Related papers: Moore and more and symmetry
We address here the issue of congestion in the modeling of crowd motion, in the non-smooth framework: contacts between people are not anticipated and avoided, they actually occur, and they are explicitly taken into account in the model. We…
We report on two series of experiments, conducted in the frame of two different collaborations designed to study how pedestrians adapt their trajectories and velocities in groups or crowds. Strong emphasis is put on the motivations for the…
This paper is devoted to the study of the dynamic optimization of several controlled crowd motion models in the general planar settings, which is an application of a class of optimal control problems involving a general nonconvex sweeping…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
This work is dedicated to the study of how uncertainty estimation of the human motion prediction can be embedded into constrained optimization techniques, such as Model Predictive Control (MPC) for the social robot navigation. We propose…
We demonstrate that the rapidity and robustness of slow contraction in homogenizing and flattening the universe found in simulations in which the initial conditions were restricted to non-perturbative variations described by a single…
We investigate dynamical properties of traffic flow using the stochastic car-following model with modified optimal velocity on circular road. The safety distance following the two-second rule and autonomous vehicles, acting as agents,…
We derive a compatible discretization method that relies heavily on the underlying geometric structure, and obeys the topological sequences and commuting properties that are constructed. As a sample problem we consider the…
The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate…
We present a new microscopic ODE-based model for pedestrian dynamics: the Gradient Navigation Model. The model uses a superposition of gradients of distance functions to directly change the direction of the velocity vector. The velocity is…
This paper presents two novel approaches to solve the classic simple harmonic motion. In one approach, the distance between the equilibrium position and the maximal displacement is divided into N equal segments. In each segment, the mass…
Mott variable range hopping is a fundamental mechanism for low-temperature electron conduction in disordered solids in the regime of Anderson localization. In a mean field approximation, it reduces to a random walk (shortly, Mott random…
Issues in modal tracking in the presence of crossings and crossing avoidances between eigenvalue traces are solved via the theory of point groups. The von Neumann-Wigner theorem is used as a key factor in predictively determining mode…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
In this paper we propose a classification of crowd models in built environments based on the assumed pedestrian ability to foresee the movements of other walkers. At the same time, we introduce a new family of macroscopic models, which make…
Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are…
The presence of symmetries in a Hamiltonian system usually implies the existence of conservation laws that are represented mathematically in terms of the dynamical preservation of the level sets of a momentum mapping. The symplectic or…
Many organisms, from flies to humans, use visual signals to estimate their motion through the world. To explore the motion estimation problem, we have constructed a camera/gyroscope system that allows us to sample, at high temporal…
Despite its importance for practical applications, not much is known about the optimal shape of a network that connects in an efficient way a set of points. This problem can be formulated in terms of a multiplex network with a fast layer…
We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be…