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Multivariate analysis of multi-domain data considering the association between data vectors

Research Project

Project/Area Number 16H02789
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Statistical science
Research InstitutionKyoto University (2017-2019)
Osaka University (2016)

Principal Investigator

Shimodaira Hidetoshi  京都大学, 情報学研究科, 教授 (00290867)

Co-Investigator(Kenkyū-buntansha) 清水 昌平  滋賀大学, データサイエンス学部, 教授 (10509871)
Project Period (FY) 2016-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥16,900,000 (Direct Cost: ¥13,000,000、Indirect Cost: ¥3,900,000)
Fiscal Year 2019: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2018: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2017: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2016: ¥8,190,000 (Direct Cost: ¥6,300,000、Indirect Cost: ¥1,890,000)
Keywords多変量解析 / パターン認識 / グラフ埋め込み / 次元削減 / 分散表現 / ニューラルネットワーク / マルチモーダル / 自然言語処理 / 漸近理論 / 画像検索
Outline of Final Research Achievements

Multi-domain association data consists of data vectors from various types of sources (called domains), such as images, tags, documents, etc., and the strength of associations between data vectors. Conventional multivariate analysis has dealt with one-to-one vector correspondence, and therefore, it cannot represent flexible data structures. In this study, we describe the relationship between vectors as a graph (network). Then, we have proposed and developed methods of information integration via dimensionality reduction, which preserves the graph structure as much as possible.

Academic Significance and Societal Importance of the Research Achievements

関連性データのグラフ構造をなるべく保存するようにデータベクトルを変換することをグラフ埋め込みという.正準相関分析など従来の多変量解析を一般化したグラフ埋め込み手法を提案し,画像と単語の相互検索などのタスクで有効性を確認した.ニューラルネットワークによる非線形変換を用いたグラフ埋め込み法を提案し,さらに外れ値の影響を軽減するロバスト化を行った.ベクトル間の内積とそれを発展させたニューラルネットワークモデルによって表現できる類似度関数のクラスを明らかにした.

Report

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

    (64 results)

All 2020 2019 2018 2017 2016 Other

All Journal Article (15 results) (of which Peer Reviewed: 15 results,  Open Access: 10 results) Presentation (48 results) (of which Int'l Joint Research: 17 results,  Invited: 2 results) Remarks (1 results)

  • [Journal Article] PAFit: An R Package for the Non-Parametric Estimation of Preferential Attachment and Node Fitness in Temporal Complex Networks2020

    • Author(s)
      Thong Pham, Paul Sheridan, Hidetoshi Shimodaira
    • Journal Title

      Journal of Statistical Software

      Volume: 92 Issue: 3 Pages: 1-30

    • DOI

      10.18637/jss.v092.i03

    • NAID

      120006950589

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Hyperlink regression via Bregman divergence2020

    • Author(s)
      Akifumi Okuno and Hidetoshi Shimodaira
    • Journal Title

      Neural Networks

      Volume: 126 Pages: 362-383

    • DOI

      10.1016/j.neunet.2020.03.026

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Joint Estimation of the Non-parametric Transitivity and Preferential Attachment Functions in Scientific Co-authorship Networks2020

    • Author(s)
      Masaaki Inoue, Thong Pham, Hidetoshi Shimodaira
    • Journal Title

      Journal of Informetrics

      Volume: -

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Segmentation-free Compositional n-gram Embedding2019

    • Author(s)
      Geewook Kim, Kazuki Fukui, Hidetoshi Shimodaira
    • Journal Title

      Proceedings of 2019 Annual Conference of the North American Chapter of the Association for Computational Linguistics (NAACL-HLT)

      Volume: - Pages: 3207-3215

    • DOI

      10.18653/v1/n19-1324

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Representation Learning with Weighted Inner Product for Universal Approximation of General Similarities2019

    • Author(s)
      Geewook Kim, Akifumi Okuno, Kazuki Fukui, Hidetoshi Shimodaira
    • Journal Title

      Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, IJCAI-19

      Volume: - Pages: 5031-5038

    • DOI

      10.24963/ijcai.2019/699

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] An Information Criterion for Auxiliary Variable Selection in Incomplete Data Analysis2019

