Related papers: Travel-time tomography from mean field game dynami…
To characterize transport in a deterministic dynamical system is to compute exit time distributions from regions or transition time distributions between regions in phase space. This paper surveys the considerable progress on this problem…
It is well-known that natural images possess statistical regularities that can be captured by bandpass decomposition and divisive normalization processes that approximate early neural processing in the human visual system. We expand on…
Marine invasive species spread through global shipping and generate substantial ecological and economic impacts. Traditional risk assessments require detailed records of ballast water and traffic patterns, which are often incomplete,…
Different observations of a relation between inputs ("sources") and outputs ("targets") are often reported in terms of histograms (discretizations of the source and the target densities). Transporting these densities to each other provides…
Traditional approaches to the design of multi-agent navigation algorithms consider the environment as a fixed constraint, despite the obvious influence of spatial constraints on agents' performance. Yet hand-designing improved environment…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
The travel time tomography problem is a coefficient inverse problem for the eikonal equation. This problem has well known applications in seismic. The eikonal equation is considered here in the circular cylinder, where point sources run…
In model-based reinforcement learning, generative and temporal models of environments can be leveraged to boost agent performance, either by tuning the agent's representations during training or via use as part of an explicit planning…
Understanding and modeling human mobility is central to challenges in transport planning, sustainable urban design, and public health. Despite decades of effort, simulating individual mobility remains challenging because of its complex,…
Based on a recent work on traveling waves in spatially nonlocal reaction-diffusion equations, we investigate the existence of traveling fronts in reaction-diffusion equations with a memory term. We will explain how such memory terms can…
The paper presents a novel approach for the analysis and control of a multi-agent system with non-identical agents and a path-graph topology. With the help of irrational wave transfer functions, the approach describes the interaction among…
Understanding human mobility is crucial for applications such as forecasting epidemic spreading, planning transport infrastructure and urbanism in general. While, traditionally, mobility information has been collected via surveys, the…
The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…
Transportation companies and organizations routinely collect huge volumes of passenger transportation data. By aggregating these data (e.g., counting the number of passengers going from a place to another in every 30 minute interval), it…
The characterization of non-stationary signals requires joint time and frequency information. However, time (t) and frequency (omega) being non-commuting variables there cannot be a joint probability density in the (t,omega) plane and the…
This article is concerned with tensor field tomography in a fairly general setting, that takes refraction, attenuation and time-dependence of tensor fields into account. The mathematical model is given by attenuated ray transforms of the…
Entry-exit dynamics are crucial in modeling crowd movement. Here, we present a novel first-order, stationary mean-field game model on a bounded domain that accurately captures these dynamics. The interior dynamics of the system are governed…
Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…
Departure time choice models play a crucial role in determining the traffic load in transportation systems. This paper introduces a new framework to model and analyze the departure time user equilibrium (DTUE) problem based on the so-called…