Linear Network Optimization

This book is on existence and necessary conditions, such as Potryagin's maximum principle, for optimal control problems described by ordinary and partial differential equations. These necessary conditions are obtained from Kuhn–Tucker theorems for nonlinear programming problems in infinite dimensional spaces. The optimal control problems include control constraints, state constraints and target conditions. Evolution partial differential equations are studied using semigroup theory, abstract differential equations in linear spaces, integral equations and interpolation theory. Existence of optimal controls is established for arbitrary control sets by means of a general theory of relaxed controls. Applications include nonlinear systems described by partial differential equations of hyperbolic and parabolic type and results on convergence of suboptimal controls.

In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. In this classic book, George Dantzig looks at a wealth of

Thisgraduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete

This book summarizes developments related to a class of methods called Stochastic Decomposition (SD) algorithms, which represent an important shift in the design of optimization algorithms. Unlike tra

Building on a base of simple economic theory and elementary linear algebra and calculus, this broad treatment of static and dynamic optimization methods discusses the importance of shadow prices, and

Based on courses taught to advanced undergraduate students, this book offers a broad introduction to the methods of numerical linear algebra and optimization. The prerequisites are familiarity with th

This introduction to optimization emphasizes the need for both a pure and an applied mathematical point of view. Beginning with a chapter on linear algebra and Euclidean geometry, the author then applies this theory with an introduction to linear programming. There follows a discussion of convex analysis, which finds application in non-linear programming. The book ends with an extensive commentary to the exercises that are given at the end of each chapter. The author's straightforward, geometrical approach makes this an attractive textbook for undergraduate students of mathematics, engineering, operations research and economics.

How a web-scale network of autonomous micromanagers can challenge the AI revolution and combat the high cost of quantitative business optimization.The artificial intelligence (AI) revolution is leaving behind small businesses and organizations that cannot afford in-house teams of data scientists. In Microprediction, Peter Cotton examines the repeated quantitative tasks that drive business optimization from the perspectives of economics, statistics, decision making under uncertainty, and privacy concerns. He asks what things currently described as AI are not “microprediction,” whether microprediction is an individual or collective activity, and how we can produce and distribute high-quality microprediction at low cost. The world is missing a public utility, he concludes, while companies are missing an important strategic approach that would enable them to benefit―and also give back. In an engaging, colloquial style, Cotton argues that market-inspired “superminds” are likely to be very e

This self-contained introduction to machine learning, designed from the start with engineers in mind, will equip students with everything they need to start applying machine learning principles and algorithms to real-world engineering problems. With a consistent emphasis on the connections between estimation, detection, information theory, and optimization, it includes: an accessible overview of the relationships between machine learning and signal processing, providing a solid foundation for further study; clear explanations of the differences between state-of-the-art techniques and more classical methods, equipping students with all the understanding they need to make informed technique choices; demonstration of the links between information-theoretical concepts and their practical engineering relevance; reproducible examples using Matlab, enabling hands-on student experimentation. Assuming only a basic understanding of probability and linear algebra, and accompanied by lecture slide

Discover the fundamental characteristics of ultra-dense networks with this comprehensive text. Featuring a consistent mathematical description of ultra-dense small cell networks while also covering real-world issues such as network deployment, operation and optimization, this book investigates performance metrics of coverage probability and area spectral efficiency (ASE) and addresses the aspects of ultra-dense networks that make them different from current networks. Insightful intuitions, which will assist decision-makers as they migrate their services, are explained and mathematically proven. The book presents the latest review of research outcomes on ultra-dense networks, based on both theoretical analyses and network simulations, includes over 200 sources from 3GPP, the Small Cell Forum, journals and conference proceedings, and covers all other related and prominent topics. This is an ideal reference text for professionals who are dealing with the development, deployment, operation

