1993 Fiscal Year Annual Research Report

力学系と位相エントロピーの研究

Research Project

Project/Area Number	04640192
Research Institution	Science University of Tokyo
Principal Investigator	戸川美郎東京理科大学, 理工学部, 助教授 (20112899)
Co-Investigator(Kenkyū-buntansha)	須鎗弘樹東京理科大学, 理工学部, 助手 (70246685) 渡辺昇東京理科大学, 理工学部, 講師 (70191781) 下井田宏雄東京理科大学, 理工学部, 教授 (00112897) 宮沢政清東京理科大学, 理工学部, 教授 (80110948) 大矢雅則東京理科大学, 理工学部, 教授 (90112896)
Keywords	エントロピー理論 / 量子力学 / カオス / 位相エントロピー / 相互エントロピー / 遺伝子解析 / 待ち行列ネットワーク / 率保存則
Research Abstract	今年度の研究実績について述べる。エントロピー理論はClausius,Boltzmann,Shannon等に始まり、その後、von Neumannによって、量子力学の数学的構築が試みられ、量子系のエントロピー理論が生まれ、現在も様々な分野において、その研究が続けられている。本研究計画においても、以上のような背景にもとづいて、次に示すような研究実績をあげてきた。(1)解がカオス的に境界に漸近する力学系において、境界が存在する相空間上の位相的エントロピーのパラメーター依存性を調べた。(2)画像処理に用いられる回路の安定性の条件を見つけることができた。(3)光通信における誤り確率の定式化並びに相互エントロピーによる変調効率の比較等を行うことができた。(4)ガウス通信過程への相互エントロピーの応用等を論じた。(5)量子系のエントロピーの最大化、ファジーエントロピーの諸性質などについても論じた。(6)遺伝子解析にエントロピー理論を応用するため、2個の生物の塩基配列、あるいはアミノ酸列をコンピュータによって、整列化する際、DP matcingを用いたアルゴリズムを提案し、従来の整列化法を比較検討した。(7)また、2個の塩基配列だけでなく、n個の塩基配列を同時に整列化する方法も提案し、その速さ等を従来の方法と比較検討した。(8)RGSMP(Reallocatable Generalized Semi-Markov Process)と呼ばれる一般の待ち行列ネットワークに応用することが出来る確率過程を提案し、その基本的な特性の解析を調べた。(9)RGSMP の定常分布の構造をあらかじめ仮定することにより、RGSMP の状態推移の構造が定常分布にどのように反映しているかを議論した。(10)ポアソン到着を持つ無限窓口待ち行列の系内仕事量のモーメントを計算しバースト型到着モデルへの応用を論じた。(11)率保存則についてサーベイを行うとともに、パルム測度関する基本的な公式や各種の確率過程の定常分布を特徴づける式などがすべて率保存則より導かれることを示した。

Research Products

(26 results)

All Other

All Publications (26 results)