    • Author(s)
      Imori, S., Shimodaira, H.
    • Journal Title

      Entropy

      Volume: 21 Issue: 3 Pages: 281-281

    • DOI

      10.3390/e21030281

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Graph Embedding with Shifted Inner Product Similarity and Its Improved Approximation Capability2019

    • Author(s)
      Akifumi Okuno, Geewook Kim, Hidetoshi Shimodaira
    • Journal Title

      Proceedings of Machine Learning Research, PMLR

      Volume: 89 Pages: 644-653

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Robust Graph Embedding with Noisy Link Weights2019

    • Author(s)
      Akifumi Okuno, Hidetoshi Shimodaira
    • Journal Title

      Akifumi Okuno, Hidetoshi Shimodaira ; Proceedings of Machine Learning Research, PMLR

      Volume: 89 Pages: 664-673

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] An information criterion for model selection with missing data via complete-data divergence2018

    • Author(s)
      Hidetoshi Shimodaira, Haruyoshi Maeda
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: 70 Issue: 2 Pages: 421-438

    • DOI

      10.1007/s10463-016-0592-7

    • Related Report
      2018 Annual Research Report 2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A probabilistic framework for multi-view feature learning with many-to-many associations via neural networks2018

    • Author(s)
      Akifumi Okuno, Tetsuya Hada, Hidetoshi Shimodaira
    • Journal Title

      Proceedings of the 35th International Conference on Machine Learning, PMLR

      Volume: 80 Pages: 3888-3897

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Transitivity vs Preferential Attachment: Determining the Driving Force Behind the Evolution of Scientific Co-Authorship Networks2018

    • Author(s)
      Masaaki Inoue, Thong Pham, Hidetoshi Shimodaira
    • Journal Title

      International Conference on Complex Systems, ICCS 2018: Unifying Themes in Complex Systems

      Volume: IX Pages: 262-271

    • DOI

      10.1007/978-3-319-96661-8_28

    • ISBN
      9783319966601, 9783319966618
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Word-like character n-gram embedding2018

    • Author(s)
      Geewook Kim, Kazuki Fukui and Hidetoshi Shimodaira
    • Journal Title

      Proceedings of the 2018 EMNLP Workshop W-NUT: The 4th Workshop on Noisy User-generated Text

      Volume: 4 Pages: 148-152

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A novel principle for causal inference in data with small error variance2018

    • Author(s)
      Patrick Bloebaum, Dominik Janzing, Takashi Washio, Shohei Shimizu, Bernhard Schoelkopf
    • Journal Title

      Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR

      Volume: 84 Pages: 900-909

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Non-Gaussian Methods for Causal Structure Learning2018

    • Author(s)
      Shimizu Shohei
    • Journal Title

      Prevention Science

      Volume: 20 Issue: 3 Pages: 431-441

    • DOI

      10.1007/s11121-018-0901-x

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Bidirectional Retrieval between Images and Multiple Tags Using Matching Correlation Analysis2016

    • Author(s)
      福井一輝, 奥野彰文, 下平英寿
    • Journal Title

      電子情報通信学会論文誌D 情報・システム

      Volume: J99-D Issue: 8 Pages: 774-777

    • DOI

      10.14923/transinfj.2015IUL0005

    • ISSN
      1880-4535, 1881-0225
    • Year and Date
      2016-08-01
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Presentation] 単語埋め込みの二種類の加法構成性2020

    • Author(s)
      Kim Geewook, 横井祥, 下平英寿
    • Organizer
      言語処理学会第26回年次大会(NLP2020)
    • Related Report
      2019 Annual Research Report
  • [Presentation] マルチスケールk-近傍法を用いた画像のタグ推定2019

    • Author(s)
      田中卓磨; 奥野彰文; 福井一輝; Kim Geewook; 下平英寿
    • Organizer
      第22回情報論的学習理論ワークショップ
    • Related Report
      2019 Annual Research Report
  • [Presentation] グラフと近傍グラフの確率的同時埋め込みによるマルチモーダルデータの可視化2019

