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A study of finite-time distributions of infection processes on finite graphs

Research Project

Project/Area Number 16K17652
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionKanazawa Institute of Technology (2019)
Japan Advanced Institute of Science and Technology (2018)
Kanagawa University (2016-2017)

Principal Investigator

Ide Yusuke  金沢工業大学, 基礎教育部, 講師 (70553999)

Project Period (FY) 2016-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords確率過程 / 量子課程 / 量子探索 / 量子ウォーク / 感染課程 / グラフ分割 / 固有解析 / equitable partition / perfect state transfer / 固有空間 / 時間発展作用素 / 感染症過程 / コンタクトプロセス / 固有空間解析 / グラフ分解 / 感染過程 / 複雑ネットワーク
Outline of Final Research Achievements

We developed a method to analyse matrices which define stochastic and/or quantum processes on graphs. This method provides "unified perspective" to
understand stochastic and/or quantum processes on graphs. More specifically, our method provides "coarse graining" of given graphs and corresponding time evolution operator of the process on it by using so-called equitable partition.

Academic Significance and Societal Importance of the Research Achievements

ネットワーク上で起こる感染症の広がりを理解するうえでも,あるいは,量子探索の効率性を議論するうえでも,個々のケースに特化した解析を進める一方で,ネットワーク(グラフ)の持つ特徴とそれぞれをモデル化したプロセスの挙動との関係を理解する必要がある.本研究で提案したグラフの隣接関係による粗視化と,その粗視化に対応する基底を用いた各種プロセスの時間発展作用素(行列)の再構成法をベースとして,研究対象となる各種プロセスを俯瞰することによって,ネットワーク上の各種プロセスに対する理解が深まり,実問題への対応策を考える際の一助となることが考えられる.

Report

(5 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (29 results)

All 2020 2019 2018 2017 2016 Other

All Journal Article (8 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 8 results,  Open Access: 1 results,  Acknowledgement Compliant: 3 results) Presentation (17 results) (of which Int'l Joint Research: 3 results,  Invited: 5 results) Book (2 results) Remarks (2 results)

  • [Journal Article] 量子ウォークによる高速探索2019

    • Author(s)
      井手勇介, 今野紀雄
    • Journal Title

      日本物理学会誌

      Volume: 74 Pages: 682-690

    • NAID

      130007807164

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Partition of graphs and quantum walk based search algorithms2019

    • Author(s)
      Ide Yusuke
    • Journal Title

      Nonlinear Theory and Its Applications, IEICE

      Volume: 10 Issue: 1 Pages: 16-27

    • DOI

      10.1587/nolta.10.16

    • NAID

      130007542509

    • ISSN
      2185-4106
    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] The spectral analysis of the unitary matrix of a 2-tessellable staggered quantum walk on a graph2018

    • Author(s)
      Konno Norio、Ide Yusuke、Sato Iwao
    • Journal Title

      Linear Algebra and its Applications

      Volume: 545 Pages: 207-225

    • DOI

      10.1016/j.laa.2018.01.022

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] A spectral analysis of discrete-time quantum walks with related to birth and death chain2018

    • Author(s)
      Choon-Lin Ho, Yusuke Ide, Norio Konno, Etsuo Segawa, Kentaro Takumi
    • Journal Title

      Journal of Statistical Physics

      Volume: 171 Issue: 2 Pages: 207-219

    • DOI

      10.1007/s10955-018-1998-9

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] New theory of diffusive and coherent nature of optical wave via a quantum walk2017

    • Author(s)
      Yusuke Ide, Norio Konno, Shigeki Matsutani, and Hideo Mitsuhashi
    • Journal Title

      Ann. Phys.,

      Volume: 383 Pages: 165-180

    • DOI

      10.1016/j.aop.2017.05.009

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Turing instability in reaction-diffusion models on complex networks2016

    • Author(s)
      Yusuke Ide, Hirofumi Izuhara, Takuya Machida
    • Journal Title

      Physica A

      Volume: 457 Pages: 331-347

    • DOI

      10.1016/j.physa.2016.03.055

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks2016

    • Author(s)
      Xin-Ping Xu, Yusuke Ide
    • Journal Title

      Annals of Physics

      Volume: 373 Pages: 682-693

    • DOI

      10.1016/j.aop.2016.08.019

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Periodicity for space-inhomogeneous quantum walks on the cycle2016

    • Author(s)
      Toshiyuki Arai, Choon-Lin Ho, Yusuke Ide, Norio Konno
    • Journal Title

      Yokohama Mathematical Journal

      Volume: 62 Pages: 39-50

    • NAID

      120006459875

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] 量子ウォークの極限分布に付随する直交多項式と対応するランダムウォークについて2020

    • Author(s)
      井手勇介, 今野紀雄
    • Organizer
      日本数学会2020年度年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Introduction to Continuous Time Quantum Walk Search2019

