scholarly journals Voter and Majority Dynamics with Biased and Stubborn Agents

2020 ◽  
Vol 181 (4) ◽  
pp. 1239-1265
Author(s):  
Arpan Mukhopadhyay ◽  
Ravi R. Mazumdar ◽  
Rahul Roy
Keyword(s):  
Majority Rule ◽  
Branching Processes ◽  
Mean Field ◽  
Opinion Dynamics ◽  
Majority Opinion ◽  
Rule Model ◽  
Interacting Agents ◽  
The Mean ◽  
Fully Connected ◽  
Mean Time

Abstract We study binary opinion dynamics in a fully connected network of interacting agents. The agents are assumed to interact according to one of the following rules: (1) Voter rule: An updating agent simply copies the opinion of another randomly sampled agent; (2) Majority rule: An updating agent samples multiple agents and adopts the majority opinion in the selected group. We focus on the scenario where the agents are biased towards one of the opinions called the preferred opinion. Using suitably constructed branching processes, we show that under both rules the mean time to reach consensus is $$\varTheta (\log N)$$ Θ ( log N ) , where N is the number of agents in the network. Furthermore, under the majority rule model, we show that consensus can be achieved on the preferred opinion with high probability even if it is initially the opinion of the minority. We also study the majority rule model when stubborn agents with fixed opinions are present. We find that the stationary distribution of opinions in the network in the large system limit using mean field techniques.

Phase transition and universality of the three-one spin interaction based on the majority-rule model

2021 ◽  
pp. 2150115
Author(s):  
Roni Muslim ◽  
Rinto Anugraha ◽  
Sholihun Sholihun ◽  
Muhammad Farchani Rosyid
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Majority Rule ◽  
Mean Field ◽  
Opinion Dynamics ◽  
Universality Class ◽  
Spin Interaction ◽  
Population Number ◽  
Infinite Population ◽  
Rule Model

In this work, we study the opinion dynamics of majority-rule model on a complete graph with additional social behavior namely anticonformity. We consider four spins with three-one interaction; three spins persuade the fourth spin in the population. We perform analytical and numerical calculations to find the critical behavior of the system. From both, we obtained the agreement results, e.g. the system undergoes a second-order phase transition and the critical point of the system only depends on the population number. In addition, the critical point decays exponentially as the number population increases. For the infinite population, the obtained critical point is [Formula: see text], which agrees well with that of the previous work. We also obtained the critical exponents [Formula: see text] and [Formula: see text] of the model, thus, the model is in the same universality class with the mean-field Ising.

Phase transition of the Sznajd model with anticonformity for two different agent configurations

2020 ◽  
Vol 31 (04) ◽  
pp. 2050052 ◽  
Author(s):  
Roni Muslim ◽  
Rinto Anugraha ◽  
Sholihun Sholihun ◽  
Muhammad Farchani Rosyid
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Mean Field ◽  
Opinion Dynamics ◽  
Universality Class ◽  
Consensus Process ◽  
The Social ◽  
The Mean ◽  
Analytical Result ◽  
Fully Connected

In this work, we study the opinion dynamics of the Sznajd model with anticonformity on a fully-connected network. We consider four agents with two different configurations; three against one (3–1) and two against two (2–2). We consider two different individual behaviors, conformity and anticonformity, and observe the effect on the critical behavior of the model. We analyze the differences between the phase transitions that occur for both agent configurations. We find that both agent configurations have a different critical point. The critical point of the 3–1 agent is smaller than that of the 2–2 agent configuration. From the simulation and analytical result, we find that the critical point for the 3–1 occurs at [Formula: see text], and for the 2–2, at [Formula: see text]. From the social viewpoint, the consensus process in a population is faster with a larger influencer in the same number of small group of the population. In addition, we find the critical exponents for both configurations are the same, that are [Formula: see text] and [Formula: see text]. Our results suggest that both models are identical and in the mean-field Ising universality class.

scholarly journals Selective model-predictive control for flocking systems

2018 ◽  
Vol 9 (2) ◽  
pp. 4-21 ◽  
Author(s):  
Giacomo Albi ◽  
Lorenzo Pareschi
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Computational Cost ◽  
Mean Field ◽  
Stochastic Algorithm ◽  
Field Limit ◽  
Mean Field Limit ◽  
Constrained Dynamics ◽  
Interacting Agents ◽  
The Mean