An updated edition of a widely used textbook, offering a clear and comprehensive presentation of mathematics for undergraduate economics students.This text offers a clear and comprehensive presentation of the mathematics required to tackle problems in economic analyses, providing not only straightforward exposition of mathematical methods for economics students at the intermediate and advanced undergraduate levels but also a large collection of problem sets. This updated and expanded fourth edition contains numerous worked examples drawn from a range of important areas, including economic theory, environmental economics, financial economics, public economics, industrial organization, and the history of economic thought. These help students develop modeling skills by showing how the same basic mathematical methods can be applied to a variety of interesting and important issues. The five parts of the text cover fundamentals, calculus, linear algebra, optimization, and dynamics. The onl

Based on TD-LTE (Time Division-Long Term Evolution), this book adopts the modular teaching mode and applies the eNodeB equipment of Datang Mobile TD-LTE. Through the specific tasks in each module, it presents such contents as base station products, equipment installation, wireless technology, network testing, network planning and optimization, etc. in a comprehensive and detailed way. This book is divided into four training modules, namely, TD-LTE Equipment Cognition, TD-LTE Key Technologies, Network Test, Network Planning and Optimization. After learning the four training modules, learners can master the basic contents involved in the operation and maintenance of the mobile communications system, such as the hardware structure, maintenance and testing of the base station equipment, network planning and optimization. This book aims to cultivate high-quality skilled personnel who master the testing and optimization skills of base station and meet the requirements of standardized field m

A detailed and up-to-date introduction to machine learning, presented through the unifying lens of probabilistic modeling and Bayesian decision theory.This book offers a detailed and up-to-date introduction to machine learning (including deep learning) through the unifying lens of probabilistic modeling and Bayesian decision theory. The book covers mathematical background (including linear algebra and optimization), basic supervised learning (including linear and logistic regression and deep neural networks), as well as more advanced topics (including transfer learning and unsupervised learning). End-of-chapter exercises allow students to apply what they have learned, and an appendix covers notation. Probabilistic Machine Learning grew out of the author’s 2012 book, Machine Learning: A Probabilistic Perspective. More than just a simple update, this is a completely new book that reflects the dramatic developments in the field since 2012, most notably deep learning. In addition, the ne

Until now, biological invasions have been conceptualised and studied mainly as a linear process: from introduction to establishment to spread. This volume charts a new course for the field, drawing on key developments in network ecology and complexity science. It defines an agenda for Invasion Science 2.0 by providing new framings and classification of research topics and by offering tentative solutions to vexing problems. In particular, it conceptualises a transformative ecosystem as an open adaptive network with critical transitions and turnover, with resident species heuristically learning and fine-tuning their niches and roles in a multiplayer eco-evolutionary game. It erects signposts pertaining to network interactions, structures, stability, dynamics, scaling, and invasibility. It is not a recipe book or a road map, but an atlas of possibilities: a 'hitchhiker's guide'.

Until now, biological invasions have been conceptualised and studied mainly as a linear process: from introduction to establishment to spread. This volume charts a new course for the field, drawing on key developments in network ecology and complexity science. It defines an agenda for Invasion Science 2.0 by providing new framings and classification of research topics and by offering tentative solutions to vexing problems. In particular, it conceptualises a transformative ecosystem as an open adaptive network with critical transitions and turnover, with resident species heuristically learning and fine-tuning their niches and roles in a multiplayer eco-evolutionary game. It erects signposts pertaining to network interactions, structures, stability, dynamics, scaling, and invasibility. It is not a recipe book or a road map, but an atlas of possibilities: a 'hitchhiker's guide'.

