It is suggested that the motion of pedestrians can be described as if they would be subject to 'social forces'. These 'forces' are not directly exerted by the pedestrians' personal environment, but they are a measure for the internal motivations of the individuals to perform certain actions (movements). The corresponding force concept is discussed in more detail and can be also applied to the description of other behaviors.

This paper uses a dynamic conditional correlation model to examine whether Bitcoin can act as a hedge and safe haven for major world stock indices, bonds, oil, gold, the general commodity index and the US dollar index. Daily and weekly data span from July 2011 to December 2015. Overall, the empirical results indicate that Bitcoin is a poor hedge and is suitable for diversification purposes only. However, Bitcoin can only serve as a strong safe haven against weekly extreme down movements in Asian stocks. We also show that Bitcoin hedging and safe haven properties vary between horizons.

Although pedestrians have individual preferences, aims, and destinations, the dynamics of pedestrian crowds is surprisingly predictable. Pedestrians can move freely only at small pedestrian densities. Otherwise their motion is affected by repulsive interactions with other pedestrians, giving rise to self-organization phenomena. Examples of the resulting patterns of motion are separate lanes of uniform walking direction in crowds of oppositely moving pedestrians or oscillations of the passing direction at bottlenecks. If pedestrians leave footprints on deformable ground (for example, in green spaces such as public parks) this additionally causes attractive interactions which are mediated by modifications of their environment. In such cases, systems of pedestrian trails will evolve over time. The corresponding computer simulations are a valuable tool for developing optimized pedestrian facilities and way systems.

Many human social phenomena, suchh as cooperation [1][2][3], the growth of settlements [4], traffic dynamics [5][6][7] and pedestrian movement [7][8][9][10], appear to be accessible to mathematical descriptions that invoke self-organization [11,12]. Here we develop a model of pedestrian motion to explore the evolution of trails in urban green spaces such as parks. Our aim is to address such questions as what the topological structures of these trail systems are [13], and whether optimal path systems can be predicted for urban planning. We use an 'active walker' model [14][15][16][17][18][19] that takes into account pedestrian motion and orientation and the concomitant feedbacks with the surrounding environment. Such models have previously been applied to the study of complex structure formation in physical [14][15][16], chemical [17] and biological [18,19] systems. We find that our model is able to reporduce many of the observed large-scale spatial features of trail systems.

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Active walker models have recently proved their great value for describing the formation of clusters, periodic patterns, and spiral waves as well as the development of rivers, dielectric breakdown patterns, and many other structures.It is shown that they also allow to simulate the formation of trail systems by pedestrians and ants, yielding a better understanding of human and ani- Whereas pedestrians leave footprints on the ground, ants produce chemical markings for their orientation. Nevertheless, it is more important that pedestrians steer towards a certain destination, while ants usually find their food sources by chance, i.e. they reach their destination in a stochastic way. As a consequence, the typical structure of the evolving trail systems depends on the respective species. Some ant species produce a dendritic trail system, whereas pedestrians generate a minimal detour system. The trail formation model can be used as a tool for the optimization of pedestrian facilities: It allows urban planners to design convenient way systems which actually meet the route choice habits of pedestrians. Typeset using REVT E XHelbing/Schweitzer/Keltsch/Molnár: Active Walker Model for Trail Formation 3

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Highlights We model stock price variation around the world during the corona crash. We use Google search volume activity as a gauge of panic and fear. Search terms are specific to the coronavirus crisis. Our sample covers 10 stock market indices. Excess search volume predicts price variation during the corona crash.