The rapidly growing availability of multigene sequence data during the past decade has enabled phylogeny estimation at phylogenomic scales. However, dealing with evolutionary process heterogeneity across the genome becomes increasingly challenging. Here we develop a mixture model approach that uses reversible jump Markov chain Monte Carlo (MCMC) estimation to permit as many distinct models as t...

In this paper we consider the problem of determining a balanced ordering of the vertices of a graph; that is, the neighbors of each vertex v are as evenly distributed to the left and right of v as possible. This problem, which has applications in graph drawing for example, is shown to be NP-hard, and remains NP-hard for bipartite simple graphs with maximum degree six. We then describe and analy...

It has been postulated that existing species have been linked in the past in a way that can be described using an additive tree structure. Any such tree structure reflecting species relationships is associated with a matrix of distances between the species considered which is called a distance matrix or a tree metric matrix. A circular order of elements of X corresponds to a circular (clockwise...

Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been studied extensively in the context of crossing number problems. We consider a natural class of simple topological drawings of complete bipartite graphs, in ...

We consider the problem of bipartitioning a circuit into two balanced components that minimizes the number of crossing nets. Previously, Kernighan and Lin type (K&L) heuristics, simulated annealing approach, and analytical methods were given to solve the problem. However, network flow (maxflow min-cut) techniques were overlooked as viable heuristics to min-cut balanced bipartition due to their ...

It has been postulated that existing species have been linked in the past in a way that can be described using an additive tree structure. Any such tree structure reflecting species relationships is associated with a matrix of distances between the species considered and called a distance matrix or a tree metric matrix. A circular order of elements of X corresponds to a circular (clockwise) sca...

The multi-copy internal transcribed spacer (ITS) region of nuclear ribosomal DNA is widely used to infer phylogenetic relationships among closely related taxa. Here we use maximum likelihood (ML) and splits graph analyses to extract phylogenetic information from approximately 600 mostly cloned ITS sequences, representing 81 species and subspecies of Acer, and both species of its sister Dipteron...

A conjecture of Luo, Tian and Wu (2022) says that for every positive integer k finite tree T with bipartition X Y (denote t=max⁡{|X|,|Y|}), k-connected bipartite graph G δ(G)≥k+t contains a subtree T′≅T such κ(G−V(T′))≥k. In this paper, we confirm caterpillars when k=3 spiders k≤3.