The full basis theorem does not imply analytic wellordering

A finite support product of ${\omega }_1$ clones of Jensen's minimal ${\Pi }_2^1$ singleton forcing is used to define a model in which any non-empty analytically definable set of reals contains an analytically definable real (the full basis theorem), but there is no analytically definable wellordering of the reals.     

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.     

How much sweetness is there in the universe?

We continue investigations of forcing notions with strong ccc properties introducing new methods of building sweet forcing notions. We also show that quotients of topologically sweet forcing notions over Cohen reals are topologically sweet while the quotients over random reals do not have to be such. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

New reals: Can live with them,can live without them

We give a self‐contained proof of the preservation theorem for proper countable support iterations known as “tools‐preservation”, “Case A” or “first preservation theorem” in the literature. We do not assume that the forcings add reals. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global Forcing Number of Benzenoid Graphs

A global forcing set in a simple connected graph G with a perfect matching is any subset S of E(G) such that the restriction of the characteristic function of perfect matchings of G on S is an injection. The number of edges in a global forcing set of the smallest cardinality is called the global forcing number of G. In this paper we prove several results concerning global forcing sets and numbers of benzenoid graphs. In particular, we prove that all catacondensed benzenoids and catafused coronoids with n hexagons have the global forcing number equal to n, and that for pericondensed benzenoids the global forcing number is always strictly smaller than the number of hexagons.     

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.