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Last Updated :2024/11/18

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Master

Affiliation (Master)

  • Research Institute for Electronic Science　Research Center of Mathematics for Social Creativity

Affiliation (Master)

  • Research Institute for Electronic Science　Research Center of Mathematics for Social Creativity

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Profile and Settings

Affiliation

  • Hokkaido University, Research Institute for Electronic Science, Assistant Professor

Degree

  • Doctor of Science（Hokkaido University）

Profile and Settings

  • Name (Japanese)

    Ishii

  • Name (Kana)

    Hiroshi

  • Name

    202201016748799553

Alternate Names

Affiliation

  • Hokkaido University, Research Institute for Electronic Science, Assistant Professor

Achievement

Research Interests

  • Localized patterns   Nonlocal reaction-diffusion equations   Nonlocal effect   Reaction-diffusion equations   

Research Areas

  • Natural sciences / Mathematical analysis
  • Natural sciences / Applied mathematics and statistics

Research Experience

  • 2023/12 - Today (Concurrent) Department of Mathematics, Hokkaido University
  • 2023/11 - Today Hokkaido University Research Institute for Electronic Science Asistant Professor
  • 2022/04 - 2023/10 Kyoto University ASHBi
  • 2021/04 - 2022/03 日本学術振興会 特別研究員DC2

Education

  • 2020/04 - 2022/03  Hokkaido University  Graduate School of Science  Department of Mathematics
  • 2018/04 - 2020/03  Hokkaido University  Graduate School of Science  Department of Mathematics
  • 2014/04 - 2018/03  Hokkaido University  School of Science  Mathematics

Committee Memberships

  • 2023/12 - Today   An organizer of Hokudai Mathematical Modeling Club Seminar

Awards

  • 2020/05 北海道大学大学院理学院 優秀研究奨励賞

Published Papers

  • Hiroshi Ishii
    Discrete and Continuous Dynamical Systems - Series B Accepted 2024/11 [Refereed]
  • Hiroshi Ishii
    Proceedings of the American Mathematical Society 152 (10) 4451 - 4461 0002-9939 2024/08/07 [Refereed][Not invited]
     

    In this paper, we consider the asymptotic profiles of zero points for the spatial variable of the solutions to the heat equation. By giving suitable conditions for the initial data, we prove the existence of zero points by extending the high-order asymptotic expansion theory for the heat equation. This reveals a previously unknown asymptotic profile of zero points diverging at . In a one-dimensional spatial case, we show the zero point’s second and third-order asymptotic profiles in a general situation. We also analyze a zero level set in high-dimensional spaces and obtain results that extend the results for the one-dimensional spatial case.

  • Ei, S.-I., Ishii, H., Sato, M., Tanaka, Y., Wang, M., Yasugi, T.
    Journal of Mathematical Biology 82 (6) 1432-1416 2021 [Not refereed]
  • Ei, S.-I., Ishii, H.
    Discrete and Continuous Dynamical Systems - Series B 26 (1) 173 - 190 1531-3492 2021 [Refereed]
  • Shin-Ichiro Ei, Hiroshi Ishii, Shigeru Kondo, Takashi Miura, Yoshitaro Tanaka
    Journal of Theoretical Biology 509 110496 - 110496 0022-5193 2021/01 [Refereed]
     
    A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary many factors can be reduced to a single or a simpler system of integro-differential equations called "effective equation" including the reduced integral kernel (called "effective kernel") in the convolution type. As one typical example, the Mexican hat shaped kernel is theoretically derived from two component activator-inhibitor systems. It is also shown that a three component system with quite different appearance from activator-inhibitor systems is reduced to an effective equation with the Mexican hat shaped kernel. It means that the two different systems have essentially the same effective equations and that they exhibit essentially the same spatial and temporal patterns. Thus, we can identify two different systems with the understanding in unified concept through the reduced effective kernels. Other two applications of this method are also given: Applications to pigment patterns on skins (two factors network with long range interaction) and waves of differentiation (called proneural waves) in visual systems on brains (four factors network with long range interaction). In the applications, we observe the reproduction of the same spatial and temporal patterns as those appearing in pre-existing models through the numerical simulations of the effective equations.
  • Naroda, Y., Endo, Y., Yoshimura, K., Ishii, H., Ei, S.-I., Miura, T.
    PLoS ONE 15 (12 December) e0235802 - e0235802 1932-6203 2020/12/17 [Refereed]
     
