Related papers: Monotone three-dimensional surface and equivalent …
We offer a simple and self-contained proof that the Follow-the-Leader model converges to the Lighthill-Whitham-Richards model for traffic flow.
Despite the availability of large empirical data sets and the long history of traffic modeling, the theory of traffic congestion on freeways is still highly controversial. In this contribution, we compare Kerner's three-phase traffic theory…
A new coupling rule for the Lighthill-Whitham-Richards model at merging junctions is introduced that imposes the preservation of the ratio between inflow from a given road to the total inflow into the junction. This rule is considered both…
Dynamic wetting poses a well-known challenge in classical sharp-interface formulation as the no-slip wall condition leads to a contact line singularity that is typically regularized with a Navier boundary condition, often requiring…
Likelihood-based deep generative models have been widely investigated for Image Anomaly Detection (IAD), particularly Normalizing Flows, yet their strict architectural invertibility needs often constrain scalability, particularly in…
We study the optimization of non-convex functions that are not necessarily smooth (gradient and/or Hessian are Lipschitz) using first order methods. Smoothness is a restrictive assumption in machine learning in both theory and practice,…
Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of domains, including physical, engineered,…
We investigate different approaches to machine learning of line bundle cohomology on complex surfaces as well as on Calabi-Yau three-folds. Standard function learning based on simple fully connected networks with logistic sigmoids is…
For a class of data-fitted macroscopic traffic models, the influence of the choice of the stagnation density on the model accuracy is investigated. This work builds on an established framework of data-fitted first-order…
We study 3D chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial "blinking" tumbler). The flow is essentially quasi-2D in any…
Jamitons are self-sustained traveling wave solutions that arise in certain second-order macroscopic models of vehicular traffic. A necessary condition for a jamiton to appear is that the local traffic density breaks the so-called…
This paper identifies the nonzero resultant and consequent unique displacement singularity of time-dependent complex variable method on quasi-three dimensional shallow tunnelling in visco-elastic and gravitational geomaterial. The…
This research effort uses vehicular traffic flow techniques to model bicyclist longitudinal motion while accounting for bicycle interactions. Specifically, an existing car-following model, the Fadhloun-Rakha (FR) model is re-parametrized to…
This article presents the dynamic interpolation problem for locomotion systems evolving on a trivial principal bundle $Q$. Given an ordered set of points in $Q$, we wish to generate a trajectory which passes through these points by…
$\textbf{This is the conference version of our paper: Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner}$. Spatiotemporal Traffic Data (STTD) measures the complex dynamical behaviors of the multiscale…
We study the dynamics of inertial particles in three dimensional incompressible maps, as representations of volume preserving flows. The impurity dynamics has been modeled, in the Lagrangian framework, by a six-dimensional dissipative…
This dissertation investigates the geometric combinatorics of convex polytopes and connections to the behavior of the simplex method for linear programming. We focus our attention on transportation polytopes, which are sets of all tables of…
A generalized unbalanced optimal transport distance ${\rm WB}_{\Lambda}$ on matrix-valued measures $\mathcal{M}(\Omega,\mathbb{S}_+^n)$ was defined in [arXiv:2011.05845] \`{a} la Benamou-Brenier, which extends the Kantorovich-Bures and the…
Tourists often go to multiple tourism destinations in one trip. The volume of tourism flow between tourism destinations, also referred to as ITF (Inter-Destination Tourism Flow) in this paper, is commonly used for tourism management on…
The emergence of congestion is a critical phenomenon in transport systems. Transport is organized along pathways abstracted by links, which connect different nodes as regions to form the network. The modeling of traffic has so far mainly…