Abstract In this paper the optimal control of alignment models composed by a large number of agents is investigated in presence of a selective action of a controller, acting in order to enhance consensus. Two types of selective controls have been presented: an homogeneous control filtered by a selective function and a distributed control active only on a selective set. As a first step toward a reduction of computational cost, we introduce a model predictive control (MPC) approximation by deriving a numerical scheme with a feedback selective constrained dynamics. Next, in order to cope with the numerical solution of a large number of interacting agents, we derive the mean-field limit of the feedback selective constrained dynamics, which eventually will be solved numerically by means of a stochastic algorithm, able to simulate effciently the selective constrained dynamics. Finally, several numerical simulations are reported to show the effciency of the proposed techniques.

scholarly journals The Effect of Different Deep Network Architectures upon CNN-Based Gaze Tracking

Algorithms ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 127
Author(s):  
Hui-Hui Chen ◽  
Bor-Jiunn Hwang ◽  
Jung-Shyr Wu ◽  
Po-Ting Liu
Keyword(s):  
Neural Network ◽  
Tracking System ◽  
Network Architectures ◽  
Gaze Tracking ◽  
Global Average ◽  
Area Of Interest ◽  
Batch Normalization ◽  
The Mean ◽  
Fully Connected ◽  
Mean Time

In this paper, we explore the effect of using different convolutional layers, batch normalization and the global average pooling layer upon a convolutional neural network (CNN) based gaze tracking system. A novel method is proposed to label the participant’s face images as gaze points retrieved from eye tracker while watching videos for building a training dataset that is closer to human visual behavior. The participants can swing their head freely; therefore, the most real and natural images can be obtained without too many restrictions. The labeled data are classified according to the coordinate of gaze and area of interest on the screen. Therefore, varied network architectures are applied to estimate and compare the effects including the number of convolutional layers, batch normalization (BN) and the global average pooling (GAP) layer instead of the fully connected layer. Three schemes, including the single eye image, double eyes image and facial image, with data augmentation are used to feed into neural network to train and evaluate the efficiency. The input image of the eye or face for an eye tracking system is mostly a small-sized image with relatively few features. The results show that BN and GAP are helpful in overcoming the problem to train models and in reducing the amount of network parameters. It is shown that the accuracy is significantly improved when using GAP and BN at the mean time. Overall, the face scheme has a highest accuracy of 0.883 when BN and GAP are used at the mean time. Additionally, comparing to the fully connected layer set to 512 cases, the number of parameters is reduced by less than 50% and the accuracy is improved by about 2%. A detection accuracy comparison of our model with the existing George and Routray methods shows that our proposed method achieves better prediction accuracy of more than 6%.

scholarly journals Learning in mean field games: The fictitious play

2017 ◽  
Vol 23 (2) ◽  
pp. 569-591 ◽  
Author(s):  
Pierre Cardaliaguet ◽  
Saeed Hadikhanloo
Keyword(s):  
Differential Games ◽  
Mean Field ◽  
Mean Field Games ◽  
Fictitious Play ◽  
Mean Field Game ◽  
Interacting Agents ◽  
Learning Procedure ◽  
Equilibrium Configurations ◽  
The Mean

Mean Field Game systems describe equilibrium configurations in differential games with infinitely many infinitesimal interacting agents. We introduce a learning procedure (similar to the Fictitious Play) for these games and show its convergence when the Mean Field Game is potential.

scholarly journals Do zealots increase or decrease the polarization of social networks?

