Related papers: The Aldous-Shields model revisited (with applicati…
Tree-size distribution is one of the most investigated subjects in plant population biology. The forestry literature reports that tree-size distribution trajectories vary across different stands and/or species, while the metabolic scaling…
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…
Modeling the distribution of high dimensional data by a latent tree graphical model is a prevalent approach in multiple scientific domains. A common task is to infer the underlying tree structure, given only observations of its terminal…
Consider a random recusive tree with n vertices. We show that the number of vertices with even depth is asymptotically normal as n tends to infinty. The same is true for the number of vertices of depth divisible by m for m=3, 4 or 5; in all…
Random forests are an ensemble method relevant for many problems, such as regression or classification. They are popular due to their good predictive performance (compared to, e.g., decision trees) requiring only minimal tuning of…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
Consider a $d$-ary rooted tree ($d\geq3$) where each edge $e$ is assigned an i.i.d. (bounded) random variable $X(e)$ of negative mean. Assign to each vertex $v$ the sum $S(v)$ of $X(e)$ over all edges connecting $v$ to the root, and assume…
Inspired by biological dynamics, we consider a growth Markov process taking values on the space of rooted binary trees, similar to the Aldous-Shields model. Fix $n\ge 1$ and $\beta>0$. We start at time 0 with the tree composed of a root…
For a labeled tree on the vertex set $\set{1,2,\ldots,n}$, the local direction of each edge $(i\,j)$ is from $i$ to $j$ if $i<j$. For a rooted tree, there is also a natural global direction of edges towards the root. The number of edges…
Rotation distances measure the differences in structure between rooted ordered binary trees. The one-dimensional skeleta of associahedra are rotation graphs, where two vertices representing trees are connected by an edge if they differ by a…
Phylogenetic networks extend phylogenetic trees to model non-vertical inheritance, by which a lineage inherits material from multiple parents. The computational complexity of estimating phylogenetic networks from genome-wide data with…
In this paper, an automatic seeded region growing algorithm is proposed for cellular image segmentation. First, the regions of interest (ROIs) extracted from the preprocessed image. Second, the initial seeds are automatically selected based…
The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching degree. Aldous's Brownian continuum random tree, the…
We consider Galton--Watson trees conditioned on both the total number of vertices $n$ and the number of leaves $k$. The focus is on the case in which both $k$ and $n$ grow to infinity and $k = \alpha n + O(1)$, with $\alpha \in (0, 1)$.…
In this paper, we use tree partition schemes and an algebraic expression for the virial coefficients in terms of the cluster coefficients in order to derve upper bounds on the virial coefficients and consequently lower bounds on the radius…
Various modifications of decision trees have been extensively used during the past years due to their high efficiency and interpretability. Tree node splitting based on relevant feature selection is a key step of decision tree learning, at…
Leaves, i.e., vertices of degree one, can play a significant role in graph structure, especially in sparsely connected settings in which leaves often constitute the largest fraction of vertices. We consider a leaf-based counterpart of the…
Using topological summaries of gene trees as a basis for species tree inference is a promising approach to obtain acceptable speed on genomic-scale datasets, and to avoid some undesirable modeling assumptions. Here we study the…
We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that…