    • Author(s)
      水谷守裕; 奥野彰文; 福井一輝; Kim Geewook; 金沢朋実; 白石 友一; 岡田眞里子; 下平英寿
    • Organizer
      第22回情報論的学習理論ワークショップ
    • Related Report
      2019 Annual Research Report
  • [Presentation] ニューラルネットワークを用いたグラフ埋め込みの表現 能力とその拡張2019

    • Author(s)
      奥野 彰文, Geewook Kim, 下平 英寿
    • Organizer
      統計関連学会連合大会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Hyperlink Regression via Bregman Divergence2019

    • Author(s)
      奥野 彰文, 下平 英寿
    • Organizer
      統計関連学会連合大会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Multiscale Bootstrap for Selective Inference with Applications to Model Selection2019

    • Author(s)
      Hidetoshi Shimodaira
    • Organizer
      Data Science, Statistics and Visualization (DSSV2019)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Multiview Graph Embedding as a Generalization of Canonical Correlation Analysis2019

    • Author(s)
      Hidetoshi Shimodaira
    • Organizer
      62nd ISI World Statistics Congress 2019 (ISI WSC 2019)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Statistical Estimation of the Effects of First and Second Order Local Structures on Growth of Complex Networks2019

    • Author(s)
      Masaaki Inoue, Thong Pham, Hidetoshi Shimodaira
    • Organizer
      ACML 2019 Workshop on Statistics & Machine Learning Researchers in Japan
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 擬ユークリッド空間への単語埋め込み2019

    • Author(s)
      Geewook Kim, 奥野 彰文, 下平 英寿
    • Organizer
      言語処理学会 第25回年次大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] On representation power of neural network-based graph embedding and beyond2018

    • Author(s)
      Akifumi Okuno and Hidetoshi Shimodaira
    • Organizer
      ICML2018 workshop Theoretical Foundations and Applications of Deep Generative Models
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] ニューラルネットワークを用いた異種データのグラフ埋め込み2018

    • Author(s)
      奥野 彰文, 下平英寿
    • Organizer
      2018年度 統計関連学会連合大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] マルチスケール・ブートストラップによるモデル選択後のselective inference2018

    • Author(s)
      寺田吉壱, 下平英寿
    • Organizer
      2018年度 統計関連学会連合大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 回帰モデルにおける補助変数を活用した推定精度の向上2018

    • Author(s)
      前田篤刀, 伊森晋平, 下平英寿
    • Organizer
      2018年度 統計関連学会連合大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 複雑ネットワーク成長メカニズムにおける優先的選択性と推移性のノンパラメトリック同時推定2018

    • Author(s)
      井上雅章, Pham THONG, 下平英寿
    • Organizer
      2018年度 統計関連学会連合大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 単語ベクトルを利用した文書の教師なし行列表現2018

    • Author(s)
      福井一輝, 下平英寿
    • Organizer
      情報論的学習理論と機械学習ワークショップ
    • Related Report
      2018 Annual Research Report
  • [Presentation] ロバストなグラフ埋め込み2018

    • Author(s)
      奥野彰文, 下平英寿
    • Organizer
      情報論的学習理論と機械学習ワークショップ
    • Related Report
      2018 Annual Research Report
  • [Presentation] ニューラルネットワークを用いたグラフ埋め込みの表現定理とその拡張2018

    • Author(s)
      奥野彰文, Geewook Kim, 下平英寿
    • Organizer
      情報論的学習理論と機械学習ワークショップ
    • Related Report
      2018 Annual Research Report
  • [Presentation] グラフ埋め込みの次数補正とその応用2018

    • Author(s)
      田中卓磨, 奥野彰文, 下平英寿
    • Organizer
      情報論的学習理論と機械学習ワークショップ
    • Related Report
      2018 Annual Research Report
  • [Presentation] 因果探索、予測、そして制御2018

    • Author(s)
      清水昌平
    • Organizer
      応用統計学会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Causal discovery, prediction mechanisms, and control2018

