Multilayer networks is a rising topic in Network Science which characterizes the structure and the function of complex systems formed by several interacting networks. Multilayer networks research has been propelled forward by the wide realm of applications in social, biological and infrastructure networks and the large availability of network data, as well as by the significance of recent results, which have produced important advances in this rapidly growing field. This book presents a comprehensive account of this emerging field. It provides a theoretical introduction to the main results of multilayer network science.

This book is a comprehensive introduction to quantitative approaches to complex adaptive systems. Practically all areas of life on this planet are constantly confronted with complex systems, be it ecosystems, societies, traffic, financial markets, opinion formation and spreading, or the internet and social media. Complex systems are systems composed of many elements that interact strongly with each other, which makes them extremely rich dynamical systems showing a huge range of phenomena. Properties of complex systems that are of particular importance are their efficiency, robustness, resilience, and proneness to collapse.
The quantitative tools and concepts needed to understand the co-evolutionary nature of networked systems and their properties are challenging. The book gives a self-contained introduction to these concepts, so that the reader will be equipped with a toolset that allows them to engage in the science of complex systems. Topics covered include random processes of path-dependent processes, co-evolutionary dynamics, dynamics of networks, the theory of scaling, and approaches from statistical mechanics and information theory. The book extends beyond the early classical literature in the field of complex systems and summarizes the methodological progress made over the past 20 years in a clear, structured, and comprehensive way.

"Simulation," writes Gary Flake in his preface, "becomes a form of experimentation in a universe of theories. The primary purpose of this book is to celebrate this fact."In this book, Gary William Flake develops in depth the simple idea that recurrent rules can produce rich and complicated behaviors. Distinguishing "agents" (e.g., molecules, cells, animals, and species) from their interactions (e.g., chemical reactions, immune system responses, sexual reproduction, and evolution), Flake argues that it is the computational properties of interactions that account for much of what we think of as "beautiful" and "interesting." From this basic thesis, Flake explores what he considers to be today's four most interesting computational topics: fractals, chaos, complex systems, and adaptation.Each of the book's parts can be read independently, enabling even the casual reader to understand and work with the basic equations and programs. Yet the parts are bound together by the theme of the computer as a laboratory and a metaphor for understanding the universe. The inspired reader will experiment further with the ideas presented to create fractal landscapes, chaotic systems, artificial life forms, genetic algorithms, and artificial neural networks.

Stuart Kauffman here presents a brilliant new paradigm for evolutionary biology, one that extends the basic concepts of Darwinian evolution to accommodate recent findings and perspectives from the fields of biology, physics, chemistry and mathematics. The book drives to the heart of the exciting debate on the origins of life and maintenance of order in complex biological systems. It focuses on the concept of the spontaneous emergence of order that is widely observed throughout nature Kauffman argues that self-organization plays an important role in the Darwinian process of natural selection. Yet until now no systematic effort has been made to incorporate the concept of self-organization into evolutionary theory. The construction requirements which permit complex systems to adapt are poorly understood, as is the extent to which selection itself can yield systems able to adapt more successfully. This book explores these themes. It shows how complex systems,
contrary to expectations, can spontaneously exhibit stunning degrees of order, and how this order, in turn, is essential for understanding the emergence and development of life on Earth. Topics include the new biotechnology of applied molecular evolution, with its important implications for developing new drugs and vaccines; the balance between order and chaos observed in many naturally occurring systems; new insights concerning the predictive power of statistical mechanics in biology; and other major issues. Indeed, the approaches investigated here may prove to be the new center around which biological science itself will evolve. The work is written for all those interested in the cutting edge of research in the life sciences.

该书是一本von Neumann关于“自复制自动机”的研究论文集，由von Neumann在密西根大学的助手Arthur Burk（大名鼎鼎的John Holland的博士导师）整理编辑。
这本书的意义不仅仅在于它实际上开创了“人工生命”、“细胞自动机”等多门复杂性研究的分支。更重要的是，该书将“自我复制”作为生命的一个本质特征加以数学建模的研究。而这套理论和可计算性理论、歌德尔定理以及热力学深深地联系到了一起。这一点也许对于我们研究复杂系统的人来说仍具有重要的意义。

