arXiv subjects

Roni Muslim

Publications and source records attributed to Roni Muslim.

15 recordsLinked to original sources

arXiv2026

Interaction size and dissent tolerance in majority-rule dynamics with collective reversal

We introduce a majority-rule model in which collective reversal can be activated in highly aligned groups even when a limited number of members dissent. The dissent tolerance $d$ extends the strict-unanimity dynamics by making near-unanimous group compositions eligible for reversal. Mean-field analysis and simulations reveal that this change qualitatively alters the phase structure. Under strict unanimity, a physically accessible transition exists only for $n=3$ and $n=4$. Allowing dissent restores transitions at larger interaction sizes, replacing the fixed interaction-size threshold with an accessibility boundary in the $(n,d)$ plane. When the activation window is sufficiently broad, directional asymmetry can eliminate one of the two ordered attractors through a saddle-node bifurcation, producing a single stable collective state. In the one-sided case, increasing the dissent tolerance can shorten the transient approach to consensus but leaves its leading logarithmic dependence on population size unchanged. Activation selectivity acts as an independent control parameter for collective ordering, bistability, and consensus dynamics.

physics.soc-ph↗

arXiv2026

Exact moment equivalence and structural nonidentifiability in nonlinear epidemics

Transmission through temporary groups does not necessarily preserve complete information about the group-size distribution in aggregate epidemic data. We show that, in finite-population SIS and SIR models, the group-size distribution enters the dynamics only through a finite set of moments selected by the order of the nonlinear transmission kernel. Consequently, markedly different distributions can generate identical stochastic dynamics when their relevant moments coincide. This equivalence extends to transient evolution, fluctuations, extinction-time statistics, and final outbreak sizes. In the deterministic limit, the first moment sets the invasion threshold, whereas the second controls the nature of the transition and the emergence of bistability and hysteresis. The two distributions become distinguishable only when a higher-order transmission mechanism activates their first unmatched moment; even a weak additional channel can shift the phase boundary and place the systems in different dynamical regimes. Solutions of the master equation and stochastic simulations support these analytical predictions. These results establish an intrinsic limit on epidemic inference: a single aggregate dynamical protocol can identify only an equivalence class of group-size distributions, rather than uniquely reconstructing the full distribution.

physics.soc-ph↗

arXiv2026

Topology-dependent criticality in triplet majority-rule dynamics with collective reversal on quenched networks

We study a triplet majority-rule opinion-dynamics model with collective reversal on quenched networks. Interactions occur on local triplets composed of one agent and two of its neighbors, while collective reversal acts only on unanimous triplets. This rule separates local conformity from external perturbations that disrupt local agreement. We show that quenched network topology shifts the order--disorder critical point away from the well-mixed value. For Barab\'asi--Albert, Erd\H{o}s--R\'enyi, random regular, and Watts--Strogatz networks, the estimated critical exponents remain close to the mean-field values, suggesting mean-field-like universal behavior within the system sizes studied. The strongest shift of the critical point occurs for Watts--Strogatz networks, where clustering and local correlations make the ordered phase less stable. A rewiring analysis of Watts--Strogatz networks further shows that the ordered phase becomes more stable as the network becomes more random. These results indicate that quenched topology primarily controls the location of the transition, while the collective-reversal mechanism largely preserves mean-field-like critical behavior.

physics.soc-ph↗

arXiv2026

Quantifying thermal-signature equivalence in infrared breast thermography using a modified Pennes bioheat model

Infrared breast thermography provides a noninvasive measurement of skin-surface temperature, but the relation between surface thermal patterns and intratumoral physiology is limited by heat diffusion and thermal screening. Here we study a steady-state modified Pennes bioheat model in a two-dimensional multilayer breast-tissue cross-section containing a finite-sized tumor with spatially heterogeneous perfusion. We compare four idealized perfusion patterns: uniform, rim-enhanced, necrotic-core, and anisotropic perfusion. To assess how well these internal differences are preserved at the surface, we compare the full temperature-rise profiles using an $L^2$ distance and define thermal-signature equivalence through an observational tolerance. The results show that distinct perfusion patterns can generate clearly different internal temperature fields, while their surface signatures may become much more similar after propagation through the surrounding tissue. Tests with noisy surface profiles indicate that this equivalence classification is sensitive to the assumed form of profile-level uncertainty. After matching the tumor-averaged perfusion, the radially heterogeneous cases become much closer to the uniform case, whereas the anisotropic case remains more distinguishable because of its directional structure. Increasing tumor depth promotes thermal-signature equivalence, whereas increasing tumor diameter enhances surface distinguishability;a depth--diameter map shows the competition between these two effects. Fat-layer thickness and mild outer-surface deformation modify the surface profiles, but their influence is secondary over the parameter ranges considered here. These results highlight a limitation of static breast thermography: a surface thermal anomaly can be detected without uniquely identifying the underlying intratumoral perfusion structure.

