This chapter presents a game-theoretic solution to several challenges in electricity markets, e.g., intermittent generation; high levels of average prices; price volatility; and fundamental aspects concerning the environment, reliability, and affordability. It proposes a stochastic bi-level optimization model to find the optimal nodal storage capacities required to achieve a certain price volatility level in a highly volatile energy-only electricity market. The decision on storage capacities is made in the upper-level problem and the operation of strategic/regulated generation, storage, and transmission players is modeled in the lower-level problem using an extended stochastic (Bayesian) Cournot-based game.

Information theory plays an indispensable role in the development of algorithm-independent impossibility results, both for communication problems and for seemingly distinct areas such as statistics and machine learning. While numerous information-theoretic tools have been proposed for this purpose, the oldest one remains arguably the most versatile and widespread: Fano’s inequality. In this chapter, we provide a survey of Fano’s inequality and its variants in the context of statistical estimation, adopting a versatile framework that covers a wide range of specific problems. We present a variety of key tools and techniques used for establishing impossibility results via this approach, and provide representative examples covering group testing, graphical model selection, sparse linear regression, density estimation, and convex optimization.

We introduce the mathematical modeling process. We also set the stage for the rest of the book by discussing systems of linear equations and their solutions, matrices, Gauss-Jordan elimination, linear combinations of vectors, basis vectors of Euclidean space, and their connection to basic solutions of a linear system. We conclude with simple optimization problems with quadratic functions.

In this chapter, we discuss the application of edge caching to enhance the physical layer security of cellular networks with limited backhaul capacity. By proactively sharing the same content across a subset of base stations (BSs) through both caching and backhaul loading, secure cooperative multiple-input multiple-output (MIMO) transmission of several BSs can be dynamically enabled in accordance with the cache status, the channel conditions, and the backhaul capacity. We formulate a two-stage nonconvex optimization problem for minimizing the total transmit power while providing quality of service (QoS) and guaranteeing communication secrecy during content delivery, where the caching and the cooperative MIMO transmission policy are optimized in an offline caching stage and an online delivery stage, respectively. Caching is shown to be beneficial as it reduces the data sharing overhead imposed on the capacity-constrained backhaul links, introduces additional secure degrees of freedom, and enables a power-efficient communication system design.

Optimization and root finding are closely aligned techniques for determining the extremums and zeros, respectively, of a function. Newton's method is the workhorse of both types of algorithms for nonlinear functions, and the conjugate-gradient and GMRES methods are also covered. Optimization of linear, quadratic, and nonlinear functions are addressed with and without constraints, which may be equality or inequality. In the linear programming case, emphasis is placed on the simplex method.

Least-squares methods provide the mathematical foundation for optimization of algebraic systems. They can be applied to overdetermined systems, having more equations than unknowns, or undertermined systems, having fewer equations than unknowns. The optimization may involve constraints or be subject to a penalty function. Numerical methods, namely the conjugate-gradient and GMRES methods, that are based on least-squares optimization method are discussed in detail and put into the context of other Krylov-based methods.

Vector and matrix calculus provides a powerful set of tools for analying and manipulating scalars, vectors, and tensors in continuum mechanics. This includes transformations between coordinate systems and provides the foundation for optimization methods.

The chapter introduces basic optimization concepts, and motivates the use of optimization models and methods to engineering and scientific practice applications. It establishes key concepts, such as the types of variables, arguments to an optimization problem as continuous, integer and control functions (for optimal control problems). Further, it introduces types of optimization problems according to their formulation (such as multiobjective, bilevel, stochastic optimization problems)

Changing practices in contemporary biosciences and biotechnology have altered definitions and understandings of what we call “life”—what we mean by this term, what constitutes life, and how human and nonhuman others experience life. This chapter explores the shifting definitions of life within the biosciences, and beyond—which have emerged due to specific bioscientific/biotech advancements and changing political-economic imperatives and governing logics that have emerged during the latter half of the twentieth century. Increasingly, now, life as we know it has come to be manipulated, customized, optimized, maximized, and commodified. The chapter considers how life is increasingly technologized, how life is now understood as an ‘open dynamism,’ how life is something now viewed as subject to self-governance, and how life has become a domain of biovalue. While concepts of life and life-making strategies might have altered, historic inequities have not receded but are instead re-secured and often exacerbated.

This book intends to be self-contained, and this chapter provides a short recap of (almost) all the necessary mathematical background that is required to understand the rest of this book.

This chapter proposes that globalization of multinational enterprises (MNEs) can be viewed as involving self-organizing swarms searching for optimal solutions to challenges presented by new and rapidly changing organizational ecologies. These challenges include developing innovative strategies for leadership, communication, training, management style, organizational design, and so forth. In this model, optimization most effectively occurs through evolutionary performance-based processes rather than more rational, analytic ones. This chapter applies recent theory and research on swarm intelligence to globalization, relates it to work on building microcultures in MNEs and suggests that the combination of these two processes can lead to more “intelligent swarming.” The latter involves a more detailed description of the past solution attempts of one’s own work team and those of other potentially comparable teams, including a fuller explication of key ecological characteristics, identification of potentially relevant comparison ecologies, and accurate evaluation of solution outcomes. It also involves better data storage and retrieval. Conditions which nurture intelligent swarming are discussed. Two training activities that have been used in a variety of organizational contexts and adaptable to enhancing intelligent swarming are described – “World Café” and “Smart Swarming.”

The Handbook of Behavior Change is the first wide-ranging compendium of theory- and evidence-based research and practice on behavior change. It provides scientists, students, and practitioners with the current evidence on behavior change and expert advice on how to develop, evaluate, and implement behavior change interventions. The handbook also sets an agenda for future research on behavior change theory and practice across multiple behaviors, contexts, and populations. This chapter outlines emerging issues and future research directions arising from the handbook. The chapter stresses the importance of theory development, including the need for greater emphasis on ecological and social theories; clearer descriptions and operationalizations of behavior change theories; and increased application of interdisciplinary approaches. Future research on intervention development should conduct more comprehensive intervention fidelity assessments; adopt novel means to improve the translation, feasibility, and optimization of interventions; ensure consideration of ethical issues in behavior change research; routinely evaluate mechanisms of action in behavior change interventions; and apply complex systems approaches to behavior change. “Best-practice” guidance on behavior change should consider emerging methods and approaches to behavior change; implement trials to evaluate the long-term maintenance of behavior change; and develop core curricula on behavior change to educate the next generation of scientists and practitioners.

Robust development of behavior change interventions is based on a sound understanding of the target group, the target behaviors that need to change, the context in which change will occur, the hypothesized mechanisms of change, and the behavior change techniques. Intervention development frameworks advocate a systematic approach to behavior change intervention development. Key tasks include (1) identify and analyze the problem addressed in behavioral terms; (2) identify intervention mechanisms, content, and delivery mode(s) and design a logic model or program theory; (3) develop materials or prototypes (e.g., interface); and (4) test the intervention iteratively through empirical optimization. The tasks apply to both developing new interventions and optimizing existing interventions. The tasks may differ somewhat for digital behavior change interventions (e.g., iterative testing and refinement of early prototypes during development). Depending on time and resources, the tasks can be completed relatively quickly or take considerable time. The current chapter presents key challenges in intervention development and describes potential solutions. Fidelity, feasibility, and acceptability should be considered during all development tasks. The chapter also provides recommendations for advancing the methodology of intervention development and the use of intervention development frameworks and approaches in practice and policy settings.