This contributed volume contains articles written by the plenary and invited speakers from the second international MATHEON Workshop 2015 that focus on applications of compressed sensing. Article authors address their techniques for solving the problems of compressed sensing, as well as connections to related areas like detecting community-like structures in graphs, curbatures on Grassmanians, and randomized tensor train singular value decompositions. Some of the novel applications covered include dimensionality reduction, information theory, random matrices, sparse approximation, and sparse recovery. This book is aimed at both graduate students and researchers in the areas of applied mathematics, computer science, and engineering, as well as other applied scientists exploring the potential applications for the novel methodology of compressed sensing. An introduction to the subject of compressed sensing is also provided for researchers interested in the field who are not as familiar with it.

The chapters in this volume highlight the state-of-the-art of compressed sensing and are based on talks given at the third international MATHEON conference on the same topic, held from December 4-8, 2017 at the Technical University in Berlin. In addition to methods in compressed sensing, chapters provide insights into cutting edge applications of deep learning in data science, highlighting the overlapping ideas and methods that connect the fields of compressed sensing and deep learning. Specific topics covered include: Quantized compressed sensing Classification Machine learning Oracle inequalities Non-convex optimization Image reconstruction Statistical learning theory This volume will be a valuable resource for graduate students and researchers in the areas of mathematics, computer science, and engineering, as well as other applied scientists exploring potential applications of compressed sensing.

This contributed volume contains articles written by the plenary and invited speakers from the second international MATHEON Workshop 2015 that focus on applications of compressed sensing. Article authors address their techniques for solving the problems of compressed sensing, as well as connections to related areas like detecting community-like structures in graphs, curbatures on Grassmanians, and randomized tensor train singular value decompositions. Some of the novel applications covered include dimensionality reduction, information theory, random matrices, sparse approximation, and sparse recovery. This book is aimed at both graduate students and researchers in the areas of applied mathematics, computer science, and engineering, as well as other applied scientists exploring the potential applications for the novel methodology of compressed sensing. An introduction to the subject of compressed sensing is also provided for researchers interested in the field who are not as familiar with it.

Caching refers to the act of replicating information at a faster (or closer) medium with the purpose of improving performance. This deceptively simple idea has given rise to some of the hardest optimization problems in the fields of computer systems, networking, and the Internet; many of which remain unsolved several years after their conception. While a wealth of research contributions exists from the topics of memory systems, data centers, Internet traffic, CDNs, and recently wireless networks, the literature is dispersed and overlapping at times. In this monograph, the authors focus on the fundamental underlying mathematical models, into a powerful framework for performing optimization of caching systems. In doing so they the present the reader with a solid background for the anticipated explosion in caching research, and provide a didactic view into how engineers have managed to infuse mathematical models into the study of caching over the last 40 years. Written by leading researchers from academia and industry, this monograph provides students, researchers and practicing engineers with a concise introduction to challenges and solutions for implementing caching in modern computing systems.

Since its introduction, Bit-Interleaved Coded Modulation (BICM) has been regarded as a pragmatic yet powerful scheme to achieve high data rates with general signal constellations. Nowadays, BICM is employed in a wide range of practical communications systems, such as DVB-S2, Wireless LANs, DSL, WiMax, the future generation of high data rate cellular systems (the so-called 4th generation). BICM has become the de-facto standard for coding over the Gaussian channel in modern systems. Bit-Interleaved Coded Modulation provides a comprehensive study of the subject. In particular, it review its information theoretic foundations, and its capacity, cutoff rate and error exponents. It further examines the error probability of BICM, focussing on the union bound and improved bounds to the error probability before turning its attention to iterative decoding of BICM. The underlying design techniques reviewed and improved BICM schemes in a unified framework introduced. Finally, a number of applications of BICM not explicitly elsewhere covered are described. Bit-Interleaved Coded Modulation provides a comprehensive review of one of the most important coding schemes in modern communication systems. It will be of interest to students, practitioners and researchers working on developing 4th generation communication systems.