Related papers: Lonely runners in function fields

Pedestrian movements can be modeled at different degrees of detail. While flux models (Predeshensky/Milinski 1971) and cellular automata models (Schreckenberg 2002) give answers to some important questions and are fast and easy to use,…

Focusing on motion of two interacting players in football games, two velocity vectors for the pair of one player and the nearest opponent player exhibit strong alignment. Especially, we find that there exists a characteristic interpersonal…

This article considers execution and analysis of laboratory experiments of pedestrians moving in a quasi-one-dimensional system with periodic boundary conditions. To analyze characteristics of jams in the system we aim to use the whole…

Visualizing the trajectory of multiple runners with videos collected at different points in a race could be useful for sports performance analysis. The videos and the trajectories can also aid in athlete health monitoring. While the runners…

Multiple people tracking is a key problem for many applications such as surveillance, animation or car navigation, and a key input for tasks such as activity recognition. In crowded environments occlusions and false detections are common,…

We review some representative results for first-passage problems involving so-called mortal or evanescent walkers, i.e., walkers with a finite lifetime. The mortality constraint plays a key role in the modeling of many real scenarios, as it…

We present experimental results obtained for a one-dimensional flow using high precision motion capture. The full pedestrians' trajectories are obtained. In this paper, we focus on the fundamental diagram, and on the relation between the…

Falls during walking are a major health issue in the elderly population. Older individuals are usually more cautious, work more slowly, take shorter steps, and exhibit increased step-to-step variability. They often have impaired dynamic…

We study the properties of random walks on complex trees. We observe that the absence of loops reflects in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and…

The explosion of data on animal behavior in more natural contexts highlights the fact that these behaviors exhibit correlations across many time scales. But there are major challenges in analyzing these data: records of behavior in single…

Despite their importance for urban planning, traffic forecasting, and the spread of biological and mobile viruses, our understanding of the basic laws governing human motion remains limited thanks to the lack of tools to monitor the time…

In some athletic races, such as cycling and types of speed skating races, athletes have to complete a relatively long distance at a high speed in the presence of direct opponents. To win such a race, athletes are motivated to hide behind…

Pedestrians adjust both speed and stride length when they navigate difficult situations such as tight corners or dense crowds. They try to avoid collisions and to preserve their personal space. State-of-the-art pedestrian motion models…

In order to directly demonstrate that in static gravitational field the rate of clocks increases with their distance from the source a simple thought experiment is proposed.

Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…

We studied simple random-walk models with asymmetric time delays. Stochastic simulations were performed for hyperbolic-tangent fitness functions and to obtain analytical results we approximated them by step functions. A novel behavior has…

At the 2005 world championships there was considerable discussion and a formal protest in the long distance race arising from a perceived advantage obtained by some athletes running together. It is shown that a statistical model presented…

We consider stable three-dimensional matchings of three categories of agents, such as women, men and dogs. This was suggested long ago by Knuth (1976), but very little seems to have been published on this problem. Based on computer…

In [1], the authors consider a random walk $(Z_{n,1},\ldots,Z_{n,K+1})\in \mathbb{Z}^{K+1}$ with the constraint that each coordinate of the walk is at distance one from the following one. A functional central limit theorem for the first…

We ask if it is possible to find some particular continuous paths of unit length in linear Brownian motion. Beginning with a discrete version of the problem, we derive the asymptotics of the expected waiting time for several interesting…