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We propose an entropic geometrical model of psycho-physical crowd dynamics (with dissipative crowd kinematics), using Feynman action-amplitude formalism that operates on three synergetic levels: macro, meso and micro. The intent is to explain the dynamics of crowds simultaneously and consistently across these three levels, in order to characterize their geometrical properties particularly with respect to behavior regimes and the state changes between them. Its most natural statistical descriptor is crowd entropy $S$ that satisfies the Prigogines extended second law of thermodynamics, $partial_tSgeq 0$ (for any nonisolated multi-component system). Qualitative similarities and superpositions between individual and crowd configuration manifolds motivate our claim that goal-directed crowd movement operates under entropy conservation, $partial_tS = 0$, while natural crowd dynamics operates under (monotonically) increasing entropy function, $partial_tS > 0$. Between these two distinct topological phases lies a phase transition with a chaotic inter-phase. Both inertial crowd dynamics and its dissipative kinematics represent diffusion processes on the crowd manifold governed by the Ricci flow, with the associated Perelman entropy-action. Keywords: Crowd psycho-physical dynamics, action-amplitude formalism, crowd manifold, Ricci flow, Perelman entropy, topological phase transition
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In this paper we analyze crowd turbulence from both classical and quantum perspective. We analyze various crowd waves and collisions using crowd macroscopic wave function. In particular, we will show that nonlinear Schr{o}dinger (NLS) equation is fundamental for quantum turbulence, while its closed-form solutions include shock-waves, solitons and rogue waves, as well as planar de Broglies waves. We start by modeling various crowd flows using classical fluid dynamics, based on Navier-Stokes equations. Then, we model turbulent crowd flows using quantum turbulence in Bose-Einstein condensation, based on modified NLS equation. Keywords: Crowd behavior dynamics, classical and quantum turbulence, shock waves, solitons and rogue waves
We study stochastic effects on the lagging anchor dynamics, a reinforcement learning algorithm used to learn successful strategies in iterated games, which is known to converge to Nash points in the absence of noise. The dynamics is stochastic when players only have limited information about their opponents strategic propensities. The effects of this noise are studied analytically in the case where it is small but finite, and we show that the statistics and correlation properties of fluctuations can be computed to a high accuracy. We find that the system can exhibit quasicycles, driven by intrinsic noise. If players are asymmetric and use different parameters for their learning, a net payoff advantage can be achieved due to these stochastic oscillations around the deterministic equilibrium.
Humans are often incapable of precisely identifying and implementing the desired control strategy in controlling unstable dynamical systems. That is, the operator of a dynamical system treats the current control effort as acceptable even if it deviates slightly from the desired value, and starts correcting the actions only when the deviation has become evident. We argue that the standard Newtonian approach does not allow to model such behavior. Instead, the physical phase space of a controlled system should be extended with an independent phase variable characterizing the operator motivated actions. The proposed approach is illustrated via a simple non-Newtonian model capturing the operators fuzzy perception of their own actions. The properties of the model are investigated analytically and numerically; the results confirm that the extended phase space may aid in capturing the intricate dynamical properties of human-controlled systems.
We present in this paper the behavior of an artificial agent who is a member of a crowd. The behavior is based on the social comparison theory, as well as the trajectory mapping towards an agents goal considering the agents field of vision. The crowd of artificial agents were able to exhibit arching, clogging, and bursty exit rates. We were also able to observe a new phenomenon we called double arching, which happens towards the end of the simulation, and whose onset is exhibited by a calm density graph within the exit passage. The density graph is usually bursty at this area. Because of these exhibited phenomena, we can use these agents with high confidence to perform microsimulation studies for modeling the behavior of humans and objects in very realistic ways.
Numerous studies and anecdotes demonstrate the wisdom of the crowd, the surprising accuracy of a groups aggregated judgments. Less is known, however, about the generality of crowd wisdom. For example, are crowds wise even if their members have systematic judgmental biases, or can influence each other before members render their judgments? If so, are there situations in which we can expect a crowd to be less accurate than skilled individuals? We provide a precise but general definition of crowd wisdom: A crowd is wise if a linear aggregate, for example a mean, of its members judgments is closer to the target value than a randomly, but not necessarily uniformly, sampled member of the crowd. Building on this definition, we develop a theoretical framework for examining, a priori, when and to what degree a crowd will be wise. We systematically investigate the boundary conditions for crowd wisdom within this framework and determine conditions under which the accuracy advantage for crowds is maximized. Our results demonstrate that crowd wisdom is highly robust: Even if judgments are biased and correlated, one would need to nearly deterministically select only a highly skilled judge before an individuals judgment could be expected to be more accurate than a simple averaging of the crowd. Our results also provide an accuracy rationale behind the need for diversity of judgments among group members. Contrary to folk explanations of crowd wisdom which hold that judgments should ideally be independent so that errors cancel out, we find that crowd wisdom is maximized when judgments systematically differ as much as possible. We re-analyze data from two published studies that confirm our theoretical results.
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