In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen. Chen made the first of several seminal contributions to the theory and application of Stein’s method. One of his most important contributions has been to turn Stein’s concentration inequality idea into an effective tool for providing error bounds for the normal approximation in many settings, and in particular for sums of random variables exhibiting only local dependence. This conference attracted a large audience that came to pay homage to Chen and to hear presentations by colleagues who have worked with him in special ways over the past 40+ years. The papers in this volume attest to how Louis Chen’s cutting-edge ideas influenced and continue to influence such areas as molecular biology and computer science. He has developed applications of his work on Poisson approximation to problems of signal detection in computational biology. The original papers contained in this book provide historical context for Chen’s work alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.

The theory of stellar atmospheres is one of the most important branches of modern astrophysics. It is first of all a major tool for understanding all aspects of stars. As the physical properties of their outer layers can now be found with high precision, firm conclusions can be drawn about the internal structure and evolution of stars. Moreover, improvements in our knowledge of the chemical composition of stars is shedding new light on the chemical evolution of galaxies and of the Universe as a whole. Because the outer layers of stars are among the best-understood astrophysical objects, the theory of stellar atmospheres plays an important role in the study of many other types of objects. These include planetary nebulae, H II regions, interstellar matter, and objects of interest in high-energy astrophysics, such as accretion disks (close binaries, dwarf novae, cataclysmic variables, quasars, active galactic nuclei), pulsar magnetospheres, and Seyfert galaxies. Finally, as stars provide a laboratory in which plasmas can be studied under more extreme conditions than on earth, the study of stellar atmospheres has strong connections with modern physics. Astronomical observations provided a vital stimulus in the early stages of quantum theory and atomic physics; even today topics such as low-temperature dielectronic recombination develop hand in hand with the interpretation of stellar and nebular spectra. Early work on MHD was similiarly motivated. Many such connections remain to be explored.

A comprehensive study in efficient multi-rate teletraffic loss models used for designing, performance analysis, and optimization of systems and networks Efficient Multirate Teletraffic Loss Models Beyond Erlang is an easy-to-read book filled with numerous efficient teletraffic loss models. Presented in three sections—Teletraffic Models of Random Input, Teletraffic Models of Quasi-Random Input, and Teletraffic Models of Batched Poisson Input—it covers everything that a professional experienced with optimization and dimensioning of telecom networks could ever need to know. This unique book provides a detailed explanation on how efficient multirate teletraffic loss models are extracted and applied, and guides readers through almost all network technologies and services. Starting from the basics, it steadily increases in difficulty to keep the book self-contained and to provide a better understanding to those who might be new to the subject. It includes detailed explanations of the complex teletraffic models—many of which were developed by the authors. Tutorial examples, several backed by supplementary software, are accompanied by intermediate results and figures. Additionally, end-of-chapter applications describe the applicability of the models to modern network technologies, updating the incorporated teletraffic models of commercial packages/tools. Uses the classic EMLM (Erlang Multirate Loss Model) as its base to present a comprehensive range of teletraffic models through detailed explanation and numerical examples Filled with the authors’ own original teletraffic models—making for a wholly unique learning experience Offers a clear, self-contained presentation with a beginning, middle, and end Starts with simple models, then moves to more complex models, before finishing with complicated ones Supplemented by an accompanying website with computer implementation of the most important models Directed primarily at telecommunication engineers, Efficient Multirate Teletraffic Loss Models Beyond Erlang is also useful for telecom operators or managers on the higher and average levels, as well a Ph.D. students, researchers, and modelers.

Beyond Chance and Credence introduces a new way of thinking of probabilities in science that combines physical and epistemic considerations. Myrvold shows that conceiving of probabilities in this way solves puzzles associated with the use of probability and statistical mechanics.

This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

To advantageously plan and design for the explosive near-future increase in the number of unmanned aerial vehicles (UAVs) and their demanding applications, integration of UAVs into cellular communication systems has seen increasing interest. This book provides a timely and comprehensive overview of the recent research efforts and results of unmanned aerial vehicles (UAVs)-integrated cellular network communications. The aim of the book is to provide a comprehensive coverage of the potential applications, networking architectures, latest research findings and key enabling technologies, experimental measurement results, as well as up-to-date industry standardizations for UAV communications in cellular systems, including the existing LTE as well as the future 5G-and-beyond systems.

This book discusses the smooth integration of optical and RF networks in 5G and beyond (5G+) heterogeneous networks (HetNets), covering both planning and operational aspects. The integration of high-frequency air interfaces into 5G+ wireless networks can relieve the congested radio frequency (RF) bands. Visible light communication (VLC) is now emerging as a promising candidate for future generations of HetNets. Heterogeneous RF-optical networks combine the high throughput of visible light and the high reliability of RF. However, when implementing these HetNets in mobile scenarios, several challenges arise from both planning and operational perspectives. Since the mmWave, terahertz, and visible light bands share similar wave propagation characteristics, the concepts presented here can be broadly applied in all such bands. To facilitate the planning of RF-optical HetNets, the authors present an algorithm that specifies the joint optimal densities of the base stations by drawing on stochastic geometry in order to satisfy the users’ quality-of-service (QoS) demands with minimum network power consumption. From an operational perspective, the book explores vertical handovers and multi-homing using a cooperative framework. For vertical handovers, it employs a data-driven approach based on deep neural networks to predict abrupt optical outages; and, on the basis of this prediction, proposes a reinforcement learning strategy that ensures minimal network latency during handovers. In terms of multi-homing support, the authors examine the aggregation of the resources from both optical and RF networks, adopting a two-timescale multi-agent reinforcement learning strategy for optimal power allocation. Presenting comprehensive planning and operational strategies, the book allows readers to gain an in-depth grasp of how to integrate future coexisting networks at high-frequency bands in a cooperative manner, yielding reliable and high-speed 5G+ HetNets.

Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory.· Probability· Measure· Integration· Random Variables and Expected Values· Convergence of Distributions· Derivatives and Conditional Probability· Stochastic Processes