Introduction to the book material.

This chapter introduces to the concepts of algorithm, model of computation, and computational resources, starting from the classic ones (time and space) and then moving to I/O complexity by introducing the two-level memory model, which constitutes a simple, yet very effective, approximation of modern hierarchical memories. Examples are given in order to motivate the importance of counting I/Os for estimating the real performance of algorithms in modern computers.

The current sharing economy suffers from system-wide deficiencies even as it produces distinctive benefits and advantages for some participants. The first generation of sharing markets has left us to question: Will there be any workers in the sharing economy? Can we know enough about these technologies to regulate them? Is there any way to avoid the monopolization of assets, information, and wealth? Using convergent, transdisciplinary perspectives, this volume examines the challenge of reengineering a sharing economy that is more equitable, democratic, sustainable, and just. The volume enhances the reader’s capacity for integrating applicable findings and theories in business, law and social science into ethical engineering design and practice. At the same time, the book helps explain how technological innovations in the sharing economy create value for different stakeholders and how they impact society at large. Reengineering the Sharing Economy is also available as Open Access on Cambridge Core.

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 provides a unified discussion of the framework for model validation. It describes how model validation developed over time across various disciplines. It then describes the various approaches that are applied for validation of risk management models at financial institutions.

In this chapter, we describe the main goal of the book, its organization, course outline, and suggestions for instructions and self-study. The textbook material is aimed for a one-semester undergraduate/graduate course for mathematics and computer science students. The course might also be recommended for students of physics, interested in networks and the evolution of large systems, as well as engineering students, specializing in telecommunication. Our textbook aims to give a gentle introduction to the mathematical foundations of random graphs and to build a platform to understand the nature of real-life networks. The text is divided into three parts and presents the basic elements of the theory of random graphs and networks. To help the reader navigate through the text, we have decided to start with describing in the preliminary part (Part I) the main technical tools used throughout the text. Part II of the text is devoted to the classic Erdős–Rényi–Gilbert uniform and binomial random graphs. Part III concentrates on generalizations of the Erdős–Rényi–Gilbert models of random graphs whose features better reflect some characteristic properties of real-world networks.