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京都大学 / 新制・課程博士 / 博士(理学) / 甲第24398号 / 理博第4897号 / 新制||理||1700(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐藤 昌利, 教授 佐々 真一, 准教授 戸塚 圭介 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

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 Informatics / Kyoto University / DFAM

Great efforts have been devoted to decipher the sequence composition of the genomes and transcriptomes of diverse organisms. Continuing advances in high-throughput sequencing technologies have led to a decline in associated costs, facilitating a rapid increase in the amount of available genetic data. In particular genome studies have undergone a fundamental paradigm shift where genome projects are no longer limited by sequencing costs, but rather by computational problems associated with assembly. There is an urgent demand for more efficient and more accurate methods. Most recently, “hybrid” methods that integrate short- and long-read data have been devised to address this need. LazyB is a new, low-cost hybrid genome assembler. It starts from a bipartite overlap graph between long reads and restrictively filtered short-read unitigs. This graph is translated into a long-read overlap graph. By design, unitigs are both unique and almost free of assembly errors. As a consequence, only few spurious overlaps are introduced into the graph. Instead of the more conventional approach of removing tips, bubbles, and other local features, LazyB extracts subgraphs whose global properties approach a disjoint union of paths in multiple steps, utilizing properties of proper interval graphs. A prototype implementation of LazyB, entirely written in Python, not only yields significantly more accurate assemblies of the yeast, fruit fly, and human genomes compared to state-of-the-art pipelines, but also requires much less computational effort. An optimized C++ implementation dubbed MuCHSALSA further significantly reduces resource demands. Advances in RNA-seq have facilitated tremendous insights into the role of both coding and non-coding transcripts. Yet, the complete and accurate annotation of the transciptomes of even model organisms has remained elusive. RNA-seq produces reads significantly shorter than the average distance between related splice events and presents high noise levels and other biases The computational reconstruction remains a critical bottleneck. Ryūtō implements an extension of common splice graphs facilitating the integration of reads spanning multiple splice sites and paired-end reads bridging distant transcript parts. The decomposition of read coverage patterns is modeled as a minimum-cost flow problem. Using phasing information from multi-splice and paired-end reads, nodes with uncertain connections are decomposed step-wise via Linear Programming. Ryūtōs performance compares favorably with state-of-the-art methods on both simulated and real-life datasets. Despite ongoing research and our own contributions, progress on traditional single sample assembly has brought no major breakthrough. Multi-sample RNA-Seq experiments provide more information which, however, is challenging to utilize due to the large amount of accumulating errors. An extension to Ryūtō enables the reconstruction of consensus transcriptomes from multiple RNA-seq data sets, incorporating consensus calling at low level features. Benchmarks show stable improvements already at 3 replicates. Ryūtō outperforms competing approaches, providing a better and user-adjustable sensitivity-precision trade-off. Ryūtō consistently improves assembly on replicates, demonstrable also when mixing conditions or time series and for differential expression analysis. Ryūtōs approach towards guided assembly is equally unique. It allows users to adjust results based on the quality of the guide, even for multi-sample assembly.:1 Preface 1.1 Assembly: A vast and fast evolving field 1.2 Structure of this Work 1.3 Available 2 Introduction 2.1 Mathematical Background 2.2 High-Throughput Sequencing 2.3 Assembly 2.4 Transcriptome Expression 3 From LazyB to MuCHSALSA - Fast and Cheap Genome Assembly 3.1 Background 3.2 Strategy 3.3 Data preprocessing 3.4 Processing of the overlap graph 3.5 Post Processing of the Path Decomposition 3.6 Benchmarking 3.7 MuCHSALSA – Moving towards the future 4 Ryūtō - Versatile, Fast, and Effective Transcript Assembly 4.1 Background 4.2 Strategy 4.3 The Ryūtō core algorithm 4.4 Improved Multi-sample transcript assembly with Ryūtō 5 Conclusion & Future Work 5.1 Discussion and Outlook 5.2 Summary and Conclusion

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A graph G is a (t,r)-regular graph if every collection of t independent vertices is collectively adjacent to exactly r vertices. In this thesis, we will present a complete characterization of (t,r)-regular graphs of order n if n is sufficiently large. Furthermore, we will show that all graphs of this type are isomorphic to Ks + mKp where t(p - 1) + s = r.

In a paper by Beeler and Hoilman, the traditional game of peg solitaire is generalized to graphs in the combinatorial sense. One of the important open problems in this paper was to classify solvable trees. In this thesis, we will give necessary and sufficient conditions for the solvability for all trees with diameter four. We also give the maximum number of pegs that can be left on such a graph under the restriction that we jump whenever possible.

In this thesis, we consider packings and coverings of various complete graphs with the 4-cycle with a pendant edge. We consider both restricted and unrestricted coverings. Necessary and sufficient conditions are given for such structures for (1) complete graphs Kv, (2) complete bipartite graphs Km,n, and (3) complete graphs with a hole K(v,w).

In this thesis, we study universal hypergraphs. What are these? Let us start with defining a universal graph as a graph on n vertices that contains each of the many possible graphs of a smaller size k < n as an induced subgraph. A hypergraph is a discrete structure on n vertices in which edges can be of any size, unlike graphs, where the edge size is always two. If all edges are of size three, then the hypergraph is said to be 3-uniform. If a 3-uniform hypergraph can have edges colored one of a colors, then it is called a 3-uniform hypergraph with a colors. Analogously with universal graphs, a universal, induced, 3-uniform, k-hypergraph, with a possible edge colors is then defined to be a 3-uniform a-colored hypergraph on n vertices that contains each of the many possible 3-uniform a-colored hypergraphs on k vertices, k < n. In this thesis, we study conditions for the existence of a such a universal hypergraph, and address the question of how large n must be, given a fixed k, so that hypergraphs on n vertices are universal with high probability. This extends the work of Alon, [2] who studied the case of a = 2, and that too for graphs (not hypergraphs).

As introduced by Slater in 2008, liar's domination provides a way of modeling protection devices where one may be faulty. Assume each vertex of a graph G is the possible location for an intruder such as a thief. A protection device at a vertex v is assumed to be able to detect the intruder at any vertex in its closed neighborhood N[v] and identify at which vertex in N[v] the intruder is located. A dominating set is required to identify any intruder's location in the graph G, and if any one device can fail to detect the intruder, then a double-dominating set is necessary. Stronger still, a liar's dominating set can identify an intruder's location even when any one device in the neighborhood of the intruder vertex can lie, that is, any one device in the neighborhood of the intruder vertex can misidentify any vertex in its closed neighborhood as the intruder location or fail to report an intruder in its closed neighborhood. In this thesis, we present the liar's domination number for the finite ladders, infinite ladder, and infinite P_3 x P_infty. We also give bounds for other grid graphs.