Related papers: Selection and Coalescence in a Finite State Model
Individuals do not respond uniformly to treatments, events, or interventions. Sociologists routinely partition samples into subgroups to explore how the effects of treatments vary by covariates like race, gender, and socioeconomic status.…
We show that a coalescence equation exhibits a variety of critical behaviors, depending on the initial condition. This equation was introduced a few years ago to understand a toy model {studied by Derrida and Retaux to mimic} the depinning…
In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching"), and particles that land on an occupied site merge with the…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
In this paper, we consider the knot matching problem arising in computational forestry. The knot matching problem is an important problem that needs to be solved to advance the state of the art in automatic strength prediction of lumber. We…
We develop a marginal treatment effect based method to learn about causal effects in multiple treatment models with discrete instruments. We allow selection into treatment to be governed by a general class of threshold crossing models that…
To model discriminative, i.e. competition induced, self-thinning in even-aged forest stands a concept has been explored that discriminative mortality alters spatial arrangement of trees which in turn alters the mortality. Function of…
Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…
Considering a random binary tree with $n$ labelled leaves, we use a pruning procedure on this tree in order to construct a $\beta(3/2,1/2)$-coalescent process. We also use the continuous analogue of this construction, i.e. a pruning…
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…
We propose a new method of analyzing the asymptotics of moments of certain linear random recurrences which is based on the technique of iterative functions. By using the method, we show that the moments of the number of collisions and the…
There has been renewed interest in understanding the mathematical structure of ecological population models that lead to overcompensation, the process by which a population recovers to a higher level after suffering a permanent increase in…
Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense…
Species tree reconstruction is complicated by effects of Incomplete Lineage Sorting (ILS), commonly modeled by the multi-species coalescent model. While there has been substantial progress in developing methods that estimate a species tree…
Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions and…
We consider the range $R^{(n)}$, the tree made up of visited vertices by a diffusive null-recurrent randomly biased walk $\mathbb{X}$ on a Galton-Watson tree $\mathbb{T}$ up to the $n$-th return time to its root and we consider the…
To learn about the past from a sample of genomic sequences, one needs to understand how evolutionary processes shape genetic diversity. Most population genetic inference is based on frameworks assuming adaptive evolution is rare. But if…
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if…
We study the problem of connecting the parts of a multipartite graph using a minimum number of edges under a matching constraint. We introduce interconnection trees, defined as matchings whose projections onto the quotient graph form a…
Natural selection acts on traits at different scales, often with opposing consequences. This article identifies the particular forces that act at each scale and how those forces combine to determine the overall evolutionary outcome. A…