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Diffusion coefficient measurements are important for many biological and material investigations, such as particle dynamics, kinetics, and size determinations. Amongst current measurement methods, single particle tracking (SPT) offers the…
Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe…
Single-molecule localization microscopy allows practitioners to locate and track labeled molecules in biological systems. When extracting diffusion coefficients from the resulting trajectories, it is common practice to perform a linear fit…
Single-particle tracking (SPT) has become a popular tool to study the intracellular transport of molecules in living cells. Inferring the character of their dynamics is important, because it determines the organization and functions of the…
Single Particle Tracking (SPT) can aid in understanding complex spatio-temporal processes. However, quantifying diffusivity and forces from individual live cell trajectories is complicated by inter- & intra-trajectory kinetic heterogeneity,…
Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single particle tracking is to determine the…
Single-molecule tracking is a powerful way to look at the dynamic organization of plasma membranes. However, there are some limitations to its use. For example, it was recently observed, using numerical simulation, that time-averaging…
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
The movement of a particle described by Brownian motion is quantified by a single parameter, $D$, the diffusion constant. The estimation of $D$ from a discrete sequence of noisy observations is a fundamental problem in biological single…
In this article we consider the estimation of static parameters for partially observed diffusion processes with discrete-time observations over a fixed time interval. In particular, when one only has access to time-discretized solutions of…
Single-particle tracking allows to infer the motion of single molecules in living cells. When we observe a long trajectory (more than 100 points), it is possible that the particle switches mode of motion over time. Then, fitting a single…
Single Particle Tracking (SPT) is a powerful class of tools for analyzing the dynamics of individual biological macromolecules moving inside living cells. The acquired data is typically in the form of a sequence of camera images that are…
Heterogeneous diffusion processes occur in many different fields such as transport in living cells or diffusion in porous media. A characterization of the transport parameters of such processes can be achieved by ensemble-based methods,…
Methods to extract information from the tracking of mobile objects/particles have broad interest in biological and physical sciences. Techniques based on simple criteria of proximity in time-consecutive snapshots are useful to identify the…
Progress on modern scientific questions regularly depends on using large-scale datasets to understand complex dynamical systems. An especially challenging case that has grown to prominence with advances in single-cell sequencing…
We present a theory for analyzing residence times of single molecules in a fixed detection area of a scanning tunneling microscope (STM). The approach is developed for one-dimensional molecule diffusion and can be extended to two dimensions…
We describe how a single-particle tracking experiment should be designed in order for its recorded trajectories to contain the most information about a tracked particle's diffusion coefficient. The precision of estimators for the diffusion…
Sampling from unnormalized target distributions is a fundamental yet challenging task in machine learning and statistics. Existing sampling algorithms typically require many iterative steps to produce high-quality samples, leading to high…
Methods of determining surface diffusion coefficients of molecules from signal fluctuations of a locally fixed probe are revisited and refined. Particular emphasis is put on the influence of the molecule's extent. In addition to the…
We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have…