Networks, Games, and Dynamics: From Dynamical Systems and Stochastic Analysis to Transportation Theory and Optimal Control
暫譯: 網絡、遊戲與動態：從動態系統與隨機分析到交通理論與最優控制
Saburov, Mansoor, Hovakimyan, Naira, Bagdasaryan, Armen
- 出版商: Birkhauser Boston
- 出版日期: 2025-12-06
- 售價: $8,730
- 貴賓價: 9.5 折 $8,294
- 語言: 英文
- 頁數: 308
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3032091756
- ISBN-13: 9783032091758
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相關分類:
控制系統 Control-systems
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商品描述
This contributed volume provides an integrated perspective on modern mathematical and computational techniques for addressing complex problems in networks, control systems, learning, and game theory. It encompasses state-of-the-art research from a diverse range of disciplines, including dynamical systems, stochastic analysis, optimization, game theory, machine learning, and transportation theory. Particular emphasis is placed on connecting rigorous theoretical developments with real-world applications.
This volume is organized into twelve chapters. The first part (Chapters 1-6) addresses the optimal transportation problem in traffic networks. The second part (Chapters 7-11) investigates Markov chains with memory by examining the geometric, algebraic, dynamical, and ergodic properties of quadratic (polynomial) stochastic operators associated with cubic stochastic hypermatrices. Finally, Chapter 12 illustrates how methods from stochastic analysis and dynamical systems can be applied to lattice models of statistical mechanics defined on a Cayley tree.
Intended to serve as a comprehensive reference for academics and researchers, this volume may also benefit practitioners and anyone interested in exploring the interplay among these fields.
商品描述(中文翻譯)
本書提供了一個綜合的視角，探討現代數學和計算技術在解決網絡、控制系統、學習和博弈論中的複雜問題的應用。它涵蓋了來自多個學科的最前沿研究，包括動態系統、隨機分析、優化、博弈論、機器學習和交通理論。特別強調將嚴謹的理論發展與現實世界的應用相連接。
本書共分為十二章。第一部分（第1-6章）探討交通網絡中的最優運輸問題。第二部分（第7-11章）通過檢視與立方隨機超矩陣相關的二次（多項式）隨機算子的幾何、代數、動態和遍歷性質，研究具有記憶的馬可夫鏈。最後，第12章說明了如何將隨機分析和動態系統的方法應用於定義在凱萊樹上的統計力學格子模型。
本書旨在作為學術界和研究人員的綜合參考資料，對於實務工作者及任何有興趣探索這些領域之間相互作用的人士也將有所裨益。
作者簡介
Mansoor Saburov is an Associate Professor at the Gulf University for Science and Technology. He received his PhD in Mathematics (2011) from the International Islamic University Malasia. His research interests lie in dynamical systems, functional analysis, quantum probability, and (p)-adic analysis.
Naira Hovakimyan is a Professor at the University of Illinois at Urbana-Champaign, USA. She received her PhD in Physics and Mathematics (1992) from the Institute of Applied Mathematics of the Russian Academy of Sciences. Her research interests include control and optimization, autonomous systems, machine learning, neural networks, and their applications.
Armen Badgasaryan is Researcher at the Institute of Mathematics of the National Academy of Sciences, Armenia, and Associate Professor at the Institute of Mathematics and Informatics of Russian-Armenian University, Armenia. He holds a Ph.D. in applied mathematics (2000) from the Russian Academy of Sciences. He does research in the fields of number theory, analysis, dynamical systems, optimization and control, and optimal transport.
作者簡介(中文翻譯)
Mansoor Saburov 是海灣科技大學的副教授。他於2011年在馬來西亞國際伊斯蘭大學獲得數學博士學位。他的研究興趣包括動態系統、泛函分析、量子概率以及(p)-進分析。
Naira Hovakimyan 是美國伊利諾伊大學香檳分校的教授。她於1992年在俄羅斯科學院應用數學研究所獲得物理與數學博士學位。她的研究興趣包括控制與優化、自主系統、機器學習、神經網絡及其應用。
Armen Badgasaryan 是亞美尼亞國家科學院數學研究所的研究員，以及亞美尼亞俄羅斯聯合大學數學與資訊學研究所的副教授。他於2000年在俄羅斯科學院獲得應用數學博士學位。他的研究領域包括數論、分析、動態系統、優化與控制以及最優運輸。
