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Hodge分解によるヘテロ・大域的な脳活動の遍歴検出

Publicly Offered Research

Project AreaThe study on the neural dynamics for understanding communication in terms of complex hetero systems
Project/Area Number 24120701
Research Category

Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)

Allocation TypeSingle-year Grants
Review Section Complex systems
Research InstitutionTohoku University

Principal Investigator

三浦 佳二  東北大学, 情報科学研究科, 助教 (60520096)

Project Period (FY) 2012-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywordsホッジ分解 / ネットワーク / 神経科学 / コミュニケーション神経情報学 / 複雑ネットワーク / Hodge分解 / 応用数学
Research Abstract

本研究においては、グラフ版のHodge-小平分解の神経科学への応用を目指した。Hodge-小平分解は、向き付けられたネットワークを流れに見立てて勾配流、大域循環流、局所渦の3成分へと分解して、ネットワークの構造解析を可能とする。例えば、大域循環流(harmonic flow)の自由度はネットワーク中のループの数に対応し、勾配流の自由度は連結成分数を反映する。
本年度は、このHodge-小平分解を青木・青柳らによる時間変化するネットワークモデルの構造解析に応用した。その結果、ネットワークの結合の時間変化を支配する学習則がSTDP則(β~0)である時に、ループが多くでき、Hebb則(β<-0.5)である時にはループができにくいことを解明した。また、ネットワークの不変量であるループの数が、従来知られていたこのモデルの分岐図(Aoki & Aoyagi 2009, 2011)を反映するだけでなく、これまでカオス領域としてひとくくりにされていたパラメタ領域(Anti-Hebb則,β>0.3)をさらに細かく特徴づけることを可能とすることを発見した。
また、Hodge-小平分解のデータ解析への応用だけでなく、脳のモデルとして、脳の触覚系がHodge-小平分解のアルゴリズムを利用して、不変量を取り出しているという仮説を提案した。数学のトポロジーの分野において導かれた(連続変形において保存する)不変量を活用することで、2次元タッチパネル上の指の形や位置に全く影響を受けず、タッチ回数を正しく数える並列アルゴリズムを提案した。

Current Status of Research Progress
Reason

25年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

25年度が最終年度であるため、記入しない。

Report

(2 results)
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • Research Products

    (28 results)

All 2013 2012 Other

All Journal Article (3 results) (of which Peer Reviewed: 3 results) Presentation (24 results) (of which Invited: 8 results) Book (1 results)

  • [Journal Article] The dorsomedial striatum encodes net expected return, critical for energizing performance vigor2013

    • Author(s)
      Alice Y. Wang, Keiji Miura, Naoshige Uchida
    • Journal Title

      Nature Neuroscience

      Volume: 16 Issue: 5 Pages: 639-647

    • DOI

      10.1038/nn.3377

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Semiparametric Covariance Estimator Immune to Arbitrary Signal Drift2013

    • Author(s)
      Keiji Miura
    • Journal Title

      Interdisciplinary Information Sciences

      Volume: 19 Issue: 1 Pages: 35-41

    • DOI

      10.4036/iis.2013.35

    • NAID

      110009795567

    • ISSN
      1340-9050, 1347-6157
    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Odor representations in olfactory cortex: distributed rate coding and decorrelated population activity2012

    • Author(s)
      Keiji Miura, Zachary F. Mainen, Naoshige Uchida
    • Journal Title

      Neuron

      Volume: 74 Issue: 6 Pages: 25-35

    • DOI

      10.1016/j.neuron.2012.04.021

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Presentation] Near zero noise correlations underlie efficient population codes in olfactory cortex2013

    • Author(s)
      三浦 佳二
    • Organizer
      脳と心のメカニズム 冬のワークショップ
    • Place of Presentation
      ルスツ、北海道
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] An unbiased estimator of noise correlations under signal drift2012

    • Author(s)
      Keiji Miura
    • Organizer
      SIAM Annual Meeting
    • Place of Presentation
      Minneapolis, USA
    • Related Report
      2012 Annual Research Report
  • [Presentation] Fast, efficient population codes in olfactory cortex through decorrelation and synchronization to theta-frequency sniffing2012

    • Author(s)
      Keiji Miura, Zachary F. Mainen, Naoshige Uchida
    • Organizer
      包括脳 脳と心のメカニズム 夏のワークショップ
    • Place of Presentation
      仙台
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] グラフのHodge分解とその周辺2012

    • Author(s)
      三浦 佳二
    • Organizer
      ヘテロ・ニューロアナリシス研究会
    • Place of Presentation
      仙台
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] グラフ上の流れのHodge分解の考察と金属ガラス時系列への応用2012

    • Author(s)
      三浦 佳二, 藤田 武志
    • Organizer
      ネットワーク科学の数理と展開
    • Place of Presentation
      仙台
    • Related Report
      2012 Annual Research Report
  • [Presentation] Near zero noise correlations underlie efficient population codes in olfactory cortex2012

    • Author(s)
      Keiji Miura, Zachary F. Mainen, Naoshige Uchida
    • Organizer
      Neuroscience 2012
    • Place of Presentation
      Nagoya
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Near zero noise correlations underlie efficient population codes in olfactory cortex2012

    • Author(s)
      Keiji Miura
    • Organizer
      RIKEN BSI Forum
    • Place of Presentation
      Saitama
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 位相縮約に基づくシリコンニューロンのダイナミカルシステムデザイン2012

