Download or read book Mathematics of Epidemics on Networks written by István Z. Kiss and published by Springer. This book was released on 2017-06-08 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate students, as well as doctoral students, postdoctoral researchers and academic experts who are engaged in modeling stochastic processes on networks; Providing software that can solve differential equation models or directly simulate epidemics on networks. Replete with numerous diagrams, examples, instructive exercises, and online access to simulation algorithms and readily usable code, this book will appeal to a wide spectrum of readers from different backgrounds and academic levels. Appropriate for students with or without a strong background in mathematics, this textbook can form the basis of an advanced undergraduate or graduate course in both mathematics and other departments alike.
Download or read book Random Graphs and Complex Networks written by Remco van der Hofstad and published by Cambridge University Press. This book was released on 2017 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
Download or read book Exponential Random Graph Models for Social Networks written by Dean Lusher and published by Cambridge University Press. This book was released on 2013 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an account of the theoretical and methodological underpinnings of exponential random graph models (ERGMs).
Download or read book Valuation of Network Effects in Software Markets written by Andreas Kemper and published by Springer Science & Business Media. This book was released on 2009-12-12 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The customer base is an important value driver of software companies and a reliable prediction of its development is fundamental for investment decisions. A particularity in software markets is that an individual’s purchasing decision is often influenced by other users’ choices. Although such customer network effects are evident, their quantitative assessment remain elusive with conventional approaches. This book contributes to closing this gap by developing methods for measuring network effects and their implications for valuation in software markets. Based on the theory of complex networks the book reveals that such diffusion processes highly depend on structural properties of customer networks. Moreover, it depicts that such insights are contributions to improve the quality of valuations in software markets. But the implications of this research also comprise social and political aspects as they can be applied in order to prevent corporate failures in all network effect markets.
Download or read book Stochastic Epidemic Models and Their Statistical Analysis written by Hakan Andersson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present lecture notes describe stochastic epidemic models and methods for their statistical analysis. Our aim is to present ideas for such models, and methods for their analysis; along the way we make practical use of several probabilistic and statistical techniques. This will be done without focusing on any specific disease, and instead rigorously analyzing rather simple models. The reader of these lecture notes could thus have a two-fold purpose in mind: to learn about epidemic models and their statistical analysis, and/or to learn and apply techniques in probability and statistics. The lecture notes require an early graduate level knowledge of probability and They introduce several techniques which might be new to students, but our statistics. intention is to present these keeping the technical level at a minlmum. Techniques that are explained and applied in the lecture notes are, for example: coupling, diffusion approximation, random graphs, likelihood theory for counting processes, martingales, the EM-algorithm and MCMC methods. The aim is to introduce and apply these techniques, thus hopefully motivating their further theoretical treatment. A few sections, mainly in Chapter 5, assume some knowledge of weak convergence; we hope that readers not familiar with this theory can understand the these parts at a heuristic level. The text is divided into two distinct but related parts: modelling and estimation.
Download or read book The Oxford Handbook of the Economics of Networks written by Yann Bramoullé and published by Oxford University Press. This book was released on 2016-03-01 with total page 857 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Oxford Handbook of the Economics of Networks represents the frontier of research into how and why networks they form, how they influence behavior, how they help govern outcomes in an interactive world, and how they shape collective decision making, opinion formation, and diffusion dynamics. From a methodological perspective, the contributors to this volume devote attention to theory, field experiments, laboratory experiments, and econometrics. Theoretical work in network formation, games played on networks, repeated games, and the interaction between linking and behavior is synthesized. A number of chapters are devoted to studying social process mediated by networks. Topics here include opinion formation, diffusion of information and disease, and learning. There are also chapters devoted to financial contagion and systemic risk, motivated in part by the recent financial crises. Another section discusses communities, with applications including social trust, favor exchange, and social collateral; the importance of communities for migration patterns; and the role that networks and communities play in the labor market. A prominent role of networks, from an economic perspective, is that they mediate trade. Several chapters cover bilateral trade in networks, strategic intermediation, and the role of networks in international trade. Contributions discuss as well the role of networks for organizations. On the one hand, one chapter discusses the role of networks for the performance of organizations, while two other chapters discuss managing networks of consumers and pricing in the presence of network-based spillovers. Finally, the authors discuss the internet as a network with attention to the issue of net neutrality.