    Sutures, the thin, soft tissue between skull bones, serve as the major craniofacial growth centers during postnatal development. In a newborn skull, the sutures are straight; however, as the skull develops, the sutures wind dynamically to form an interdigitation pattern. Moreover, the final winding pattern had been shown to have fractal characteristics. Although various molecules involved in suture development have been identified, the mechanism underlying the pattern formation remains unknown. In a previous study, we reproduced the formation of the interdigitation pattern in a mathematical model combining an interface equation and a convolution kernel. However, the generated pattern had a specific characteristic length, and the model was unable to produce a fractal structure with the model. In the present study, we focused on the anterior part of the sagittal suture and formulated a new mathematical model with time–space-dependent noise that was able to generate the fractal structure. We reduced our previous model to represent the linear dynamics of the centerline of the suture tissue and included a time–space-dependent noise term. We showed theoretically that the final pattern from the model follows a scaling law due to the scaling of the dispersion relation in the full model, which we confirmed numerically. Furthermore, we observed experimentally that stochastic fluctuation of the osteogenic signal exists in the developing skull, and found that actual suture patterns followed a scaling law similar to that of the theoretical prediction.
  • Ei, S.-I., Ishii, H., Sato, M., Tanaka, Y., Wang, M., Yasugi, T.
    Journal of Mathematical Biology 81 (4-5) 981 - 1028 1432-1416 2020/11 [Refereed]
     
    Abstract In this paper, we introduce a continuation method for the spatially discretized models, while conserving the size and shape of the cells and lattices. This proposed method is realized using the shift operators and nonlocal operators of convolution types. Through this method and using the shift operator, the nonlinear spatially discretized model on the uniform and nonuniform lattices can be systematically converted into a spatially continuous model; this renders both models point-wisely equivalent. Moreover, by the convolution with suitable kernels, we mollify the shift operator and approximate the spatially discretized models using the nonlocal evolution equations, rendering suitable for the application in both experimental and mathematical analyses. We also demonstrate that this approximation is supported by the singular limit analysis, and that the information of the lattice and cells is expressed in the shift and nonlocal operators. The continuous models designed using our method can successfully replicate the patterns corresponding to those of the original spatially discretized models obtained from the numerical simulations. Furthermore, from the observations of the isotropy of the Delta–Notch signaling system in a developing real fly brain, we propose a radially symmetric kernel for averaging the cell shape using our continuation method. We also apply our method for cell division and proliferation to spatially discretized models of the differentiation wave and describe the discrete models on the sphere surface. Finally, we demonstrate an application of our method in the linear stability analysis of the planar cell polarity model.
  • Ei, S.-I., Guo, J.-S., Ishii, H., Wu, C.-C.
    Journal of Mathematical Analysis and Applications 487 (2) 124007 - 124007 1096-0813 2020/07 [Refereed]
  • Seirin-Lee, S., Sukekawa, T., Nakahara, T., Ishii, H., Ei, S.-I.
    Journal of Mathematical Biology 80 (6) 1885 - 1917 1432-1416 2020/05 [Refereed]
     
    Abstract Cell polarity is an important cellular process that cells use for various cellular functions such as asymmetric division, cell migration, and directionality determination. In asymmetric cell division, a mother cell creates multiple polarities of various proteins simultaneously within her membrane and cytosol to generate two different daughter cells. The formation of multiple polarities in asymmetric cell division has been found to be controlled via the regulatory system by upstream polarity of the membrane to downstream polarity of the cytosol, which is involved in not only polarity establishment but also polarity positioning. However, the mechanism for polarity positioning remains unclear. In this study, we found a general mechanism and mathematical structure for the multiple streams of polarities to determine their relative position via conceptional models based on the biological example of the asymmetric cell division process of C. elegans embryo. Using conceptional modeling and model reductions, we show that the positional relation of polarities is determined by a contrasting role of regulation by upstream polarity proteins on the transition process of diffusion dynamics of downstream proteins. We analytically prove that our findings hold under the general mathematical conditions, suggesting that the mechanism of relative position between upstream and downstream dynamics could be understood without depending on a specific type of bio-chemical reaction, and it could be the universal mechanism in multiple streams of polarity dynamics of the cell.

