This paper presents a review and critical analysis on the modeling of the dynamics of
vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It …

Transformers play a central role in the inner workings of large language models. We
develop a mathematical framework for analyzing Transformers based on their interpretation …

Time (or clock) synchronization is a large and vital field of research, as synchronization is a
precondition for many applications. A few example applications are distributed data …

Recent work has exposed the idea that interesting quantum-like (QL) probability laws,
including interference effects, can be manifest in classical systems. Here, we propose a …

We present and analyze a nonabelian version of the Kuramoto system, which we call the
Quantum Kuramoto system. We study the stability of several classes of special solutions to …

Orthogonal group synchronization is the problem of estimating elements from the orthogonal
group given some relative measurements. The least-squares formulation is nonconvex. To …

We present a relativistic model for a mixture of Euler gases with multiple temperatures. For
the proposed relativistic model, we explicitly determine production terms resulting from the …

We introduce a Lohe group which is a new class of matrix Lie groups and present a
continuous dynamical system for the synchronization of group elements in a Lohe group …

We present a new aggregation model on the space of rank-m tensors with the same size,
and study emergent dynamics of the proposed model. Our proposed new aggregation …

We study a system of N identical interacting particles moving on the unit sphere in d-
dimensional space. The particles are self-propelled and coupled all to all, and their motion is …