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Register a new userLong route to consensus: Two stage coarsening in a binary choice voting model
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Formation of consensus, in binary yes/no type of voting, is a well defined process. However, even in presence of clear incentives, the dynamics involved can be incredibly complex. Specifically, formations of large groups of similarly opinionated individuals could create a condition of `support-bubbles or spontaneous polarization that renders consensus virtually unattainable (e.g., the question of the UK exiting the EU). There have been earlier attempts in capturing the dynamics of consensus formation in societies through simple $Z_2$-symmetric models hoping to capture the essential dynamics of average behaviorof a large number of individuals in a statistical sense. However, in absence of external noise, they tend to reach a frozen state with fragmented and polarized states i.e., two or more groups of similarly opinionated groups with frozen dynamics. Here we show in a kinetic exchange opinion model (KEM) considered on $L times L$ square lattices, that while such frozen states could be avoided, an exponentially slow approach to consensus is manifested. Specifically, the system could either reach consensus in a time that scales as $L^2$ or a long lived metastable state (termed a domain-wall state) for which formation of consensus takes a time scaling as $L^{3.6}$. The latter behavior is comparable to some voter-like models with intermediate states studied previously. The late-time anomaly in the time scale is reflected in the persistence probability of the model. Finally, the interval of zero-crossing of the average opinion i.e., the time interval over which the average opinion does not change sign is shown to follow a scale free distribution, which is compared with that seen in the opinion surveys regarding Brexit and associated issues in the last 40 years. The issue of minority spreading is also addressed by calculating the exit probability.
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We investigate the nonequilibrium dynamics following a quench to zero temperature of the non-conserved Ising model with power-law decaying long-range interactions $propto 1/r^{d+sigma}$ in $d=2$ spatial dimensions. The zero-temperature coarsening is always of special interest among nonequilibrium processes, because often peculiar behavior is observed. We provide estimates of the nonequilibrium exponents, viz., the growth exponent $alpha$, the persistence exponent $theta$, and the fractal dimension $d_f$. It is found that the growth exponent $alphaapprox 3/4$ is independent of $sigma$ and different from $alpha=1/2$ as expected for nearest-neighbor models. In the large $sigma$ regime of the tunable interactions only the fractal dimension $d_f$ of the nearest-neighbor Ising model is recovered, while the other exponents differ significantly. For the persistence exponent $theta$ this is a direct consequence of the different growth exponents $alpha$ as can be understood from the relation $d-d_f=theta/alpha$; they just differ by the ratio of the growth exponents $approx 3/2$. This relation has been proposed for annihilation processes and later numerically tested for the $d=2$ nearest-neighbor Ising model. We confirm this relation for all $sigma$ studied, reinforcing its general validity.
To alleviate traffic congestion, a variety of route guidance strategies has been proposed for intelligent transportation systems. A number of the strategies are proposed and investigated on a symmetric two-route traffic system over the past decade. To evaluate the strategies in a more general scenario, this paper conducts eight prevalent strategies on a asymmetric two-route traffic network with different slowdown behaviors on alternative routes. The results show that only mean velocity feedback strategy is able to equalize travel time, i.e., approximate user optimality; while the others fail due to incapability of establishing relations between the feedback parameters and travel time. The paper helps better understand these strategies, and suggests mean velocity feedback strategy if the authority intends to achieve user optimality.
We explore simple models aimed at the study of social contagion, in which contagion proceeds through two stages. When coupled with demographic turnover, we show that two-stage contagion leads to nonlinear phenomena which are not present in the basic `classical models of mathematical epidemiology. These include: bistability, critical transitions, endogenous oscillations, and excitability, suggesting that contagion models with stages could account for some aspects of the complex dynamics encountered in social life. These phenomena, and the bifurcations involved, are studied by a combination of analytical and numerical means.
How should one combine noisy information from diverse sources to make an inference about an objective ground truth? This frequently recurring, normative question lies at the core of statistics, machine learning, policy-making, and everyday life. It has been called combining forecasts, meta-analysis, ensembling, and the MLE approach to voting, among other names. Past studies typically assume that noisy votes are identically and independently distributed (i.i.d.), but this assumption is often unrealistic. Instead, we assume that votes are independent but not necessarily identically distributed and that our ensembling algorithm has access to certain auxiliary information related to the underlying model governing the noise in each vote. In our present work, we: (1) define our problem and argue that it reflects common and socially relevant real world scenarios, (2) propose a multi-arm bandit noise model and count-based auxiliary information set, (3) derive maximum likelihood aggregation rules for ranked and cardinal votes under our noise model, (4) propose, alternatively, to learn an aggregation rule using an order-invariant neural network, and (5) empirically compare our rules to common voting rules and naive experience-weighted modifications. We find that our rules successfully use auxiliary information to outperform the naive baselines.
We investigate the coarsening dynamics in the two-dimensional Hamiltonian XY model on a square lattice, beginning with a random state with a specified potential energy and zero kinetic energy. Coarsening of the system proceeds via an increase in the kinetic energy and a decrease in the potential energy, with the total energy being conserved. We find that the coarsening dynamics exhibits a consistently superdiffusive growth of a characteristic length scale with 1/z > 1/2 (ranging from 0.54 to 0.57). Also, the number of point defects (vortices and antivortices) decreases with exponents ranging between 1.0 and 1.1. On the other hand, the excess potential energy decays with a typical exponent of 0.88, which shows deviations from the energy-scaling relation. The spin autocorrelation function exhibits a peculiar time dependence with non-power law behavior that can be fitted well by an exponential of logarithmic power in time. We argue that the conservation of the total Josephson (angular) momentum plays a crucial role for these novel features of coarsening in the Hamiltonian XY model.
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