physics.soc-ph↗

arXiv2026

Effect of higher-order interactions on noisy majority-rule dynamics with random group sizes

We study opinion dynamics with higher-order interactions, motivated by the fact that social influence often takes place in groups rather than only through pairwise contacts. We introduce a noisy majority-rule model on annealed hypergraphs with heterogeneous group sizes and investigate how the distribution of interaction sizes affects collective ordering and relaxation. Using analytical theory and Monte Carlo simulations, we show that group-size heterogeneity strongly shapes both the transition between ordered and mixed states and the associated time scales. In particular, broader and heavier-tailed distributions make ordering more robust by enhancing the effect of rare large-group events. They also modify the finite-size scaling of relaxation, producing a crossover from the standard logarithmic behavior to faster ordering in sufficiently broad ensembles. In the pure majority-rule limit, we further show that the exit probability near coexistence obeys a universal error-function scaling form controlled by a single structural parameter. Our results demonstrate that the full distribution of group sizes is a key determinant of nonequilibrium ordering in higher-order opinion dynamics.

physics.soc-ph↗

arXiv2025

Ordering-disordering dynamics of the $q$-voter model under random external bias

We investigate a variant of the two-state $q$-voter model in which agents update their states under a random external field (which points upward with probability $s$ and downward with probability $1-s$) with probability $p$ or adopt the unanimous opinion of $q$ randomly selected neighbors with probability $ 1-p$. Using mean-field analysis and Monte Carlo simulations, we identify an order-disorder transition at $p_c$ when $s=\tfrac{1}{2}$. Notably, in the regime of $p>p_c$, we estimate the time for systems to reach disordered state from consensus state and find the logarithmic scaling $T_{\text{dis}} \sim \mathcal{B}\ln N$, with $\mathcal{B} = 1/(2p)$ for $q = 1$, while for $q > 1$, $\mathcal{B}$ depends on both $p > p_c$ and $q$. We observe that disordering dynamics slow down significantly for nonlinear strengths $q$ between $2$ and $3$, independent of the probability $p$. On the other hand, when $s=0$ or $s=1$, the system is bound to reach consensus, with the consensus time scaling logarithmically with system size as $T_{\text{con}} \sim \mathcal{B}\ln N$, where $\mathcal{B} = 1/p$ for $q = 1$ and $\mathcal{B} = 1$ for $q > 1$. Furthermore, in the limit of $p = 0$, we derive a closed-form exit probability valid for arbitrary values of $q$ and demonstrate a finite-size scaling collapse. These results clarify how external cues and peer conformity jointly control ordering and disordering in binary opinion dynamics.

physics.soc-ph↗

arXiv2024

Opinion formation under mass media influence on the Barabasi-Albert network

We study numerically the dynamics of opinion formation under the influence of mass media using the $q$-voter model on a Barabasi-Albert network. We investigate the scenario where a voter adopts the mass media's opinion with a probability $p$ when there is no unanimity among a group of $q$ agents. Through numerical simulation, we identify a critical probability threshold, $p_t$, at which the system consistently reaches complete consensus. This threshold probability $p_t$ decreases as the group size $q$ increases, following a power-law relation $p_t \propto q^{\gamma}$ with $\gamma \approx -1.187$. Additionally, we analyze the system's relaxation time, the time required to reach a complete consensus state. This relaxation time increases with the population size $N$, following a power-law $\tau \propto N^{\nu}$, where $\nu \approx 1.093$. Conversely, an increase in the probability $p$ results in a decrease in relaxation time following a power-law relationship $\tau \propto p^{\delta}$, with $\delta \approx -0.596$. The value of the exponent $ \nu $ is similar to the exponents obtained in the voter and $q$-voter models across various network topologies.

