Polarization Model of Online Social Networks Based on the Concept of Spontaneous Symmetry Breaking

Abstract

The online echo-chamber effect is a phenomenon in which beliefs that are far from common sense are strengthened within relatively small communities formed within online social networks. Since it is significantly degrading social activities in the real world, we should understand how the echo-chamber effect arises in an engineering framework to realize countermeasure technologies. This paper proposes a model of the online echo-chamber effect by introducing the concept of spontaneous symmetry breaking to the oscillation model framework used for describing online user dynamics.

Derivation and Characteristics of Closed-Form Solutions of the Fundamental Equations for Online User Dynamics

“…There are two types of fundamental equations: boson-type and fermion-type [16]. The boson-type fundamental equation cannot consider the structure of links, whereas the fermion-type can take account of characteristics such as the sparseness of the link structure of OSNs.…”

Derivation and characteristics of closed‐form solutions of the fundamental equations for online user dynamics

“…5,6 There are two types of fundamental equations: boson-type and fermion-type. 18 The naming of boson-type and fermion-type comes from quantum field theory. 19 The fermion-type fundamental equation has a similar structure to the Dirac equation (more precisely, the Dirac equation for massless particles, called the Weyl equation) which describes Fermi particles.…”

“…This means x b (t) is a solution of the original wave equation (1). Since the original wave equation ( 1) is the second-order differential equation, solution (18) that includes two arbitrary constants x + (0) and x − (0) as the initial conditions, is a general solution of the original wave equation (1).…”

“…There are two types of fundamental equations: boson‐type and fermion‐type 18 . The naming of boson‐type and fermion‐type comes from quantum field theory 19 .…”

Closed-Form Solutions of the Fundamental Equation That Describes User Dynamics in Online Social Networks

“…There are two types of fundamental equations: boson-type and fermion-type [15]. The boson-type fundamental equation cannot consider the structure of links, whereas the fermiontype can take account of characteristics such as the sparseness of the link structure of OSNs.…”