Related papers: Branching Processes -- A General Concept
This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…
The general theory of the branching processes is used for establishing the relation between the parameters $k$ and $\bar n$ of the negative binomial distribution. This relation gives the possibility to describe the overall data on…
Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical…
Consider a branching Markov process with values in some general type space. Conditional on survival up to generation $N$, the genealogy of the extant population defines a random marked metric measure space, where individuals are marked by…
The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank (consisting of dormant individuals) when facing fluctuating…
In a supercritical branching particle system, the trimmed tree consists of those particles which have descendants at all times. We develop this concept in the superprocess setting. For a class of continuous superprocesses with Feller…
We introduce the notion of a hereditary property for rooted real trees and we also consider reduction of trees by a given hereditary property. Leaf-length erasure, also called trimming, is included as a special case of hereditary reduction.…
Consider the diffusion process defined by the forward equation $u_t(t, x) = \tfrac{1}{2}\{x u(t, x)\}_{xx} - \alpha \{x u(t, x)\}_{x}$ for $t, x \ge 0$ and $-\infty < \alpha < \infty$, with an initial condition $u(0, x) = \delta(x - x_0)$.…
Phylogenetic trees represent the evolutionary relationships between extant lineages, where extinct or non-sampled lineages are omitted. Extending the work of Stadler and collaborators, this paper focuses on the branch lengths in…
We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that is…
We consider an indecomposable Galton-Watson branching process with countably infinitely many types. Assuming that the process is critical and allowing for infinite variance of the offspring sizes of some (or all) types of particles we…
Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…
It is well-known that conditioning a supercritical (multi-type) branching process on the event that it eventually becomes extinct yields a subcritical branching process. We study the corresponding inverse problem: given a subcritical…
This note investigates core properties of martingales, emphasizing the measure-theoretic formulation of conditional expectation, the martingale transform, and the upcrossing lemma. These results lead to the Martingale Convergence Theorem,…
Learning a categorical distribution comes with its own set of challenges. A successful approach taken by state-of-the-art works is to cast the problem in a continuous domain to take advantage of the impressive performance of the generative…
We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…
Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply…
We prove an invariance principle for a general class of continuous time critical branching processes with finite variance (non-local) branching mechanism. We show that the genealogical trees, viewed as random compact metric measure spaces,…
To offer a view into the rapidly developing theory of fractional diffusion processes we describe in some detail three topics of present interest: (i) the well-scaled passage to the limit from continuous time random walk under power law…
We propose a framework for solving evolution equations within parametric function classes, especially ones that are specified by neural networks. We call this framework the minimal neural evolution (MNE) because it is motivated by the goal…