2019 ◽  
Vol 8 (4) ◽  
Author(s):  
Snehal M Shekatkar
Keyword(s):  
Social Networks ◽  
Social Network ◽  
Majority Rule ◽  
Initial Conditions ◽  
Opinion Dynamics ◽  
Network Density ◽  
Configuration Model ◽  
Rule Model ◽  
Total Fraction ◽  
Topological Characteristics

Abstract Zealots are the vertices in a social network who do not change their opinions under social pressure and are crucial to the study of opinion dynamics on complex networks. In this article, we study the effect of zealots on the polarization dynamics of a deterministic majority rule model using the configuration model as a substrate. To this end, we propose a novel quantifier, called ‘correlated polarization’, for measuring the amount of polarization in the network when vertices can exist in two opposite states. The quantifier takes into account not only the fraction of vertices with each opinion but also how they are connected to each other. We then show that the presence of zealots does not have a fixed effect on the polarization, and can change it in positive, negative or neutral way depending upon their topological characteristics like degree, their total fraction in the network, density and degree heterogeneity of the network and the type of initial conditions of the dynamics. Our results particularly highlight the importance of the role played by the initial conditions in drifting the polarization towards lower or higher values as the total number of zealots is increased.

scholarly journals RESHUFFLING SPINS WITH SHORT RANGE INTERACTIONS: WHEN SOCIOPHYSICS PRODUCES PHYSICAL RESULTS

2005 ◽  
Vol 16 (10) ◽  
pp. 1507-1517 ◽  
Author(s):  
A. O. SOUSA ◽  
K. MALARZ ◽  
S. GALAM
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Nonlinear Behavior ◽  
Opinion Dynamics ◽  
Monte Carlo Step ◽  
Square Lattice ◽  
The Mean ◽  
Dynamics Models

Galam reshuffling introduced in opinion dynamics models, is investigated under the nearest neighbor Ising model on a square lattice using Monte Carlo simulations. While the corresponding Galam analytical critical temperature TC≈3.09 [J/kB] is recovered almost exactly, it is proved to be different from both values, not reshuffled (TC =2/ arcsinh (1)≈2.27 [J/kB]) and mean-field (TC =4 [J/kB]). On this basis, gradual reshuffling is studied as function of 0≤p≤1 where p measures the probability of spin reshuffling after each Monte Carlo step. The variation of TC as function of p is obtained and exhibits a nonlinear behavior. The simplest Solomon network realization is noted to reproduce Galam p =1 result. Similarly to the critical temperature, critical exponents are found to differ from both, the classical Ising case and the mean field values.

Emergence of Abstaining in Glauber Opinion Dynamics

2013 ◽  
Vol 347-350 ◽  
pp. 3827-3831
Author(s):  
Bao Long Niu ◽  
Wei Wei
Keyword(s):  
Phase Diagram ◽  
Random Graphs ◽  
Initial Density ◽  
Mean Field ◽  
Opinion Dynamics ◽  
Wide Spread ◽  
The Mean ◽  
Frozen State ◽  
Two Parameters

We study the evolution of Glauber opinion dynamics with abstaining and tunable threshold on random graphs. The phase diagram shows plentiful features in the space of the two parameters of the model, the threshold and the abstaining probability. It is found that the threshold that limits the agents to be stable plays an important role in the emerging of abstaining in a wide spread. And it can be obtained that the observables stay the same in frozen state whatever the initial density of 0 is. We also use the mean field calculations to verify the fact of linearity between the density of 0 and the abstaining probability.

scholarly journals Mean-field optimal control as Gamma-limit of finite agent controls

2019 ◽  
Vol 30 (6) ◽  
pp. 1153-1186 ◽  
Author(s):  
M. FORNASIER ◽  
S. LISINI ◽  
C. ORRIERI ◽  
G. SAVARÉ
Keyword(s):  
Optimal Control ◽  
Superposition Principle ◽  
Large Population ◽  
Mean Field ◽  
Optimal Controls ◽  
Mean Field Limit ◽  
Interacting Agents ◽  
The Mean ◽  
Γ Convergence

This paper focuses on the role of a government of a large population of interacting agents as a meanfield optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a Partial Differential Equation of continuity-type without diffusion, governing the dynamics of the probability distribution of the agent population. We derive existence of optimal controls in a measure-theoretical setting as natural limits of finite agent optimal controls without any assumption on the regularity of control competitors. In particular, we prove the consistency of mean-field optimal controls with corresponding underlying finite agent ones. The results follow from a Γ -convergence argument constructed over the mean-field limit, which stems from leveraging the superposition principle.

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