Related papers: Detection of cellular aging in a Galton-Watson pro…
We study locally interacting processes in discrete time, often called probabilistic cellular automata, indexed by locally finite graphs. For infinite regular trees and certain generalized Galton-Watson trees, we show that the marginal…
We consider a discrete-time host-parasite model for a population of cells which are colonized by proliferating parasites. The cell population grows like an ordinary Galton-Watson process, but in reflection of real biological settings the…
We present a new pruning procedure on discrete trees by adding marks on the nodes of trees. This procedure allows us to construct and study a tree-valued Markov process $\{{\cal G}(u)\}$ by pruning Galton-Watson trees and an analogous…
In this paper, we study the Galton-Watson process in the random environment for the particular case when the number of the offsprings in each generation has the fractional linear generation function with random parameters. In this case, the…
Multi-model inference covers a wide range of modern statistical applications such as variable selection, model confidence set, model averaging and variable importance. The performance of multi-model inference depends on the availability of…
Consider a branching process with a homogeneous reproduction law. Sampling a single cell uniformly from the population at a time $T > 0$ and looking along the sampled cell's ancestral lineage, we find that the reproduction law is…
We introduce a simple tree growth process that gives rise to a new two-parameter family of discrete fragmentation trees that extends Ford's alpha model to multifurcating trees and includes the trees obtained by uniform sampling from…
We consider the problem of estimating the elapsed time since the most recent common ancestor of a finite random sample drawn from a population which has evolved through a Bienayme-Galton-Watson branching process. More specifically, we are…
We study the exponential growth of bifurcating processes with ancestral dependence. We suppose here that the lifetimes of the cells are dependent random variables, that the numbers of new cells are random and dependent. Lifetimes and new…
In this paper we consider inhomogeneous Galton-Watson trees, and derive various moments for such processes: the number of vertices, the number of leaves, and the height of the tree. Also we make a simple condition of finiteness. We use…
Lifespan distributions of populations of quite diverse species such as humans and yeast seem to surprisingly well follow the same empirical Gompertz-Makeham law, which basically predicts an exponential increase of mortality rate with age.…
Consider any supercritical Galton-Watson process which may become extinct with positive probability. It is a well-understood and intuitively obvious phenomenon that, on the survival set, the process may be pathwise decomposed into a…
We present a new technique to segregate old and young stellar populations in galactic spectra using machine learning methods. We used an ensemble of classifiers, each classifier in the ensemble specializes in young or old populations and…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
Recent methods have been developed to map single-cell lineage statistics to population growth. Because population growth selects for exponentially rare phenotypes, these methods inherently depend on sampling large deviations from finite…
Recent methodological advances are enabling better examination of speciation and extinction processes and patterns. A major open question is the origin of large discrepancies in species number between groups of the same age. Existing…
We consider multi-type Galton Watson trees, and find the distribution of these trees when conditioning on very general types of recursive events. It turns out that the conditioned tree is again a multi-type Galton Watson tree, possibly with…
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 a multi-type Galton-Watson branching processes, where the largest in magnitude positive eigenvalue $\rho$ of the first moments matrix is close to unity. Specifically, we examine the random vector representing the number of…
We study the long-term behavior of weighted multi-type branching processes, focusing on extending classical laws of large numbers and martingale convergence to settings with infinitely many weighted particles, arbitrary type spaces and…