13 research outputs found
Asymptotic analysis of the Friedkin-Johnsen model when the matrix of the susceptibility weights approaches the identity matrix
In this paper we analyze the Friedkin-Johnsen model of opinions when the
coefficients weighting the agent susceptibilities to interpersonal influence
approach 1. We will show that in this case, under suitable assumptions, the
model converges to a quasi-consensus condition among the agents. In general the
achieved consensus value will be different to the one obtained by the
corresponding DeGroot mode
Novel Multidimensional Models of Opinion Dynamics in Social Networks
Unlike many complex networks studied in the literature, social networks
rarely exhibit unanimous behavior, or consensus. This requires a development of
mathematical models that are sufficiently simple to be examined and capture, at
the same time, the complex behavior of real social groups, where opinions and
actions related to them may form clusters of different size. One such model,
proposed by Friedkin and Johnsen, extends the idea of conventional consensus
algorithm (also referred to as the iterative opinion pooling) to take into
account the actors' prejudices, caused by some exogenous factors and leading to
disagreement in the final opinions.
In this paper, we offer a novel multidimensional extension, describing the
evolution of the agents' opinions on several topics. Unlike the existing
models, these topics are interdependent, and hence the opinions being formed on
these topics are also mutually dependent. We rigorous examine stability
properties of the proposed model, in particular, convergence of the agents'
opinions. Although our model assumes synchronous communication among the
agents, we show that the same final opinions may be reached "on average" via
asynchronous gossip-based protocols.Comment: Accepted by IEEE Transaction on Automatic Control (to be published in
May 2017
Opinion Dynamics and the Evolution of Social Power in Social Networks
A fundamental aspect of society is the exchange and discussion of
opinions between individuals, occurring in mediums and situations
as varied as company boardrooms, elementary school classrooms and
online social media. This thesis studies several mathematical
models of how an individual’s opinion(s) evolves via
interaction with others in a social network, developed to reflect
and capture different socio-psychological processes that occur
during the interactions.
In the first part, and inspired by Solomon E. Asch’s seminal
experiments on conformity, a novel discrete-time model of opinion
dynamics is proposed, with each individual having both an
expressed and a private opinion on the same topic. Crucially, an
individual’s expressed opinion is altered from the
individual’s private opinion due to pressures to conform to the
majority opinion of the social network. Exponential convergence
of the opinion dynamical system to a unique configuration is
established for general networks. Several conclusions are
established, including how differences between an individual’s
expressed and private opinions arise, and how to estimate
disagreement among the private opinions at equilibrium. Asch’s
experiments are revisited and re-examined, and then it is shown
that a few extremists can create “pluralistic ignorance”,
where people believe there is majority support for a position but
in fact the position is privately rejected by the majority of
individuals!
The second part builds on the recently proposed discrete-time
DeGroot–Friedkin model, which describes the evolution of an
individual’s self-confidence (termed social power) in his/her
opinion over the discussion of a sequence of issues. Using
nonlinear contraction analysis, exponential convergence to a
unique equilibrium is established for networks with constant
topology. Networks with issue-varying topology (which remain
constant for any given issue) are then studied; exponential
convergence to a unique limiting trajectory is established. In a
social context, this means that each individual forgets his/her
initial social power exponentially fast; in the limit, his/her
social power for a given issue depends only on the previously
occurring sequence of dynamic topology. Two further related works
are considered; a network modification problem, and a different
convergence proof based on Lefschetz Fixed Point Theory.
In the final part, a continuous-time model is proposed to capture
simultaneous discussion of logically interdependent topics; the
interdependence is captured by a “logic matrix”. When no
individual remains attached to his/her initial opinion, a
necessary and sufficient condition for the network to reach a
consensus of opinions is provided. This condition depends on the
interplay between the network interactions and the logic matrix;
if the network interactions are too strong when compared to the
logical couplings, instability can result. Last, when some
individuals remain attached to their initial opinions, sufficient
conditions are given for opinions to converge to a state of
persistent disagreement
Dynamical Networks of Social Influence: Modern Trends and Perspectives
Dynamics and control of processes over social networks, such as the evolution of opinions, social influence and interpersonal appraisals, diffusion of information and misinformation, emergence and dissociation of communities, are now attracting significant attention from the broad research community that works on systems, control, identification and learning. To provide an introduction to this rapidly developing area, a Tutorial Session was included into the program of IFAC World Congress 2020. This paper provides a brief summary of the three tutorial lectures, covering the most “mature” directions in analysis of social networks and dynamics over them: 1) formation of opinions under social influence; 2) identification and learning for analysis of a network’s structure; 3) dynamics of interpersonal appraisals
Learning Hidden Influences in Large-Scale Dynamical Social Networks: A Data-Driven Sparsity-Based Approach, in Memory of Roberto Tempo
The processes of information diffusion across social networks (for example, the spread of opinions and the formation of beliefs) are attracting substantial interest in disciplines ranging from behavioral sciences to mathematics and engineering (see "Summary"). Since the opinions and behaviors of each individual are infl uenced by interactions with others, understanding the structure of interpersonal infl uences is a key ingredient to predict, analyze, and, possibly, control information and decisions [1]. With the rapid proliferation of social media platforms that provide instant messaging, blogging, and other networking services (see "Online Social Networks") people can easily share news, opinions, and preferences. Information can reach a broad audience much faster than before, and opinion mining and sentiment analysis are becoming key challenges in modern society [2]. The first anecdotal evidence of this fact is probably the use that the Obama campaign made of social networks during the 2008 U.S. presidential election [3]. More recently, several news outlets stated that Facebook users played a major role in spreading fake news that might have infl uenced the outcome of the 2016 U.S. presidential election [4]. This can be explained by the phenomena of homophily and biased assimilation [5]-[7] in social networks, which correspond to the tendency of people to follow the behaviors of their friends and establish relationships with like-minded individuals
