研究活動情報

• Quasimorphisms of free products of racks and quandles
  Masamitsu Aoki
  2024年04月23日
  We show that the second bounded cohomology of the free product of racks and quandles is infinite-dimensional as a real vector space. This is similar to the case of groups. As a corollary, we show that the second bounded cohomology of the free rack and the free quandle is infinite-dimensional. We also give another proof of this corollary using homogeneous group quasimorphisms.
• Reproducing the Reaction Route Map on the Shape Space from Its Quotient by the Complete Nuclear Permutation-Inversion Group
  Hiroshi Teramoto; Takuya Saito; Masamitsu Aoki; Burai Murayama; Masato Kobayashi; Takenobu Nakamura; Tetsuya Taketsugu
  Journal of Chemical Theory and Computation, 19, 17, 5886, 5896, American Chemical Society (ACS), 2023年08月29日
  研究論文（学術雑誌）, This study develops an algorithm to reproduce reaction route maps (RRMs) in shape space from the outputs of potential search algorithms. To demonstrate this, GRRM is utilized as a potential search algorithm but the proposed algorithm should work with other potential search algorithms in principle. The proposed algorithm does not require any encoding of the molecular configurations and is thus applicable to complicated realistic molecules for which efficient encoding is not readily available. We show subgraphs of a RRM mapped to each other by the action of the symmetry group are isomorphic and also provide an algorithm to compute the set of feasible transformations in the sense of Longuet--Higgins. We demonstrate the proposed algorithm in toy models and in more realistic molecules. Finally, we remark on absolute rate theory from our perspective.
• Characterizing Reaction Route Map of Realistic Molecular Reactions Based on Weight Rank Clique Filtration of Persistent Homology
  Murayama, Burai; Kobayashi, Masato; Aoki, Masamitsu; Ishibashi, Suguru; Saito, Takuya; Nakamura, Takenobu; Teramoto, Hiroshi; Taketsugu, Tetsuya
  Journal of chemical theory and computation, 19, 15, 5007, 5023, 2023年08月08日
  英語, 研究論文（学術雑誌）, A reaction route map (RRM) constructed using the GRRM program is a collection of elementary reaction pathways, each of which comprises two equilibrium (EQ) geometries and one transition state (TS) geometry connected by an intrinsic reaction coordinate (IRC). An RRM can be mathematically represented by a graph with weights assigned to both vertices, corresponding to EQs, and edges, corresponding to TSs, representing the corresponding energies. In this study, we propose a method to extract topological descriptors of a weighted graph representing an RRM based on persistent homology (PH). The work of Mirth et al. [J.Chem.Phys.2021,154,114114], in which PH analysis was applied to the (3N - 6)-dimensional potential energy surface of an N atomic system, is related to the present method, but our method is practically applicable to realistic molecular reactions. Numerical assessments revealed that our method can extract the same information as the method proposed by Mirth et al. for the 0-th and 1-st PHs, except for the death of the 1-st PH. In addition, the information obtained from the 0-th PH corresponds to the analysis using the disconnectivity graph. The results of this study suggest that the descriptors obtained using the proposed method accurately reflect the characteristics of the chemical reactions and/or physicochemical properties of the system.

• ポテンシャルエネルギー曲面の新記述子:反応経路地図のパーシステント・ホモロジー
  村山 武来; 小林 正人; 青木 雅允; 石橋 卓; 齋藤 琢弥; 中村 壮伸; 寺本 央; 武次 徹也, Journal of Computer Chemistry, Japan, 23, 1, 33, 36, 2024年
  A reaction route map (RRM), which is a collection of elementary reaction pathways, contracts the potential energy surface (PES) with 3N − 6 variables (N: the number of atoms) into a weighted graph representation. Although the automated construction of RRMs has greatly contributed to the accurate understanding of chemical reaction mechanisms, only a small fraction of networks with low activation energies are relevant to actual chemical reactions, and thus studies focusing on the entire RRM have not been conducted. In this letter, we summarize our recent approach to applying the persistent homology (PH) analysis to the graph structure of an RRM., 日本コンピュータ化学会, 日本語
• パーシステントホモロジーによるGRRMの表示
  中村 壮伸; 村山 武; 小林 正人; 青木 雅允; 石橋 卓; 齋藤 琢弥; 寺本 央; 武次 徹也, 日本物理学会講演概要集, 77.1, 2271, 2271, 2022年
  一般社団法人 日本物理学会, 日本語
• 第15回数学総合若手研究集会 : 数学の交叉点
  福田 一貴; 青木 雅允; 植田 優基; 上島 芳倫; 矢不 俊文; 新村 貴之; 佐藤 直飛; 豊川 永喜; 松坂 公暉; 山形 颯; 吉田 啓佑, Hokkaido University technical report series in Mathematics, 176, 1, 646, 2019年03月12日
  Department of Mathematics, Hokkaido University, 日本語
• 第14回数学総合若手研究集会 : 数学の交叉点—The 14th Mathematics Conference for Young Researchers ： MCYR14
  半田 悟; 小森 大地; 藤沢 好; ロドリゲス ムレー アルベール; 青木 雅允; 上島 芳倫; 福田 一貴; 矢不 俊文, 173, 1, 569, 2018年02月28日
  日本語

• ラックの自由積上の擬準同型と 2 次有界コホモロジーの無限次元性
  青木雅允
  研究集会「結び目の数理Ⅷ」, 2025年12月18日, 日本語, 口頭発表（一般）
  2025年12月17日 - 2025年12月20日, 日本大学, Kędra によってラックとカンドルに対する有界コホモロジーと擬準同型が導入された。
  この講演では、自由積の 2 次有界コホモロジーが無限次元であるという、群の場合で既
  に知られている結果の類似がラックやカンドルでも成り立つことを紹介する。