    • Author(s)
      S. Shimizu
    • Organizer
      The 5th meeting of the Institute of Mathematical Statistics (IMS) meeting series, the IMS Asia Pacific Rim Meeting (IMS-APRM)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Causal discovery, prediction, and control2018

    • Author(s)
      S. Shimizu
    • Organizer
      Causal Modeling and Machine Learning (CaMaL) Workshop
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 単語らしい文字n-gramの埋め込みによる単語の分散表現2018

    • Author(s)
      Kim Geewook, 福井一輝 , 羽田哲也 , 下平英寿
    • Organizer
      言語処理学会第24回年次大会(NLP2018)
    • Related Report
      2017 Annual Research Report
  • [Presentation] 単語分割を経由しない単語埋め込み2017

    • Author(s)
      押切孝将, 下平英寿
    • Organizer
      言語処理学会第23回年次大会
    • Place of Presentation
      筑波大学(茨城県・つくば市)
    • Year and Date
      2017-03-14
    • Related Report
      2016 Annual Research Report
  • [Presentation] 多対多対応を扱う相関分析の一致性について2017

    • Author(s)
      奥野彰文, 下平英寿
    • Organizer
      第11回日本統計学会春季集会
    • Place of Presentation
      政策研究大学院大学(東京都・港区)
    • Year and Date
      2017-03-05
    • Related Report
      2016 Annual Research Report
  • [Presentation] Leveraging local data structure for multi-view analysis with many-to-many associations2017

    • Author(s)
      Akifumi Okuno and Hidetoshi Shimodaira
    • Organizer
      Conference of the International Federation of Classification Societies (IFCS-2017)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Statistical consistency of multi-view correlation analysis with many-to-many associations2017

    • Author(s)
      Akifumi Okuno and Hidetoshi Shimodaira
    • Organizer
      Joint Statistical Meeting 2017
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Robust Multi-view Graph Embedding2017

    • Author(s)
      Akifumi Okuno and Hidetoshi Shimodaira
    • Organizer
      International Conference on Robust Statistics 2017
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Segmentation-Free Word Embedding for Unsegmented Languages2017

    • Author(s)
      Takamasa Oshikiri
    • Organizer
      Conference on Empirical Methods in Natural Language Processing (EMNLP 2017)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Spectral Graph-Based Method of Multimodal Word Embedding2017

    • Author(s)
      Kazuki Fukui, Takamasa Oshikiri, Hidetoshi Shimodaira
    • Organizer
      Workshop on Graph-based Methods for Natural Language Processing (TextGraphs-11)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Deep Multi-view Representation Learning Based on Adaptive Weighted Similarity2017

    • Author(s)
      Tetsuya Hada, Akifumi Okuno, Hidetoshi Shimodaira
    • Organizer
      First International Workshop on Symbolic-Neural Learning (SNL-2017)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] An Information Criterion For Prediction With Auxiliary Variables Under Covariate Shift2017

    • Author(s)
      Takahiro Ido, Shinpei Imori, Hidetoshi Shimodaira
    • Organizer
      IASC-ARS/NZSA 2017
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Cross-view link prediction with attribute vectors and its information criterion2017

    • Author(s)
      Akifumi Okuno, Hidetoshi Shimodaira
    • Organizer
      2017年度統計関連学会連合大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] クロスドメインマッチング相関分析による画像情報を反映した単語埋め込み2017

    • Author(s)
      福井 一輝, 押切 孝将, 下平 英寿
    • Organizer
      2017年度統計関連学会連合大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] マルチスケールブートストラップによる近似的に不偏なselective inference2017

    • Author(s)
      寺田 吉壱, 下平 英寿
    • Organizer
      2017年度統計関連学会連合大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 共変量シフトにおける補助変数を用いた予測と情報量規準2017

    • Author(s)
      井戸 貴大, 伊森 晋平, 下平 英寿
    • Organizer
      2017年度統計関連学会連合大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 属性ベクトルとニューラルネットワークを用いた異種データ間のリンク構造の最尤推定2017

    • Author(s)
      奥野彰文, 羽田哲也, 下平英寿
    • Organizer
      第20回情報論的学習理論ワークショップ
    • Related Report
      2017 Annual Research Report
  • [Presentation] クロスドメインマッチング相関分析を用いた画像とキャプションの同時埋め込み2017

