Related papers: Transport maps as flows of control-affine systems
In this article, we give a condition for the global controllability of affine nonlinear control systems with drifts on Euclidean spaces. Under regularity assumptions, the condition is necessary and sufficient in the codimension-1 and…
A shift-periodic map is a one-dimensional map from the real line to itself which is periodic up to a linear translation and allowed to have singularities. It is shown that iterative sequences $x_{n+1}=F(x_n)$ generated by such maps display…
This paper considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible…
We study an approximate controllability problem for the continuity equation and its application to constructing transport maps with normalizing flows. Specifically, we construct time-dependent controls $\theta=(w, a, b)$ in the vector field…
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we…
In potential flow networks, the equilibrium flow rates are usually not proportional to the demands and flow control elements are required to regulate the flow. The control elements can broadly be classified into two types - discrete and…
In many scientific fields imaging is used to relate a certain physical quantity to other dependent variables. Therefore, images can be considered as a map from a real-world coordinate system to the non-negative measurements being acquired.…
The goal of traffic management is efficiently utilizing network resources via adapting of source sending rates and routes selection. Traditionally, this problem is formulated into a utilization maximization problem. The single-path routing…
How to free a road from vehicle traffic as efficiently as possible and in a given time, in order to allow for example the passage of emergency vehicles? We are interested in this question which we reformulate as an optimal control problem.…
A model for autonomous feedback control of particle transport through a large number of channels is introduced. Interactions among the particles can lead to a strong suppression of fluctuations in the particle number statistics. Within a…
We collect some examples of optimal transports in order to explore the (in)stability of the identity map as an optimal transport. First, we consider density and domain perturbations near regular portions of domains. Second, we investigate…
Autonomous vehicles (AVs) allow new ways of regulating the traffic flow on road networks. Most of available results in this direction are based on microscopic approaches, where ODEs describe the evolution of regular cars and AVs. In this…
Inspired by the question of whether one can create a visually informative map in which distances reflect travel-times rather than physical proximity, we examine whether it is possible to construct a meaningful travel time function between…
Optimal transport has numerous applications, particularly in machine learning tasks involving generative models. In practice, the transportation process often encounters an information bottleneck, typically arising from the conversion of a…
Statistical mechanics of a disordered system of cars on a single-lane road is developed. Behaviour of cars is defined by conditional probability of car velocity depending on the distance and velocity of the car ahead. A system consisting of…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…
This paper explores the controllability and state tracking of ensembles from the perspective of optimal transport theory. Ensembles, characterized as collections of systems evolving under the same dynamics but with varying initial…
The probability of shortage absence is estimated for the storage of some transport system. The intensive computer methods of statistics are used in corresponding processes simulation. The efficiency of suggested approach, taking the mean…
There are two standard ways of classifying transport behavior of systems. The first is via time scaling of spread of correlations in the isolated system in thermodynamic limit. The second is via system size scaling of conductance in the…
Flows over time have received substantial attention from both an optimization and (more recently) a game-theoretic perspective. In this model, each arc has an associated delay for traversing the arc, and a bound on the rate of flow entering…