This book introduces a class of alignment models based on the so-called Cucker-Smale system as well as its kinetic and hydrodynamic counterparts. Cutting edge research in the area of collective behavior is presented, including emerging techniques from fluid mechanics, fractional analysis, and kinetic theory. Analytical aspects are highlighted throughout, such as regularity theory and long time behavior of solutions. Featuring open problems, readers will be motivated to apply these breakthrough methods to future research. The chapters offer an overview of state of the art research with introductions to core concepts. Chapter One introduces the central focus of the book: The agent-based Cucker-Smale system. Further agent-based systems and alignment systems are covered in chapters Two and Three. Following this are chapters covering the kinetic and hydrodynamic variants of the Cucker-Smale system. The core well-posedness theory of both smooth and singular models is then presented. Chapter Eight discusses the fully developed one-dimensional theory. The final chapter presents some of the known partial results concerning the regularity of multidimensional Euler Alignment systems. Dynamics and Analysis of Alignment Models of Collective Behavior is ideal for graduate students and researchers studying PDEs, especially those interested in the active areas of collective behavior and alignment models.
The topics dealt with in this thesis are all part of the general problem of social consensus, namely how a convention flourish and decay and what motivates people to conform to it. Examples range from driving on the right side of the street, to language, rules of courtesy or moral judgments. Some conventions arise directly from the need to coordinate or conform, such as fashion or speaking the same language, others, instead, apply to situations where there is a tension between individual and collective interest, such as cooperation, reciprocity, etc. This thesis is developed around three main questions still open in the research field of collective human behavior: how coexistence of concurrent conventions is possible, why cooperation in real systems is more common than predicted and how a population undergoes collective behavioral change, namely how an initially minority norm can supplant a majority ones. In the first work, we study the impact of concurrent social pressures in consensus processes. We propose a model of opinion competition where individuals participate in different social networks and receive conflicting social influences. The dynamics take place in two distinct domains, which we model as layers of a multiplex network. The novelty of our study lies to the fact that individuals can have different options in the different layers. This naturally reflects a common situation where an individual can possess some different opinions in different social contexts as a result of consensus with other individuals in the one context but not in the other. Our analysis shows that the latter property enriches the system's dynamics and allows not only for consensus into a single state for both layers, but also for active dynamical states of coexistence of both options. In the second model, we analyze the influence of opinion dynamic in competitive strategical games. Cooperation between humans is quite common and stable behavior even in situations where both game theory and experiments predict defection prevalence. One of the reasons could be just the fact that individuals engaging in strategic interactions are also exposed to social influence and, consequently, to the spread of opinions. We present a new evolutionary game model where game and opinions dynamics take place in different layers of a multiplex network. We show that the coupling between the two dynamical processes can lead to cooperation in scenarios where the pure game dynamics predicts defection and, in some particular setting, gives rise to a metastable state in which nodes that adopt the same strategy self-organize into local groups. In the last work, we present the first extensive quantitative analysis of the phenomenon of norm change by looking at 2,365 orthographic and lexical norms shifts occurred in English and Spanish over the last two centuries as recorded by millions of digitized books. We are able to identify three distinct patterns in the data depending on the nature of the norm shift. Furthermore, we propose a simple evolutionary model that captures all the identified mechanisms and reproduces quantitatively the transitions between norms. This work advances the current understanding of norm shifts in language change, most often limited to qualitative illustrations (e.g., the observation that adoption curve of the new norm follows an ‘S-shaped' behavior.
This book constitutes the thoroughly refereed post-proceedings of the 2nd SAB 2006 International Workshop on Swarm Robotics held in Rome, Italy in September/October 2006 as a satellite event of SAB 2006, the 9th Conference on Simulation of Adaptive Behavior. The 14 revised full papers are organized in topical sections on algorithms, modeling and analysis, hardware, and evolutionary approaches.
Polymer and cell dynamics play an important role in processes like tumor growth, metastasis, embryogenesis, immune reactions and regeneration. Based on an international workshop on numerical simulations of polymer and cell dynamics in Bad Honnef (Germany) in 2000, this volume provides an overview of the relevant mathematical and numerical methods, their applications and limits. Polymer and Cell Dynamics will be of interest to scientists and advanced undergraduates.
In this work we provide mathematical and computational tools that allow us to model the “physics” of human group behavior: how the relationship between the individuals’ characteristics, interaction dynamics, and environmental factors translates into changes in the behavior of the group. We characterize the group dynamics for four specific situations, and show the importance of these models to improve the performance of task-solving groups in organizational management, to design strategies that prevent high-risk behaviors, and to motivate collective action and cooperation in situations that lead to social dilemmas.
"This book compiles real-world case studies on discovering, understanding and engineering emergent behaviors in a computational environment across multiple application domains such as wargaming, biology, IoT, disaster management and space architecting. All the application domains are described through an undercurrent of System of Systems (SoS) engineering in conjunction with theoretical foundations required for engineering a Modeling and Simulation SoS capable of displaying valid emergent behavior. An excellent read and state-of-the-art in M&S of emergent behavior in complex systems!" --Dr. Saurabh Mittal, Department Chief Scientist, The MITRE Corporation This book is the of its kind to address real-world applications of the phenomenon of emergent behavior in real-world system of systems. It launches from the foundation of theory and basic understanding of the subject of emergent behavior as found in system of systems applications. It includes real-world examples where emergent behavior is manifested. Each chapter addresses the following major points, which are exploratory in nature: the physical results of the presence of emergent behavior; the implications for the existence of emergent behavior; the manifestation of emergent behavior; and methods to either control emergent behavior assuming its effects are negative in nature, or capitalize on emergent behavior given its effects are positive in nature.
A comprehensive treatment of visual ecology Visual ecology is the study of how animals use visual systems to meet their ecological needs, how these systems have evolved, and how they are specialized for particular visual tasks. Visual Ecology provides the first up-to-date synthesis of the field to appear in more than three decades. Featuring some 225 illustrations, including more than 140 in color, spread throughout the text, this comprehensive and accessible book begins by discussing the basic properties of light and the optical environment. It then looks at how photoreceptors intercept light and convert it to usable biological signals, how the pigments and cells of vision vary among animals, and how the properties of these components affect a given receptor's sensitivity to light. The book goes on to examine how eyes and photoreceptors become specialized for an array of visual tasks, such as navigation, evading prey, mate choice, and communication. A timely and much-needed resource for students and researchers alike, Visual Ecology also includes a glossary and a wealth of examples drawn from the full diversity of visual systems. The most up-to-date overview of visual ecology available Features some 225 illustrations, including more than 140 in color, spread throughout the text Guides readers from the basic physics of light to the role of visual systems in animal behavior Includes a glossary and a wealth of real-world examples