Master the practical aspects of implementing deep learning solutions with PyTorch, using a hands-on approach to understanding both theory and practice. This updated edition will prepare you for applying deep learning to real world problems with a sound theoretical foundation and practical know-how with PyTorch, a platform developed by Facebook's Artificial Intelligence Research Group.You'll start with a perspective on how and why deep learning with PyTorch has emerged as an path-breaking framework with a set of tools and techniques to solve real-world problems. Next, the book will ground you with the mathematical fundamentals of linear algebra, vector calculus, probability and optimization. Having established this foundation, you'll move on to key components and functionality of PyTorch including layers, loss functions and optimization algorithms. You'll also gain an understanding of Graphical Processing Unit (GPU) based computation, which is essential for training deep learning models

This excellent resource synthesizes the theory and practice of PLC, providing a straightforward introduction to the fundamentals of PLC, as well as an exhaustive review of the performance, evaluation, security, and heterogeneous network that combine PLC with other means of communications. It advances the groundwork on power-line communication (PLC), a tool which has the potential to boost the performance of local networks, and provides useful worked practical problems on, for example, PLC protocol optimization. Covering the PHY and MAC layers of the most popular PLC specifications, including tutorials and experimental frameworks, and featuring many examples of real-world applications and performance, it is ideal for university researchers and professional engineers designing and maintaining PLC or hybrid devices and networks.

There are no silver bullets in algorithm design, and no single algorithmic idea is powerful and flexible enough to solve every computational problem. Nor are there silver bullets in algorithm analysis, as the most enlightening method for analyzing an algorithm often depends on the problem and the application. However, typical algorithms courses rely almost entirely on a single analysis framework, that of worst-case analysis, wherein an algorithm is assessed by its worst performance on any input of a given size. The purpose of this book is to popularize several alternatives to worst-case analysis and their most notable algorithmic applications, from clustering to linear programming to neural network training. Forty leading researchers have contributed introductions to different facets of this field, emphasizing the most important models and results, many of which can be taught in lectures to beginning graduate students in theoretical computer science and machine learning.

The advanced text covers dynamical systems, single variable and multi-variable optimization, linear algebra, advanced model fitting techniques, game theory, and multi-attribute decision processes.

本書立足於思想政治教育學科前沿，著重引入和探討了思想政治教育研究的一種新視角。本研究將網絡輿論置於生態學視域下，對高校網絡輿論生態系統優化的基本內涵、思維特點、本真訴求進行了梳理，對輿論生態系統的發生要素、生成邏輯、演進機理探究分析。同時以外部性生成環境、內生性組織狀況、現實性演進困境三個角度揭示了當下高校網絡輿論生態系統的現狀，並試圖構建切實可行的優化機制和優化路徑等。

A thorough treatment of UAV wireless communications and networking research challenges and opportunities. Detailed, step-by-step development of carefully selected research problems that pertain to UAV network performance analysis and optimization, physical layer design, trajectory path planning, resource management, multiple access, cooperative communications, standardization, control, and security is provided. Featuring discussion of practical applications including drone delivery systems, public safety, IoT, virtual reality, and smart cities, this is an essential tool for researchers, students, and engineers interested in broadening their knowledge of the deployment and operation of communication systems that integrate or rely on unmanned aerial vehicles.

Master the usage of s-parameters in signal integrity applications and gain full understanding of your simulation and measurement environment with this rigorous and practical guide. Solve specific signal integrity problems including calculation of the s-parameters of a network, linear simulation of circuits, de-embedding, and virtual probing, all with expert guidance. Learn about the interconnectedness of s-parameters, frequency responses, filters, and waveforms. This invaluable resource for signal integrity engineers is supplemented with the open-source software SignalIntegrity, a Python package for scripting solutions to signal integrity problems.

