Related Experiment Video
Updated: Sep 27, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain
Published on: October 13, 2023
Contrasting Resilience Diagnostics in Route-Preserving Multimodal Transit Hypergraphs
1Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, Saint Petersburg 199034, Russia.
Abstract:
Most multimodal transit studies use pairwise or multilayer graphs that discard route membership. We construct route-preserving bus-metro hypergraphs for 45 Chinese cities. A route-support rule makes node viability depend on the fraction of incident routes that remain viable. Transfer-first attack is the most damaging static strategy in 33 cities. PPCR is associated with greater connectivity retention under random disruption (r=0.807), but with deeper route-support pruning under targeted triggering. Connectivity retention, route-support outcomes, and recovery are only moderately aligned (mean |ρ|=0.52). Three principal components are needed to explain 90% of their variance. Multimodal resilience, therefore, cannot be summarized by one ranking. The hypergraph preserves route-dependent failure as a native model property.
Related Concept Videos
Short-distance Transport of Resources
Graphs of Two-Variable Functions
Woodward–Hoffmann Selection Rules and Microscopic Reversibility
Design Example: Analyzing Capacity Contours for Flood Risk Assessment
Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
Multimachine Stability
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by: