arXiv subjects

Pratik Mullick

Publications and source records attributed to Pratik Mullick.

18 recordsLinked to original sources

arXiv2026

Persistence probability based dynamics and phase diagrams in biased q-voter models

Persistence probability in opinion dynamics models estimates the tendency of the agents not to change their initial opinion till the present time. Here we consider two nonlinear q-voter models with binary opinions, where the dynamics are governed by a biased choice when the q panel is not unanimous. The models are studied for different parameter ranges corresponding to the known stationary states. Mean field theory and numerical simulations are used to compute the persistence probability for the two types of opinion separately. The long time behavior in general is either a saturation or a decay that can be approximated by an exponential form, depending on the chosen parameters. Based on this, phase diagrams in the parameter space are presented for both the models. The regions in the phase diagrams indicate a strong correlation with the behavior of fixed points in the corresponding models, which is non-trivial as far as the persistence probability is concerned.

cond-mat.stat-mech↗

arXiv2026

I see you, do you see me? Perception-based crowdedness and behavioral responses in pedestrian dynamics

Pedestrian traffic is commonly characterized using local density, yet the interactions experienced by individuals depend on the relative positions and perceptual relevance of surrounding pedestrians. This raises the question of whether behavioral relationships inferred from local crowdedness are robust to the representation of perceptual anisotropy, and how interaction geometry shapes pedestrian adaptation over time. We analyze experimental pedestrian crossing flows over angles from 0 to 180 degrees using a distance-weighted measure of local crowdedness. Perceptual anisotropy is varied by reducing the contribution of pedestrians outside the focal pedestrian's field of view. We examine the temporal evolution of crowdedness and its relationships with velocity, directional deviation, and acceleration. Anisotropy primarily changes the numerical scale of crowdedness, while the qualitative dynamics, temporal progression, and crossing-angle dependence remain largely preserved. Pedestrians deviate appreciably from their expected group directions, but changes between successive walking directions remain small, indicating adaptation through smooth, incremental corrections rather than abrupt turns. Acceleration dynamics reveal an asymmetry between disruption and recovery: initial deceleration varies strongly with crossing geometry, whereas recovery accelerations are more similar across angles. Non-retracing trajectories in the behavioral phase spaces show that similar instantaneous conditions can correspond to different phases of the interaction. Overall, interaction geometry has a stronger influence on the organization of crossing flows than the perceptual weighting used to quantify local crowdedness. More broadly, dynamic fundamental diagrams provide a more complete characterization of transient pedestrian interactions than conventional relationships based on instantaneous state variables alone.

physics.soc-ph↗

arXiv2025

Analysing contrarian behaviour using nonlinear biased $q$-voter model

We investigate the role of contrarians in a recently proposed weighted-influence variant of the $q$-voter model. In this framework, non-unanimous influence groups affect the focal agent through weighted contributions governed by a bias parameter $p$. We extend this setting by introducing a fraction $\alpha$ ($\alpha> 0$) of contrarians, defined as agents who systematically oppose the prevailing influence irrespective of whether the group is unanimous or divided. Analytical mean-field calculations and Monte Carlo simulations reveal that the final states of the system are governed by simple phase boundaries: regions of positive and negative majority separated by the lines $p=1/2$ and $\alpha=1/2$, with equally-mixed states confined to these boundaries. While low contrarian densities are insufficient to overturn the bias, higher values of $\alpha$ systematically drive the system closer to a balanced coexistence of opinions, though exact parity is prevented by the presence of bias $p$. We further analyze the temporal relaxation of opinions and extract the characteristic timescales of convergence. Our findings highlight how contrarians, acting as structured non-conformists, can suppress consensus and maintain opinion diversity, while internal biases ultimately hinder a perfectly even split.

