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Video anomaly detection (VAD) is a vital yet complex open-set task in computer vision, commonly tackled through reconstruction-based methods. However, these methods struggle with two key limitations: (1) insufficient robustness in open-set…
Fractional Brownian motion (FBM) is the only Gaussian self-similar process with stationary increments. Its increment process, called fractional Gaussian noise, is ergodic and exhibits a property of power-like decaying autocorrelation…
We describe a method to probe the spectral fluctuations of a transition over broad ranges of frequencies and timescales with the high spectral resolution of Fourier spectroscopy, and a temporal resolution as high as the excited state…
We introduce the concept of Randomly Modulated Gaussian Processes as a unifying framework for modeling, analyzing and classifying anomalous diffusion models in heterogeneous media. This formulation incorporates correlations in the…
Anomalous diffusion is discussed in the context of quantum Brownian motion with colored noise. It is shown that earlier results follow simply and directly from the fluctuation-dissipation theorem. The limits on the long-time dependence of…
A robust and efficient anomaly detection technique is proposed, capable of dealing with crowded scenes where traditional tracking based approaches tend to fail. Initial foreground segmentation of the input frames confines the analysis to…
Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) which converges back to a Brownian motion with reduced diffusion coefficient at long times, after the anomalous…
Optical tweezers setup is often used to probe the motion of individual tracer particle, which promotes the study of relaxation dynamics of a generic process confined in a harmonic potential. We uncover the dependence of ensemble- and…
Anomalous diffusion occurs in a wide range of systems, including protein transport within cells, animal movement in complex habitats, pollutant dispersion in groundwater, and nanoparticle motion in synthetic materials. Accurately estimating…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
Automatic detection and tracking of cells in microscopy images are major applications of computer vision technologies in both biomedical research and clinical practice. Though machine learning methods are increasingly common in these…
Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic…
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…
Advanced microscopy techniques are essential in biomedical research for visualising and tracking biomolecules within living cells and their compartments. Conventional fluorescence microscopy methods, however, often struggle with accurately…
Modern online mass spectrometry generates multi-terabyte data streams critical for understanding Earth's environmental systems. However, extracting actionable chemical insights from these repositories is impeded by a computational…
Motion models (i.e., transition probability densities) are often deduced from fluorescence widefield tracking experiments by analyzing single-particle trajectories post-processed from data. This analysis immediately raises the question: To…
Clustering is a central tool in biomedical research for discovering heterogeneous patient subpopulations, where group boundaries are often diffuse rather than sharply separated. Traditional methods produce hard partitions, whereas soft…
We propose a robust alignment technique for Standard Fundus Images (SFIs) and Ultra-Widefield Fundus Images (UWFIs), which are challenging to align due to differences in scale, appearance, and the scarcity of distinctive features. Our…
Supervised machine learning has enabled accurate pathology detection in brain MRI, but requires training data from diseased subjects that may not be readily available in some scenarios, for example, in the case of rare diseases.…
Diffusion processes in biological membranes are of interest to understand the macromolecular organisation and function of several molecules. Fluorescence Recovery After Photobleaching (FRAP) has been widely used as a method to analyse this…