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The original Hardenberg's model of biomass patterns in arid and semi-arid regions is revisited to extend it to more general non flat regions. It is proposed a technique to study these more generalized (non-flat) regions using both a…
We introduce random survival forests, a random forests method for the analysis of right-censored survival data. New survival splitting rules for growing survival trees are introduced, as is a new missing data algorithm for imputing missing…
The Drossel-Schwabl Forest Fire Model is one of the best studied models of non-conservative self-organised criticality. However, using a new algorithm, which allows us to study the model on large statistical and spatial scales, it has been…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
Random forests are a very effective and commonly used statistical method, but their full theoretical analysis is still an open problem. As a first step, simplified models such as purely random forests have been introduced, in order to shed…
We consider the one-dimensional generalized forest fire process: at each site of $\zz$, seeds and matches fall according some i.i.d. stationary renewal processes. When a seed falls on an empty site, a tree grows immediately. When a match…
We discuss the scaling behavior of the self-organized critical forest-fire model on large length scales. As indicated in earlier publications, the forest-fire model does not show conventional critical scaling, but has two qualitatively…
Prescribed burns have been increasingly utilized in forest management in the past few decades. However, their effectiveness in reducing the risk of destructive wildfires has been debated. The sandpile model of self-organized criticality,…
Species extinction is a core process that affects the diversity of life on Earth. Competition between species in a population is considered by ecological niche-based theories as a key factor leading to different severity of species…
Forecasting bushfire spread is an important element in fire prevention and response efforts. Empirical observations of bushfire spread can be used to estimate fire response under certain conditions. These observations form rate-of-spread…
Using local detailed balance we rewrite the Kirchhoff formula for stationary distribution of Markov jump processes in terms of a physically interpretable tree-ensemble. We use that arborification of path-space integration to derive a…
The issue of estimating residual variance in regression models has experienced relatively little attention in the machine learning community. However, the estimate is of primary interest in many practical applications, e.g. as a primary…
Vegetation in semi-arid ecosystems frequently organizes into spatially heterogeneous mosaics that regulate ecosystem functioning, productivity, and resilience. These patterns arise from local biological interactions, including facilitation…
Simple stochastic models for phylogenetic trees on species have been well studied. But much paleontology data concerns time series or trees on higher-order taxa, and any broad picture of relationships between extant groups requires use of…
We give examples of data-generating models under which Breiman's random forest may be extremely slow to converge to the optimal predictor or even fail to be consistent. The evidence provided for these properties is based on mostly intuitive…
Random forests are a learning algorithm proposed by Breiman [Mach. Learn. 45 (2001) 5--32] that combines several randomized decision trees and aggregates their predictions by averaging. Despite its wide usage and outstanding practical…
Tree-based methods are popular nonparametric tools in studying time-to-event outcomes. In this article, we introduce a novel framework for survival trees and ensembles, where the trees partition the dynamic survivor population and can…
We study generalizations of the Forest Fire model introduced in [van den Berg, J., and J\'arai, A. A. "On the asymptotic density in a one-dimensional self-organized critical forest-fire model". Comm. Math. Phys. 253 (2005)] and [Volkov,…
Thanks to recent advances in generative AI, computers can now simulate realistic and complex natural processes. We apply this capability to predict how wildfires spread, a task made difficult by the unpredictable nature of fire and the…