The rapid spread of infectious diseases and online rumors share similarities in terms of their speed, scale, and patterns of contagion. Although these two phenomena have historically been studied separately, the COVID-19 pandemic has highlighted the devastating consequences that simultaneous crises of epidemics and misinformation can have on the world. Soon after the outbreak of COVID-19, the World Health Organization launched a campaign against the COVID-19 Infodemic, which refers to the dissemination of pandemic-related false information online that causes widespread panic and hinders recovery efforts. Undoubtedly, nothing spreads faster than fear. Networks serve as a crucial platform for viral spreading, as the actions of highly influential users can quickly render others susceptible to the same. The potential for contagion in epidemics and rumors hinges on the initial source, underscoring the need for rapid and efficient digital contact tracing algorithms to identify super-spreaders or Patient Zero. Similarly, detecting and removing rumour mongers is essential for preventing the proliferation of harmful information in online social networks. Identifying the source of large-scale contagions requires solving complex optimization problems on expansive graphs. Accurate source identification and understanding the dynamic spreading process requires a comprehensive understanding of surveillance in massive networks, including topological structures and spreading veracity. Ultimately, the efficacy of algorithms for digital contact tracing and rumour source detection relies on this understanding. This monograph provides an overview of the mathematical theories and computational algorithm design for contagion source detection in large networks. By leveraging network centrality as a tool for statistical inference, we can accurately identify the source of contagions, trace their spread, and predict future trajectories. This approach provides fundamental insights into surveillance capability and asymptotic behaviour of contagion spreading in networks. Mathematical theory and computational algorithms are vital to understanding contagion dynamics, improving surveillance capabilities, and developing effective strategies to prevent the spread of infectious diseases and misinformation.

A basic question in wireless networking is how to optimize the wireless network resource allocation for utility maximization and interference management. How can we overcome interference to efficiently optimize fair wireless resource allocation, under various stochastic constraints on quality of service demands? Network designs are traditionally divided into layers. How does fairness permeate through layers? Can physical layer innovation be jointly optimized with network layer routing control? How should large complex wireless networks be analyzed and designed with clearly-defined fairness using beamforming? Wireless Network Optimization by Perron-Frobenius Theory provides a comprehensive survey of the models, algorithms, analysis, and methodologies using a Perron-Frobenius theoretic framework to solve wireless utility maximization problems. This approach overcomes the notorious non-convexity barriers in these problems, and the optimal value and solution of the optimization problems can be analytically characterized by the spectral property of matrices induced by nonlinear positive mappings. It can even solve several previously open problems in the wireless networking literature. This survey will be of interest to all researchers, students and engineers working on wireless networking.

Power Control in Wireless Cellular Networks provides a comprehensive survey of the models, algorithms, analysis, and methodologies in this vast and growing research area. It starts with a taxonomy of the wide range of power control problem formulations, and progresses from the basic formulation to more sophisticated ones. When transmit power is the only set of optimisation variables, algorithms for fixed SIR are presented first, before turning to their robust versions and joint SIR and power optimization. This is followed by opportunistic and non-cooperative power control. Then joint control of power together with beamforming pattern, base station assignment, spectrum allocation, and transmit schedule are surveyed one by one. Power Control in Wireless Cellular Networks highlights the use of mathematical language and tools in the study of power control, including optimisation theory, control theory, game theory, and linear algebra. Practical implementations of some of the algorithms in operational networks are discussed in the concluding chapter.