研究者詳細 - 藤田　敏治

論文 - 藤田　敏治

分割表示61 件中 1 - 20 件目／全件表示 >>

COMPLEMENTARY DUALS—BOTH FIXED POINTS (III)— 国際誌

Iwamoto S., Kimura Y., Fujita T.

Bulletin of the Kyushu Institute of Technology - Pure and Applied Mathematics 2024 ( 71 ) 13 - 42 2024年03月

担当区分：責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

We consider a quadratic minimization problem with both fixed endpoints and its associated maximization problem from a viewpoint of complementarity. We show that a complementary identity with an elementary inequality generates a pair of (n-1)-variable minimization problem (primal) and (n + 1)-variable maximization one (dual). The identity produces an equality condition, which is a linear system of 2n-equation on 2n-variable. The condition splits into a pair of linear systems of (n-1)-equation on (n - 1)-variable and of (n + 1)-equation on (n + 1)-variable. The former solves the primal, while the latter does the dual. Both the optimal solutions are characterized by the Fibonacci sequence. The solutions are also given through dynamic programming.

DOI： 10.18997/0002000380

Scopus

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Golden Ratio Flap Designed Using the Golden Ratio Rectangle 査読有り国際誌

Sakamoto A., Fujita T., Noguchi T., Matsuda S.

Plastic and Reconstructive Surgery - Global Open 12 ( 1 ) 2024年01月

記述言語：英語掲載種別：研究論文（学術雑誌）

Background: Rotation flaps are arcuate repairs that redistribute tension vectors and recruit adjacent and/or distant tissue laxity. The incision curve could be a logarithmic spiral curve to reduce the length of an incision. We propose a rotation flap - the golden ratio flap - designed using a golden rectangle. Methods: The flap incision is an arc though the major square which is beside the minor square of a golden rectangle. The defect is attached to the line of another minor square and diagonal to the major square. The bottom line runs from the incision end to the tangent point of the circle or the oval, and the perpendicular height line runs from the bottom line to the cross point of the flap incision. These parameters were analyzed retrospectively for four superficial sarcomas that were treated using a rotation flap with an incision approximating the logarithmic spiral curve. Results: The ratio of height to bottom of the golden ratio flap design was highly similar to the preoperative flap design in the four cases assessed. With the new design, the ratio of bottom to the defect diameter (minor axis in the oval defect) was 1.3, and for the height, it was 1.4. Conclusions: The golden ratio flap, designed using the golden rectangle, is reproducible. The parameters of height and bottom approximate the flap shape, or the length and width, respectively. For clinical applications, step-by-step guidance for drawing the new flap are also proposed.

DOI： 10.1097/GOX.0000000000005508

Kyutacar

Scopus

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CONVERGING MARKOV DECISION PROCESSES WITH MULTIPLICATIVE REWARD SYSTEM 国際誌

Fujita T.

Bulletin of the Kyushu Institute of Technology - Pure and Applied Mathematics 2023 ( 70 ) 33 - 41 2023年03月

担当区分：筆頭著者,　最終著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

We consider multiplicative reward system on a finite-stage converging decision process in stochastic environment. In this paper, we give a recursive method by dynamic programming under the assump-tion that the order in which decisions are taken is predetermined.

DOI： 10.18997/00009112

Scopus

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85158091522&origin=inward

ON COMPLEMENTARY DUALS—BOTH FIXED POINTS (II) 国際誌

Iwamoto S., Kimura Y., Fujita T.

Bulletin of the Kyushu Institute of Technology - Pure and Applied Mathematics 69 7 - 34 2022年03月

担当区分：最終著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

We consider a quadratic minimization (primal) problem with both fixed endpoints and its associated maximization (dual) problem from a view point of complementarity. We show that a new complementary identity produces the pair with an equality condition. The condition is a linear system of (2n + 1)-equation on (2n + 1)-variable. The system yields a couple of solutions; one is a minimum solution to n-variable primal and the other is a maximum one to (n + 1)-variable dual. Both the solutions turn out to be complementary. The optimal solution is characterized by the backward Fibonacci sequence. The duality is enhanced through conjugate function. The optimal solution is also given by dynamic programming.

DOI： 10.18997/00008773

Scopus

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85135371991&origin=inward

Converging decision processes with multiplicative reward system

Fujita T.

Bulletin of the Kyushu Institute of Technology - Pure and Applied Mathematics 2021 ( 68 ) 9 - 26 2021年03月

担当区分：責任著者記述言語：英語掲載種別：研究論文（大学，研究機関等紀要）

Converging decision process is a decision process model with converging transition, which is one of the nonserial branch systems proposed by Nemhauser. This paper deals with multiplicative reward system on a finite-stage deterministic converging decision process. The purpose of this work is to give a recursive method to solve our model by bidecision approach.

Scopus

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On Complementary Duals—Both Fixed Points—

Iwamoto S., Kimura Y., Fujita T.

Bulletin of the Kyushu Institute of Technology - Pure and Applied Mathematics 2020 ( 67 ) 1 - 28 2020年03月

担当区分：責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

© 2020, Kyushu Institute of Technology. All rights reserved. We consider a quadratic minimization (primal) problem with both ﬁxed endpoints and its associated maximization (dual) problem from a view point of complementarity. We focus on a pair of linear terms, which generates the respective quadratic functions (sums of squares) through an elementary inequality. We show that a complementary identity plays a fundamental part in establishing a dual relation between primal and dual. The identity produces the pair with an equality condition. The condition turns out to be a linear system of 2n-equation in 2n-variable. The system yields a couple of solutions, one is a minimum solution and the other is a maximum one. In the n-variable pair, both the solutions turn out to be complementary. The optimal solution is characterized by the backward Fibonacci sequence. The duality is enhanced through conjugate function. The solution is also given by dynamic programming. Thus Fibonacci complementary duality is established through the complementary identity approach.