physics.soc-ph↗

arXiv2025

Sociophysics models inspired by the Ising model

The Ising model, originally developed for understanding magnetic phase transitions, has become a cornerstone in the study of collective phenomena across diverse disciplines. In this review, we explore how Ising and Ising-like models have been successfully adapted to sociophysical systems, where binary-state agents mimic human decisions or opinions. By focusing on key areas such as opinion dynamics, financial markets, social segregation, game theory, language evolution, and epidemic spreading, we demonstrate how the models describing these phenomena, inspired by the Ising model, capture essential features of collective behavior, including phase transitions, consensus formation, criticality, and metastability. In particular, we emphasize the role of the dynamical rules of evolution in the different models that often converge back to Ising-like universality. We end by outlining the future directions in sociphysics research, highlighting the continued relevance of the Ising model in the analysis of complex social systems.

physics.soc-ph↗

arXiv2025

Analyzing stripes in crossing pedestrian flows using temporal matrices and a geometric model

Understanding pattern formation in crossing pedestrian flows is essential for analyzing and managing high-density crowd dynamics in urban environments. This study presents two complementary methodological approaches to detect and characterize stripe formations, an emergent structure observed when two pedestrian groups cross at various angles. First, we propose a matrix-based method that utilizes time-resolved trajectory data to determine the relative crossing order of pedestrians from opposing groups. By identifying points of minimal spatial separation between individuals and analyzing associated time differences, we construct a crossing matrix that captures the sequence and composition of stripes. Second, we introduce a geometric model based on elliptical approximations of pedestrian groups, enabling analytical prediction of two key macroscopic quantities: the number of stripes and the interaction time between groups. The model captures how these quantities vary with the crossing angle and shows strong agreement with experimental data. Further analysis reveals that group elongation during crossing correlates with the vertical cross-section of the elliptical shape. These methods provide effective tools for analyzing large-scale movement datasets, informing the design of public spaces, and calibrating mechanistic models. The study also presents hypotheses about pattern transitions in continuous pedestrian streams, suggesting promising directions for future research on collective motion under varying flow geometries and densities.

physics.soc-ph↗

arXiv2025

Modeling biases in binary decision-making within the generalized nonlinear q-voter model

Collective decision-making is a process by which a group of individuals determines a shared outcome that shapes societal dynamics; from innovation diffusion to organizational choices. A common approach to model these processes is using binary dynamics, where the choices are reduced to two alternatives. One of the most popular models in this context is the $q$-voter model, which assumes that opinion changes are driven by peer pressure from a unanimous group. However, real-world decisions are also shaped by prior personal choices and external influences, such as mass media, which introduce biases that can favor certain options over others. To address this, we propose a generalized $q$-voter model that incorporates these biases. In our model, when the influence group is not unanimous, the probability that an individual changes its opinion depends on its current state, breaking the symmetry between opinions. In limiting cases, our model recovers both the original $q$-voter model and several recently introduced modifications of the $q$-voter model, while extending the framework to capture a broader range of scenarios. We analyze the model on a complete graph using analytical methods and Monte Carlo simulations. Our results highlight two key findings: (1) for larger influence groups ($q>3$), a phase emerges where both adopted and partially adopted states coexist, (2) in small systems, greater initial support for an opinion does not necessarily increase its likelihood of widespread adoption, as reflected in the unique form of the exit probability. These results point to one of the key issues in social science, the importance of group size in collective action.

physics.soc-ph↗

arXiv2024

Classifying pedestrian crossing flows: A data-driven approach using fundamental diagrams and machine learning

This study investigates the dynamics of pedestrian crossing flows with varying crossing angles $α$ to classify different scenarios and derive implications for crowd management. Probability density functions of four key features$-$velocity $v$, density $ρ$, avoidance number $Av$, and intrusion number $In$$-$were analyzed to characterize pedestrian behavior. Velocity-density fundamental diagrams were constructed for each $α$ and fitted with functional forms from existing literature. Classification attempts using $Av$-$In$ and $v$-$ρ$ phase spaces revealed significant overlaps, highlighting the limitations of these metrics alone for scenario differentiation. To address this, machine learning models, including logistic regression and random forest, were employed using all four features. Results showed robust classification performance, with $v$ and $Av$ contributing most significantly. Insights from feature importance metrics and classification accuracy offer practical guidance for managing high-density crowds, optimizing pedestrian flow, and designing safer public spaces. These findings provide a data-driven framework for advancing pedestrian dynamics research.

