1st Edition
Information Spread in a Social Media Age Modeling and Control
The rise of social networks and social media has led to a massive shift in the ways information is dispersed. Platforms like Twitter and Facebook allow people to more easily connect as a community, but they can also be avenues for misinformation, fake news, and polarization. The need to examine, model, and analyze the trajectory of information spread within this new paradigm has never been greater. This text expands upon the authors’ combined teaching experience, engineering knowledge, and multiple academic journal publications on these topics to present an intuitive and easy to understand exploration of social media information spread alongside the technical and mathematical concepts. By design, this book uses simple language and accessible and modern case studies (including those centered around United States mass shootings, the #MeToo social movement, and more) to ensure it is accessible to the casual reader. At the same time, readers with prior knowledge of the topics will benefit from the mathematical model and control elements and accompanying sample simulation code for each main topic.
By reading this book and working through the included exercises, readers will gain a general understanding of modern social media systems, network fundamentals, model development techniques, and social marketing. The mathematical modeling of information spread over social media is heavily emphasized through a review of existing epidemiology and marketing based models. The book then presents novel models developed by the authors to account for modern social media concerns such as community filter bubbles, strongly polarized groups, and contentious information spread. Readers will learn how to build and execute simple case studies using Twitter data to help verify the text’s proposed models.
Once the reader is armed with a fundamental understanding of mathematical modeling and social media-based system considerations, the book introduces more complex engineering control concepts, including controller design, PID control, and optimal control. Examples of control methods for social campaigns and misinformation mitigation applications are covered in a step-by-step format from problem formulation to solution simulation and results discussions. While many of the examples and methods are framed in the context of controlling social media information spread, the material is also directly applicable to many different types of controllable systems.
With the essential background, models, and tools presented within, any interested reader can take the first steps toward exploring and taming the growing complexity of the modern social media age.
1 Introduction
1.1 Expressions of Information
1.2 Why Information Spread Matters?
1.3 Modern Information Spread Scenarios
1.4 Controllable Information Spread
1.5 How to Read This Book
1.6 Exercises
I Understanding Social Networking Systems
2 Social Media in Popular Culture
2.1 The Topology of Social Media
2.2 Social Networking Sites
2.3 Content Sharing Sites
2.4 Discussion Forums
2.5 News and Blogs
2.6 Shopping and Reviews
2.7 Games and Music
2.8 Hybrid Social Media
2.9 Exercises
3 Social Theory and Networks
3.1 Philosophy, Science, and Information Spread
3.2 Social Theory and Social Networks
3.3 Social Exchange Theory
3.4 Exercises
4 Social Network Relationships and Structures
4.1 Social Network Relationship Overview
4.2 Core Social Network Relationships
4.3 Homophily and Filter Bubbles
4.4 Dyadic Relationships and Reciprocity
4.5 Triads and Balanced Relationships
4.6 Social Network Analysis Software
4.7 Exercises
5 Social Network Analysis
5.1 Density and Structural Holes
5.2 Weak and Strong Ties
5.3 Centrality and Distance
5.4 Small World Networks
5.5 Clusters, Cohesion, and Polarization
5.6 The Adjacency Matrix
5.7 Exercises
II Macroscopic Modeling and Information Spread
6 Modeling Basics
6.1 What is a Model?
6.2 Models in Decision Making
6.3 Standard Models
6.4 Models, Assumptions, and Approximations
6.5 Mathematical Systems Modeling
6.6 Microscopic and Macroscopic Models
6.7 Basic Steps to Develop a Mathematical Model
6.8 Model Validation
6.9 Modeling and the State-Space Representation
6.10 Example 1: A Spring-Mass System
6.11 Example 2: A Predator-Prey System
6.12 Example 3: An RLC Circuit
6.13 Example 4: An Epidemic Model
6.14 Example 5: Vehicular Traffic Modeling
7 Epidemiology-Based Models for Information Spread
7.1 Epidemiology Models
7.2 Information Spread Models: Overview and Conventions
7.3 The Ignorant-Spreader (IS) Model
7.4 The Ignorant-Spreader-Ignorant (ISI) Model
7.5 The Ignorant-Spreader-Recovered (ISR) Model
7.6 Reproductive Number and Herd Immunity
7.7 ISR Model for Social Media
7.8 ISCR Model for Contentious Information Spread
7.9 Hybrid ISCR Model
7.10 ISSRR Model for Contentious Information
7.11 Exercises
8 Stochastic Modeling of Information Spread
8.1 Brownian Motion
8.2 Deterministic and Stochastic Realizations of Processes
8.3 Stochastic Modeling Considerations for Social Media Systems
8.4 Stochastic ISI Information Model
8.5 Stochastic ISR Information Modeling and Social Media
8.6 Exercises
9 Social Marketing-Based Models for Information Spread
9.1 Vidale-Wolfe Model
9.2 Bass Model
9.3 Sethi Model
9.4 Event-triggered Social Media Chatter Model
9.5 Exercises
10 Case Studies
10.1 Selecting Case Studies
10.2 Case Study-1: 2017 Mass Shootings
10.3 Case Study-2: The #MeToo Social Movement
10.4 Case Study-3: 2018 Golden Globe Awards
10.5 Case Study-4: Viral Internet Debates
10.6 Exercises
III Control Methods For Information Spread
11 Control Basics
11.1 Introduction
11.2 Open-loop and Closed-loop Control Systems
11.3 SISO and MIMO Control Systems
11.4 Continuous-time and Discrete-time Control Systems
11.5 Control System Design
12 Control Methods
12.1 State Variable Feedback Controller
12.2 PID Controller
12.3 Optimal Control
12.4 Exercises
13 Information Spread and Control
13.1 Controlling Socio-technical Systems
13.2 The Control Action and Social Media Systems
13.3 Optimal Control and Social Media
13.4 Exercises
14 Control Application 1: Advertisements and Social Crazes
14.1 Scenario Description
14.2 Problem Formulation
14.3 Dynamic Programming Approach
14.4 Pontryagin’s Approach
14.5 Numerical Solution and Discussion
15 Control Application 2: Stopping a Fake News Outbreak
15.1 Scenario Description
15.2 Problem Formulation
15.3 Pontryagin’s Approach
15.4 Numerical Solution and Discussion
16 Concluding Thoughts
16.1 What Have We Learned?
16.2 But Now What?
16.3 The Future and Beyond
Biography
Michael Muhlmeyer provides engineering consulting services at Sabre Engineering Consulting in Los Angeles, CA. His areas of interest include mathematical modeling, control systems, computational social systems, information spread on social media, fake news, and novel applications of engineering to multidisciplinary research.
Shaurya Agarwal is currently an Assistant Professor in the Civil, Environmental, and Construction Engineering Department at the University of Central Florida. His research focuses on interdisciplinary areas of cyber-physical systems, smart and connected communities, and socio-technical-infrastructures systems.
