Related papers: Dimensional analysis in forest mensuration
We study the random m-ary search tree model (where m stands for the number of branches of a search tree), an important problem for data storage in computer science, using a variety of statistical physics techniques that allow us to obtain…
In this paper, we show how the notion of tree dimension can be used in the verification of constrained Horn clauses (CHCs). The dimension of a tree is a numerical measure of its branching complexity and the concept here applies to Horn…
Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy and medicine. Although trees are estimated, their uncertainties are discarded by mathematicians working in tree space. Here we explicitly…
Empirical observations suggest that in pure even-aged forests, the mean diameter of forest trees (D, diameter at breast height, 1.3 m above ground) tends to remain a constant proportion of stand height (H, average height of the largest…
The properties of scale-free random trees are investigated using both preconditioning on non-extinction and fixed size averages, in order to study the thermodynamic limit. The scaling form of volume probability is found, the connectivity…
Trees are key components of the terrestrial biosphere, playing vital roles in ecosystem function, climate regulation, and the bioeconomy. However, large-scale monitoring of individual trees remains limited by inadequate modelling. Available…
Let $T$ be a weighted tree. The weight of a subtree $T_1$ of $T$ is defined as the product of weights of vertices and edges of $T_1$. We obtain a linear-time algorithm to count the sum of weights of subtrees of $T$. As applications, we…
Decision trees are popular machine learning models that are simple to build and easy to interpret. Even though algorithms to learn decision trees date back to almost 50 years, key properties affecting their generalization error are still…
The diameter distribution of a given species of deciduous trees in mature, temperate zone forests is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data…
By computations on generating functions, Szekeres proved in 1983 that the law of the diameter of a uniformly distributed rooted labelled tree with n vertices, rescaled by a factor n^{1/2} , converges to a distribution whose density is…
Vegetation, trees in particular, sequester carbon by absorbing carbon dioxide from the atmosphere. However, the lack of efficient quantification methods of carbon stored in trees renders it difficult to track the process. We present an…
In this paper we give some estimates for nonlinear harmonic measures on trees. In particular, we estimate in terms of the size of a set $D$ the value at the origin of the solution to $ u(x)=F((x,0),\dots,(x,m-1))$ for every…
Treemaps are a popular technique to visualize hierarchical data. The input is a weighted tree $\tree$ where the weight of each node is the sum of the weights of its children. A treemap for $\tree$ is a hierarchical partition of a rectangle…
Nation-wide Sentinel-2 mosaics were used with National Forest Inventory (NFI) data for modelling and subsequent mapping of spruce, pine and deciduous forest in Norway in 16 m $\times$ 16 m resolution. The accuracies of the best model ranged…
Density Estimation Trees can play an important role in exploratory data analysis for multidimensional, multi-modal data models of large samples. I briefly discuss the algorithm, a self-optimization technique based on kernel density…
Dimensional analysis, and in particular the Buckingham $\Pi$ theorem is widely used in fluid mechanics. In this article we obtain an expression for the impact parameter from Buckingham's theorem and we compare our result with Rutherford's…
Forest inventories rely on accurate measurements of the diameter at breast height (DBH) for ecological monitoring, resource management, and carbon accounting. While LiDAR-based techniques can achieve centimeter-level precision, they are…
The Buckingham's $\pi$, theorem has been recently introduced in the context of Non destructive Testing \& Evaluation (NdT\&E) , giving a theoretical basis for developing simple but effective methods for multi-parameter estimation via…
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…
We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new…