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Title: Characterization of uncertain experimental diffusion trajectories via calibration surfaces
Abstract: Modern live-imaging fluorescent microscopy techniques following the stochastic motion of labeled tracer particles, i.e. single particle tracking (SPT) experiments, have uncovered significant deviations from the laws of Brownian motion in a variety of biological systems. Accurately characterizing the anomalous diffusion for SPT experiments has become a central issue in biophysics. However, measurement errors raise difficulty in the analysis of single trajectories. We introduce a novel surface calibration method based on fractionally integrated moving average (FIMA) process as an effective tool for extracting both the anomalous exponent and the magnitude of the measurement error for autocorrelated processes of various origins. This method is developed using a toy model fractional Brownian motion disturbed by independent Gaussian white noise and is illustrated on both simulated and experimental biological and telecommunication data. We also compare this new method with the mean-squared displacement (MSD) technique, extended to capture the measurement noise in the toy model, which shows inferior results. The introduced procedure is expected to allow for more accurate analysis of trajectories with measurement errors across different experimental fields and without the need for any calibration measurements.