Related papers: Constant Delay Lattice Train Schedules
We study one-dimensional hardcore lattice gases, with nearest-neighbor interactions, in the presence of an external potential barrier, that moves on the periodic lattice with a constant speed. We investigate how the nature of the…
In this paper, we study the stochastic optimal control problem for control system with time-varying delay. The corresponding stochastic differential equation is a kind of stochastic differential delay equation. We prove the existence and…
Two mobile agents, starting from different nodes of a network modeled as a graph, and woken up at possibly different times, have to meet at the same node. This problem is known as rendezvous. We consider deterministic distributed rendezvous…
In this paper, we study the problem of map matching with travel time constraints. Given a sequence of $k$ spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by…
We consider a single particle tunnelling in a tight-binding model with nearest-neighbour couplings, in the presence of a periodic high-frequency force. An effective Hamiltonian for the particle is derived using an averaging method…
Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…
The Erd\H{o}s distance problem concerns the least number of distinct distances that can be determined by $N$ points in the plane. The integer lattice with $N$ points is known as \textit{near-optimal}, as it spans $\Theta(N/\sqrt{\log(N)})$…
We introduce a problem in which a service vehicle seeks to guard a deadline (boundary) from dynamically arriving mobile targets. The environment is a rectangle and the deadline is one of its edges. Targets arrive continuously over time on…
In this paper, we propose a new interpretation of local limit theorems for univariate and multivariate distributions on lattices. We show that - given a local limit theorem in the standard sense - the distributions are approximated well by…
We study realizable continual linear regression under random task orderings, a common setting for developing continual learning theory. In this setup, the worst-case expected loss after $k$ learning iterations admits a lower bound of…
In this paper, we present some properties of time optimal controls for linear ODEs with the ball-type control constraint. More precisely, for an optimal control, we build up an upper bound for the number of its switching points; show that…
This paper deals with the problem of string stability in a chain of acceleration-controlled vehicles. It is known that string stability cannot be achieved, with any linear controller, when the vehicles' control inputs are based on relative…
In this paper, we study dynamical optimal transport on a connected graph from the perspective of the Benamou-Brenier formulation, where densities are assigned to vertices and velocities to edges. However, directly using Newton's method on…
A \emph{$(k,t)$-track layout} of a graph $G$ consists of a (proper) vertex $t$-colouring of $G$, a total order of each vertex colour class, and a (non-proper) edge $k$-colouring such that between each pair of colour classes no two…
A key measure of performance and comfort in a road traffic network is the travel time that the users of the network experience to complete their journeys. Travel times on road traffic networks are stochastic, highly variable, and dependent…
A problem that arises in drawings of transportation networks is to minimize the number of crossings between different transportation lines. While this can be done efficiently under specific constraints, not all solutions are visually…
Assurance of asymptotic trajectory tracking in robotic manipulators with a smooth control law in the presence of unmodeled dynamics or external disturbance is a challenging problem. Recently, it is asserted that it is achieved via a…
Public transit systems are the backbone of urban mobility systems in the era of urbanization. The design of transit schedules is important for the efficient and sustainable operation of public transit. However, previous studies usually…
We study the two-player communication problem of determining whether two vertices $x, y$ are nearby in a graph $G$, with the goal of determining the graph structures that allow the problem to be solved with a constant-cost randomized…
We study map lattices coupled by collision and show how perturbations of transfer operators associated with the spatially periodic approximation of the model can be used to extract information about collisions per lattice unit. More…