    • Author(s)
      福井一輝,下平英寿
    • Organizer
      第20回情報論的学習理論ワークショップ
    • Related Report
      2017 Annual Research Report
  • [Presentation] 単語辞書を併用した単語分割しない単語埋め込み2017

    • Author(s)
      Geewook Kim,福井 一輝,羽田 哲也,下平 英寿
    • Organizer
      第20回情報論的学習理論ワークショップ
    • Related Report
      2017 Annual Research Report
  • [Presentation] 深層クロスドメインマッチング相関分析の提案とその応用2016

    • Author(s)
      羽田哲也, 福井一輝, 下平英寿
    • Organizer
      第19回情報論的学習理論ワークショップ
    • Place of Presentation
      京都大学(京都府・京都市)
    • Year and Date
      2016-11-16
    • Related Report
      2016 Annual Research Report
  • [Presentation] Image and tag retrieval by leveraging image-group links with multi-domain graph embedding2016

    • Author(s)
      Fukui, Kazuki and Okuno, Akifumi and Shimodaira, Hidetoshi
    • Organizer
      2016 IEEE International Conference on Image Processing
    • Place of Presentation
      Phoenix(アメリカ)
    • Year and Date
      2016-09-26
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] データベクトルのマッチングに関する情報統合の多変量解析とその最尤推定2016

    • Author(s)
      下平英寿
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      金沢大学(石川県・金沢市)
    • Year and Date
      2016-09-07
    • Related Report
      2016 Annual Research Report
  • [Presentation] マッチング相関分析を用いた多言語単語埋め込み2016

    • Author(s)
      押切孝将, 福井一輝, 下平英寿
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      金沢大学(石川県・金沢市)
    • Year and Date
      2016-09-07
    • Related Report
      2016 Annual Research Report
  • [Presentation] 多ドメインマッチング相関分析の深層ニューラルネットによる非線形化2016

    • Author(s)
      羽田哲也, 下平英寿
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      金沢大学(石川県・金沢市)
    • Year and Date
      2016-09-07
    • Related Report
      2016 Annual Research Report
  • [Presentation] 多対多対応を利用したマッチング相関分析の一致性について2016

    • Author(s)
      奥野彰文, 下平英寿
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      金沢大学(石川県・金沢市)
    • Year and Date
      2016-09-07
    • Related Report
      2016 Annual Research Report
  • [Presentation] Cross-Lingual Word Representations via Spectral Graph Embeddings2016

    • Author(s)
      Oshikiri, Takamasa and Fukui, Kazuki and Shimodaira, Hidetoshi
    • Organizer
      54th Annual Meeting of the Association for Computational Linguistics
    • Place of Presentation
      Berlin(ドイツ)
    • Year and Date
      2016-08-10
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A non-Gaussian approach for causal structure learning in the presence of hidden common causes2016

    • Author(s)
      Shimizu, Shohei
    • Organizer
      CRM Workshop: Statistical Causal Inference and its Applications to Genetics
    • Place of Presentation
      Montreal (Canada)
    • Year and Date
      2016-07-25
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 多ドメインマッチング相関分析のL1正則化法2016

    • Author(s)
      小嶋啓右, 廣瀬慧,下平英寿
    • Organizer
      情報論的学習理論と機械学習(IBISML)研究会
    • Place of Presentation
      沖縄科学技術大学院大学メインキャンパス(沖縄県・国頭郡恩納村)
    • Year and Date
      2016-07-06
    • Related Report
      2016 Annual Research Report
  • [Presentation] A non-Gaussian model for causal discovery in the presence of hidden common causes2016

    • Author(s)
      Shimizu, Shohei
    • Organizer
      Munich Workshop on Causal Inference and Information Theory
    • Place of Presentation
      Munich (Germany)
    • Year and Date
      2016-05-23
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Remarks] Shimodaira Lab

    • URL

      http://www.sigmath.es.osaka-u.ac.jp/shimo-lab/

    • Related Report
      2016 Annual Research Report

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

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