Opinion fluctuations and disagreement in social networks

We study a tractable opinion dynamics model that generates long-run disagreements and persistent opinion fluctuations. Our model involves an inhomogeneous stochastic gossip process of continuous opinion dynamics in a society consisting of two types of agents: regular agents, who update their beliefs according to information that they receive from their social neighbors; and stubborn agents, who never update their opinions. When the society contains stubborn agents with different opinions, the belief dynamics never lead to a consensus (among the regular agents). Instead, beliefs in the society fail to converge almost surely, the belief profile keeps on fluctuating in an ergodic fashion, and it converges in law to a non-degenerate random vector. The structure of the network and the location of the stubborn agents within it shape the opinion dynamics. The expected belief vector evolves according to an ordinary differential equation coinciding with the Kolmogorov backward equation of a continuous-time Markov chain with absorbing states corresponding to the stubborn agents and converges to a harmonic vector, with every regular agent's value being the weighted average of its neighbors' values, and boundary conditions corresponding to the stubborn agents'. Expected cross-products of the agents' beliefs allow for a similar characterization in terms of coupled Markov chains on the network. We prove that, in large-scale societies which are highly fluid, meaning that the product of the mixing time of the Markov chain on the graph describing the social network and the relative size of the linkages to stubborn agents vanishes as the population size grows large, a condition of \emph{homogeneous influence} emerges, whereby the stationary beliefs' marginal distributions of most of the regular agents have approximately equal first and second moments.Comment: 33 pages, accepted for publication in Mathematics of Operation Researc

Critical phenomena in complex networks

The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years, researchers have made important steps toward understanding the qualitatively new critical phenomena in complex networks. We review the results, concepts, and methods of this rapidly developing field. Here we mostly consider two closely related classes of these critical phenomena, namely structural phase transitions in the network architectures and transitions in cooperative models on networks as substrates. We also discuss systems where a network and interacting agents on it influence each other. We overview a wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, k-core percolation, phenomena near epidemic thresholds, condensation transitions, critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks. We also discuss strong finite size effects in these systems and highlight open problems and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references, extende

Opinion Fluctuations and Disagreement in Social Network

We study a stochastic gossip model of continuous opinion dynamics in a society consisting of two types of agents: regular agents, who update their beliefs according to information that they receive from their social neighbors; and stubborn agents, who never update their opinions and might represent leaders, political parties or media sources attempting to influence the beliefs in the rest of the society. When the society contains stubborn agents with different opinions, opinion dynamics never lead to a consensus (among the regular agents). Instead, beliefs in the society almost surely fail to converge, and the belief of each regular agent converges in law to a non-degenerate random variable. The model thus generates long-run disagreement and continuous opinion fluctuations. The structure of the social network and the location of stubborn agents within it shape opinion dynamics. When the society is “highly fluid,” meaning that the mixing time of the random walk on the graph describing the social network is small relative to (the inverse of) the relative size of the linkages to stubborn agents, the ergodic beliefs of most of the agents concentrate around a certain common value. We also show that under additional conditions, the ergodic beliefs distribution becomes “approximately chaotic”, meaning that the variance of the aggregate belief of the society vanishes in the large population limit while individual opinions still fluctuate significantly

Glosarium Matematika

273 p.; 24 cm

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Radiation effects studies for the high-resolution spectrograph

The generation and collection of charge carriers created during the passage of energetic protons through a silicon photodiode array are modeled. Pulse height distributions of noise charge collected during exposure of a digicon type diode array to 21 and 75 MeV protons were obtained. The magnitude of charge collected by a diode from each proton event is determined not only by diffusion, but by statistical considerations involving the ionization process itself. Utilizing analytical solutions to the diffusion equation for transport of minority carriers, together with the Vavilov theory of energy loss fluctuations in thin absorbers, simulations of the pulse height spectra which follow the experimental distributions fairly well are presented and an estimate for the minority carrier diffusion length L sub d is provided