Prediction of collective opinion in consensus formation

2014 ◽  
Vol 25 (04) ◽  
pp. 1450002 ◽  
Author(s):  
Lei Hou ◽  
Jianguo Liu ◽  
Xue Pan ◽  
Wen-Jun Song ◽  
Xu-Dong Li
Keyword(s):  
Steady State ◽  
Theoretical Analysis ◽  
Linear Relationship ◽  
Correlation Coefficient ◽  
Opinion Leaders ◽  
Formation Model ◽  
Opinion Formation ◽  
Consensus Formation ◽  
Final State ◽  
Formation Dynamics

In the consensus formation dynamics, the effect of leaders and interventions have been widely studied for it has many applications such as in politics and commerce. However, the problem is how to know if it is necessary for one to make an intervention. In this paper, we theoretically propose a method for predicting the tendency and final state of collective opinion. By giving each agent a conviction ci which measures the ability to insist on his opinion, we present an opinion formation model in which agents with high convictions naturally show up properties of the opinion leaders. Results reveal that, although each agent initially gets an opinion evenly distributed in the range [-1, 1], the collective opinion of the steady-state may deviate to the positive or negative direction because of the initial bias of the leaders' opinions. We further get the correlation coefficient of the linear relationship between the collective opinion and the initial bias according to both the experimental and theoretical analysis. Thus, we could predict the final state at the very beginning of the dynamic only if we get the opinions of a small portion of the population. The prediction would afford us more time and opportunities to make reactions and interventions.

DYNAMICS WITH CO-EVOLUTION OF INDIVIDUAL INCLINATION AND OPINION

2011 ◽  
Vol 22 (01) ◽  
pp. 51-62 ◽  
Author(s):  
FEI XIONG ◽  
YUN LIU ◽  
ZHENJIANG ZHANG
Keyword(s):  
Opinion Dynamics ◽  
Spin Systems ◽  
Voter Model ◽  
Formation Model ◽  
Opinion Formation ◽  
Final State ◽  
Memory Length ◽  
Slowing Down ◽  
The Past ◽  
The Individual

Based on the voter model, we present a new opinion formation model which takes into account the evolution of both opinions and individual inclinations. A memory-based inclination is developed gradually during the process of social interaction; however, if the individual inclination gets strong enough, it will react to opinion dynamics. We assume that an individual inclination increases with the number of times the individual has held its most frequent opinion in the past interactions. As a result of inclination choices the transition rate following neighbors decreases, thus slowing down the microscopic dynamics. Analytical and simulation results indicate the system under the action of opinion inclinations evolves to a more polarized state for average opinion. The appearance of extremists holding the minority opinion is observed in the final state, where one opinion predominates. It is also found that the stable opinion and relaxation time depend on network topology and memory length. Moreover, this model is not only valid to the voter model, but can also be applied to other spin systems.

scholarly journals Boltzmann and Fokker–Planck equations modelling opinion formation in the presence of strong leaders

2009 ◽  
Vol 465 (2112) ◽  
pp. 3687-3708 ◽  
Author(s):  
Bertram Düring ◽  
Peter Markowich ◽  
Jan-Frederik Pietschmann ◽  
Marie-Therese Wolfram
Keyword(s):  
Mathematical Model ◽  
Opinion Leaders ◽  
Ordinary People ◽  
Formation Model ◽  
Opinion Formation ◽  
Macroscopic Description ◽  
Microscopic Interactions ◽  
Theory Of Mixtures ◽  
Fokker Planck Equations ◽  
Fokker Planck

We propose a mathematical model for opinion formation in a society that is built of two groups, one group of ‘ordinary’ people and one group of ‘strong opinion leaders’. Our approach is based on an opinion formation model introduced in Toscani (Toscani 2006 Commun. Math. Sci. 4 , 481–496) and borrows ideas from the kinetic theory of mixtures of rarefied gases. Starting from microscopic interactions among individuals, we arrive at a macroscopic description of the opinion formation process that is characterized by a system of Fokker–Planck-type equations. We discuss the steady states of this system, extend it to incorporate emergence and decline of opinion leaders and present numerical results.

Theoretical analysis of RNA polymerase fidelity: a steady-state copolymerization approach

2021 ◽  
Author(s):  
Wenbo Fu ◽  
Qiushi Li ◽  
Yongshun Song ◽  
Yaogen Shu ◽  
Zhongcan Ouyang ◽  
...  
Keyword(s):  
Steady State ◽  
Dna Replication ◽  
Theoretical Analysis ◽  
Rna Polymerase ◽  
Higher Order ◽  
Simplified Models ◽  
Rna Transcription ◽  
Dna Transcription ◽  
Polymerase Fidelity ◽  
Neighbor Effects

Abstract The fidelity of DNA transcription catalyzed by RNA polymerase (RNAP) has long been an important issue in biology. Experiments have revealed that RNAP can incorporate matched nucleotides selectively and proofread the incorporated mismatched nucleotides. However, systematic theoretical researches on RNAP fidelity are still lacking. In the last decade, several theories on RNA transcription have been proposed, but they only handled highly simplified models without considering the high-order neighbor effects and the oligonucleotides cleavage both of which are critical for the overall fidelity. In this paper, we regard RNA transcription as a binary copolymerization process and calculate the transcription fidelity by the steady-state copolymerization theory recently proposed by us for DNA replication. With this theory, the more realistic models considering higher-order neighbor effects, oligonucleotides cleavage, multi-step incorporation and multi-step cleavage can be rigorously handled.