physics.soc-ph↗

arXiv2024

Phase transition and universality of the majority-rule model on complex networks

We investigate the phenomena of order-disorder phase transition and the universality of the majority-rule model defined on three complex networks, namely the Barabasi-Albert, Watts-Strogatz, and Erdos-Renyi networks. Assume each agent holds two possible opinions distributed randomly across the networks' nodes. Agents adopt anticonformity and independence behaviors, represented by the probability (p), where with a probability (p), agents adopt anticonformity or independence behavior. Based on our numerical simulation results and finite-size scaling analysis, it is found that the model undergoes a continuous phase transition for all networks, with critical points for the independence model greater than those for the anticonformity model in all three networks. We obtain critical exponents identical to the opinion dynamics model defined on a complete graph, indicating that the model exhibits the same universality class as the mean-field Ising model.

physics.soc-ph↗

arXiv2023

The impact of social noise on the majority rule model across various network topologies

We explore the impact of social noise, characterized by nonconformist behavior, on the phase transition within the framework of the majority rule model. The order-disorder transition can reflect the consensus-polarization state in a social context. This study covers various network topologies, including complete graphs, two-dimensional (2-D) square lattices, three-dimensional (3-D) square lattices, and heterogeneous or complex networks such as Watts-Strogatz (W-S), Barab\'asi-Albert (B-A), and Erd\H{o}s-R\'enyi (E-R) networks, as well as their combinations (multilayer network). Social behavior is represented by the parameter $ p $, which indicates the probability of agents exhibiting nonconformist behavior. Our results show that the model exhibits a continuous phase transition across all networks. Through finite-size scaling analysis and evaluation of critical exponents, our results suggest that the model falls into the same universality class as the Ising model.

physics.soc-ph↗

arXiv2023

Independence role in the generalized Sznajd model

The Sznajd model is one of sociophysics's well-known opinion dynamics models. Based on social validation, it has found application in diverse social systems and remains an intriguing subject of study, particularly in scenarios where interacting agents deviate from prevailing norms. This paper investigates the generalized Sznajd model, featuring independent agents on a complete graph and a two-dimensional square lattice. Agents in the network act independently with a probability $p$, signifying a change in their opinion or state without external influence. This model defines a paired agent size $r$, influencing a neighboring agent size $n$ to adopt their opinion. This study incorporates analytical and numerical approaches, especially on the complete graph. Our results show that the macroscopic state of the system remains unaffected by the neighbor size $n$ but is contingent solely on the number of paired agents $r$. Additionally, the time required to reach a stationary state is inversely proportional to the number of neighboring agents $n$. For the two-dimensional square lattice, two critical points $p = p_c$ emerge based on the configuration of agents. The results indicate that the universality class of the model on the complete graph aligns with the mean-field Ising universality class. Furthermore, the universality class of the model on the two-dimensional square lattice, featuring two distinct configurations, is identical and falls within the two-dimensional Ising universality class.

physics.soc-ph↗

arXiv2023

Nonlinear $q$-voter model involving nonconformity on networks

The order-disorder phase transition is a fascinating phenomenon in opinion dynamics models within sociophysics. This transition emerges due to noise parameters, interpreted as social behaviors such as anticonformity and independence (nonconformity) in a social context. In this study, we examine the impact of nonconformist behaviors on the macroscopic states of the system. Both anticonformity and independence are parameterized by a probability $ p $, with the model implemented on a complete graph and a scale-free network. Furthermore, we introduce a skepticism parameter $ s $, which quantifies a voter's propensity for nonconformity. Our analytical and simulation results reveal that the model exhibits continuous and discontinuous phase transitions for nonzero values of $ s $ at specific values of $ q $. We estimate the critical exponents using finite-size scaling analysis to classify the model's universality. The findings suggest that the model on the complete graph and the scale-free network share the same universality class as the mean-field Ising model. Additionally, we explore the scaling behavior associated with variations in $ s $ and assess the influence of $ p $ and $ s $ on the system's opinion dynamics.

