Short-time Monte Carlo simulation of the majority-vote model on cubic lattices

We study a nonequilibrium model with up–down symmetry and a noise parameter q known as majority-vote model (MVM) of Oliveira 1992 on opinion-dependent network or Stauffer–Hohnisch–Pittnauer (SHP) networks. By Monte Carlo (MC) simulations and finite-size scaling relations the critical exponents β∕ν, γ∕ν and 1∕ν and points qc and U* are obtained. After extensive simulations, we obtain β∕ν = 0.230(3), γ∕ν = 0.535(2) and 1∕ν = 0.475(8). The calculated values of the critical noise parameter and Binder cumulant are qc = 0.166(3) and U* = 0.288(3). Within the error bars, the exponents obey the relation 2β∕ν + γ∕ν = 1 and the results presented here demonstrate that the MVM belongs to a different universality class than the equilibrium Ising model on SHP networks, but to the same class as majority-vote models on some other networks.

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Short-time dynamics of a two-dimensional majority vote model

Physical Review E ◽

10.1103/physreve.57.108 ◽

1998 ◽

Vol 57 (1) ◽

pp. 108-110 ◽

Cited By ~ 29

Author(s):

J. F. F. Mendes ◽

M. A. Santos

Keyword(s):

Majority Vote ◽

Two Dimensional ◽

Vote Model ◽

Time Dynamics ◽

Short Time

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Monte Carlo simulation of the short-time behaviour of the dynamicXY-model

Journal of Physics A General Physics ◽

10.1088/0305-4470/30/13/009 ◽

1997 ◽

Vol 30 (13) ◽

pp. 4527-4535 ◽

Cited By ~ 16

Author(s):

K Okano ◽

L Schülke ◽

K Yamagishi ◽

B Zheng

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Time Behaviour ◽

Short Time

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Nonequilibrium opinion dynamics on triangular, honeycomb, and Kagome lattices

International Journal of Modern Physics C ◽

10.1142/s0129183117501236 ◽

2017 ◽

Vol 28 (10) ◽

pp. 1750123 ◽

Cited By ~ 2

Author(s):

F. W. S. Lima ◽

N. Crokidakis

Keyword(s):

Phase Transition ◽

Monte Carlo ◽

Ising Model ◽

Critical Exponents ◽

Majority Vote ◽

Opinion Dynamics ◽

Dynamics Model ◽

Vote Model ◽

Disorder Phase Transition ◽

Disorder Parameter

The Ising model on all Archimedean lattices exhibits spontaneous ordering. Three examples of these lattices, namely triangular ([Formula: see text]), honeycomb [Formula: see text] and Kagome [Formula: see text] lattices, are considered to study the kinetic continuous opinion dynamics model (KCOD) through extensive Monte Carlo simulations. The order/disorder phase transition is observed in all lattices for the KCOD. The estimated values of the critical disorder parameter are [Formula: see text], [Formula: see text], and [Formula: see text] for [Formula: see text], [Formula: see text] and [Formula: see text] lattices, respectively. The critical exponents [Formula: see text], [Formula: see text] and [Formula: see text] for the model are [Formula: see text], [Formula: see text], and [Formula: see text]; [Formula: see text], [Formula: see text], and [Formula: see text]; [Formula: see text], [Formula: see text], and [Formula: see text], for [Formula: see text], [Formula: see text] and [Formula: see text] lattices, respectively. These results agree with the majority-vote model on ([Formula: see text]), ([Formula: see text]), and [Formula: see text] lattices but are different from KCOD model results on square lattices [Formula: see text].

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Price Index Modeling and Risk Prediction of Sharia Stocks in Indonesia

Economies ◽

10.3390/economies10010017 ◽

2022 ◽

Vol 10 (1) ◽

pp. 17

Author(s):

Hersugondo Hersugondo ◽

Imam Ghozali ◽

Eka Handriani ◽

Trimono Trimono ◽

Imang Dapit Pamungkas

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Risk Prediction ◽

Stock Prices ◽

Value At Risk ◽

Stock Price ◽

Price Index ◽

Simulation Approach ◽

Trading Period ◽

Short Time

This study aimed to predict the JKII (Jakarta Islamic Index) price as a price index of sharia stocks and predict the loss risk. This study uses geometric Brownian motion (GBM) and Value at Risk (VaR; with the Monte Carlo Simulation approach) on the daily closing price of JKII from 1 August 2020–13 August 2021 to predict the price and loss risk of JKII at 16 August 2021–23 August 2021. The findings of this study were very accurate for predicting the JKII price with a MAPE value of 2.03%. Then, using VaR with a Monte Carlo Simulation approach, the loss risk prediction for 16 August 2021 (one-day trading period after 13 August 2021) at the 90%, 95%, and 99% confidence levels was 2.40%, 3.07%, and 4.27%, respectively. Most Indonesian Muslims have financial assets in the form of Islamic investments as they offer higher returns within a relatively short time. The movement of all Islamic stock prices traded on the Indonesian stock market can be seen through the Islamic stock price index, namely the JKII (Jakarta Islamic Index). Therefore, the focus of this study was predicting the price and loss risk of JKII as an index of Islamic stock prices in Indonesia. This study extends the previous literature to determine the prediction of JKII price and the loss risk through GBM and VaR using a Monte Carlo simulation approach.

