Parameter Estimation of Social Forces in Crowd Dynamics Models via a Probabilistic Method

Focusing on a specific crowd dynamics situation, including real life experiments and measurements, our paper targets a twofold aim: (1) we present a Bayesian probabilistic method to estimate the value and the uncertainty (in the form of a probability density function) of parameters in crowd dynamic models from the experimental data; and (2) we introduce a fitness measure for the models to classify a couple of model structures (forces) according to their fitness to the experimental data, preparing the stage for a more general model-selection and validation strategy inspired by probabilistic data analysis. Finally, we review the essential aspects of our experimental setup and measurement technique.Comment: 20 pages, 9 figure

Continuous measurements of real-life bidirectional pedestrian flows on a wide walkway

Employing partially overlapping overhead \kinectTMS sensors and automatic pedestrian tracking algorithms we recorded the crowd traffic in a rectilinear section of the main walkway of Eindhoven train station on a 24/7 basis. Beside giving access to the train platforms (it passes underneath the railways), the walkway plays an important connection role in the city. Several crowding scenarios occur during the day, including high- and low-density dynamics in uni- and bi-directional regimes. In this paper we discuss our recording technique and we illustrate preliminary data analyses. Via fundamental diagrams-like representations we report pedestrian velocities and fluxes vs. pedestrian density. Considering the density range $0$ - $1.1\,$ped/m$^2$, we find that at densities lower than $0.8\,$ped/m$^2$ pedestrians in unidirectional flows walk faster than in bidirectional regimes. On the opposite, velocities and fluxes for even bidirectional flows are higher above $0.8\,$ped/m$^2$.Comment: 9 pages, 7 figure

Modeling Routing Choices in Unidirectional Pedestrian Flows

In this work we present a simple routing model capable of capturing pedestrians path choices in the presence of a herding effect. The model is tested and validated against data from a large scale tracking campaign which we have conducted during the GLOW 2019 festival. The choice between alternative paths is modeled as an individual cost minimization procedure, with the cost function being associated to the (estimated) traveling time. In order to trigger herding effects the cost function is supplemented with a penalty term, modulated as a function of the fraction of pedestrians walking along each route. The model is shown to provide an accurate quantitative description of the decision process

Path-integral representation of diluted pedestrian dynamics

We frame the issue of pedestrian dynamics modeling in terms of path-integrals, a formalism originally introduced in quantum mechanics to account for the behavior of quantum particles, later extended to quantum field theories and to statistical physics. Path-integration enables a trajectory-centric representation of the pedestrian motion, directly providing the probability of observing a given trajectory. This appears as the most natural language to describe the statistical properties of pedestrian dynamics in generic settings. In a given venue, individual trajectories can belong to many possible usage patterns and, within each of them, they can display wide variability. We provide first a primer on path-integration, and we introduce and discuss the path-integral functional probability measure for pedestrian dynamics in the diluted limit. As an illustrative example, we connect the path-integral description to a Langevin model that we developed previously for a particular crowd flow condition (the flow in a narrow corridor). Building on our previous real-life measurements, we provide a quantitatively correct path-integral representation for this condition. Finally, we show how the path-integral formalism can be used to evaluate the probability of rare-events (in the case of the corridor, U-turns)

Importance of d-p Coulomb interaction for high TC_C cuprates and other oxides

Current theoretical studies of electronic correlations in transition metal oxides typically only account for the local repulsion between d-electrons even if oxygen ligand p-states are an explicit part of the effective Hamiltonian. Interatomic interactions such as Upd between d- and (ligand) p-electrons, as well as the local interaction between p-electrons, are neglected. Often, the relative d-p orbital splitting has to be adjusted "ad hoc" on the basis of the experimental evidence. By applying the merger of local density approximation and dynamical mean field theory (LDA+DMFT) to the prototypical case of the 3-band Emery dp model for the cuprates, we demonstrate that, without any "ad hoc" adjustment of the orbital splitting, the charge transfer insulating state is stabilized by the interatomic interaction Upd. Our study hence shows how to improve realistic material calculations that explicitly include the p-orbitals.Comment: 17 pages, 6 figures, our study shows that U_pd is the physics behind previous ad-hoc shifts of the d-p level splittin

Lifshitz transition driven by spin fluctuations and spin-orbit renormalization in NaOsO3_3

In systems where electrons form both dispersive bands and small local spins, we show that changes of the spin configuration can tune the bands through a Lifshitz transition, resulting in a continuous metal-insulator transition associated with a progressive change of the Fermi surface topology. In contrast to a Mott-Hubbard and Slater pictures, this spin-driven Lifshitz transition appears in systems with small electron-electron correlation and large hybridization. We show that this situation is realized in 5$d$ distorted perovskites with an half-filled $t_{2g}$ bands such as NaOsO$_3$, where the strong $p-d$ hybridization reduces the local moment, and spin-orbit coupling causes a large renormalization of the electronic mobility. This weakens the role of electronic correlations and drives the system towards an itinerant magnetic regime which enables spin-fluctuations