生命体、城市、公司，乃至一切复杂万物，是否都存在相通的内在生长逻辑？制约生命与死亡、城市化的扩张及公司寿命的决定因素究竟是什么？人类能否通过融汇生物学、物理学、社会学、经济学等跨学科知识，找到揭开复杂万物生长背后的简单法则？
享誉全球的复杂系统性科学研究中心圣塔菲研究所前所长杰弗里•韦斯特潜心研究数十年，经过反复试验和求证，终于找到了解构复杂世界的简单逻辑——规模法则。在韦斯特眼中，规模成为衡量世间万物的不变标准，利用规模法则，复杂世界变得可量化、可预测、清晰明了且极度统一。规模法则阐明了从生命体到城市、从经济体到公司的生长与衰败都离不开其自身规模的制约，并与其规模呈一定比例关系，遵守统一的公式。这一算法框架不仅为人类思考未知世界提供了难得的简单法则，而且能解答不同生命体的生长极限之谜，优化城市发展架构并找到推动经济实现可持续发展、公司从初创到卓越的生长曲线。
《规模》将帮助你重新思考生命、认识自身、了解你的生活与工作，并告诉你复杂世界其实充满简单的逻辑，只要跳脱思维框架，打破学科限制，你就会重新看清你周遭的一切。

The articles in this "Control & Chaos" volume are an outgrowth of a US-Australia workshop held in Hawaii in 1995. Experts in dynamical systems theory and control theory from the US and Australia, as well as England and Japan, focused on the problem of controlling nonlinear and potentially chaotic systems using limited control effort. The formal contributions take into account the discussions and commentaries of the participants and are reflected at the end of each article. Part I contains papers dealing with modeling, behavior, reconstruction, prediction and numerics. Part II deals with controlling complex systems by means of embedding unstable periodic orbits, targeting, filtering, optimization and adaptive methods. Part III contains four applications papers including the control of a bouncing ball, evolutionary stability, chaos in ecosystems, and neural networks.

This text is intended for the general reader who is interested in science. The author is a physicist who is well known for his development of the property called "self organized criticality", a property or phenomenon that lies at the heart of large dynamical systems. It can be used to analyze systems that are complicated, and which are part of the new science of complexity. It is a unifying concept that can be used to study phenomena in fields as diverse as economics, astronomy, the earth sciences, and physics. The author discusses his discovery of self organized criticality, its relation to the world of classical physics computer simulations and experiments which aid scientists' understanding of the property and the relation of the subject to popular areas such as fractal geometry and power laws cellular automata, and a wide range of practical applications.

This book comprehensively discusses the neural network models from a statistical mechanics perspective. It starts with one of the most influential developments in the theory of neural networks: Hopfield's analysis of networks with symmetric connections using the spin system approach and using the notion of an energy function from physics. Introduction to the Theory of Neural Computation uses these powerful tools to analyze neural networks as associative memory stores and solvers of optimization problems. A detailed analysis of multi-layer networks and recurrent networks follow. The book ends with chapters on unsupervised learning and a formal treatment of the relationship between statistical mechanics and neural networks. Little information is provided about applications and implementations, and the treatment of the material reflects the background of the authors as physicists. However the book is essential for a solid understanding of the computational potential of neural networks. Introduction to the Theory of Neural Computation assumes that the reader is familiar with undergraduate level mathematics, but does not have any background in physics. All of the necessary tools are introduced in the book.

Physics and computer science genius Stephen Wolfram, whose Mathematica computer language launched a multimillion-dollar company, now sets his sights on a more daunting goal: understanding the universe. Wolfram lets the world see his work in
, a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modeling complex systems.

This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set.
Contents
Part I. Basic Complexity Classes: 1. The computational model - and why it doesn’t matter; 2. NP and NP completeness; 3. Diagonalization; 4. Space complexity; 5. The polynomial hierarchy and alternations; 6. Boolean circuits; 7. Randomized computation; 8. Interactive proofs; 9. Cryptography; 10. Quantum computation; 11. PCP theorem and hardness of approximation: an introduction; Part II. Lower Bounds for Concrete Computational Models: 12. Decision trees; 13. Communication complexity; 14. Circuit lower bounds; 15. Proof complexity; 16. Algebraic computation models; Part III. Advanced Topics: 17. Complexity of counting; 18. Average case complexity: Levin’s theory; 19. Hardness amplification and error correcting codes; 20. Derandomization; 21. Pseudorandom constructions: expanders and extractors; 22. Proofs of PCP theorems and the Fourier transform technique; 23. Why are circuit lower bounds so difficult?; Appendix A: mathematical background.
Reviews
Pre-Publication Review: "This text is a major achievement that brings together all of the important developments in complexity theory. Student and researchers alike will find it to be an immensely useful resource."
Michael Sipser, MIT, author of Introduction to the Theory of Computation
Pre-Publication Review: "Computational complexity theory is at the core of theoretical computer science research. This book contains essentially all of the (many) exciting developments of the last two decades, with high level intuition and detailed technical proofs. It is a must for everyone interested in this field."
Avi Wigderson, Professor, Institute for Advanced Study, Princeton
Pre-Publication Review: "This book by two leading theoretical computer scientists provides a comprehensive,insightful and mathematically precise overview of computational complexity theory, ranging from early foundational work to emerging areas such as quantum computation and hardness of approximation. It will serve the needs of a wide audience, ranging from experienced researchers to graduate students and ambitious undergraduates seeking an introduction to the mathematical foundations of computer science. I will keep it at my side as a useful reference for my own teaching and research."
Richard M. Karp, University Professor, University of California at Berkeley

