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Modeling Information Diffusion in Online Social Networks with Partial Differential Equations

  • Haiyan Wang
  • Feng Wang
  • Kuai Xu
Book
  • 311 Downloads

Part of the Surveys and Tutorials in the Applied Mathematical Sciences book series (STAMS, volume 7)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Haiyan Wang, Feng Wang, Kuai Xu
    Pages 1-2
  3. Haiyan Wang, Feng Wang, Kuai Xu
    Pages 3-13
  4. Haiyan Wang, Feng Wang, Kuai Xu
    Pages 15-25
  5. Haiyan Wang, Feng Wang, Kuai Xu
    Pages 27-41
  6. Haiyan Wang, Feng Wang, Kuai Xu
    Pages 43-58
  7. Haiyan Wang, Feng Wang, Kuai Xu
    Pages 59-68
  8. Haiyan Wang, Feng Wang, Kuai Xu
    Pages 69-112
  9. Haiyan Wang, Feng Wang, Kuai Xu
    Pages 113-132
  10. Back Matter
    Pages 133-144

About this book

Introduction

The book lies at the interface of mathematics, social media analysis, and data science. Its authors aim to introduce a new dynamic modeling approach to the use of partial differential equations for describing information diffusion over online social networks. The eigenvalues and eigenvectors of the Laplacian matrix for the underlying social network are used to find communities (clusters) of online users. Once these clusters are embedded in a Euclidean space, the mathematical models, which are reaction-diffusion equations, are developed based on intuitive social distances between clusters within the Euclidean space. The models are validated with data from major social media such as Twitter. In addition, mathematical analysis of these models is applied, revealing insights into information flow on social media. Two applications with geocoded Twitter data are included in the book: one describing the social movement in Twitter during the Egyptian revolution in 2011 and another predicting influenza prevalence. The new approach advocates a paradigm shift for modeling information diffusion in online social networks and lays the theoretical groundwork for many spatio-temporal modeling problems in the big-data era.

Keywords

Information Diffusion Online Social Networks Partial Differential Equations Reaction-Diffusion Equations Social Media Spectral Graph Clustering Logistic Equations Spatio-temporal modeling Twitter Social movement Influenza prediction

Authors and affiliations

  • Haiyan Wang
    • 1
  • Feng Wang
    • 2
  • Kuai Xu
    • 3
  1. 1.School of Mathematical & Natural SciencesArizona State UniversityGlendaleUSA
  2. 2.School of Mathematical & Natural SciencesArizona State UniversityGlendaleUSA
  3. 3.School of Mathematical & Natural SciencesArizona State UniversityGlendaleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-38852-2
  • Copyright Information Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-38850-8
  • Online ISBN 978-3-030-38852-2
  • Series Print ISSN 2199-4765
  • Series Online ISSN 2199-4773
  • Buy this book on publisher's site