This paper introduces two new crossover operators for Genetic Programming (GP). Contrary to the regular GP crossover, the operators presented attempt to preserve the context in which subtrees appeared in the parent trees. A simple coordinate scheme for nodes in an S-expression tree is proposed, and crossovers are only allowed between nodes with exactly or partially matching coordinates.

Binary trees are essential structures in Computer Science. The leaf (leaves) of a binary tree is one of the most significant aspects of it. In this study, we prove that the order of a leaf (leaves) of a binary tree is the same in the main tree traversals; preorder, inorder, and postorder. Then, we prove that given the preorder and postorder traversals of a binary tree, the leaf (leaves) of a bi...

We offer some new identities for a bipartition function, which has a relation to a Hecke-type identity of Andrews. Further, we show this partition function is lacunary, and relate it to a real quadratic field.

Introduction: Children with Apert syndrome have hypertelorism and midfacial hypoplasia, which can be treated facial bipartition (FB), often aided by rigid external distraction. The technique involves a midline osteotomy that lateralizes the maxillary segments, resulting in posterior cross-bites diastema. Varying degrees of spontaneous realignment dental arches occurs postoperatively. This study...

Bipartition support in maximum-likelihood (ML) analysis is most commonly assessed using the nonparametric bootstrap. Although bootstrap replicates should theoretically be analyzed in the same manner as the original data, model selection is almost never conducted for bootstrap replicates, substitution-model parameters are often fixed to their maximum-likelihood estimates (MLEs) for the empirical...

We show two results related to the Hamiltonicity and k-Path algorithms in undirected graphs by Björklund [FOCS’10], and Björklund et al., [arXiv’10]. First, we demonstrate that the technique used can be generalized to finding some k-vertex tree with l leaves in an n-vertex undirected graph in O(1.6572) time. It can be applied as a subroutine to solve the k-Internal Spanning Tree (k-IST) problem...