Ira Schwartz | Search arXiv

arXiv2026

Multi-rank Subspace Change-point Detection with Application in Monitoring Robotic Swarms

We study real-time detection of low-rank changes in the covariance structure of high-dimensional streaming data, motivated by robotic swarm monitoring. Building on the spiked covariance model, we propose the Multi-rank Subspace-CUSUM (MRS-C) procedure, which extends classical CUSUM by tracking projection energy onto an estimated signal subspace. We analyze the immediate-change expected detection delay (EDD), deriving closed-form choices of the window size and drift parameter that minimize the leading-order asymptotic EDD approximation. We further establish an oracle-relative asymptotic efficiency result, with an explicit efficiency constant that depends on heterogeneity in spike strengths. When the signal rank is unknown, we propose a practical parallel procedure. Simulations and robotic swarm-behavior data illustrate robustness and effectiveness.

stat.ME↗

arXiv2023

The chaotic milling behaviors of interacting swarms after collision

We consider the problem of characterizing the dynamics of interacting swarms after they collide and form a stationary center of mass. Modeling efforts have shown that the collision of near head-on interacting swarms can produce a variety of post-collision dynamics including coherent milling, coherent flocking, and scattering behaviors. In particular, recent analysis of the transient dynamics of two colliding swarms has revealed the existence of a critical transition whereby the collision results in a combined milling state about a stationary center of mass. In the present work we show that the collision dynamics of two swarms that form a milling state transitions from periodic to chaotic motion as a function of the repulsive force strength and its length scale. We used two existing methods as well as one new technique: Karhunen-Loeve decomposition to show the effective modal dimension chaos lives in, the 0-1 test to identify chaos, and then Constrained Correlation Embedding to show how each swarm is embedded in the other when both swarms combine to form a single milling state after collision. We expect our analysis to impact new swarm experiments which examine the interaction of multiple swarms.

nlin.PS↗