Related papers: Labeled Chip-firing on Binary Trees with $2^n-1$ C…
We extend Schaeffer's bijection between rooted quadrangulations and well-labeled trees to the general case of Eulerian planar maps with prescribed face valences, to obtain a bijection with a new class of labeled trees, which we call…
Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…
Rooted binary perfect phylogenies provide a generalization of rooted binary unlabeled trees in which each leaf is assigned a positive integer value that corresponds in a biological setting to the count of the number of indistinguishable…
We describe symbolic constructions for listing and enumerating graphs having the same induced edge label sequence. We settle in the affirmative R. Whitty's [W08] conjectured existence of determinantal constructions for listing and…
We study a variant of the chip-firing game called the diffusion game. In the diffusion game, we begin with some integer labelling of the vertices of a graph, interpreted as a number of chips on each vertex, and then for each subsequent step…
Binary relations derived from labeled rooted trees play an import role in mathematical biology as formal models of evolutionary relationships. The (symmetrized) Fitch relation formalizes xenology as the pairs of genes separated by at least…
We demonstrate a method for proving precise concentration inequalities in uniformly random trees on $n$ vertices, where $n\geq1$ is a fixed positive integer. The method uses a bijection between mappings…
Pondering upon the grammatical labeling of 0-1-2 increasing plane trees, we come to the realization that the grammatical labels play a role as records of chopped off leaves of the original increasing binary trees. While such an…
Learning structured outputs with general structures is computationally challenging, except for tree-structured models. Thus we propose an efficient boosting-based algorithm AdaBoost.MRF for this task. The idea is based on the realization…
A modular or distributive lattice is `diamond-colored' if its order diagram edges are colored in such a way that, within any diamond of edges, parallel edges have the same color. Such lattices arise naturally in combinatorial representation…
We propose a generalization of the graphical chip-firing model allowing for the redistribution dynamics to be governed by any invertible integer matrix while maintaining the long term critical, superstable, and energy minimizing behavior of…
We investigate pattern avoidance in permutations satisfying some additional restrictions. These are naturally considered in terms of avoiding patterns in linear extensions of certain forest-like partially ordered sets, which we call binary…
The pivot algorithm is the most efficient known method for sampling polymer configurations for self-avoiding walks and related models. Here we introduce two recent improvements to an efficient binary tree implementation of the pivot…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
The aim of this paper is to study lattice properties of the sharp partial order for complex matrices having index at most 1. We investigate the down-set of a fixed matrix $B$ under this partial order via isomorphisms with two different…
Motivated by the notion of chip-firing on the dual graph of a planar graph, we consider `integral flow chip-firing' on an arbitrary graph $G$. The chip-firing rule is governed by ${\mathcal L}^*(G)$, the dual Laplacian of $G$ determined by…
This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a…
A labeling scheme for nearest common ancestors assigns a distinct binary string, called the label, to every node of a tree, so that given the labels of two nodes (and no further information about the topology of the tree) we can compute the…
We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the…
When genetic algorithms are used to evolve decision trees, key tree quality parameters can be recursively computed and re-used across generations of partially similar decision trees. Simply storing instance indices at leaves is enough for…