Obesity-related behaviors in adolescent friendship networks

This study examines obesity-related behaviors within adolescent friendship networks, because adolescent peers have been identified as being important determinants of many health behaviors. We applied ERGM selection models for single network observations to determine if close adolescent friends engage in similar behaviors and to explore associations between behavior and popularity. Same-sex friends were found to be similar on measures of organized physical activity in two out of three school-based friendship networks. Female friends were found to engage in similar screen-based behaviors, and male friends tended to be similar in their consumption of high-calorie foods. Popularity (receiving ties) was also associated with some behaviors, although these effects were gender specific and differed across networks.     

几乎无桥的连通图具有控制闭迹的一个充分条件

在研究一个图是否具有生成闭迹时，Ｐ．Ａ．Ｃａｔｌｉｎ提供一个有效的化简方法，而Ｈ．Ｊ．Ｂｒｏｅｒｓｍａ，Ｈ．Ｊ．Ｖｅｌｄｍａｎ 利用禁用导出子图给出控制闭迹、控制圈的若干充条件，本文结合这两种方法得到了一个图具有控制闭迹的一个充分条件。     

Tracking Edges, Corners and Vertices in an Image

Abstract.  In a range of imaging problems, particularly those where the images are of man-made objects, edges join at points which comprise three or more distinct boundaries between textures. In such cases the set of edges in the plane forms what a mathematician would call a planar graph. Smooth edges in the graph meet one another at junctions, called 'vertices', the 'degrees' of which denote the respective numbers of edges that join there. Conventional image reconstruction methods do not always draw clear distinctions among different degrees of junction, however. In such cases the algorithm is, in a sense, too locally adaptive; it inserts junctions without checking more globally to determine whether another configuration might be more suitable. In this paper we suggest an alternative approach to edge reconstruction, which combines a junction classification step with an edge-tracking routine. The algorithm still makes its decisions locally, so that the method retains an adaptive character. However, the fact that it focuses specifically on estimating the degree of a junction means that it is relatively unlikely to insert multiple low-degree junctions when evidence in the data supports the existence of a single high-degree junction. Numerical and theoretical properties of the method are explored, and theoretical optimality is discussed. The technique is based on local least-squares, or local likelihood in the case of Gaussian data. This feature, and the fact that the algorithm takes a tracking approach which does not require analysis of the full spatial data set, mean that it is relatively simple to implement.     

On the impact of contaminations in graphical Gaussian models

This paper analyzes the impact of some kinds of contaminant on model selection in graphical Gaussian models. We investigate four different kinds of contaminants, in order to consider the effect of gross errors, model deviations, and model misspecification. The aim of the work is to assess against which kinds of contaminant a model selection procedure for graphical Gaussian models has a more robust behavior. The analysis is based on simulated data. The simulation study shows that relatively few contaminated observations in even just one of the variables can have a significant impact on correct model selection, especially when the contaminated variable is a node in a separating set of the graph.     

A better constant-factor approximation for weighted dominating set in unit disk graph

This paper presents a (10+ε)-approximation algorithm to compute minimum-weight connected dominating set (MWCDS) in unit disk graph. MWCDS is to select a vertex subset with minimum weight for a given unit disk graph, such that each vertex of the graph is contained in this subset or has a neighbor in this subset. Besides, the subgraph induced by this vertex subset is connected. Our algorithm is composed of two phases: the first phase computes a dominating set, which has approximation ratio 6+ε (ε is an arbitrary positive number), while the second phase connects the dominating sets computed in the first phase, which has approximation ratio 4. This work is supported in part by National Science Foundation under grant CCF-9208913 and CCF-0728851; and also supported by NSFC (60603003) and XJEDU.     

New 3-level response surface designs constructed from incomplete block designs

Box and Behnken [1958. Some new three level second-order designs for surface fitting. Statistical Technical Research Group Technical Report No. 26. Princeton University, Princeton, NJ; 1960. Some new three level designs for the study of quantitative variables. Technometrics 2, 455–475.] introduced a class of 3-level second-order designs for fitting the second-order response surface model. These 17 Box–Behnken designs (BB designs) are available for 3–12 and 16 factors. Although BB designs were developed nearly 50 years ago, they and the central-composite designs of Box and Wilson [1951. On the experimental attainment of optimum conditions. J. Royal Statist. Soc., Ser. B 13, 1–45.] are still the most often recommended response surface designs. Of the 17 aforementioned BB designs, 10 were constructed from balanced incomplete block designs (BIBDs) and seven were constructed from partially BIBDs (PBIBDs). In this paper we show that these seven BB designs constructed from PBIBDs can be improved in terms of rotatability as well as average prediction variance, D$D$- and G$G$-efficiency. In addition, we also report new orthogonally blocked solutions for 5, 8, 9, 11 and 13 factors. Note that an 11-factor BB design is available but cannot be orthogonally blocked. All new designs can be found at http://www.math.montana.edu/∼$\sim$jobo/bbd/.     

On the Addition and Comparison of Graphs Labeled with Stochastic Variables: Learnable Anatomical Catalogs

We provide an operator for the addition of a pair of graphs, labeled with continuous variables which are subject to stochastic variation. We also provide an operator for measuring dissimilarity between a pair of such graphs. We use such a representation and operators to model a collection of vascular anatomy which accounts for inter-individual variations in both branching structure and in vessel shape. The model may be incrementally acquired, and is thus a catalog of anatomy whose content may be learned. The model may be used in applications such as the reconstruction of vasculature in three-dimensions from x-ray images, which we briefly outline.     

A new recombination lower bound and the minimum perfect phylogenetic forest problem

Understanding recombination is a central problem in population genetics. In this paper, we address an established computational problem in this area: compute lower bounds on the minimum number of historical recombinations for generating a set of sequences (Hudson and Kaplan in Genetics 111, 147–164, 1985; Myers and Griffiths in Genetics 163, 375–394, 2003; Gusfield et al. in Discrete Appl. Math. 155, 806–830, 2007; Bafna and Bansal in IEEE/ACM Trans. Comput. Biol. Bioinf. 1, 78–90, 2004 and in J. Comput. Biol. 13, 501–521, 2006; Song et al. in Bioinformatics 421, i413–i244, 2005). In particular, we propose a new recombination lower bound: the forest bound. We show that the forest bound can be formulated as the minimum perfect phylogenetic forest problem, a natural extension to the classic binary perfect phylogeny problem, which may be of interests on its own. We then show that the forest bound is provably higher than the optimal haplotype bound (Myers and Griffiths in Genetics 163, 375–394, 2003), a very good lower bound in practice (Song et al. in Bioinformatics 421, i413–i422, 2005). We prove that, like several other lower bounds (Bafna and Bansal in J. Comput. Biol. 13, 501–521, 2006), computing the forest bound is NP-hard. Finally, we describe an integer linear programming (ILP) formulation that computes the forest bound precisely for certain range of data. Simulation results show that the forest bound may be useful in computing lower bounds for low quality data. A preliminary version of this paper appeared in the Proceedings of COCOON 2007, LNCS, vol. 4598, pp. 16–26. The work was performed while Y. Wu was with UC Davis and supported by grants CCF-0515278 and IIS-0513910 from National Science Foundation. D. Gusfield supported by grants CCF-0515278 and IIS-0513910 from National Science Foundation.     

计算机在优美图研究中的应用

本文通过n∪i=1Fmi,4是交错图的证明过程,说明了在优美图研究的过程中计算机和计算程序所起的重要作用。