Jacob Sriraman | Searcharxiv

arXiv2026

Parametric Shortest Paths in a Linearly Interpolated Graph

We consider the parametric shortest paths problem in a linearly interpolated graph. Given two positively-weighted directed graphs $G_0=(V,E,\omega_0)$ and $G_1=(V,E,\omega_1),$ the linearly interpolated graph is the family of graphs $(1-\lambda)G_0+\lambda G_1$, parameterized by $\lambda\in [0,1]$. The problem is to compute all distinct parametric shortest paths. We compute a data structure in $\Theta(k|E|\log |V|)$ time, where~$k$ is the number of distinct parametric shortest paths over all~$\lambda\in [0,1]$ that exist for a nontrivial interval of parameters, each corresponding to a linear function in a maximal sub-interval of $[0,1]$. Using this data structure, a shortest path query takes~$\Theta(\log k)$ time.

cs.CG↗

arXiv2025

Topology of The Polar Vortex and Montana Weather

This paper explores the use of Topological Data Analysis (TDA) to investigate patterns in zonal-mean zonal winds of the Arctic, which make up the polar vortex, in order to better explain polar vortex dynamics. We demonstrate how TDA reveals significant topological features in this polar vortex data, and how they may relate these features to the collapse of the stratospheric vortex during the winter in the northern hemisphere. Using a time series representation of this data, we build a point cloud using the principles of Takens' Embedding theorem and apply persistent homology to uncover nontrivial topological structures that provide insight into the dynamical system's chaotic and periodic behaviors. These structures can offer new perspectives on the dynamics of the polar vortex, and perhaps other weather regimes, all of which have a global impact. Our results show clear transitions between seasons, with substantial increases in topological activity during periods of extreme cold. This is particularly evident in the historically strong polar vortex event of early 2016. Our analysis captures the persistence of topological features during such events and may even offer insights into vortex splitting, as indicated by the number of distinct persistent features. This work highlights the potential of TDA in climate science, offering a novel approach to studying complex dynamical systems.

math.DS↗