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every cha

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every cha

This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Löf in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exerc

This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Löf in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exerc

Integer linear programming (ILP) is a versatile modeling and optimization technique that is increasingly used in non-traditional ways in biology, with the potential to transform biological computation. However, few biologists know about it. This how-to and why-do text introduces ILP through the lens of computational and systems biology. It uses in-depth examples from genomics, phylogenetics, RNA, protein folding, network analysis, cancer, ecology, co-evolution, DNA sequencing, sequence analysis, pedigree and sibling inference, haplotyping, and more, to establish the power of ILP. This book aims to teach the logic of modeling and solving problems with ILP, and to teach the practical 'work flow' involved in using ILP in biology. Written for a wide audience, with no biological or computational prerequisites, this book is appropriate for entry-level and advanced courses aimed at biological and computational students, and as a source for specialists. Numerous exercises and accompanying soft

This book focuses on the suitable methods to solve optimization problems in wireless network system utilizing digital sensors like Wireless Sensor Network. This kind of system has been emerging as the

Computational Intelligence for Multimedia Big Data on the Cloud with Engineering Applications covers timely topics, including the neural network (NN), particle swarm optimization (PSO), evolutionary a

Discover a modern approach to the analysis, modeling and design of high sensitivity phased arrays. Network theory, numerical methods and computational electromagnetic simulation techniques are uniquely combined to enable full system analysis and design optimization. Beamforming and array signal processing theory are integrated into the treatment from the start. Digital signal processing methods such as polyphase filtering and RFI mitigation are described, along with technologies for real-time hardware implementation. Key concepts from interferometric imaging used in radio telescopes are also considered. A basic development of theory and modeling techniques is accompanied by problem sets that guide readers in developing modeling codes that retain the simplicity of the classical array factor method while incorporating mutual coupling effects and interactions between elements. Combining current research trends with pedagogical material suitable for a first-year graduate course, this is an

Updated new edition covering all aspects of network planning and optimization This welcome new edition provides comprehensive coverage of all aspects of network planning in all the technologies,

Achieve faster and more efficient network design and optimization with this comprehensive guide. Some of the most prominent researchers in the field explain the very latest analytic techniques and results from stochastic geometry for modelling the signal-to-interference-plus-noise ratio (SINR) distribution in heterogeneous cellular networks. This book will help readers to understand the effects of combining different system deployment parameters on key performance indicators such as coverage and capacity, enabling the efficient allocation of simulation resources. In addition to covering results for network models based on the Poisson point process, this book presents recent results for when non-Poisson base station configurations appear Poisson, due to random propagation effects such as fading and shadowing, as well as non-Poisson models for base station configurations, with a focus on determinantal point processes and tractable approximation methods. Theoretical results are illustrate

This book deals with averaging dynamics, a paradigmatic example of network based dynamics in multi-agent systems. The book presents all the fundamental results on linear averaging dynamics, proposing

Covering network designs, discrete convex analysis, facility location and clustering problems, matching games, and parameterized complexity, this book discusses theoretical aspects of combinatorial op

From basic architecture, interconnection, and parallelization to power optimization, this book provides a comprehensive description of emerging multicore systems-on-chip (MCSoCs) hardware and software

This new edition covers linear and nonlinear methods as well as optimization, numerical simulation, and eigenvalue methods. Independent of the implementation approach, this book includes numerical exa

This book is for all those who are looking for a non-conventional mathematical model of electrical network systems. It presents a modern approach using linear algebra and derives various commonly unkn

This book introduces readers to titanium matrix composites (TMCs) with novel network microstructures. The bottleneck problem of extreme brittleness and low strengthening effect surrounding TMCs fabric

Learn about the key technologies and understand the state of the art in research for full-duplex communication networks and systems with this comprehensive and interdisciplinary guide. Incorporating physical, MAC, network, and application layer perspectives, it explains the fundamental theories on which full-duplex communications are built, and lays out the techniques needed for network design, analysis and optimization. Techniques covered in detail include self-interference cancellation and signal processing algorithms, physical layer algorithms, methods for efficient resource allocation, and game theory. Potential applications and networking schemes are discussed, including full-duplex cognitive radio networks, cooperative networks, and heterogeneous networks. The first book to focus exclusively on full-duplex communications, this is an indispensable reference for both researchers and practitioners designing the next generation of wireless networks.

This book presents cutting-edge research contributions that address various aspects of network design, optimization, implementation, and application of cognitive radio technologies. It demonstrates ho