Related papers: Time reversal dualities for some random forests
Recently, a first step was made by the authors towards a systematic investigation of the effect of reaction-step-size noise - uncertainty in the step size of the reaction - on the dynamics of stochastic populations. This was done by…
As a model of trapping by biased motion in random structure, we study the time taken for a biased random walk to return to the root of a subcritical Galton-Watson tree. We do so for trees in which these biases are randomly chosen,…
We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…
Forward-time models of diversification (i.e., speciation and extinction) produce phylogenetic trees that grow "vertically" as time goes by. Pruning the extinct lineages out of such trees leads to natural models for reconstructed trees…
We consider a population with two types of individuals, distinguished by the resources required for reproduction: type-$0$ (small) individuals need a fractional resource unit of size $\vartheta \in (0,1)$, while type-$1$ (large) individuals…
In the absence of horizontal gene transfer it is possible to reconstruct the history of gene families from empirically determined orthology relations, which are equivalent to event-labeled gene trees. Knowledge of the event labels…
Rooted trees with probabilities are used to analyze properties of a variable length code. A bound is derived on the difference between the entropy rates of the code and a memoryless source. The bound is in terms of normalized informational…
We calculate the density and expectation for the number of lineages in a reconstructed tree with $n$ extant species. This is done with conditioning on the age of the tree as well as with assuming a uniform prior for the age of the tree.
We consider a family of fragmentation processes where the rate at which a particle splits is proportional to a function of its mass. Let $F\_{1}^{(m)}(t),F\_{2}^{(m)}(t),...$ denote the decreasing rearrangement of the masses present at time…
A classical result, fundamental to evolutionary biology, states that an edge-weighted tree $T$ with leaf set $X$, positive edge weights, and no vertices of degree 2 can be uniquely reconstructed from the set of leaf-to-leaf distances…
Random survival forest and survival trees are popular models in statistics and machine learning. However, there is a lack of general understanding regarding consistency, splitting rules and influence of the censoring mechanism. In this…
The ongoing explosion of genome sequence data is transforming how we reconstruct and understand the histories of biological systems. Across biological scales, from individual cells to populations and species, trees-based models provide a…
We consider a branching population where individuals live and reproduce independently. Their lifetimes are i.i.d. and they give birth at a constant rate b. The genealogical tree spanned by this process is called a splitting tree, and the…
This review paper presents the known results on the asymptotics of the survival probability and limit theorems conditioned on survival of critical and subcritical branching processes in IID random environments. The key assumptions of the…
We consider the model of random trees introduced by Devroye [SIAM J. Comput. 28 (1999) 409-432]. The model encompasses many important randomized algorithms and data structures. The pieces of data (items) are stored in a randomized fashion…
We analyse a simple discrete-time stochastic process for the theoretical modeling of the evolution of protein lengths. At every step of the process a new protein is produced as a modification of one of the proteins already existing and its…
In a population with haploid reproduction any individual has a single parent in the previous generation. If all genealogical distances among pairs of individuals (generations from the closest common ancestor) are known it is possible to…
The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
An early burst of speciation followed by a subsequent slowdown in the rate of diversification is commonly inferred from molecular phylogenies. This pattern is consistent with some verbal theory of ecological opportunity and adaptive…