Dynamical networks of social influence: Modern trends and perspectives
Dynamics and control of processes over social networks, such as the evolution of opinions, social influence and interpersonal appraisals, diffusion of information and misinfor-mation, emergence and dissociation of communities, are now attracting significant attention from the broad research community that works on systems, control, identification and learning. To provide an introduction to this rapidly developing area, a Tutorial Session was included into the program of IFAC World Congress 2020. This paper provides a brief summary of the three tutorial lectures, covering the most "mature"directions in analysis of social networks and dynamics over them: 1) formation of opinions under social influence; 2) identification and learning for analysis of a network's structure; 3) dynamics of interpersonal appraisals
Recommended from our members
Analysis, Modeling, and Control of Dynamic Processes in Networks
Dynamic network processes have surrounded people for millennia. Information spread through social networks, alliance formation in financial and organizational networks, heat diffusion through material networks, and distributed synchronization in robotic networks are just a few examples. Network processes are studies along three dimensions: analysis of network processes through the data produced by them; designing complex plausible, yet, tractable mathematical models for network processes; and designing control mechanisms that would guide network processes towards desirable evolution patterns. This thesis advances the frontier of knowledge about network processes along each of these three dimensions, emphasizing applications to social networks.The first part of the thesis is dedicated to the design of a method for model-driven analysis of a polar opinion formation process in social networks. The core of the method is a distance measure quantifying the likelihood of a social network's transitioning between different states with respect to a chosen opinion dynamics model characterizing expected evolution of the network's state. I describe how to design such a distance measure relying upon the classical transportation problem, compute it in linear time, and use it in applications.In the second part of the thesis, I focus on designing a model for polar opinion formation in social networks, and define a class of non-linear models that capture the dependence of the users' opinion formation behavior upon the opinions themselves. The obtained models are connected to socio-psychological theories, and their behavior is theoretically analyzed employing tools from non-smooth analysis and a generalization of LaSalle Invariance Principle.The third part of the thesis targets the problem of defense against social control. While the existing socio-psychological theories as well as influence maximization techniques expose the opinion formation process in social networks to external attacks, I propose an algorithm that nullifies the effect of such attacks by strategically recommending a small number of new edges to the network's users. The optimization problem underlying the algorithm is NP-hard, and I provide a pseudo-linear time heuristic---drawing upon the theory of Markov chains---that solves the problem approximately and performs well in experiments
Diffusion and Supercritical Spreading Processes on Complex Networks
Die große Menge an Datensätzen, die in den letzten Jahren verfügbar wurden, hat es ermöglicht, sowohl menschlich-getriebene als auch biologische komplexe Systeme in einem beispiellosen Ausmaß empirisch zu untersuchen.
Parallel dazu ist die Vorhersage und Kontrolle epidemischer Ausbrüche für Fragen der öffentlichen Gesundheit sehr wichtig geworden.
In dieser Arbeit untersuchen wir einige wichtige Aspekte von Diffusionsphänomenen und Ausbreitungsprozeßen auf Netzwerken. Wir untersuchen drei verschiedene Probleme im Zusammenhang mit Ausbreitungsprozeßen im überkritischen Regime. Zunächst untersuchen wir die Reaktionsdiffusion auf Ensembles zufälliger Netzwerke, die durch die beobachteten Levy-Flugeigenschaften der menschlichen Mobilität charakterisiert sind.
Das zweite Problem ist die Schätzung der Ankunftszeiten globaler Pandemien. Zu diesem Zweck leiten wir geeignete verborgene Geometrien netzgetriebener Streuprozeße, unter Nutzung der Random-Walk-Theorie, her und identifizieren diese.
Durch die Definition von effective distances wird das Problem komplexer raumzeitlicher Muster auf einfache, homogene Wellenausbreitungsmuster reduziert. Drittens führen wir durch die Einbettung von Knoten in den verborgenen Raum, der durch effective distances im Netzwerk definiert ist, eine neuartige Netzwerkzentralität ein, die ViralRank genannt wird und quantifiziert, wie nahe ein Knoten, im Durchschnitt, den anderen Knoten im Netzwerk ist.
Diese drei Studien bilden einen einheitlichen Rahmen zur Charakterisierung von Diffusions- und Ausbreitungsprozeßen, die sich auf komplexen Netzwerken allgemein abzeichnen, und bieten neue Ansätze für herausfordernde theoretische Probleme, die für die Bewertung künftiger Modelle verwendet werden können.The large amount of datasets that became available in recent years has made it possible to empirically study humanly-driven, as well as biological complex systems to an unprecedented extent.
In parallel, the prediction and control of epidemic outbreaks have become very important for public health issues.
In this thesis, we investigate some important aspects of diffusion phenomena and spreading processes unfolding on networks.
We study three different problems related to spreading processes in the supercritical regime.
First, we study reaction-diffusion on ensembles of random networks characterized by the observed Levy-flight properties of human mobility.
The second problem is the estimation of the arrival times of global pandemics. To this end, we derive and identify suitable hidden geometries of network-driven spreading processes, leveraging on random-walk theory. Through the definition of network effective distances, the problem of complex spatiotemporal patterns is reduced to simple, homogeneous wave propagation patterns.
Third, by embedding nodes in the hidden space defined by network effective distances, we introduce a novel network centrality, called ViralRank, which quantifies how
close a node is, on average, to the other nodes.
These three studies constitute a unified framework to characterize diffusion and spreading processes unfolding on complex networks in very general settings, and provide new approaches to challenging theoretical problems that can be used to benchmark future models