Related papers: Pruning, cut trees, and the reconstruction problem
We study a random fragmentation process and its associated random tree. The process has earlier been studied by Dean and Majumdar (J. Phys. A: Math. Gen., vol. 35, L501--L507), who found a phase transition: the number of fragmentations is…
In recent years, dynamically growing data and incrementally growing number of classes pose new challenges to large-scale data classification research. Most traditional methods struggle to balance the precision and computational burden when…
The broadcasting models on trees arise in many contexts such as discrete mathematics, biology statistical physics and cs. In this work, we consider the colouring model. A basic question here is whether the root's assignment affects the…
Molecular phylogenetic techniques do not generally account for such common evolutionary events as site insertions and deletions (known as indels). Instead tree building algorithms and ancestral state inference procedures typically rely on…
We consider the process of uncovering the vertices of a random labeled tree according to their labels. First, a labeled tree with $n$ vertices is generated uniformly at random. Thereafter, the vertices are uncovered one by one, in order of…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…
This work suggests fundamentally rethinking the current practice of pruning large language models (LLMs). The way it is done is by divide and conquer: split the model into submodels, sequentially prune them, and reconstruct predictions of…
Tree Containment is a fundamental problem in phylogenetics useful for verifying a proposed phylogenetic network, representing the evolutionary history of certain species. Tree Containment asks whether the given phylogenetic tree (for…
The goal of this work is to decompose random populations with a genealogy in subfamilies of a given degree of kinship and to obtain a notion of infinitely divisible genealogies. We model the genealogical structure of a population by…
We study the problem of sampling a uniformly random directed rooted spanning tree, also known as an arborescence, from a possibly weighted directed graph. Classically, this problem has long been known to be polynomial-time solvable; the…
A shift from even-aged forest management to uneven-aged management practices leads to a problem rather different from the existing straightforward practice that follows a rotation cycle of artificial regeneration, thinning of inferior trees…
Trees have long been used as a graphical representation of species relationships. However complex evolutionary events, such as genetic reassortments or hybrid speciations which occur commonly in viruses, bacteria and plants, do not fit into…
We consider a network where an infection cascade has taken place and a subset of infected nodes has been partially observed. Our goal is to reconstruct the underlying cascade that is likely to have generated these observations. We reduce…
We introduce the notion of a hereditary property for rooted real trees and we also consider reduction of trees by a given hereditary property. Leaf-length erasure, also called trimming, is included as a special case of hereditary reduction.…
Reconciling gene trees with a species tree is a fundamental problem to understand the evolution of gene families. Many existing approaches reconcile each gene tree independently. However, it is well-known that the evolution of gene families…
Markov random fields are common prior distributions used in Bayesian inverse imaging problems. In particular, difference priors assign probability distributions to differences between neighbouring pixels, such as Gaussian, Laplace, or…
In this paper, we consider the prediction of the helium concentrations as function of a spatially variable source term perturbed by fractional Brownian motion. For the direct problem, we show that it is well-posed and has a unique mild…
We study the problem of learning tree-structured Markov random fields (MRF) on discrete random variables with common support when the observations are corrupted by a $k$-ary symmetric noise channel with unknown probability of error. For…
The reconstruction of transmission trees for epidemics from genetic data has been the subject of some recent interest. It has been demonstrated that the transmission tree structure can be investigated by augmenting internal nodes of a…
Trace reconstruction is the problem of learning an unknown string $x$ from independent traces of $x$, where traces are generated by independently deleting each bit of $x$ with some deletion probability $q$. In this paper, we initiate the…