Related papers: Tree size distribution as the stationary limit of …
Generalized gamma distributions arise as limits in many settings involving random graphs, walks, trees, and branching processes. Pek\"oz, R\"ollin, and Ross (2016, arXiv:1309.4183 [math.PR]) exploited characterizing distributional fixed…
The adoption of agroecological practices will be crucial to address the challenges of climate change and biodiversity loss. Such practices favor the cultivation of plants in complex mixtures with layouts differing from the monoculture…
The appropriate description of fluctuations within the framework of evolutionary game theory is a fundamental unsolved problem in the case of finite populations. The Moran process recently introduced into this context [Nowak et al., Nature…
We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…
The tree-based ensembles are known for their outstanding performance in classification and regression problems characterized by feature vectors represented by mixed-type variables from various ranges and domains. However, considering…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions:…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
An incremental evolution equation, i.e. a Master equation in statistical mechanics, is introduced for force distributions in polydisperse frictional particle packings. As basic ingredients of the Master equation, the conditional probability…
Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field…
A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one…
Over the past decade, random forest models have become widely used as a robust method for high-dimensional data regression tasks. In part, the popularity of these models arises from the fact that they require little hyperparameter tuning…
Many biological studies involve inferring the evolutionary history of a sample of individuals from a large population and interpreting the reconstructed tree. Such an ascertained tree typically represents only a small part of a…
A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age,…
Evolution Strategies (ES) are stochastic derivative-free optimization algorithms whose most prominent representative, the CMA-ES algorithm, is widely used to solve difficult numerical optimization problems. We provide the first rigorous…
We propose a tree-level biomass estimation model approximating allometric equations by LiDAR data. Since tree crown diameters estimation is challenging from spaceborne LiDAR measurements, we develop a model to correlate tree height with…
Conventional grain growth is rate-limited by the mobility of grain boundary. To describe similar phenomena limited by the mobility of other grain junctions, we have developed a general theory allowing for size-dependent mobility and its…
In this paper, we present the description of a simplified model of the dynamic of a mono-specific even-aged forest. The model studied is a tree-growth model based on a system of two ordinary differential equations concerning the tree basal…
Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…
In this work, we investigate the spectrum of singularities of random stable trees with parameter $\gamma\in(1,2)$. We consider for that purpose the scaling exponents derived from two natural measures on stable trees: the local time $\ell^a$…