Unravelling intermittent features in single particle trajectories by a local convex hull method

TL;DR

This paper introduces a novel, model-free local convex hull method to detect change points in single particle trajectories, effectively distinguishing different phases of intermittent stochastic processes.

Contribution

The paper presents a new geometric approach using local convex hulls to identify phase transitions in stochastic trajectories without relying on specific models.

Findings

Validated on six models of intermittent motion including Brownian and fractional Brownian motion.

Effective in detecting active and passive phases in intracellular transport.

Applicable to various biological and physical systems involving phase changes.

Abstract

We propose a new model-free method to detect change points between distinct phases in a single random trajectory of an intermittent stochastic process. The local convex hull (LCH) is constructed for each trajectory point, while its geometric properties (e.g., the diameter or the volume) are used as discriminators between phases. The efficiency of the LCH method is validated for six models of intermittent motion, including Brownian motion with different diffusivities or drifts, fractional Brownian motion with different Hurst exponents, and surface-mediated diffusion. We discuss potential applications of the method for detection of active and passive phases in the intracellular transport, temporal trapping or binding of diffusing molecules, alternating bulk and surface diffusion, run and tumble (or search) phases in the motion of bacteria and foraging animals, and instantaneous firing rates in neurons.