physics.soc-ph↗

arXiv2023

Phase transition in the majority rule model with the nonconformist agents

Independence and anticonformity are two types of social behaviors known in social psychology literature and the most studied parameters in the opinion dynamics model. These parameters are responsible for continuous (second-order) and discontinuous (first-order) phase transition phenomena. Here, we investigate the majority rule model in which the agents adopt independence and anticonformity behaviors. We define the model on several types of graphs: complete graph, two-dimensional (2D) square lattice, and one-dimensional (1D) chain. By defining $p$ as a probability of independence (or anticonformity), we observe the model on the complete graph undergoes a continuous phase transition where the critical points are $p_c \approx 0.334$ ($p_c\approx 0.667$) for the model with independent (anticonformist) agents. On the 2D square lattice, the model also undergoes a continuous phase transition with critical points at $p_c \approx 0.0608$ ($p_c \approx 0.4035$) for the model with independent (anticonformist) agents. On the 1D chain, there is no phase transition either with independence or anticonformity. Furthermore, with the aid of finite-size scaling analysis, we obtain the same sets of critical exponents for both models involving independent and anticonformist agents on the complete graph. Therefore they are identical to the mean-field Ising model. However, in the case of the 2D square lattice, the models with independent and anticonformist agents have different sets of critical exponents and are not identical to the 2D Ising model. Our work implies that the existence of independence behavior in a society makes it more challenging to achieve consensus compared to the same society with anticonformists.

physics.soc-ph↗

arXiv2023

Mass media and its impact on opinion dynamics of the nonlinear $q$-voter model

With the success of general conceptual frameworks of statistical physics, many scholars have tried to apply these concepts to other interdisciplinary fields, such as socio-politics, economics, biology, medicine, and many more. In this work, we study the effect of mass media on opinion evolution based on the nonlinear $q$-voter by means with probability $p$ a voter adopts the mass media opinion whenever a $q$-sized agent in the population is not in unanimous agreement. We perform analytical and numerical calculations for some quantities of macroscopic parameters of the model such as order parameter (representing an average of public opinion), consensus (relaxation) time, and exit probability, and obtain the agreement results. We find the power-law relations for some quantities of the model. (1) The probability threshold $p_t$, i.e a probability that makes the system reaches a homogeneous state, follows the power-law relation $p_t \sim q^{\gamma}$ with the $q$-sized agent, where $\gamma = -1.00 \pm 0.01$ is the best fitting parameter. The probability threshold $p_t$ also eliminates the {coexistence two ordered states} of the model. (2) The relaxation time (the time needed by the system to reach consensus) $\tau$ with the population size $N$ is obtained in the form of $\tau \sim N^{\delta}$, where $\delta$ depends on the probability $p$ and $q$-sized agent. We also approximate the {separator} point {$r_s$} and the system's scaling parameters by employing the standard finite-size scaling relation.

physics.soc-ph↗

arXiv2023

The external field effect on the opinion formation based on the majority rule and the $q$-voter models on the complete graph

We investigate the external field effect on opinion formation based on the majority rule and $q$-voter models on a complete graph. The external field can be considered as the mass media in the social system, with the probability $p$ agents following the mass media opinion. Based on our Monte Carlo simulation, the mass media effect is not strong enough to make the system reach a homogeneous state (complete consensus) with the magnetization $m = 1$ for all values of $p$, indicates that the existence of a usual phase transition for all values of $p$. In the $q$-voter model, the mass media eliminates the usual phase transition at $p \approx 0.21$. We obtain the model's critical point and scaling parameters using the finite-size scaling analysis and obtain that both models have the same scaling parameters. The external field effect decreases both models' relaxation time and the relaxation time following the power-law relation such as $\tau \sim N^{\beta}$, where $N$ is the population size, and $\beta$ depends on the probability $p$. In the majority rule model, $\beta$ follows a linear relation, and in the $q$-voter model, $\beta$ follows a power-law relation.

physics.soc-ph↗

arXiv2022

Opinion dynamics involving contrarian and independence behaviors based on the Sznajd model with two-two and three-one agent interactions

We investigate the opinion evolution of outflow dynamics based on the Sznajd model on a complete graph involving contrarian and independence behaviors. We consider a group of four spins representing the social agents with the following scenarios: (1) scenario two-two with contrarian agents or independence agents and (2) scenario three-one with contrarian or independence agents. All of them undergo a second-order phase transition according to our simulation. The critical point decreases exponentially as $\lambda$ and $f$ increases, where $\lambda$ and $f$ are contrarian and flexibility factors, respectively. Furthermore, we find that the critical point of scenario three-one is smaller than that of scenario two-two. For the same level of $\lambda$ and $f$, the critical point of the scenario involving independence is smaller than the scenario with contrarian agents. From a sociophysics point of view, we observe that scenario three-one can likely reach a stalemate situation rather than scenario two-two. Surprisingly, the scenarios involving contrarians have a higher probability of achieving a consensus than a scenario involving independence. Our estimates of the critical exponents indicate that the model is still in the same universality class as the mean-field Ising model.

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