Download or read book Complex Spreading Phenomena in Social Systems written by Sune Lehmann and published by Springer. This book was released on 2018-06-21 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is about spreading of information and influence in complex networks. Although previously considered similar and modeled in parallel approaches, there is now experimental evidence that epidemic and social spreading work in subtly different ways. While previously explored through modeling, there is currently an explosion of work on revealing the mechanisms underlying complex contagion based on big data and data-driven approaches. This volume consists of four parts. Part 1 is an Introduction, providing an accessible summary of the state of the art. Part 2 provides an overview of the central theoretical developments in the field. Part 3 describes the empirical work on observing spreading processes in real-world networks. Finally, Part 4 goes into detail with recent and exciting new developments: dedicated studies designed to measure specific aspects of the spreading processes, often using randomized control trials to isolate the network effect from confounders, such as homophily. Each contribution is authored by leading experts in the field. This volume, though based on technical selections of the most important results on complex spreading, remains quite accessible to the newly interested. The main benefit to the reader is that the topics are carefully structured to take the novice to the level of expert on the topic of social spreading processes. This book will be of great importance to a wide field: from researchers in physics, computer science, and sociology to professionals in public policy and public health.
Download or read book Networks written by Sanjeev Goyal and published by MIT Press. This book was released on 2023-04-18 with total page 823 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible and comprehensive overview of the economic theory and the realities of networks written by a pioneering economics researcher. Networks are everywhere: the infrastructure that brings water into our homes, the social networks made up of our friends and families, the supply chains connecting cities, people, and goods. These interconnections contain economic trade-offs: for example, should an airline operate direct flights between cities or route all its flights through a hub? Viewing networks through an economics lens, this textbook considers the costs and benefits that govern their formation and functioning. Networks are central to an understanding of the production, consumption, and information that lie at the heart of economic activity. Sanjeev Goyal provides advanced undergraduate and graduate students with an accessible and comprehensive introduction to the economics research on networks of the past twenty-five years. Each chapter introduces a theoretical model illustrated with the help of case studies and formal proofs. After introducing the theoretical concepts, Goyal examines economic networks, including infrastructure, security, market power, and financial networks. He then covers social networks, with chapters on coordinating activity, communication and learning, information networks, epidemics, and impersonal markets. Finally, Goyal locates social and economic networks in a broader context covering networked markets, economic development, trust, and group networks in their relation to markets and the state. First textbook to provide a broad and comprehensive overview of twenty-first-century economic theory of networks Features engaging case studies and accessible exercises Written by a pioneering economics researcher
Download or read book Stochastic Interacting Systems in Life and Social Sciences written by Nicolas Lanchier and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-07-01 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an overview of two of the most important examples of interacting particle systems, the contact process, and the voter model, as well as their many variants introduced in the past 50 years. These stochastic processes are organized by domains of application (epidemiology, population dynamics, ecology, genetics, sociology, econophysics, game theory) along with a flavor of the mathematical techniques developed for their analysis.
