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The methodology named LIFE (Linear-in-Flux-Expressions) was developed with the purpose of simulating and analyzing large metabolic systems. With LIFE, the number of model parameters is reduced by accounting for correlations among the…
We study a dynamic routing game motivated by traffic flows. The base model for an edge is the Vickrey bottleneck model. That is, edges are equipped with a free flow transit time and a capacity. When the inflow into an edge exceeds its…
This note introduces a piecewise-deterministic queueing (PDQ) model to study the stability of traffic queues in parallel-link transportation systems facing stochastic capacity fluctuations. The saturation rate (capacity) of the PDQ model…
We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…
We present a theoretical framework for analyzing linear attention models through matrix-valued state space models (SSMs). Our approach, Parallel Flows, provides a perspective that systematically decouples temporal dynamics from…
The symmetric low-rank matrix factorization serves as a building block in many learning tasks, including matrix recovery and training of neural networks. However, despite a flurry of recent research, the dynamics of its training via…
A dynamic transit flow estimation model based on congested schedule-based transit equilibrium assignment is proposed using observations from stop count data. A solution algorithm is proposed for the mathematical program with schedule-based…
A seminal result of [Fleischer et al. and Karakostas and Kolliopulos, both FOCS 2004] states that system optimal multi-commodity static network flows are always implementable as tolled Wardrop equilibrium flows even if users have…
The problem of load balancing in a distribution network under unknown time- varying demand and supply is studied. A set of distributed controllers which regulate the amount of flow through the edges is designed to guarantee convergence of…
It is by now well-known that wireless networks with file arrivals and departures are stable if one uses alpha-fair congestion control and back-pressure based scheduling and routing. In this paper, we examine whether ?alpha-fair congestion…
External flows, such as shear flow, add directional biases to particle motion, introducing anisotropic behavior into the system. Here, we explore the non-equilibrium dynamics that emerge from the interplay between linear shear flow and…
Recent advances in dynamic graph processing have enabled the analysis of highly dynamic graphs with change at rates as high as millions of edge changes per second. Solutions in this domain, however, have been demonstrated only for…
Simulating turbulent flows is crucial for a wide range of applications, and machine learning-based solvers are gaining increasing relevance. However, achieving temporal stability when generalizing to longer rollout horizons remains a…
Motivated by the possibility of noise to cure equations of finite-time blowup, recent work arXiv:2109.09892 by the second and third named authors showed that with quantifiable high probability, random diffusion restores global existence for…
This paper discusses the effect of sequential conflict resolution maneuvers of an infinite aircraft flow through a finite control volume. Aircraft flow models are utilized to simulate traffic flows and determine stability. Pseudo-random…
Dynamical flow networks serve as macroscopic models for, e.g., transportation networks, queuing networks, and distribution networks. While the flow dynamics in such networks follow the conservation of mass on the links, the outflow from…
Dynamic Flows were introduced by Ford and Fulkerson in 1958 to model flows over time. They define edge capacities to be the total amount of flow that can enter an edge {\em in one time unit}. Each edge also has a length, representing the…
Communication networks are time-varying and hence, fair sharing of network resources among the users in such a dynamic environment is a challenging task. In this context, a time-varying network model is designed and the shortest user's…
In this work, we present a high-order finite volume framework for the numerical simulation of shallow water flows. The method is designed to accurately capture complex dynamics inherent in shallow water systems, particularly suited for…
Many active biological particles, such as swimming microorganisms or motor-proteins, do work on their environment by going though a periodic sequence of shapes. Interactions between particles can lead to the phase-synchronization of their…