MISC

  • 非局所反応拡散方程式における定常フロント解同士の相互作用
    石井宙志, 栄伸一郎  第17回数学総合若手研究集会-北海道大学数学講究録-,  180-  471  -478  2021/03  [Not refereed][Not invited]
  • Existence of traveling wave solutions to a nonlocal scalar equation with sign-changing kernel
    Hiroshi Ishii  Proceedings of 45th Sapporo Symposium on Partial Differential Equations-北海道大学数学講究録-  71  -79  2020/08  [Not refereed][Invited]
  • 符号変化する積分核を有する時間発展方程式における進行波解の存在について
    栄伸一郎, Jong-Shenq Guo, 石井宙志, Chin-Chin Wu  第16回数学総合若手研究集会-北海道大学数学講究録-, 北海道大学  178-  473  -480  2020/03  [Not refereed][Not invited]
  • 符号変化が伴う非局所分散項を持つFisher-KPP方程式における進行波解の存在について
    石井宙志  第41回若手発展方程式セミナー報告集  67  -74  2020/02
  • 球面上における分化の波の数値計算
    石井宙志, 栄伸一郎, 佐藤純, 八杉徹雄  第15回数学総合若手研究集会-北海道大学数学講究録-  176-  631  -638  2019/03  [Not refereed][Not invited]

Presentations

Teaching Experience

  • Calculus ICalculus I Hokkaido University

Association Memberships

  • JSIAM   日本数学会   日本数理生物学会   

Research Projects

  • Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research
    Date (from‐to) : 2024/04 -2029/03 
    Author : 村川 秀樹, 野津 裕史, 石井 宙志, 佐藤 純, 田中 吉太郎, 富樫 英
  • 日本学術振興会：科学研究費助成事業 若手研究
    Date (from‐to) : 2023/04 -2028/03 
    Author : 石井 宙志
  • Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows
    Date (from‐to) : 2021/04 -2023/03 
    Author : 石井 宙志
     
    今年度はまず，非局所効果が十分小さい場合に非局所反応拡散方程式の空間パターンがどのように時間変化するか考察した．ある仮定の下では複数のフロント型局在パターンの重ね合わせで近似可能な時間発展する解の存在を示し，それぞれの局在パターンの位置の時間発展を積分核の不定積分を含む常微分方程式によって特徴づけすることに成功した．この結果により積分核の与え方によって多様な解の挙動が現れることを数学的に厳密に示すことができた．現在は仮定をより一般化することを試みている． また，単独の局在パターンについての数理解析も進めており，存在や安定性の他に局在パターンの性質を数理モデルに含まれるパラメータで特徴づけすることを試みている．この研究で得られた形式的な結果の一部は，共同研究で提案された数理モデルに対する数理解析の結果としてまとめ，学術論文として投稿中である． 次に，反応拡散ネットワークから形式的に導出される，ネットワークの情報が縮約された非局所効果を持つ数理モデルを導出するEffective nonlocal kernelを用いたモデリング手法の数学的妥当性について考察を行った．ある特定の条件を満たす反応拡散ネットワークから定まる線形の非局所反応拡散方程式の解は，十分時間が立てば情報が縮約された数理モデルの解に収束することを明らかにした．今後はより一般的な仮定の下で妥当性を示し，モデリングへの応用に向けた解析を行っていく． さらに，縮約された方程式の解の挙動の考察，および非局所効果による空間伝搬について考察するために，空間2階微分で記述される拡散方程式と畳み込み積分で記述される非局所拡散方程式の解の零点の漸近挙動について解析した．これら2つの方程式の場合には零点集合の上界や零点の漸近挙動で違いが現れることを明らかにした．これらの成果の一部は研究集会で発表するとともに，学術論文として投稿中である．

Academic Contribution

  • RIES international symposium 2024 Organizing member
    Date (from-to) :2024/04/01-Today
    Role: Planning etc
    Type: Competition etc
    Organizer, responsible person: Hokkaido University RIES
  • Mathematics in biological pattern formation problems
    Date (from-to) :2023/08/23
    Role: Planning etc
    Type: Competition etc
    Organizer, responsible person: Shin-Ichiro Ei, Hiroshi Ishii
  • Methods and Applications in Mathematical Life Sciences
    Date (from-to) :2023/02/17
    Role: Planning etc
    Type: Academic society etc
    Organizer, responsible person: Antoine Diez, Hiroshi Ishii, Clément Moreau
  • 日本応用数理学会2022年度年会 正会員OS「複雑系における発生・発展現象の数理」
    Date (from-to) :2022/09/09
    Role: Planning etc
    Type: Competition etc
    Organizer, responsible person: Antoine Diez, 石井宙志
  • 第18回数学総合若手研究集会 世話人
    Role: Planning etc
    Type: Academic society etc
  • 第17回数学総合若手研究集会 世話人
    Role: Planning etc
    Type: Academic society etc
  • 第16回数学総合若手研究集会（Covid-19により中止） 世話人
    Role: Planning etc
    Type: Academic society etc

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