Irreversible 2-conversion set in graphs of bounded degree

An irreversible $k$-threshold process (also a $k$-neighbor bootstrap percolation) is a dynamic process on a graph where vertices change color from white to black if they have at least $k$ black neighbors. An irreversible $k$-conversion set of a graph $G$ is a subset $S$ of vertices of $G$ such that the irreversible $k$-threshold process starting with $S$ black eventually changes all vertices of $G$ to black. We show that deciding the existence of an irreversible 2-conversion set of a given size is NP-complete, even for graphs of maximum degree 4, which answers a question of Dreyer and Roberts. Conversely, we show that for graphs of maximum degree 3, the minimum size of an irreversible 2-conversion set can be computed in polynomial time. Moreover, we find an optimal irreversible 3-conversion set for the toroidal grid, simplifying constructions of Pike and Zou.Comment: 18 pages, 12 figures; journal versio

Feedback vertex number of Sierpi\'{n}ski-type graphs

The feedback vertex number $\tau(G)$ of a graph $G$ is the minimum number of vertices that can be deleted from $G$ such that the resultant graph does not contain a cycle. We show that $\tau(S_p^n)=p^{n-1}(p-2)$ for the Sierpi\'{n}ski graph $S_p^n$ with $p\geq 2$ and $n\geq 1$. The generalized Sierpi\'{n}ski triangle graph $\hat{S_p^n}$ is obtained by contracting all non-clique edges from the Sierpi\'{n}ski graph $S_p^{n+1}$. We prove that $\tau(\hat{S}_3^n)=\frac {3^n+1} 2=\frac{|V(\hat{S}_3^n)|} 3$, and give an upper bound for $\tau(\hat{S}_p^n)$ for the case when $p\geq 4$

生物情報ネットワークのグラフ理論に基づく解析法

京都大学新制・課程博士博士(情報学)甲第24730号情博第818号新制||情||138(附属図書館)京都大学大学院情報学研究科知能情報学専攻(主査)教授 阿久津 達也, 教授 山本 章博, 教授 岡部 寿男学位規則第4条第1項該当Doctor of InformaticsKyoto UniversityDFA

Individual Based Model to Simulate the Evolution of Insecticide Resistance

Insecticides play a critical role in agricultural productivity. However, insecticides impose selective pressures on insect populations, so the Darwinian principles of natural selection predict that resistance to the insecticide is likely to form in the insect populations. Insecticide resistance, in turn, severely reduces the utility of the insecticides being used. Thus there is a strong economic incentive to reduce the rate of resistance evolution. Moreover, resistance evolution represents an example of evolution under novel selective pressures, so its study contributes to the fundamental understanding of evolutionary theory. Insecticide resistance often represents a complex interplay of multiple fitness trade-offs for individual insects. Resistant individuals tend to suffer significant decreases in fitness when no insecticide is present, resulting in non-resistant individuals having the tendency to outcompete resistant ones in areas with no insecticide. In the use of standard modeling practices, difficulties arise when trying to incorporate these complexities in a fashion which facilitates the simulation of the model and analyzing the results. Individual based models (IBMs) are one approach to overcoming these difficulties by leveraging modern computational techniques and modern computer power. In an IBM each member of the population is simulated to follow a set of stochastic rules, which includes rules about the behaviors and interactions of individuals. We propose to apply an IBM approach to modeling the evolution of insecticide resistance in an insect species population. The fall armyworm is an economically damaging pest which has recently become invasive in Africa, India, and China. A common type of insecticide used control fall armyworms is Bacillus thuringiensis (Bt). We hypothesize that individuals that are resistant to Bt grow at slower rates than their counterparts. This creates a strong fitness disadvantage when Bt is not present because the fall armyworms are cannibalistic, where smaller individuals have a large disadvantage. Thus we use our IBM to explore the nature of the fitness trade-offs between resistance and growth rate in order to understand how it could be exploited to lessen the rate of resistance evolution in the species. Adviser: Richard Rebarber and Brigitte Tenhumber

Feedback message passing for inference in Gaussian graphical models

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Includes bibliographical references (p. 89-92).For Gaussian graphical models with cycles, loopy belief propagation often performs reasonably well, but its convergence is not guaranteed and the computation of variances is generally incorrect. In this paper, we identify a set of special vertices called a feedback vertex set whose removal results in a cycle-free graph. We propose a feedback message passing algorithm in which non-feedback nodes send out one set of messages while the feedback nodes use a different message update scheme. Exact inference results can be obtained in O(k²n), where k is the number of feedback nodes and n is the total number of nodes. For graphs with large feedback vertex sets, we describe a tractable approximate feedback message passing algorithm. Experimental results show that this procedure converges more often, faster, and provides better results than loopy belief propagation.by Ying Liu.S.M