physics.soc-ph↗

arXiv2024

Social Influence and Consensus Building: Introducing a q-Voter Model with Weighted Influence

We investigate a dynamical model of opinion formation in which an individual's opinion is influenced by interactions with a group of other agents. We introduce a bias towards one of the opinions in a manner not considered earlier to the best of our knowledge. When the bias is neutral, the model is reduced to a mean-field voter model. We analyze the behavior and steady states of the system, identifying three distinct regimes based on the bias level: one favoring negative opinions, one favoring positive opinions, and a neutral case. In large systems, the equilibrium properties become independent of the size of the group, indicating that only the bias influences the final outcome. However, for small groups, the time to reach equilibrium depends on the size of the group. Our results show that even a small initial bias leads to a consensus where all agents eventually share the same opinion when the bias is not neutral. The system exhibits universal behavior, with critical slowing down occurring near the neutral bias point, marking it as a critical dynamical threshold. The time required to reach consensus scales logarithmically when the bias is non-neutral and linearly when it is neutral. Although short-term dynamics depends on group size for small groups, long-term behavior is governed solely by the bias.

physics.soc-ph↗

arXiv2024

Eliminating Bias in Pedestrian Density Estimation: A Voronoi Cell Perspective

For pedestrians moving without spatial constraints, extensive research has been devoted to develop methods of density estimation. In this paper we present a new approach based on Voronoi cells, offering a means to estimate density for individuals in small, unbounded pedestrian groups. A thorough evaluation of existing methods, encompassing both Lagrangian and Eulerian approaches employed in similar contexts, reveals notable limitations. Specifically, these methods turn out to be ill-defined for realistic density estimation along a pedestrian's trajectory, exhibiting systematic biases and fluctuations that depend on the choice of parameters. There is thus a need for a parameter-independent method to eliminate this bias. We propose a modification of the widely used Voronoi-cell based density estimate to accommodate pedestrian groups, irrespective of their size. The advantages of this modified Voronoi method are that it is an instantaneous method that requires only knowledge of the pedestrians' positions at a give time, does not depend on the choice of parameter values, gives us a realistic estimate of density in an individual's neighborhood, and has appropriate physical meaning for both small and large human crowds in a wide variety of situations. We conclude with general remarks about the meaning of density measurements for small groups of pedestrians.

physics.soc-ph↗

arXiv2024

Statistical Evolution of ODI Cricket: Analyzing Performance Trends and Effect Sizes

In the dynamic realm of One Day International (ODI) cricket, the sport has undergone significant transformations over the past four decades. This study digs into the intricate evolution of ODI cricket from 1987 to 2023, analyzing about 4000 matches to uncover pivotal performance indicators such as batting prowess, bowling efficiency, and partnership dynamics. Employing statistical methodologies, including Cohen's effect size, we scrutinize the observed changes that have shaped ODI cricket's landscape. Our findings reveal nuanced trends: while first innings scores have shown stability with sporadic high outliers in recent years, the impact of achieving scores exceeding 300 has notably increased. Furthermore, batting depth and early wickets lost in the first innings continue to significantly influence match outcomes, highlighting strategic shifts in team approaches. We also observe improvements in second innings bowling effectiveness, particularly in wicket-taking ability, underscoring evolving defensive strategies. This research contributes a statistical foundation to comprehensively understand the evolving dynamics of ODI cricket, offering insights crucial for strategic decision-making and further analysis in sports analytics.

stat.AP↗

arXiv2024

Detecting self-organising patterns in crowd motion: Effect of optimisation algorithms

