Related papers: On the Dynamical Hierarchy in Gathering Protocols …
Two-dimensional (2D) particulate aggregates formed due to competing interactions exhibit a range of non-equilibrium steady state morphologies from finite-size compact crystalline structures to non-compact string-like conformations. 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…
Urban systems are composed by complex couplings of several components, and more particularly between the built environment and transportation networks. Their interaction is involved in the emergence of the urban form. We propose in this…
Collective motion in animal groups, such as swarms of insects, flocks of birds, and schools of fish, are some of the most visually striking examples of emergent behavior. Empirical analysis of these behaviors in experiment or computational…
The emerging collective motions of swarms of interacting agents are a subject of great interest in application areas ranging from biology to physics and robotics. In this paper, we conduct a careful analysis of the collective dynamics of a…
This paper addresses the problem of detecting coherent motions in crowd scenes and presents its two applications in crowd scene understanding: semantic region detection and recurrent activity mining. It processes input motion fields (e.g.,…
We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…
Dynamical System has been widely used for encoding trajectories from human demonstration, which has the inherent adaptability to dynamically changing environments and robustness to perturbations. In this paper we propose a framework to…
Over the last two decades, network science has greatly advanced our understanding of how the collective behaviors of a complex system emerge from the interactions among its basic units. Multiplex networks, i.e. networks with many layers,…
Growing graphs describe a multitude of developing processes from maturing brains to expanding vocabularies to burgeoning public transit systems. Each of these growing processes likely adheres to proliferation rules that establish an…
The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: We first define a spontaneous velocity which corresponds to the velocity each individual…
We study step bunching under conditions of attachment/detachment limited kinetics in the presence of a deposition or sublimation flux, which leads to bunch motion. Analysis of the discrete step dynamics reveals that the bunch velocity is…
We introduce a model for active transport on inhomogeneous networks embedded in a diffusive environment and investigate the formation of particle clusters. In the presence of a hard-core interaction, cluster sizes exhibit an algebraically…
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…
Recently, the existence of so-called granular bubbles and droplets has been demonstrated experimentally. Granular bubbles and droplets are clusters of particles that respectively rise and sink if submerged in an aerated and vibrated bed of…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
Many dynamical systems exhibit similar structure, as often captured by hand-designed simplified models that can be used for analysis and control. We develop a method for learning to correspond pairs of dynamical systems via a learned latent…
We introduce a new class of models for emergent dynamics. It is based on a new communication protocol which incorporates two main features: short-range kernels which restrict the communication to local geometric balls, and anisotropic…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…