    • Author(s)
      中田 一紀, 三浦 佳二, 浅井 哲也
    • Organizer
      ニューロコンピューティング研究会(NC)
    • Place of Presentation
      北九州
    • Related Report
      2012 Annual Research Report
  • [Presentation] Clock Synchronization Protocol Using Resonate-and-Fire Type of Pulse-Coupled Oscillators for Wireless Sensor Networks2012

    • Author(s)
      Kazuki Nakada, Keiji Miura
    • Organizer
      ICONIP 2012
    • Place of Presentation
      Doha, Qatar
    • Related Report
      2012 Annual Research Report
  • [Presentation] Silicon Neuron Design based on Phase Reduction Analysis2012

    • Author(s)
      Kazuki Nakada, Keiji Miura, Tetsuya Asai
    • Organizer
      SCIS-ISIS 2012
    • Place of Presentation
      Kobe
    • Related Report
      2012 Annual Research Report
  • [Presentation] Synchronization Analysis of Resonate-and-Fire Neuron Models with Delayed Resets2012

    • Author(s)
      Keiji Miura, Kazuki Nakada
    • Organizer
      SCIS-ISIS 2012
    • Place of Presentation
      Kobe
    • Related Report
      2012 Annual Research Report
  • [Presentation] Effects of Noise Correlations on Population Coding2012

    • Author(s)
      Keiji Miura
    • Organizer
      SCIS-ISIS 2012
    • Place of Presentation
      Kobe
    • Related Report
      2012 Annual Research Report
  • [Presentation] Dynamical Systems Design of Nonlinear Oscillators using Phase Reduction Approach2012

    • Author(s)
      Kazuki Nakada, Keiji Miura, Tetsuya Asai, Hisa- aki Tanaka
    • Organizer
      IEEE APCCAS 2012
    • Place of Presentation
      Kaohsiung, Taiwan
    • Related Report
      2012 Annual Research Report
  • [Presentation] Estimating intrinsic noise correlations under arbitrary signal drift2012

    • Author(s)
      三浦 佳二
    • Organizer
      情報統計力学の最前線 ―確率が繋ぐ自然現象と情報処理 の数理―」(YSM-SPIP 2012)
    • Place of Presentation
      仙台
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Dynamical System Design for Silicon Neurons using Phase Reduction Approach

    • Author(s)
      Kazuki Nakada, Keiji Miura, Tetsuya Asai
    • Organizer
      35th Annual International Conference of the IEEE EMBS
    • Place of Presentation
      Osaka
    • Related Report
      2013 Annual Research Report
  • [Presentation] Phase Response Curves Explain How Multiplicative Feedback on Neural Phase Elements Differs from Adaptive Physical Feedback in Robotic Motion Controls

    • Author(s)
      Kazuki Nakada, Keiji Miura and Hiroaki Wagatsuma
    • Organizer
      IJCNN 2013 (The International Joint Conference on Neural Networks)
    • Place of Presentation
      Dallas, USA
    • Related Report
      2013 Annual Research Report
  • [Presentation] Effects of Noise Correlations on Population Coding

    • Author(s)
      Keiji Miura
    • Organizer
      Francis Crick Symposium on Neuroscience: The Changing Brain
    • Place of Presentation
      Shanghai, China
    • Related Report
      2013 Annual Research Report
  • [Presentation] Dynamical Systems Design of Silicon Neurons using Phase Reduction Method

    • Author(s)
      Kazuki Nakada, Keiji Miura, Tetsuya Asai
    • Organizer
      Neuro2013
    • Place of Presentation
      Kyoto
    • Related Report
      2013 Annual Research Report
  • [Presentation] Hodge-Kodaira Decomposition of Evolving Neural Networks

    • Author(s)
      Keiji Miura, Takaaki Aoki
    • Organizer
      SIAM Applied Algebraic Geometry
    • Place of Presentation
      Fort Collins, Colorado, USA
    • Related Report
      2013 Annual Research Report
  • [Presentation] グラフ上の流れのHodge-小平分解入門

    • Author(s)
      三浦佳二
    • Organizer
      SMART研究会「応用現代幾何学」
    • Place of Presentation
      仙台
    • Related Report
      2013 Annual Research Report
  • [Presentation] Hodge-小平分解から見た現代幾何学入門

    • Author(s)
      三浦佳二
    • Organizer
      ヘテロ・ニューロアナリシス研究会
    • Place of Presentation
      仙台
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Neural implementation of shape-invariant touch counter based on Euler calculus

    • Author(s)
      Keiji Miura, Kazuki Nakada
    • Organizer
      ISNNE(The 1st International Symposium on Neuromorphic and Nonlinear Engineering)
    • Place of Presentation
      Tokyo
    • Related Report
      2013 Annual Research Report
  • [Presentation] Hodge-Kodaira Decomposition of Evolving Neural Networks

    • Author(s)
      Keiji Miura, Takaaki Aoki
    • Organizer
      Workshop on cortical dynamics: from the architecture to functions
    • Place of Presentation
      Kyoto
    • Related Report
      2013 Annual Research Report
  • [Presentation] 非定常な神経活動からのノイズ相関の推定

    • Author(s)
      三浦佳二
    • Organizer
      神経科学と統計科学の対話4
    • Place of Presentation
      東京
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Book] 嗅覚と匂い・香りの産業利用最前線2013

    • Author(s)
      三浦佳二
    • Publisher
      NTS
    • Related Report
      2012 Annual Research Report

URL: 

Published: 2013-05-15   Modified: 2019-07-29  

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