[Publications] T.Matsumoto,H.Kobayashi and Y.Togawa: "Spatial versus temporal stability issues in image processing neuro chips" IEE Trans.on Neural Networks. 3. 540-569 (1992)
[Publications] M.Ohya: "Quantum entropies and their maximizations" Maximum Entropy and Bayesian Methods. 12. 189-194 (1993)
[Publications] M.Ohya and N.watanabe: "Information dynamics and its application to Gaussian communication processes" Maximum Entropy and Bayesian Methods. 12. 195-203 (1993)
[Publications] M.Ohya and N.Muraki: "Note on continuity of information rate" Illinois J.of Math.36. 529-550 (1992)
[Publications] M.Ohya and Y.Uesaka: "Amino acids sequances and DP matching:A new methods for alignment" Journal of Information Sciences. 63. 139-151 (1992)
[Publications] M.Ohya,S.Miyazaki and K. Ogata: "On multiple alignment of genome sequences" Trans.of IEICE. E75-B. 453-457 (1992)
[Publications] M.Ohya and S.Naritsuka: "On fuzzy relative entropy" Open Systems and Information Dynamics. 1. 397-408 (1993)
[Publications] M.Ohya,N.Muraki and D.Petz: "Entropies of general quantum states" Open Systems and Information Dynamics. 1. 43-56 (1992)
[Publications] G.Yamazaki,K.Sigman and M.Miyazawa: "Moments in infinite channel queues" Computer and Mathematics with Applications. 24. 1-6 (1992)
[Publications] M.Miyazawa: "On the system queue length distributions of LCFS-P queues with arbitrary acceptance and restarting policies" J.Appl.Prob.29. 430-440 (1992)
[Publications] M.Miyazawa and G.Yamazaki: "Loss probability of a burst arrival finite queue with synchronized service" Probability in the Engineering and Informational Science. 5. 201-216 (1992)
[Publications] M.Miyazawa and G.Yamazaki: "Relationships in stationary jump processes with countable state space and their applications to queues" Stochastic Processes and their Applications. 43. 177-189 (1992)
[Publications] M.Miyazawa and Y.Takahashi: "Rate conservation principle for discrete time queues" Queueing Systems. 12. 215-229 (1992)
[Publications] M.Miyazawa and H.Tijms: "Comparison of twe approximations for the loss probability in finite buffer queues" Probability in the Engineering and Informational Science. 7. 19-27 (1993)
[Publications] I.Kino and M.Miyazawa: "The stationary work in system of a G/G/〓 gradual input queue" J.Appl.Prob.30. 207-222 (1993)
[Publications] H.Sakasegawa,M.Miyazawa and G.Yamazaki: "Evaluating the overflow probability using the infinite queue" Management Science. 39. 1238-1245 (1993)
[Publications] M.Miyazawa: "Insensitivity and product-form decomposability of Reallocatable GSMP" Adv.Appl.Prob.25. 415-437 (1993)
[Publications] M.Miyazawa and V.Schmidt: "On ladder height distributions of general risk processes" Annals of Applied Probability. 3. 763-776 (1993)
[Publications] M.Miyazawa and G.Yamazaki: "Note on batch arrival LCFS and related symmetric queues" OR letters. 43. 177-189 (1993)
[Publications] M.Miyazawa: "Rate conservation laws:a survey" Queueing Systems. 15 発表予定.
[Publications] 渡辺昇: "雑音のある通信路における光変調の効率について" 電子情報通信学会. J75-B-I. 744-750 (1992)
[Publications] N.Watanabe: "Efficiency of opetical modulations for channel with noise" 発表予定.
[Publications] M.Ohya,H.Suyari: "The Effect of Squeezing in the Attenuation Process" 京都大学数理解析研講究録. 発表予定.
[Publications] 須鎗弘樹: "量子マルコフ過程と情報力学" 京都大学数理解析研講究録. 発表予定.
[Publications] M.Ohya and D.Petz: "Quantum Entropy and its Use" Springer-Verlag, 335 (1993)
[Publications] 宮沢政清: "確率と確率過程" 近代科学社, 199 (1993)

1993 Fiscal Year Annual Research Report

力学系と位相エントロピーの研究

Principal Investigator

戸川 美郎 東京理科大学, 理工学部, 助教授 (20112899)

Research Products

[Publications] T.Matsumoto,H.Kobayashi and Y.Togawa: "Spatial versus temporal stability issues in image processing neuro chips" IEE Trans.on Neural Networks. 3. 540-569 (1992)

[Publications] M.Ohya: "Quantum entropies and their maximizations" Maximum Entropy and Bayesian Methods. 12. 189-194 (1993)

[Publications] M.Ohya and N.watanabe: "Information dynamics and its application to Gaussian communication processes" Maximum Entropy and Bayesian Methods. 12. 195-203 (1993)

[Publications] M.Ohya and N.Muraki: "Note on continuity of information rate" Illinois J.of Math.36. 529-550 (1992)