Download or read book Epidemics written by Ottar N. Bjørnstad and published by Springer. This book was released on 2018-10-30 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed to be a practical study in infectious disease dynamics. The book offers an easy to follow implementation and analysis of mathematical epidemiology. The book focuses on recent case studies in order to explore various conceptual, mathematical, and statistical issues. The dynamics of infectious diseases shows a wide diversity of pattern. Some have locally persistent chains-of-transmission, others persist spatially in ‘consumer-resource metapopulations’. Some infections are prevalent among the young, some among the old and some are age-invariant. Temporally, some diseases have little variation in prevalence, some have predictable seasonal shifts and others exhibit violent epidemics that may be regular or irregular in their timing. Models and ‘models-with-data’ have proved invaluable for understanding and predicting this diversity, and thence help improve intervention and control. Using mathematical models to understand infectious disease dynamics has a very rich history in epidemiology. The field has seen broad expansions of theories as well as a surge in real-life application of mathematics to dynamics and control of infectious disease. The chapters of Epidemics: Models and Data using R have been organized in a reasonably logical way: Chapters 1-10 is a mix and match of models, data and statistics pertaining to local disease dynamics; Chapters 11-13 pertains to spatial and spatiotemporal dynamics; Chapter 14 highlights similarities between the dynamics of infectious disease and parasitoid-host dynamics; Finally, Chapters 15 and 16 overview additional statistical methodology useful in studies of infectious disease dynamics. This book can be used as a guide for working with data, models and ‘models-and-data’ to understand epidemics and infectious disease dynamics in space and time.
Download or read book Social and Economic Networks written by Matthew O. Jackson and published by Princeton University Press. This book was released on 2010-11-01 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Networks of relationships help determine the careers that people choose, the jobs they obtain, the products they buy, and how they vote. The many aspects of our lives that are governed by social networks make it critical to understand how they impact behavior, which network structures are likely to emerge in a society, and why we organize ourselves as we do. In Social and Economic Networks, Matthew Jackson offers a comprehensive introduction to social and economic networks, drawing on the latest findings in economics, sociology, computer science, physics, and mathematics. He provides empirical background on networks and the regularities that they exhibit, and discusses random graph-based models and strategic models of network formation. He helps readers to understand behavior in networked societies, with a detailed analysis of learning and diffusion in networks, decision making by individuals who are influenced by their social neighbors, game theory and markets on networks, and a host of related subjects. Jackson also describes the varied statistical and modeling techniques used to analyze social networks. Each chapter includes exercises to aid students in their analysis of how networks function. This book is an indispensable resource for students and researchers in economics, mathematics, physics, sociology, and business.
Download or read book Genetics Abstracts written by and published by . This book was released on 1973 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spatial Dynamics and Pattern Formation in Biological Populations written by Ranjit Kumar Upadhyay and published by CRC Press. This book was released on 2021-02-24 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction to deterministic (and some stochastic) modeling of spatiotemporal phenomena in ecology, epidemiology, and neural systems. A survey of the classical models in the fields with up to date applications is given. The book begins with detailed description of how spatial dynamics/diffusive processes influence the dynamics of biological populations. These processes play a key role in understanding the outbreak and spread of pandemics which help us in designing the control strategies from the public health perspective. A brief discussion on the functional mechanism of the brain (single neuron models and network level) with classical models of neuronal dynamics in space and time is given. Relevant phenomena and existing modeling approaches in ecology, epidemiology and neuroscience are introduced, which provide examples of pattern formation in these models. The analysis of patterns enables us to study the dynamics of macroscopic and microscopic behaviour of underlying systems and travelling wave type patterns observed in dispersive systems. Moving on to virus dynamics, authors present a detailed analysis of different types models of infectious diseases including two models for influenza, five models for Ebola virus and seven models for Zika virus with diffusion and time delay. A Chapter is devoted for the study of Brain Dynamics (Neural systems in space and time). Significant advances made in modeling the reaction-diffusion systems are presented and spatiotemporal patterning in the systems is reviewed. Development of appropriate mathematical models and detailed analysis (such as linear stability, weakly nonlinear analysis, bifurcation analysis, control theory, numerical simulation) are presented. Key Features Covers the fundamental concepts and mathematical skills required to analyse reaction-diffusion models for biological populations. Concepts are introduced in such a way that readers with a basic knowledge of differential equations and numerical methods can understand the analysis. The results are also illustrated with figures. Focuses on mathematical modeling and numerical simulations using basic conceptual and classic models of population dynamics, Virus and Brain dynamics. Covers wide range of models using spatial and non-spatial approaches. Covers single, two and multispecies reaction-diffusion models from ecology and models from bio-chemistry. Models are analysed for stability of equilibrium points, Turing instability, Hopf bifurcation and pattern formations. Uses Mathematica for problem solving and MATLAB for pattern formations. Contains solved Examples and Problems in Exercises. The Book is suitable for advanced undergraduate, graduate and research students. For those who are working in the above areas, it provides information from most of the recent works. The text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.