In a rented convent in Santa Fe, a revolution has been brewing. The activists are not anarchists, but rather Nobel Laureates in physics and economics such as Murray Gell-Mann and Kenneth Arrow, and pony-tailed graduate students, mathematicians, and computer scientists down from Los Alamos. They've formed an iconoclastic think tank called the Santa Fe Institute, and their radical idea is to create a new science called complexity. These mavericks from academe share a deep impatience with the kind of linear, reductionist thinking that has dominated science since the time of Newton. Instead, they are gathering novel ideas about interconnectedness, coevolution, chaos, structure, and order - and they're forging them into an entirely new, unified way of thinking about nature, human social behavior, life, and the universe itself. They want to know how a primordial soup of simple molecules managed to turn itself into the first living cell - and what the origin of life some four billion years ago can tell us about the process of technological innovation today. They want to know why ancient ecosystems often remained stable for millions of years, only to vanish in a geological instant - and what such events have to do with the sudden collapse of Soviet communism in the late 1980s. They want to know why the economy can behave in unpredictable ways that economists can't explain - and how the random process of Darwinian natural selection managed to produce such wonderfully intricate structures as the eye and the kidney. Above all, they want to know how the universe manages to bring forth complex structures such as galaxies, stars, planets, bacteria, plants, animals, and brains. There are commonthreads in all of these queries, and these Santa Fe scientists seek to understand them. Complexity is their story: the messy, funny, human story of how science really happens. Here is the tale of Brian Arthur, the Belfast-born economist who stubbornly pushed his theories of economic ch

本书是诺贝尔经济学奖得主司马贺的代表作之一，是1996年修订出版的第三版的中译本。第三版增加了全新的一章“复杂性面面观”，修改了文字内容并更新了部分数据。
作者率先构造出“人工科学”的概念，据以将经济学、思维心理学、学习科学、设计科学、管理学、复杂性研究等领域贯穿联系起来，使人获得很多启迪。本书对传统思维提出挑战，指出人工智能所期望达到的领域，揭示了人工性和层级对于复杂性的意义，从多个领域说明人工科学何以是可能的，并试图说明它的性质。本书的基本主题是：物质符号系统具备必要和充分的手段来采取智能行动。

本书是首部全面、清晰且令人易于理解地阐述复杂适应社会系统的著作，由该领域两位权威学者联袂完成。复杂适应社会系统——不论是“政治党派”、“股票市场”，还是蚂蚁群落——都体现了社会科学在理论上与实践上所面临的一些最有趣的挑战。通过引人入胜的文字描述和难易适中且附有直观解释的技术细节，本书着重介绍了自20世纪90年代中期以来在该领域出现的关键工具与思想，以及研究此类系统所需要的支撑技术。本书详细介绍了一些相关概念，比如涌现性、自组织临界性、自动机、网络、多样性、适应性以及反馈等。它还展示了如何利用从数学到适应性主体计算模型等一系列广泛的方法来探索复杂适应系统。

《混沌与分形:科学的新疆界(第2版)》介绍了分形与混沌理论的基础知识、基本原理和特性，包括：分形与自相似、分形的维数与测度、分形与图像数据压缩编码、随机性与确定性、分形的递归结构、细胞元自动机与吸引子、分形构造中的随机性、确定性混沌：灵敏度、混合与周期点、有序与混沌、奇异吸引子、典型的分形集如Julia集、Mandelbrot集等，重点介绍了分形与混沌的物理意义、两者之间的关系、与数学的其它方面以及自然现象的联系，展示出分形与混沌的在视觉、图像方面的优美结构和图案。