[Publications] M.Ohya and Y.Uesaka: "Amino acids sequances and DP matching:A new methods for alignment" Journal of Information Sciences. 63. 139-151 (1992)

[Publications] M.Ohya,S.Miyazaki and K. Ogata: "On multiple alignment of genome sequences" Trans.of IEICE. E75-B. 453-457 (1992)

[Publications] M.Ohya and S.Naritsuka: "On fuzzy relative entropy" Open Systems and Information Dynamics. 1. 397-408 (1993)

[Publications] M.Ohya,N.Muraki and D.Petz: "Entropies of general quantum states" Open Systems and Information Dynamics. 1. 43-56 (1992)

[Publications] G.Yamazaki,K.Sigman and M.Miyazawa: "Moments in infinite channel queues" Computer and Mathematics with Applications. 24. 1-6 (1992)

[Publications] M.Miyazawa: "On the system queue length distributions of LCFS-P queues with arbitrary acceptance and restarting policies" J.Appl.Prob.29. 430-440 (1992)

[Publications] M.Miyazawa and G.Yamazaki: "Loss probability of a burst arrival finite queue with synchronized service" Probability in the Engineering and Informational Science. 5. 201-216 (1992)

[Publications] M.Miyazawa and G.Yamazaki: "Relationships in stationary jump processes with countable state space and their applications to queues" Stochastic Processes and their Applications. 43. 177-189 (1992)

[Publications] M.Miyazawa and Y.Takahashi: "Rate conservation principle for discrete time queues" Queueing Systems. 12. 215-229 (1992)

[Publications] M.Miyazawa and H.Tijms: "Comparison of twe approximations for the loss probability in finite buffer queues" Probability in the Engineering and Informational Science. 7. 19-27 (1993)

[Publications] I.Kino and M.Miyazawa: "The stationary work in system of a G/G/〓 gradual input queue" J.Appl.Prob.30. 207-222 (1993)

[Publications] H.Sakasegawa,M.Miyazawa and G.Yamazaki: "Evaluating the overflow probability using the infinite queue" Management Science. 39. 1238-1245 (1993)

[Publications] M.Miyazawa: "Insensitivity and product-form decomposability of Reallocatable GSMP" Adv.Appl.Prob.25. 415-437 (1993)

[Publications] M.Miyazawa and V.Schmidt: "On ladder height distributions of general risk processes" Annals of Applied Probability. 3. 763-776 (1993)

[Publications] M.Miyazawa and G.Yamazaki: "Note on batch arrival LCFS and related symmetric queues" OR letters. 43. 177-189 (1993)

[Publications] M.Miyazawa: "Rate conservation laws:a survey" Queueing Systems. 15 発表予定.

[Publications] 渡辺 昇: "雑音のある通信路における光変調の効率について" 電子情報通信学会. J75-B-I. 744-750 (1992)

[Publications] N.Watanabe: "Efficiency of opetical modulations for channel with noise" 発表予定.

[Publications] M.Ohya,H.Suyari: "The Effect of Squeezing in the Attenuation Process" 京都大学数理解析研講究録. 発表予定.

[Publications] 須鎗 弘樹: "量子マルコフ過程と情報力学" 京都大学数理解析研講究録. 発表予定.

[Publications] M.Ohya and D.Petz: "Quantum Entropy and its Use" Springer-Verlag, 335 (1993)

[Publications] 宮沢 政清: "確率と確率過程" 近代科学社, 199 (1993)

戸川美郎東京理科大学, 理工学部, 助教授 (20112899)

[Publications] 渡辺昇: "雑音のある通信路における光変調の効率について" 電子情報通信学会. J75-B-I. 744-750 (1992)

[Publications] 須鎗弘樹: "量子マルコフ過程と情報力学" 京都大学数理解析研講究録. 発表予定.

[Publications] 宮沢政清: "確率と確率過程" 近代科学社, 199 (1993)