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We introduce a new definition of distinguished trajectory that generalises the concepts of fixed point and periodic orbit to aperiodic dynamical systems. This new definition is valid for identifying distinguished trajectories with…
We study the dynamical behaviour of weighted backward shift operators defined on sequence spaces over a directed tree. We provide a characterization of chaos on very general Fr\'echet sequence spaces in terms of the existence of a large…
The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide…
Husky Carbon, a robot developed by Northeastern University, serves as a research platform to explore unification of posture manipulation and thrust vectoring. Unlike conventional quadrupeds, its joint actuators and thrusters enable enhanced…
In this work, we propose a learning based neural model that provides both the longitudinal and lateral control commands to simultaneously navigate multiple vehicles. The goal is to ensure that each vehicle reaches a desired target state…
We study the multi-scale description of large-time collective behavior of agents driven by alignment. The resulting multi-flock dynamics arises naturally with realistic initial configurations consisting of multiple spatial scaling, which in…
We present a unified probabilistic model that learns a representative set of discrete vehicle actions and predicts the probability of each action given a particular scenario. Our model also enables us to estimate the distribution over…
We study heaps of pieces for lattice paths, which give a combinatorial visualization of lattice paths. We introduce two types of heaps: type $I$ and type $II$. A heap of type $I$ is characterized by peaks of a lattice path. We have a…
In this paper we study parameter families of truncated horseshoes as models of multiscattering systems which show a transition to chaos without losing hyperbolicity, so that the topological features of the transition are completely…
We introduce a stochastic lattice gas model including two particle species and two parallel lanes. One lane with exclusion interaction and directed motion and the other lane without exclusion and unbiased diffusion, mimicking a micotubule…
Animal movement exhibits complex behavior which can be influenced by unobserved environmental conditions. We propose a model which allows for a spatially-varying movement rate and spatially-varying drift through a semiparametric potential…
The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially…
Characterizing the movement patterns of animals is crucial to improve our understanding of their behavior and thus develop adequate conservation strategies. Such investigations, which could not have been implemented in practice only a few…
Modeling and evaluation of automated vehicles (AVs) in mixed-autonomy traffic is essential prior to their safe and efficient deployment. This is especially important at urban junctions where complex multi-agent interactions occur. Current…
We study controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling such system with a control being a Lipschitz vector field on a fixed control set $\omega$. We prove…
The task of maneuvering a multi-steered articulated vehicle in confined environments is difficult even for experienced drivers. In this work, we present an optimization-based trajectory planner targeting low-speed maneuvers in unstructured…
Hand-drawn objects usually consist of multiple semantically meaningful parts. For example, a stick figure consists of a head, a torso, and pairs of legs and arms. Efficient and accurate identification of these subparts promises to…
Starting from recent experimental observations of starlings and jackdaws, we propose a minimal agent-based mathematical model for bird flocks based on a system of second-order delayed stochastic differential equations with discontinuous…
May and Leonard (SIAM J. Appl. Math 1975) introduced a three-species Lotka-Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete…
We introduce a mesoscopic model for natural network formation processes, acting as a bridge between the discrete and continuous network approach proposed by Hu and Cai. The models are based on a common approach where the dynamics of the…