22 papers · ranked by Valyu relevance
Larry Riddle
Mandelbrot and Frame studied the geometry of self-contracting symmetric binary trees in which they stated that the height of such trees occurred at the branch tip of the path consisting of branches that alternate left and right. Taylor proved that this happens for both self-avoiding as well as self-contacting symmetric…
Ziad Ismaili Alaoui, Detlef Plump
We present an approach to implement binary search trees in the rule-based graph programming language GP 2. (See [[4]] for a brief introduction to GP 2.) Our implementation uses GP 2's rooted graph transformation rules to be fast [[1]] and supports insertion, deletion and query operations. We argue that the worst-case…
Daniel Brosch, Diane Puges
The inducibility of a graph represents its maximum density as an induced subgraph over all possible sequences of graphs of size growing to infinity. This invariant of graphs has been extensively studied since its introduction in 1975 by Pippenger and Golumbic. In 2017, Czabarka, Székely and Wagner extended this notion…
Olivier Bodini, Antoine Genitrini, Khaydar Nurligareev
We study the extreme local structure of plane binary trees through the distribution of leaves at maximum depth. We first address two basic questions: (i) the asymptotic probability that exactly two leaves occur at the deepest level, and (ii) the asymptotic mean number of leaves at that level. These problems lead to…
Mathieu Gascon, Mattéo Delabre, Nadia El-Mabrouk
We present FullSynesth, a tree reconciliation algorithm predicting the evolution of a set of homologous genomic regions or syntenies, inside a species tree. The considered evolutionary model involves segmental events (i.e. acting on multiple genes) including duplications (D), losses (L), synteny fissions and transfers…
Luc Devroye, Michael R. Doboli, Noah A. Rosenberg, Stephan Wagner
The Colijn-Plazzotta ranking is a bijective encoding of the unlabeled binary rooted trees with positive integers. We show that the rank f(t) of a tree t is closely related to its height h, the maximal path length from a leaf to the root. We consider the rank $f\tau _n$ of a random n-leaf tree $\tau _n$ under each of…
Michael Goodrich, Yan Gu, Ryuto Kitagawa, Yihan Sun
Balanced search trees are widely used in computer science to efficiently maintain dynamic ordered data. To support efficient set operations (e.g., union, intersection, difference) using trees, the join-based framework is widely studied. This framework has received particular attention in the parallel setting, and has…
Chris Jennings-Shaffer, Cherith Chen, Julia A Palacios, Frederick A Matsen IV
Phylogenetic tree shapes capture fundamental signatures of evolution. We consider “ranked” tree shapes, which are equipped with a total order on the internal nodes compatible with the tree graph. Recent work has established an elegant bijection of ranked tree shapes and a class of integer matrices, called $F$-matrices…
Chris Jennings-Shaffer, Ziyue Cherith Chen, Julia A Palacios, Frederick A Matsen IV
Phylogenetic tree shapes capture fundamental signatures of evolution. We consider “ranked” tree shapes, which are equipped with a total order on the internal nodes compatible with the tree graph. Recent work has established an elegant bijection between ranked tree shapes and a class of integer matrices, called…
Rachel Parsons, Yunzhuo Liu, Parth Dua, Alexey Markin + 1 more
ASTRAL-pro is the leading method for reconstructing species trees under complex evolutionary scenarios involving gene duplication, loss, and coalescence. A major open question is whether ASTRAL-pro is statistically consistent under a unified model of these processes, called DLCoal. This question is challenging to…
Sean P. Svihla, Manuel E. Lladser
Haar-like wavelets sparsify the phylogenetic covariance matrices of large, uniformly random k-regular trees with overwhelmingly high probability. This motivates the Haar-like distance, a β-diversity metric that implicitly ranks the splits of a reference phylogeny by their relevance in differentiating two microbial…
Jiaqi Wu
Many comparative analyses operate on rectangular matrices whose columns represent the same variables across observations. Phylogenomic measurements, however, are attached to tree branches. Converting locus-specific trees into a common locus-by-coordinate matrix is straightforward only when loci contain the same taxa…
Gryte Satas, Matthew A. Myers, Sohrab P. Shah
The binary perfect phylogeny, in which each mutation arises exactly once on an evolutionary tree and is never lost, is a well-studied idealized phylogenetic model. When observed data has errors, a common approach to phylogeny inference is to seek a tree that minimizes the number of error corrections (“flips”) needed to…
Yuki Takazawa, Atsushi Takeda, Momoko Hayamizu, Olivier Gascuel
Phylogenetic analyses often require the summarization of multiple trees, e.g., in Bayesian analyses to obtain the centroid of the posterior distribution of trees, or to determine the consensus of a set of bootstrap trees. The majority-rule consensus tree is the most commonly used. It is easy to compute and minimizes…
Sarthak R. Mishra, Matthew W. Hahn
Many methods can be used to infer the number and timing of gene duplication and loss events from gene trees. Most such reconciliation methods use a model of gene duplication that does not include the coalescent process, or that restricts it in important ways. As a result, changes to tree topologies due to coalescence…
Sabino Francesco Roselli, Eibe Frank
Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to “classic” decision trees with constant values in their leaves, model trees can use linear combinations of predictor variables in their leaf nodes to form predictions, which can…
Luise Häuser, Alexandros Stamatakis
While there exists a plethora of prior research on phylogenetic tree shape indices, a largescale analysis of the behavior of these indices on empirical trees has not yet been conducted. Here, we address this by computing 54 indices on more than 45,000,000 empirical trees retrieved from the EvoNAPS and RAxML Grove…
Russell A. Brown
Two methods have been proposed for building and modifying a dynamic k-d tree. One method stores the dynamic tree as a single k-d tree and rebalances that tree by rebuilding subtrees within the tree when those subtrees become unbalanced due to insertion of a k-dimensional tuple into the tree or deletion of a tuple from…
Anik Saha, Md. Shamsuzzoha Bayzid
Summary methods reconstruct species trees from collections of gene trees while accounting for gene tree discordance and provide a statistically consistent framework for phylogenomic inference under the multispecies coalescent model. While existing triplet- and quartet-based approaches such as ASTRAL and STELAR have…
Authors not listed
Phase equilibrium calculations are crucial in chemical engineering design and optimization processes. The PC-SAFT equation of state (EoS) can precisely calculate phase equilibrium, but is relatively complex and computationally intensive. Surrogate models are mathematically simple models that map or regress the…
Authors not listed
RNA molecules fold into complex three-dimensional structures that determine their function. A wide range of mathematical frameworks, such as chord diagrams, fatgraphs, and context-free grammars, have been used to represent these structures; however, these models have largely been developed from mathematical motivations…
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Terminally labeled DNA oligonucleotides have wide applications in modern biology and biotechnological applications. It has been observed that the fluorescent intensity of light released from these fluorescent labels is heavily influenced by the terminal sequence of nucleotides. Recent studies have assayed and published…