This chapter delves into the complexities and challenges of data science, emphasizing the potential pitfalls and ethical considerations inherent in decision-making based on data. It explores the intricate nature of data, which can be multifaceted, noisy, temporally and spatially disjointed, and often a result of the interplay among numerous interconnected components. This complexity poses significant difficulties in drawing causal inferences and making informed decisions.

A central theme of the chapter is the compromise of privacy that individuals may face in the quest for data-driven insights, which raises ethical concerns regarding the use of personal data. The discussion extends to the concept of algorithmic fairness, particularly in the context of racial bias, shedding light on the need for mitigating biases in data-driven decision-making processes.

Through a series of examples, the chapter illustrates the challenges and potential pitfalls associated with data science, underscoring the importance of robust methodologies and ethical considerations. It concludes with a thought-provoking examination of income inequality as a controversial example of data science in practice. The example highlights the nuanced interplay between data, decisions, and societal impacts.

This chapter describes the thirty-seven autistic academics who share their stories in this book. In a different world they would be introduced to the reader by name, with their unique personalities, interests, and gifts described. However, we live in a world where autism is still very much stigmatised and where disclosure comes with significant risks to career progression and social inclusion. Thus, many of the participants have asked to remain anonymous, and their combined stories are shared in a way that gives the reader a sense of their diversity while maintaining their anonymity.

This chapter gives basic information about molecular communication. It introduces the concept and gives simple examples, explores the history of molecular communication, and discusses several examples to motivate the rest of the book.

The book starts out with a motivating chapter to answer the question: Why is it worthwhile to develop system theory? To do so, we jump fearlessly in the very center of our methods, using a simple and straight example in optimization: optimal tracking. Although optimization is not our leading subject– which is system theory– it provides for one of the main application areas, namely the optimization of the performance of a dynamical system in a time-variant environment (for example, driving a car or sending a rocket to the moon). The chapter presents a recursive matrix algebra approach to the optimization problem, known as dynamic programming. Optimal tracking is based on a powerful principle called “dynamic programming,” which lies at the very basis of what ”dynamical” means.

The so-called magnetic communication makes use of the time-varying magnetic field produced by the transmitting antenna, so that the receiving antenna receives the energy signal by mutual inductance. Research studies show that the penetrability of a magnetic communication system depends on the magnetic permeability of the medium. Because the magnetic permeability of the layer, rock, ice, soil, and ore bed is close to that of the air, channel conditions have less effects on magnetic transmission than electric transmission. Therefore, the communication network based on deep-penetrating MI can expand the perception ability and sensing range of information technology effectively, which can be applied to complex environments such as underground, underwater, tunnel, mountain, rock, ice, and forest. We conclude that the network construction of IoT based on magnetic communication is of great value and can be regarded as one of the reliable technologies to improve the connectivity of a wireless network.

We provide a short, self-contained introduction to deep neural networks that is aimed at mathematically inclined readers. We promote the use of a vect--matrix formalism that is well suited to the compositional structure of these networks and that facilitates the derivation/description of the backpropagation algorithm. We present a detailed analysis of supervised learning for the two most common scenarios, (i) multivariate regression and (ii) classification, which rely on the minimization of least squares and cross-entropy criteria, respectively.

Optimization on Riemannian manifolds–the result of smooth geometry and optimization merging into one elegant modern framework–spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing.

This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade sprinkled throughout the book for conducting research in this area and for writing effective numerical implementations.

This chapter discusses the fundamentally different mental images of large-dimensional machine learning (versus its small-dimensional counterpart), through the examples of sample covariance matrices and kernel matrices, on both synthetic and real data. Random matrix theory is presented as a flexible and powerful tool to assess, understand, and improve classical machine learning methods in this modern large-dimensional setting.

Chapter 1 introduces the capacity challenge faced by modern wireless communication systems and presents ultra-dense wireless networks as an appealing solution to address it. Moreover, it provides background on the small cell concept – the fundamental building block of an ultra-dense wireless network – describing its main characteristics, benefits and drawbacks. This chapter also presents the structure of the book and the fundamental concepts required for its systematic understanding.

In this introductory chapter, we outline the ways in which various problems in data analysis can be formulated as optimization problems. Specifically, we discuss least squares problems, problems in matrix optimization (particularly those involving low-rank matrices), linear and kernel support vector machines, binary and multiclass logistic regression, and deep learning. We also outline the scope of the remainder of the book.

In this chapter, we first provide some motivation for the type of modeling problems we address in this book. Then we provide an overview of the type of mathematical models used to describe the behavior of the classes of systems of interest. We also describe the types of uncertainty models adopted and how they fit into the mathematical models describing system behavior. In addition, we provide a preview of the applications discussed throughout the book, mostly centered around electric power systems. We conclude the chapter by providing a brief summary of the content of subsequent chapters.