starting with a single vertex of $$G$$ and repeatedly selecting, uniformly at random, an edge of $$G$$ with exactly one endpoint in $$T$$ and adding this edge to $$T$$. 

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2. On tree longevity

   https://doi.org/10.1111/nph.17148  

   Piovesan, Gianluca; Biondi, Franco (January 2021, New Phytologist)

   Summary Large, majestic trees are iconic symbols of great age among living organisms. Published evidence suggests that trees do not die because of genetically programmed senescence in their meristems, but rather are killed by an external agent or a disturbance event. Long tree lifespans are therefore allowed by specific combinations of life history traits within realized niches that support resistance to, or avoidance of, extrinsic mortality. Another requirement for trees to achieve their maximum longevity is either sustained growth over extended periods of time or at least the capacity to increase their growth rates when conditions allow it. The growth plasticity and modularity of trees can then be viewed as an evolutionary advantage that allows them to survive and reproduce for centuries and millennia. As more and more scientific information is systematically collected on tree ages under various ecological settings, it is becoming clear that tree longevity is a key trait for global syntheses of life history strategies, especially in connection with disturbance regimes and their possible future modifications. In addition, we challenge the long‐held notion that shade‐tolerant, late‐successional species have longer lifespans than early‐successional species by pointing out that tree species with extreme longevity do not fit this paradigm. Identifying extremely old trees is therefore the groundwork not only for protecting and/or restoring entire landscapes, but also to revisit and update classic ecological theories that shape our understanding of environmental change. 

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3. Shared Information for a Markov Chain on a Tree

   https://doi.org/10.1109/ISIT50566.2022.9834365  

   Bhattacharya, Sagnik; Narayan, Prakash (June 2022, Proceedings of the 2022 IEEE Symposium on Information Theory)
4. Shared Information for a Markov Chain on a Tree

   https://doi.org/10.1109/TIT.2024.3353769  

   Bhattacharya, Sagnik; Narayan, Prakash (January 2024, IEEE Transactions on Information Theory)

   Veeravalli, V. V. (Ed.)

   Abstract—Shared information is a measure of mutual de- pendence among multiple jointly distributed random variables with finite alphabets. For a Markov chain on a tree with a given joint distribution, we give a new proof of an explicit characterization of shared information. The Markov chain on a tree is shown to possess a global Markov property based on graph separation; this property plays a key role in our proofs. When the underlying joint distribution is not known, we exploit the special form of this characterization to provide a multiarmed bandit algorithm for estimating shared information, and analyze its error performance. 

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5. Shared Information for a Markov Chain on a Tree

   Bhattacharya, S; Narayan, P. (January 2024, IEEE transactions on information theory)