Related papers: Estimates for Nonlinear Harmonic Measures on Trees
The mutational heterogeneity of tumours can be described with a tree representing the evolutionary history of the tumour. With noisy sequencing data there may be uncertainty in the inferred tree structure, while we may also wish to study…
Binary rooted trees, both in the ordered and in the un-ordered case, are well studied structures in the field of combinatorics. The aim of this work is to study particular patterns in these classes of trees. We consider completely…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
The trace $\tr(q(\ma{L} + q\ma{I})^{-1})$, where $\ma{L}$ is a symmetric diagonally dominant matrix, is the quantity of interest in some machine learning problems. However, its direct computation is impractical if the matrix size is large.…
Effects like selection in evolution as well as fertility inheritance in the development of populations can lead to a higher degree of asymmetry in evolutionary trees than expected under a null hypothesis. To identify and quantify such…
We propose a new, direct, correlation-free approach based on central moments of profiles to the asymptotics of width (size of the most abundant level) in some random trees of logarithmic height. The approach is simple but gives precise…
We apply dimensional analysis with Buckinghams "Pi" theorem to estimate the volume of wood in a tree stem, given the tree's height and diameter. We use Meyer's (1953) data on 31 cherry trees from the Allegheny National forest as the main…
We establish an inequality which involves a non-negative function defined on the vertices of a finite $m$-ary regular rooted tree. The inequality may be thought of as relating an interaction energy defined on the free vertices of the tree…
In this paper, we use the H2 norm associated with a communication graph to characterize the robustness of consensus to noise. In particular, we restrict our attention to trees and by systematic attention to the effect of local changes in…
Regression methods for interval-valued data have been increasingly studied in recent years. As most of the existing works focus on linear models, it is important to note that many problems in practice are nonlinear in nature and therefore…
Many scientific and engineering challenges -- ranging from personalized medicine to customized marketing recommendations -- require an understanding of treatment effect heterogeneity. In this paper, we develop a non-parametric causal forest…
Tree-based ensemble methods, as Random Forests and Gradient Boosted Trees, have been successfully used for regression in many applications and research studies. Furthermore, these methods have been extended in order to deal with uncertainty…
Machine learning methods for estimating treatment effect heterogeneity promise greater flexibility than existing methods that test a few pre-specified hypotheses. However, one problem these methods can have is that it can be challenging to…
Large deviation estimates for the following linear parabolic equation are studied: \[ \frac{\partial u}{\partial t}=\tr\Big(a(x)D^2u\Big) + b(x)\cdot D u + \int_{\R^N} \Big\{(u(x+y)-u(x)-(D u(x)\cdot y)\ind{|y|<1}(y)\Big\}\d\mu(y), \] where…
In a rooted tree, we call a vertex {\em balanced} if it is at equal distance from all its descendant leaves. We count balanced vertices in three different tree varieties. For decreasing binary trees, we can prove that the probability that a…
The goal of branch length estimation in phylogenetic inference is to estimate the divergence time between a set of sequences based on compositional differences between them. A number of software is currently available facilitating branch…
The buildup and release of a sense of tension is one of the most essential aspects of the process of listening to music. A veridical computational model of perceived musical tension would be an important ingredient for many music…
In this paper, we prove that any subset with an appropriate sub-linear horizontal growth has a non-zero stationary harmonic measure. On the other hand, we also show any subset with super-linear horizontal growth will have a $0$ stationary…
Let $T$ be a tree with induced partial order $\preceq$. We investigate centered Gaussian processes $X=(X_t)_{t\in T}$ represented as $$ X_t=\sigma(t)\sum_{v \preceq t}\alpha(v)\xi_v $$ for given weight functions $\alpha$ and $\sigma$ on $T$…
The analysis of the internal structure of trees is highly important for both forest experts, biological scientists, and the wood industry. Traditionally, CT-scanners are considered as the most efficient way to get an accurate inner…