Download or read book Random Walks and Diffusion written by Open University Course Team and published by . This book was released on 2009-10-21 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This block explores the diffusion equation which is most commonly encountered in discussions of the flow of heat and of molecules moving in liquids, but diffusion equations arise from many different areas of applied mathematics. As well as considering the solutions of diffusion equations in detail, we also discuss the microscopic mechanism underlying the diffusion equation, namely that particles of matter or heat move erratically. This involves a discussion of elementary probability and statistics, which are used to develop a description of random walk processes and of the central limit theorem. These concepts are used to show that if particles follow random walk trajectories, their density obeys the diffusion equation.
Download or read book The Oxford Handbook of Political Networks written by Jennifer Nicoll Victor and published by Oxford University Press. This book was released on 2018 with total page 1011 pages. Available in PDF, EPUB and Kindle. Book excerpt: Politics is intuitively about relationships, but until recently the network perspective has not been a dominant part of the methodological paradigm that political scientists use to study politics. This volume is a foundational statement about networks in the study of politics.
Download or read book Machine Learning in Complex Networks written by Thiago Christiano Silva and published by Springer. This book was released on 2016-01-28 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the features and advantages offered by complex networks in the machine learning domain. In the first part, an overview on complex networks and network-based machine learning is presented, offering necessary background material. In the second part, we describe in details some specific techniques based on complex networks for supervised, non-supervised, and semi-supervised learning. Particularly, a stochastic particle competition technique for both non-supervised and semi-supervised learning using a stochastic nonlinear dynamical system is described in details. Moreover, an analytical analysis is supplied, which enables one to predict the behavior of the proposed technique. In addition, data reliability issues are explored in semi-supervised learning. Such matter has practical importance and is not often found in the literature. With the goal of validating these techniques for solving real problems, simulations on broadly accepted databases are conducted. Still in this book, we present a hybrid supervised classification technique that combines both low and high orders of learning. The low level term can be implemented by any classification technique, while the high level term is realized by the extraction of features of the underlying network constructed from the input data. Thus, the former classifies the test instances by their physical features, while the latter measures the compliance of the test instances with the pattern formation of the data. We show that the high level technique can realize classification according to the semantic meaning of the data. This book intends to combine two widely studied research areas, machine learning and complex networks, which in turn will generate broad interests to scientific community, mainly to computer science and engineering areas.
Download or read book Theoretical Ecology written by Robert May and published by OUP Oxford. This book was released on 2007-02-15 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robert May's seminal book has played a central role in the development of ecological science. Originally published in 1976, this influential text has overseen the transition of ecology from an observational and descriptive subject to one with a solid conceptual core. Indeed, it is a testament to its influence that a great deal of the novel material presented in the earlier editions has now been incorporated into standard undergraduate textbooks. It is now a quarter of a century since the publication of the second edition, and a thorough revision is timely. Theoretical Ecology provides a succinct, up-to-date overview of the field set in the context of applications, thereby bridging the traditional division of theory and practice. It describes the recent advances in our understanding of how interacting populations of plants and animals change over time and space, in response to natural or human-created disturbance. In an integrated way, initial chapters give an account of the basic principles governing the structure, function, and temporal and spatial dynamics of populations and communities of plants and animals. Later chapters outline applications of these ideas to practical issues including fisheries, infectious diseases, tomorrow's food supplies, climate change, and conservation biology. Throughout the book, emphasis is placed on questions which as yet remain unanswered. The editors have invited the top scientists in the field to collaborate with the next generation of theoretical ecologists. The result is an accessible, advanced textbook suitable for senior undergraduate and graduate level students as well as researchers in the fields of ecology, mathematical biology, environment and resources management. It will also be of interest to the general reader seeking a better understanding of a range of global environmental problems.