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Global Analysis of Stochastic Systems by the Digraph Cell Mapping Method Based on Short-Time Gaussian Approximation

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420500716 ◽

2020 ◽

Vol 30 (05) ◽

pp. 2050071

Author(s):

Qun Han ◽

Wei Xu ◽

Huibing Hao ◽

Xiaole Yue

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Stochastic Systems ◽

Gaussian Approximation ◽

Global Analysis ◽

Mapping Method ◽

Periodic Excitation ◽

Cell Mapping ◽

One Step ◽

Short Time

The digraph cell mapping method is popular in the global analysis of stochastic systems. Traditionally, the Monte Carlo simulation is used in finding the image cells of one-step mapping, and it is notably costly in the computation time. In this paper, a novel short-time Gaussian approximation (STGA) scheme is incorporated into the digraph cell mapping method to study the global analysis of nonlinear dynamical systems under Gaussian white noise excitations. In order to find out all the active image cells in one-step cell mapping quickly, the STGA scheme together with a probability truncation method is introduced for systems without periodic excitation, and then in the case with periodic excitation. The global structures, such as the stochastic attractors, stochastic basins of attraction and stochastic saddles, are calculated by the digraph analysis algorithm. The proposed methodology has been applied to three typical stochastic dynamical systems. For each system, the effectiveness and superiority of the proposed STGA scheme are verified by checking the image cells of one-step mapping and comparing with the results of Monte Carlo simulation. It is found in the global analysis that the change of the amplitude of periodic excitation induces stochastic bifurcations in the stochastic Duffing system. Moreover, a stochastic bifurcation occurs in the stochastic Lorenz system with the increase of noise intensities.

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TAX EVASION AND NONEQUILIBRIUM MODEL ON APOLLONIAN NETWORKS

International Journal of Modern Physics C ◽

10.1142/s0129183112500799 ◽

2012 ◽

Vol 23 (11) ◽

pp. 1250079 ◽

Cited By ~ 4

Author(s):

F. W. S. LIMA

Keyword(s):

Phase Transition ◽

Monte Carlo ◽

Critical Temperature ◽

Ising Model ◽

Tax Evasion ◽

Majority Vote ◽

Vote Model ◽

Agent Based ◽

Equilibrium Dynamics ◽

Economics Model

The Zaklan model had been proposed and studied recently using the equilibrium Ising model on square lattices (SLs) by [G. Zaklan, F. Westerhoff and D. Stauffer, J. Econ. Interact. Coord.4, 1 (2008), arXiv:0801.2980; G. Zaklan, F. W. S. Lima and F. Westerhoff, Physica A387, 5857 (2008)], near the critical temperature of the Ising model presenting a well-defined phase transition; but on normal and modified Apollonian networks (ANs), [J. S. Andrade, Jr., H. J. Herrmann, R. F. S. Andrade, and L. R. da Silva, Phys. Rev. Lett.94, 018702 (2005); R. F. S. Andrade, J. S. Andrade Jr. and H. J. Herrmann, Phys. Rev. E79, 036105 (2009)] studied the equilibrium Ising model. They showed the equilibrium Ising model not to present on ANs a phase transition of the type for the 2D Ising model. Here, using agent-based Monte Carlo simulations, we study the Zaklan model with the well-known majority-vote model (MVM) with noise and apply it to tax evasion on ANs, to show that differently from the Ising model the MVM on ANs presents a well-defined phase transition. To control the tax evasion in the economics model proposed by Zaklan et al., MVM is applied in the neighborhood of the critical noise qc to the Zaklan model. Here we show that the Zaklan model is robust because this can also be studied, besides using equilibrium dynamics of Ising model, through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.

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MAJORITY-VOTE ON DIRECTED SMALL-WORLD NETWORKS

International Journal of Modern Physics C ◽

10.1142/s0129183107011297 ◽

2007 ◽

Vol 18 (08) ◽

pp. 1251-1261 ◽

Cited By ~ 26

Author(s):

EDINA M. S. LUZ ◽

F. W. S. LIMA

Keyword(s):

Phase Transition ◽

Monte Carlo ◽

Critical Exponents ◽

Order Parameter ◽

Majority Vote ◽

Small World ◽

Small World Network ◽

Small World Networks ◽

Vote Model ◽

Disorder Phase Transition

On directed small-world networks the majority-vote model with noise is now studied through Monte Carlo simulations. In this model, the order-disorder phase transition of the order parameter is well defined. We calculate the value of the critical noise parameter qc for several values of rewiring probability p of the directed small-world network. The critical exponents β/ν, γ/ν and 1/ν were calculated for several values of p.

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