The Linear Relationship between Concentrations and UV Absorbance of Nitrobenzene

2014 ◽  
Vol 955-959 ◽  
pp. 1376-1379 ◽  
Author(s):  
Dan Wu ◽  
Kai Xiao Zhang
Keyword(s):  
Linear Relationship ◽  
Correlation Coefficient ◽  
Absorption Peak ◽  
Maximum Absorption ◽  
Uv Absorbance ◽  
Wavelength Interval ◽  
Vis Spectroscopy

This paper researched the linear relationship between UV absorbance and concentrations of nitrobenzene. It used the UV-1700 UV/VIS spectroscopy to get the absorbance diagram and analyze it. Then it calculated the absorbance of maximum absorption peak and the absorbance integration in a wavelength interval. There is a linear relationship between absorbance and concentration, the correlation coefficient is 0.981 of the maximum absorption peaks and the concentrations, and the largest correlation coefficient between concentrations and the integration of absorbance is 0.995 with the wavelength interval of 235-245 nm, which is between the two absorption peaks of 210 nm and 270 nm. Therefore, it’s a good way to use integration of absorbance in the middle of two absorption peaks to measure the concentration of nitrobenzene, which is more accurate and reliable.

Macro-Micro Dual-Drive Stages Based on Dual Switching Condition and Local Closed Loop

2015 ◽  
Author(s):  
Jiwen Fang ◽  
Zhili Long ◽  
Lufan Zhang
Keyword(s):  
Steady State ◽  
Theoretical Analysis ◽  
Closed Loop ◽  
Voice Coil Motor ◽  
Switching Control ◽  
Positioning Error ◽  
Vibration Displacement ◽  
Pzt Actuator ◽  
Output Displacement ◽  
State Error

This paper presents macro-micro dual-drive stages using the hybrid actuators composed of voice coil motor (VCM) and piezoelectric actuator (PZT actuator). The macro stage driven by voice coil motor can achieve large travel range and coarse positioning. The micro stage with an embedded flexure hinges mechanism, actuated by the PZT actuator, can realize short range but high precision positioning. To gain precise performance, the dynamic modes of macro stage and micro stage are equivalent to mass-damping-spring system in this research. According to theoretical analysis, the output displacement of micro stage is proportional to the extension of the PZT Actuator. The linear relationship will be used to the motion control of micro stage. To realize perfect performance, the variable gain PID controller is designed to control the macro stage. In order to prevent saturation and damage of PZT actuator, dual switching control, positioning error threshold and small vibration displacement, are applied to the switching control. Beyond the micro stage range, the micro stage must be kept in its equilibrium position while the VCM instead reaches a long travel. The PZT actuator controller is used to compensate for position error after switching control. When the error is less than a set thres hold value, the error signal is added into the micro control loop. So the macro-micro dual-drive stages are working together to reduce the positioning error. The relationship between PZT actuator of closed loop and input voltage is linear by theoretical analysis and experiment test. So the micro stage uses an open servo loop structure, but the PZT actuator is controlled with PI controller in local closed loop in order to eliminate the nonlinear of PZT. The experimental system used in this study is single-axis dual-driving stages. Turbo PMAC PCI-Lite is the core of the whole system and executes PLC programs with motion programs. Experiments show that the steady state error of dual-drive stage is nano level. The steady state error of dual-drive stage can be improved. So dual-drive stages can increase the positioning accuracy of the whole system and the performance is superior to the single VCM stage.

scholarly journals A three-state opinion formation model for financial markets

2021 ◽  
pp. 126527
Author(s):  
Bernardo J. Zubillaga ◽  
André L.M. Vilela ◽  
Chao Wang ◽  
Kenric P. Nelson ◽  
H. Eugene Stanley
Keyword(s):  
Financial Markets ◽  
Formation Model ◽  
Opinion Formation

Distributed prediction of solar farm status by probabilistic fuzzy opinion formation model

2018 ◽  
Vol 10 (4) ◽  
pp. 043508 ◽  
Author(s):  
Masoud Bashari ◽  
Mohammad-Reza Akbarzadeh-Totonchi
Keyword(s):  
Formation Model ◽  
Opinion Formation
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