The escalating process of urbanization has raised concerns about incidents arising from overcrowding, necessitating a deep understanding of large human crowd behavior and the development of effective crowd management strategies. This study employs computational methods to analyze real-world crowd behaviors, emphasizing self-organizing patterns. Notably, the intersection of two streams of individuals triggers the spontaneous emergence of striped patterns, validated through both simulations and live human experiments. Addressing a gap in computational methods for studying these patterns, previous research utilized the pattern-matching technique, employing the Nelder-Mead Simplex algorithm for fitting a two-dimensional sinusoidal function to pedestrian coordinates. This paper advances the pattern-matching procedure by introducing Simulated Annealing as the optimization algorithm and employing a two-dimensional square wave for data fitting. The amalgamation of Simulated Annealing and the square wave significantly enhances pattern fitting quality, validated through statistical hypothesis tests. The study concludes by outlining potential applications of this method across diverse scenarios.

math.OC↗

arXiv2022

Methods of density estimation for pedestrians moving in small groups without a spatial boundary

For a group of pedestrians without any spatial boundaries, the methods of density estimation is a wide area of research. Besides, there is a specific difficulty when the density along one given pedestrian trajectory is needed in order to plot an `individual-based' fundamental diagram. We illustrate why several methods become ill-defined in this case. We then turn to the widely used Voronoi-cell based density estimate. We show that for a typical situation of crossing flows of pedestrians, Voronoi method has to be adapted to the small sample size. We conclude with general remarks about the meaning of density measurements in such context.

physics.soc-ph↗

arXiv2021

Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of `stripe' formation in human data

When two streams of pedestrians cross at an angle, striped patterns spontaneously emerge as a result of local pedestrian interactions. This clear case of self-organized pattern formation remains to be elucidated. In counterflows, with a crossing angle of 180°, alternating lanes of traffic are commonly observed moving in opposite directions, whereas in crossing flows at an angle of 90° diagonal stripes have been reported. Naka (1977) hypothesized that stripe orientation is perpendicular to the bisector of the crossing angle. However, studies of crossing flows at acute and obtuse angles remain underdeveloped. We tested the bisector hypothesis in experiments on small groups (18-19 participants each) crossing at seven angles (30° intervals), and analyzed the geometric properties of stripes. We present two novel computational methods for analyzing striped patterns in pedestrian data: (i) an edge-cutting algorithm, which detects the dynamic formation of stripes and allows us to measure local properties of individual stripes; and (ii) a pattern-matching technique, based on the Gabor function, which allows us to estimate global properties (orientation and wavelength) of the striped pattern at a time T. We find an invariant property: stripes in the two groups are parallel and perpendicular to the bisector at all crossing angles. In contrast, other properties depend on the crossing angle: stripe spacing (wavelength), stripe size (number of pedestrians per stripe), and crossing time all decrease as the crossing angle increases from 30° to 180°, whereas the number of stripes increases with crossing angle. We also observe that the width of individual stripes is dynamically squeezed as the two groups cross each other. The findings thus support the bisector hypothesis at a wide range of crossing angles, although the theoretical reasons for this invariant remain unclear.

physics.soc-ph↗

arXiv2019

Active-absorbing phase transition and small world behaviour in Ising model on finite addition type networks in two dimensions

We consider the ordering dynamics of the Ising model on a square lattice where an additional fixed number of bonds connect any two sites chosen randomly. The total number of shortcuts added is controlled by two parameters $p$ and $α$. The structural properties of the network are investigated which show that that the small world behaviour is obtained along the line $α=\frac{\ln (N/2p)}{\ln N}$, which separates regions with ultra small world like behaviour and short ranged lattice like behaviour. We obtain a rich phase diagram in the $p-α$ plane showing the existence of different types of active and absorbing states to which Ising model evolves and their boundaries.

cond-mat.stat-mech↗

arXiv2019

Effect of bias in a reaction diffusion system in two dimensions

We consider a single species reaction diffusion system on a two dimensional lattice where the particles $A$ are biased to move towards their nearest neighbours and annihilate as they meet; $A + A \to \emptyset$. Allowing the bias to take both negative and positive values parametrically, any nonzero bias is seen to drastically affect the behaviour of the system compared to the unbiased (simple diffusive) case. For positive bias, a finite number of dimers, which are isolated pairs of particles occurring as nearest neighbours, exist while for negative bias, a finite density of particles survive. Both the quantities vanish in a power law manner close to the diffusive limit with different exponents. In addition, a discontinuity is observed at the fully positive bias limit. The persistence behaviour is also analysed for the system.

