Trachette L. Jackson | Searcharxiv

arXiv2025

A Saturation-Based Optimal Velocity Model for Traffic Flow Dynamics

Many headway-based car-following models describe longitudinal adaptation through linear relaxation laws, which can produce unrealistically large accelerations and limit the physical consistency of microscopic traffic dynamics. Motivated by this limitation, we develop a saturation-based extension of the classical Optimal Velocity Model (OVM) that preserves the headway-dependent desired-speed structure while introducing bounded nonlinear acceleration dynamics. Linear stability analysis shows that the proposed formulation preserves the classical long-wave instability mechanism associated with stop-and-go waves while modifying the stability threshold and enforcing bounded acceleration. Ring-road simulations support the analysis and illustrate how the model alters perturbation growth, wave amplitude, and relaxation behavior relative to the classical OVM. The resulting framework provides a compact and analytically tractable extension for studying nonlinear traffic-wave dynamics and physically constrained car-following behavior.

eess.SY↗

arXiv2008

Stochastic Network Model of Receptor Cross-Talk Predicts Anti-Angiogenic Effects

Cancer invasion and metastasis depend on angiogenesis. The cellular processes (growth, migration, and apoptosis) that occur during angiogenesis are tightly regulated by signaling molecules. Thus, understanding how cells synthesize multiple biochemical signals initiated by key external stimuli can lead to the development of novel therapeutic strategies to combat cancer. In the face of large amounts of disjoint experimental data generated from multitudes of laboratories using various assays, theoretical signal transduction models provide a framework to distill this vast amount of data. Such models offer an opportunity to formulate and test new hypotheses, and can be used to make experimentally verifiable predictions. This study is the first to propose a network model that highlights the cross-talk between the key receptors involved in angiogenesis, namely growth factor, integrin, and cadherin receptors. From available experimental data, we construct a stochastic Boolean network model of receptor cross-talk, and systematically analyze the dynamical stability of the network under continuous-time Boolean dynamics with a noisy production function. We find that the signal transduction network exhibits a robust and fast response to external signals, independent of the internal cell state. We derive an input-output table that maps external stimuli to cell phenotypes, which is extraordinarily stable against molecular noise with one important exception: an oscillatory feedback loop between the key signaling molecules RhoA and Rac1 is unstable under arbitrarily low noise, leading to erratic, dysfunctional cell motion. Finally, we show that the network exhibits an apoptotic response rate that increases with noise, suggesting that the probability of programmed cell death depends on cell health.

q-bio.MN↗