Related papers: Moore and more and symmetry
For the modelling of pedestrian dynamics we treat persons as self-driven objects moving in a continuous space. On the basis of a modified social force model we qualitatively analyze the influence of various approaches for the interaction…
Computationally efficient solutions for pseudometrics quantifying deviation from topological conjugacy between dynamical systems are presented. Deviation from conjugacy is quantified in a Pareto optimal sense that accounts for spectral…
Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has…
Common measures of neural representational (dis)similarity are designed to be insensitive to rotations and reflections of the neural activation space. Motivated by the premise that the tuning of individual units may be important, there has…
Discrete mechanics is used to present fluid mechanics, fluid-structure interactions, electromagnetism and optical physics in a coherent theoretical and numerical approach. Acceleration considered as an absolute quantity is written as a sum…
We present a detailed analysis of random motions moving in higher spaces with a natural number of velocities. In the case of the so-called minimal random dynamics, under some wide assumptions, we show the joint distribution of the position…
Experiments with pedestrians revealed that the geometry of the domain, as well as the incentive of pedestrians to reach a target as fast as possible have a strong influence on the overall dynamics. In this paper, we propose and validate…
Crowd simulation is used for evacuation and crowd safety inspections, study of performance in crowd systems and animations. Cellular automata has been extensively used in modelling the crowd. In regular cellular automata models, each…
We provide a numerical realisation of an optimal control problem for pedestrian motion with agents that was analysed in Herzog, Pietschmann, Winkler: "Optimal Control of Hughes' Model for Pedestrian Flow via Local Attraction.", arXiv…
In this note, we address formally the issue of symmetry for probabilities of different dynamical pathways in the forward and reverse directions of a conformational transition. Our discussion is based on a decomposition of equilibrium into…
Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge…
In this paper the computational challenges of time-optimal path following are addressed. The standard approach is to minimize the travel time, which inevitably leads to singularities at zero path speed, when reformulating the optimization…
For the planning of large pedestrian facilities, the movement of pedestrians in various situations has to be modelled. Many tools for pedestrian planning are based on cellular automata (CA), discrete in space and time, some use self driven…
We study the asymptotic behavior of a discrete-in-time minimizing movement scheme for square lattice interfaces when both the lattice spacing and the time step vanish. The motion is assumed to be driven by minimization of a weighted random…
When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…
We present a novel, real-time algorithm to track the trajectory of each pedestrian in moderately dense crowded scenes. Our formulation is based on an adaptive particle-filtering scheme that uses a combination of various multi-agent…
A complete overview of the surrounding vehicle environment is important for driver assistance systems and highly autonomous driving. Fusing results of multiple sensor types like camera, radar and lidar is crucial for increasing the…
In one-dimensional random walks, the waiting time for each direction transitions is the same, even in the presence of bias, as a consequence of the microscopic-reversibility. We study the symmetry breaking of forward/ backward transition…
In this paper, we introduce and study one-dimensional models for the behavior of pedestrians in a narrow street or corridor. We begin at the microscopic level by formulating a stochastic cellular automata model with explicit rules for…
This paper presents and proves an equation for the time horizon of symmetric trajectories with zero boundary conditions and bounded derivatives of arbitrary order. This equation holds regardless of the number of phases comprising the…