Associate Professor, Institute of Statistical Mathematics.
<aside> 💡 In this two-hour lecture, I will give a quick overview of selected topics in graph theory for beginners. Starting with basic concepts in graph theory (nodes, edges, trees, cycles, etc.), I will explain fundamental results in graph theory, including connectivity, planar graphs and graph minors, and matchings. Various examples of these concepts as well as algorithms will be also presented. No prior knowledge of graph theory is required for this lecture.
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Associate Professor, Institute for Life and Medical Sciences, Kyoto University.
<aside> 💡 In living cells, biochemical reactions form intricate networks, such as metabolic pathways, whose dynamics give rise to critical cellular functions. However, the intricacy of these network structures, coupled with our incomplete knowledge of their detailed kinetics, poses significant challenges to understanding how cellular functions emerge from the network dynamics. In this talk, I review the dynamical system of chemical reaction networks and introduce 'Structural Sensitivity Analysis,' a novel method that enables us to determine system responses based solely on network structure information. Through this technique, we established that the impact of parameter perturbation on the steady state is limited to subnetworks satisfying certain topological conditions. Furthermore, these subnetworks govern the steady-state bifurcations of the reaction system, such as which parameters control the onset of bifurcations and which chemicals exhibit bifurcating behaviors. Our findings highlight the pivotal role of network topology in producing robustness and plasticity --- two essential attributes of living systems.
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Associate Professor, Waseda University.
<aside> 💡 Phylogenetic trees are a standard model of evolution, but more general network models are often needed to represent complicated evolutionary histories or real-world data that are not tree-like. Tree-based networks, a prominent subclass of phylogenetic networks, include many of the other well-known subclasses. In this talk, I will present some theoretical work on trees in a complicated network. The main result is a structure theorem for rooted almost-binary phylogenetic networks, which leads to linear time (or linear delay) algorithms for various computational problems, including but not limited to counting, listing, optimizing, and ranking spanning phylogenetic trees within a given tree-based network. To stimulate discussion and collaboration, I will mention some open problems that may be of interest to researchers in discrete mathematics, and also touch on some possible avenues and ideas for biological applications, including links to cactus graphs.(Part of this work, more specifically the ranking algorithm, is a joint work with Kazuhisa Makino.)
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Professor in Honor, Yokohama National University.
<aside> 💡 Topological graph theory is a hybrid of graph theory and topology and mainly deals with embeddings of graphs on surfaces, discussing many combinatorial properties of embedded graphs. It may be said that a new stage of topological graph theory began after Four Color Problem was settled, around 1980. There have been found many types of phenomena that cannot be controlled only by Euler's formula; re-embedding structures, graph minors, graph coverings and so on. In this talk, we shall introduce the whole history about them briefly.
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Faculty of Engineering, Kyoto University.