Scopus

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85084918862&origin=inward

A dynamic programming algorithm for optimizing baseball strategies 査読有り

Kira Akifumi, Inakawa Keisuke, Fujita Toshiharu

Journal of the Operations Research Society of Japan 62 ( 2 ) 64 - 82 2019年04月

記述言語：英語掲載種別：研究論文（学術雑誌）

<p>In this paper, baseball is formulated as a finite non-zero-sum Markov game with approximately 6.45 million states. We give an effective dynamic programming algorithm which computes equilibrium strategies and the equilibrium winning percentages for both teams in less than 2 second per game. Optimal decision making can be found depending on the situation—for example, for the batting team, whether batting for a hit, stealing a base or sacrifice bunting will maximize their win percentage, or for the fielding team, whether to pitch to or intentionally walk a batter, yields optimal results. Based on this model, we discuss whether the last-batting team has an advantage. In addition, we compute the optimal batting order, in consideration of the decision making in a game.</p>

DOI： 10.15807/jorsj.62.64

Kyutacar

CiNii Article

その他リンク： https://ci.nii.ac.jp/naid/130007636494

Three recursive approaches for decision processes with a converging branch system

Fujita T.

Bulletin of the Kyushu Institute of Technology - Pure and Applied Mathematics 2018 ( 65 ) 1 - 21 2018年03月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（学術雑誌）

© 2018, Kyushu Institute of Technology. All rights reserved. In this paper, we consider a decision process model with a converging branch system that is a nonserial transition system. The model is treated by three approaches. Thus we introduce three types of recursive equations by using a dynamic programming technique.

Scopus

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Sure Way to Win a Game Using a Mutually Dependent Decision Process Model 招待有り査読有り国際誌

Toshiharu Fujita

Journal of the Operations Research Society of Japan ( 公益社団法人日本オペレーションズ・リサーチ学会 ) 60 ( 2 ) 110 - 121 2017年04月

担当区分：筆頭著者,　最終著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

The purpose of this study is to consider the problem of finding a guaranteed way of winning a certain two-player combinatorial game of perfect knowledge from the standpoint of mutually dependent decision processes (MDDPs). Our MDDP model comprises two one-stage deterministic decision processes. Each decision process expresses every turn of a player. We analyze a MDDP problem in which the length of turns taken by a player is minimized, allowing him to win regardless of the decisions made by his opponent. The model provides a formulation for finding the shortest guaranteed strategy. Although computational complexity remains, the concept introduced in this paper can also be applied to other two-player combinatorial games of perfect knowledge.

DOI： 10.15807/jorsj.60.110

Scopus

CiNii Article

CiNii Research

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合流型推移をもつ決定過程 : ある種の最大加法型評価について (確率的環境下での数理的意思決定とその周辺) 査読有り

藤田敏治

数理解析研究所講究録 ( 京都大学数理解析研究所 ) 2242 60 - 68 2023年04月

ある種の分岐・合流型決定過程について : 決定過程としてのニューラルネットワーク査読有り

藤田敏治

数理解析研究所講究録 ( 京都大学数理解析研究所 ) 2220 19 - 29 2022年05月

折り紙ユニットで構成可能な凸多面体の合同判定

藤田　敏治

京都大学数理解析研究所講究録 2044 182 - 192 2017年09月

Complementary Versus Shift Dualities 査読有り

Seiichi Iwamoto, Yutaka Kimura, Toshiharu Fujita

Journal of Nonlinear and Convex Analysis 17 ( 8 ) 1547 - 1555 2016年08月

相互依存型決定過程－１ステージモデル－

藤田　敏治

京都大学数理解析研究所講究録 1990 204 - 212 2016年04月

Mutually dependent decision processes models 国際誌

Fujita T.

Bulletin of the Kyushu Institute of Technology - Pure and Applied Mathematics 2016 ( 63 ) 15 - 26 2016年03月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（学術雑誌）

© 2016, Kyushu Institute of Technology. All Rights Reserved.We introduce a new framework for dynamic programming called mutually dependent decision processes (MDDPs). Each MDDPs model is constructed from two or more finite-stage deterministic decision processes. At each stage, the reward in one process depends on the optimal values of the other processes, whose initial state is determined by the current state and decision of the original process. We formulate the MDDPs models and derive their mutually dependent recursive equations by dynamic programming.

Scopus

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A dynamic programming algorithm for optimizing baseball strategies

Akifumi Kira, Keisuke Inakawa, Toshiharu Fujita and Kotaro Ohori

MI Preprint Series, Kyushu University MI2015 ( 10 ) 1 - 18 2015年10月

Primal-Dual Optimization through A-G Inequality (Nonlinear Analysis and Convex Analysis)

岩本誠一, 木村寛, 藤田敏治

数理解析研究所講究録 ( 京都大学数理解析研究所 ) ( 1963 ) 122 - 129 2015年10月

相互依存型マルコフ決定過程－結合型評価－

藤田　敏治

京都大学数理解析研究所講究録 1939 189 - 195 2015年04月

A Golden Complementary Duality in Quadratic Optimization Problem 査読有り

Seiichi Iwamoto, Yutaka Kimura, Toshiharu Fujita

Proceedings of the Third Asian Conference on Nonlinear Analysis and Optimization 115 - 125 2015年03月

SURE WAYS TO WIN A GAME - NONDETERMINISTIC DYNAMIC PROGRAMMING APPROACH -

Toshiharu Fujita

Bulletin of the Kyushu Institute of Technology 62 1 - 14 2015年03月

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