Unified Filtered Operator Analysis of Experimental Single-Particle Tracking in Cellular Nucleus: Validation on Lu et al. (2018) Zenodo Dataset

We apply the unified filtered operator to experimental single-particle tracking data from Lu et al. (2018), recorded in live cell nuclei. Comparing classical and unified operator analyses, we demonstrate that the unified method robustly detects physically meaningful events—such as jumps and rapid transitions—in a random, crowded biological environment, while suppressing noise and static segments. This approach is illustrated with trajectory data, graphical analysis, and reference to relevant literature.The author acknowledges the use of OpenAI’s language model for assistance in drafting certain sections of this worklDisclaimer on Reference Accuracy:<br>The author acknowledges the use of OpenAI’s language model for assistance in drafting certain sections of this work. Due to the nature of generative language models, some reference years or citation details may be imprecise or outdated. All critical sources have been verified manually; however, readers are advised to cross-check dates if exact historical accuracy is required.