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Traffic data forecasting has become an integral part of the intelligent traffic system. Great efforts are spent developing tools and techniques to estimate traffic flow patterns. Many existing approaches lack the ability to model the complex and dynamic spatio-temporal relations in the traffic data, which are crucial in capturing the traffic dynamic. In this work, we propose AJSTGL, a novel adaptive joint spatio-temporal graph learning network for traffic data forecasting. The proposed model utilizes static and adaptive graph learning modules to capture the static and dynamic spatial traffic patterns and optimize the graph learning process. A sequence-to-sequence fusion model is proposed to learn the temporal correlation and combine the output of multiple parallelized encoders. We also develop a spatio-temporal graph transformer module to complement the sequence-to-sequence fusion module by dynamically capturing the time-evolving node relations in long-term intervals. Experiments on three large-scale traffic flow datasets demonstrate that our model could outperform other state-of-the-art baseline methods. 

Abstract The Eden Model in $${\mathbb {R}}^n$$ constructs a blob as follows: initially a single unit hypercube is infected, and each second a hypercube adjacent to the infected ones is selected randomly and infected. Manin, Roldán, and Schweinhart investigated the topology of the Eden model in $${\mathbb {R}}^{n}$$ by considering the possible shapes which can appear on the boundary. In particular, they give probabilistic lower bounds on the Betti numbers of the Eden model. In this paper, we prove analogous results for the Eden model on any infinite, vertex-transitive, locally finite graph: with high probability as time goes to infinity, every “possible” subgraph (with mild conditions on what “possible” means) occurs on the boundary of the Eden model at least a number of times proportional to an isoperimetric profile of the graph. Using this, we can extend the results about the topology of the Eden model to non-Euclidean spaces, such as hyperbolic n-space and universal covers of certain Riemannian manifolds. 

Polyelectrolytes, macromolecules with ionizable groups, play a critical role in applications ranging from energy storage and drug delivery to adhesives, owing to their strong interactions with ionic solutes and water. Despite their widespread utility, an atomistic understanding of how polyelectrolytes interact with ions remains incomplete, limiting the ability to precisely control their conformation and functional properties. To bridge this knowledge gap, we conducted molecular dynamics simulations of two representative polyelectrolytes, poly(vinylbenzyl trimethylammonium chloride) (PVBTACl) and sodium polystyrene sulfonate (NaPSS), across varying salt concentrations. We observed distinct salt-responsive behaviors: as the salt (NaCl) concentration increases from 0 to 2 M, the radius of gyration (Rg) of NaPSS decreases, indicating polymer compaction, while PVBTACl remains relatively unaffected. When the salt concentration is further increased to 6 M, PVBTACl undergoes significant collapse, whereas NaPSS remains in a compact state with minimal further conformational change. The difference in the salt-responsive behavior results from the local counterion structures, where the counterions of PVBTACl are less ordered than those of NaPSS. We further examined the PVBTACl/NaPSS complex to assess deviations from the behavior of isolated polymers, revealing enhanced association in contrast to the conventionally observed dissociation at the high salt concentration. Experimental transmittance measurements of equimolar PVBTACl/NaPSS mixtures across increasing salt concentrations confirmed stable complexation behavior under high-salt conditions, supporting the simulation-based observations of persistent association between PVBTACl and NaPSS. This study offers a mechanistic understanding of salt-induced conformational changes, providing design principles for tuning polyelectrolyte properties in functional materials.