7学期講義/数理情報工学輪講

新着情報

13:00~16:00

科目区分

計数数理:必修

教員

各教員

場所


教科書・参考書

山本教員
  • Thomas M. Cover and Joy A. Thomas, Elements of Information Theory (2nd Ed.) Wiley, 2006

牧野教員
  • W. J. Cook, W. H. Cunningham, W. R. Pulleyblank, and A. Schrijver, Combinatorial Optimization, John Wiley and Sons, New York, 1998. (ISBN : 0-471-55894-X)

松尾教員
  • E. Zeidler, Applied Functional Analysis, Speringer-Verlag, New York, 1995.

竹村教員
  • R. Stanley, An introduction to hyperplane arrangements, In: Geometric Combinatorics, (eds. E. Miller, V. Reiner and B. Sturmfels), IAS/Park CityMathematics Series, 13, American Mathematical Society, 007, pp. 389-496

山西教員
  • Pattern Recognition and Machine Learning, Christopher M. Bishop, Springer (2006)

國廣教員
  • Hans Delfs and H. Knebl, Introduction to Cryptography : Principles and Applications, 2007.

室田教員
  • H. Akaike: A new look at the statistcal model identification, IEEE Transactions on Automatic Control, Vol. AC-19 (1974) pp. 716-723. [情報量規準AIC]
  • H. Akaike: On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method, Annals of the Institute of Statistical Mathematics, Vol. 11 (1959), pp. 1-16. [最急降下法]
  • J. Edmonds: Submodular functions, matroids and certaion polyhedra, in : R. Guy, H. Hanani, N. Sauer, and J. Schoenheim, eds. , Combinatorial Structures and Their Applications, Gordon and Breach, New York, 1970, pp.69-87.
  • M. Juenger, G. Reinelt, G. Rinaldi, eds. , Combinatorial Optimization -- Eureka, You Shrink!, Lecture Notes in Computer Science, 2570, Springer-Verlag, 2003, pp. 11-26. [劣モジュラ関数]
  • J. Edmonds: Matroid and the greedy algorithm, Mathematical Programming, Vol. 1 (1971), pp. 127-136. [貪欲算法]
  • W. Fenchel: On conjugate convex functions, Canadian Journal of Mathematics, Vol. 1 (1949), pp. 73-77. [共役凸関数]
  • L. R. Ford and D. R. Fulkerson: Maximum flow through a network, Canadian Journal of Mathematics, Vol. 8 (1956), pp. 399-404. [最大流問題]
  • J. B. Kruskal: On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical Society, Vol. 7 (1956), pp. 48-50. [最小木の算法]
  • L. Lovasz: On the Shannon capacity of graphs, IEEE Transactions on Information Theory, Vol. 25 (1979), pp. 1-7. [離散最適化における半正定値計画]
  • R. T. Rockafellar: Extension of Fenchel's duality theorem for convex functions, Duke Mathematical Journal, Vol. 33 (1966), pp. 81-89. [凸関数のFenchel 双対定理]

増田教員
  • D. J. Watts, S. H. Strogatz. Collective dynamics of `small-world' networks. Nature, Vol. 393, pp. 440-442 (1998).
  • A. L. Barabasi, R. Albert. Emergence of scaling in random networks. Science, Vol. 286, pp. 509-512 (1999).
  • R. Albert, H. Jeong, A. L. Barabasi. Error and attack tolerance of complex networks, Nature. Vol. 406, pp. 378-382 (2000).
  • L. A. Adamic, R. M. Lukose, A. R. Puniyani, B. A. Huberman. Search in power-law networks. Physical Review E, Vol. 64, article No. 046135 (2001).
  • R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, U. Alon. Network motifs: simple building blocks of complex networks. Science, Vol. 298, pp. 824-827 (2002).
  • M. Girvan, M. E. J. Newman. Community structure in social and biological networks. Proceedings of the National Academy of Sciences of the United States of America, Vol. 99, pp. 7821-7826 (2002).
  • A. Clauset, C. Moore, M. E. J. Newman. Hierarchical structure and the prediction of missing links in networks. Nature, Vol. 453, pp. 98-101 (2008).

寒野教員
  • R. E. Leine and N. van de Wouw, Stability and Convergence of Mechanical Systems with Unilateral Constraints, Springer-Verlag, Berlin, 2008.

鈴木(秀)教員
  • J. D. Murray, Mathematical Biology (3rd ed.), Vol I & II, Springer, 2002-2003.

成績評価


過去問


シケプリ


シラバス

科学文献の輪講を通して,文献調査の方法,理解したことの伝え方,科学論文の書き方などを学習する。

関連サイト


講義まとめ

前半(4/19-5-24): 山本、牧野、松尾、竹村、山西教員から1名選択
後半(5/31-7/5): 國廣、室田、増田、寒野、鈴木(秀)教員から1名選択

  • 最終更新:2010-04-10 20:13:06

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