cond-mat.stat-mech↗

arXiv2018

Virtual walks in spin space: a study in a family of two-parameter models

We investigate the dynamics of classical spins mapped as walkers in a virtual "spin" space using a generalised two-parameter family of spin models characterized by parameters $y$ and $z$ [M. J. de Oliveira, J. F. F. Mendes and M. A. Santos, J. Phys. A Math. Gen. \textbf{26}, 2317 (1993)]. The behavior of $S(x,t)$, the probability that the walker is at position $x$ at time $t$ is studied in detail. In general $S(x,t) \sim t^{-α}f(x/t^α)$ with $α\simeq 1$ or $0.5$ at large times depending on the parameters. In particular, $S(x,t)$ for the point $y=1, z=0.5$ corresponding to the voter model shows a crossover in time; associated with this crossover, two timescales can be defined which vary with the system size $L$ as $L^2\log L$. We also show that as the voter model point is approached from the disordered regions along different directions, the width of the Gaussian distribution $S(x,t)$ diverges in a power law manner with different exponents. For the majority voter case, the results indicate that the the virtual walk can detect the phase transition perhaps more efficiently compared to other non-equilibrium methods.

cond-mat.stat-mech↗

arXiv2017

Zero temperature coarsening in Ising model with asymmetric second neighbour interaction in two dimensions

We consider the zero temperature coarsening in the Ising model in two dimensions where the spins interact within the Moore neighbourhood. The Hamiltonian is given by $H = - \sum_{ }{S_iS_j} - κ\sum_{ }{S_iS_{j'}}$ where the two terms are for the first neighbours and second neighbours respectively and $κ\geq 0$. The freezing phenomena, already noted in two dimensions for $κ=0$, is seen to be present for any $κ$. However, the frozen states show more complicated structure as $κ$ is increased; e.g. local anti-ferromagnetic motifs can exist for $κ>2$. Finite sized systems also show the existence of an iso-energetic active phase for $κ> 2$, which vanishes in the thermodynamic limit. The persistence probability shows universal behaviour for $κ>0$, however it is clearly different from the $κ=0$ results when non-homogeneous initial condition is considered. Exit probability shows universal behaviour for all $κ\geq 0$. The results are compared with other models in two dimensions having interactions beyond the first neighbour.

cond-mat.stat-mech↗

arXiv2016

Minority spin dynamics in non-homogeneous Ising model: diverging timescales and exponents

We investigate the dynamical behaviour of the Ising model under a zero temperature quench with the initial fraction of up spins $0\leq x\leq 1$. In one dimension, the known results for persistence probability are verified; it shows algebraic decay for both up and down spins asymptotically with different exponents. It is found that the conventional finite size scaling is valid here. In two dimensions however, the persistence probabilities are no longer algebraic; in particular for $x\leq 0.5$, persistence for the up (minority) spins shows the behaviour $P_{min}(t) \sim t^{-γ}\exp(-(t/τ)^δ)$ with time $t$, while for the down (majority) spins, $P_{maj}(t)$ approaches a finite value. We find that the timescale $τ$ diverges as $(x_c-x)^{- λ}$, where $x_c=0.5$ and $λ\simeq2.31$. The exponent $γ$ varies as $θ_{2d}+c_0(x_c-x)^β$ where $θ_{2d}\simeq0.215$ is very close to the persistence exponent in two dimensions; $β\simeq1$. The results in two dimensions can be understood qualitatively by studying the exit probability, which for different system size is found to have the form $E(x) = f\big[(\frac{x-x_c}{x_c})L^{1/ν}\big]$, with $ν\approx 1.47$. This result suggests that $τ\sim L^{\tilde{z}}$, where $\tilde{z} = \fracλν = 1.57 \pm 0.11$ is an exponent not explored earlier.

cond-mat.stat-mech↗