Recursive partition and amalgamation with the exponential family: Theory and applications

The theory of tree-growing (RECPAM approach) is developed for outcome variables which are distributed as the canonical exponential family. The general RECPAM approach (consisting of three steps: recursive partition, pruning and amalgamation), is reviewed. This is seen as constructing a partition with maximal information content about a parameter to be predicted, followed by simplification by the elimination of ‘negligible’ information. The measure of information is defined for an exponential family outcome as a deviance difference, and appropriate modifications of pruning and amalgamation rules are discussed. It is further shown how the proposed approach makes it possible to develop tree-growing for situations usually treated by generalized linear models (GLIM). In particular, Poisson and logistic regression can be tree-structured. Moreover, censored survival data can be treated, as in GLIM, by observing a formal equivalence of the likelihood under random censoring and an appropriate Poisson model. Three examples are given of application to Poisson, binary and censored survival data.     

Cyclic permutations and evolutionary trees

Given a tree with leaf set X, there are certain ways of arranging the elements of X in a circular order so that can be embedded in the plane and ‘preserve’ this ordering. We investigate some new combinatorial properties of these ‘circular orderings.’ We then use these properties to establish two results concerning dissimilarity maps on X that are induced by edge-weighted trees with leaf set X.     

树映射的分布混沌

设T是个有限树,f是T上的连续映射．证明了f是分布混沌的当且仅当它的拓扑熵是正数．一些已知结论得到了改进．     

Decomposition algorithms for the tree edit distance problem

We study the behavior of dynamic programming methods for the tree edit distance problem, such as [P. Klein, Computing the edit-distance between unrooted ordered trees, in: Proceedings of 6th European Symposium on Algorithms, 1998, p. 91–102; K. Zhang, D. Shasha, SIAM J. Comput. 18 (6) (1989) 1245–1262]. We show that those two algorithms may be described as decomposition strategies. We introduce the general framework of cover strategies, and we provide an exact characterization of the complexity of cover strategies. This analysis allows us to define a new tree edit distance algorithm, that is optimal for cover strategies.     

Correlation of mercury concentrations in tree core and lichen samples in southeastern Louisiana

To determine if a correlation exists between mercury concentrations in lichens and wood from tree cores, tree core and lichen samples were taken from sites under mercury advisories and analyzed for mercury using a Bacharach 50B Mercury Analyzer System employing the Manual Cold Vapor Atomic Absorption EPA method 7471A. Wood from tree cores was dated using tree ring data. Wood samples from the cores were analyzed for various depths in the tree core (periods of time) to determine if variations occur throughout the cores. Preliminary data indicate that a strong correlation exists between mercury concentrations in tree core and lichen samples. Samples were analyzed for the 6-month period of summer 2003–winter 2004. A correlation coefficient of 0.882 was found between the tree core and lichen data sets. The derived correlations were used to estimate concentrations of mercury in tree rings for sites in lichen samples which were previously analyzed. These predicted values compared favorably to recently determined concentrations of Hg in tree cores. The strong correlation between lichen and tree core Hg concentrations suggests similar uptake mechanism for the two types of biota.     

List star edge coloring of k-degenerate graphs

A star edge coloring of a graph is a proper edge coloring such that every connected 2-colored subgraph is a path with at most 3 edges. Deng et al. and Bezegová et al. independently show that the star chromatic index of a tree with maximum degree $\Delta$ is at most $?\frac{3\Delta }{2}?$, which is tight. In this paper, we study the list star edge coloring of $k$-degenerate graphs. Let $c{h}_{st}^{\prime }\left(G\right)$ be the list star chromatic index of $G$: the minimum $s$ such that for every $s$-list assignment $L$ for the edges, $G$ has a star edge coloring from $L$. By introducing a stronger coloring, we show with a very concise proof that the upper bound on the star chromatic index of trees also holds for list star chromatic index of trees, i.e. $c{h}_{st}^{\prime }\left(T\right)\le ?\frac{3\Delta }{2}?$ for any tree $T$ with maximum degree $\Delta$. And then by applying some orientation technique we present two upper bounds for list star chromatic index of $k$-degenerate graphs.     

Caterpillars with maximum degree 3 are antimagic

Let $G=(V,E)$ be a connected graph with $m$ edges. An antimagic labeling of $G$ is a one-to-one mapping from $E$ to $\{1,2,\dots ,m\}$ such that the vertex sum (i.e., sum of the labels assigned to edges incident to a vertex) for distinct vertices are different. A graph $G$ is called antimagic if $G$ has an antimagic labeling. It was conjectured by Hartsfield and Ringel that every tree other than $K_2$ is antimagic. The conjecture remains open though it was verified for trees with some constrains. Caterpillars are an important subclass of trees. This paper shows caterpillars with maximum degree 3 are antimagic, which gives an affirmative answer to an open problem of Lozano et al. (2019).     

Learning extended tree augmented naive structures

This work proposes an extended version of the well-known tree-augmented naive Bayes (TAN) classifier where the structure learning step is performed without requiring features to be connected to the class. Based on a modification of Edmonds' algorithm, our structure learning procedure explores a superset of the structures that are considered by TAN, yet achieves global optimality of the learning score function in a very efficient way (quadratic in the number of features, the same complexity as learning TANs). We enhance our procedure with a new score function that only takes into account arcs that are relevant to predict the class, as well as an optimization over the equivalent sample size during learning. These ideas may be useful for structure learning of Bayesian networks in general. A range of experiments shows that we obtain models with better prediction accuracy than naive Bayes and TAN, and comparable to the accuracy of the state-of-the-art classifier averaged one-dependence estimator (AODE). We release our implementation of ETAN so that it can be easily installed and run within Weka.