    • Author(s)
      Yusuke Ide
    • Organizer
      The 20th Asia Pacific Industrial Engineering And Management Systems
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] グラフ分割と固有解析による連続時間量子ウォーク探索の解析2019

    • Author(s)
      井手勇介
    • Organizer
      日本数学会2019年度秋季総合分科会
    • Related Report
      2019 Annual Research Report
  • [Presentation] グラフ分割と固有解析を用いた量子ウォーク探索の解析2019

    • Author(s)
      井手勇介
    • Organizer
      RIMS共同研究(グループ型)量子ウォークとスペクトル散乱理論の数理
    • Related Report
      2019 Annual Research Report
  • [Presentation] 量子完全状態遷移と量子探索2019

    • Author(s)
      井手勇介
    • Organizer
      Workshop on Quantum Walks at SPring-8
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] グラフの分割と単純ランダムウォーク・量子ウォーク探索2018

    • Author(s)
      井手勇介
    • Organizer
      電気学会情報システム研究会
    • Related Report
      2018 Research-status Report
  • [Presentation] グラフ上のランダムウォークの到達時刻評価2018

    • Author(s)
      井手勇介,林幸雄
    • Organizer
      第15回ネットワーク生態学シンポジウム
    • Related Report
      2018 Research-status Report
  • [Presentation] Graph partition and quantum walk search2018

    • Author(s)
      Yusuke Ide
    • Organizer
      The 8th Workshop on Quantum Simulation and Quantum Walks
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Spectral analysis for discrete-time quantum walks on the path2017

    • Author(s)
      Yusuke Ide
    • Organizer
      International Conference on Computational Modeling and Simulation (ICCMS) 2017, Special Session on Quantum Computation and Quantum Information
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 連続時間量子ウォークと量子探索2017

    • Author(s)
      井手勇介
    • Organizer
      ドレスト光子・光合成・量子ウォーク
    • Related Report
      2017 Research-status Report
  • [Presentation] path上の離散時間量子ウォークの固有解析2017

    • Author(s)
      井手勇介
    • Organizer
      IMI短期共同研究「レーザー同位体分離の実用化における量子ウォークの数理」
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] 連続時間量子ウォークとグラフ構造2017

    • Author(s)
      井手勇介
    • Organizer
      オペレーションズ・リサーチ学会研究部会「確率モデルとその応用」第22回研究会
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] グラフのmodular partitionと量子ウォークの解析2017

    • Author(s)
      井手勇介
    • Organizer
      第2回グラフゼータと量子ウォークの諸相
    • Related Report
      2017 Research-status Report
  • [Presentation] はじめに2017

    • Author(s)
      井手勇介
    • Organizer
      日本物理学会第72回年次大会シンポジウム「量子ウォークの深化とその周辺」
    • Place of Presentation
      大阪大学
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] スワームシステムにおけるネットワークの生成過程2016

    • Author(s)
      右田正夫, 井手勇介
    • Organizer
      ロボティクス・メカトロニクス講演会2016 in Yokohama
    • Place of Presentation
      パシフィコ横浜
    • Related Report
      2016 Research-status Report
  • [Presentation] 円環上の離散時間量子ウォークの周期性2016

    • Author(s)
      井手勇介
    • Organizer
      グラフゼータと量子ウォークの諸相
    • Place of Presentation
      室蘭工業大学
    • Related Report
      2016 Research-status Report
  • [Presentation] 2-step 離散時間量子ウォークの固有分解2016

    • Author(s)
      井手勇介
    • Organizer
      量子ウォークの代数的考察と光学との融合
    • Place of Presentation
      佐世保工業高等専門学校
    • Related Report
      2016 Research-status Report
  • [Book] 量子ウォークの新展開―数理構造の深化と応用2019

    • Author(s)
      今野紀雄, 井手勇介(共編著)
    • Total Pages
      321
    • Publisher
      培風館
    • ISBN
      9784563011628
    • Related Report
      2019 Annual Research Report
  • [Book] 不動点定理の話題 コンタクトプロセスの最近の話題2017

    • Author(s)
      井手勇介, 竹内幸雄
    • Total Pages
      137
    • Publisher
      慶應義塾大学
    • Related Report
      2016 Research-status Report
  • [Remarks] 金沢工業大学 研究者/教育・研究業績情報

    • URL

      https://kitap01.kanazawa-it.ac.jp/researcherdb/gyousekiIndex/GIBJAAF_0001.html

    • Related Report
      2019 Annual Research Report
  • [Remarks] 神奈川大学研究者情報

    • URL

      http://kenkyu.kanagawa-u.ac.jp/kuhp/KgApp?kyoinId=ymbygoosggg

    • Related Report
      2016 Research-status Report

URL: 

Published: 2016-04-21   Modified: 2021-02-19  

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