Related papers: What can one learn from two-state single molecule …
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…
A central concern across the natural sciences is a quantitative understanding of the mechanism governing rare transitions between two metastable states. Recent research has uncovered a fundamental equality between the time-reversal…
A recent description of the motion of atoms in a classical monatomic system in liquid and supercooled liquid states divides the motion into two parts: oscillations within a given many-particle potential valley, and transit motion which…
"Oscillations" occur in quite different kinds of many-particle-systems when two groups of particles with different directions of motion meet or intersect at a certain spot. We present a model of pedestrian motion that is able to reproduce…
We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet.…
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…
The conductance of a single metal-molecule-metal junction depends critically on the conformations of the molecule. In the simple case of a biphenyl, two phenyl rings linked together by a single C-C bond, the conductance is expected to…
Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement $\overline{\delta^2}$ of individual particles remains a random variable while indicating that the particle…
We consider an interacting particle system on the one dimensional lattice $\bf Z$ modeling combustion. The process depends on two integer parameters $2\le a<M<\infty$. Particles move independently as continuous time simple symmetric random…
Trajectory inference is used to order single-cell omics data along a path that reflects a continuous transition between cells. This approach is useful for studying processes like cell differentiation, where a stem cell matures into a…
From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field $\bu(\bx)$, we derive different dynamical regimes when $\bu(\bx)$ is iterated to…
Learning a policy using only observational data is challenging because the distribution of states it induces at execution time may differ from the distribution observed during training. We propose to train a policy by unrolling a learned…
A major impediment to a more complete understanding of barrier crossing and other single-molecule processes is the inability to directly visualize the trajectories and dynamics of atoms and molecules in reactions. Rather, the kinetics are…
Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…
The thermodynamics of proteins indicate that folding/unfolding takes place either through stable intermediates or through a two-state process without intermediates. The rather short folding times of the two-state process indicate that…
We study kinetic transport through modular networks consisting of alternating domains using both analytical and numerical methods. We demonstrate that the mean velocity is insensitive to the local structure of the network, and it indicates…
The orientational memory of particles can serve as an effective measure of diffusivity, spreading, and search efficiency in complex stochastic processes. We develop a theoretical framework to describe the decay of directional correlations…
Time course measurement of single molecules on a cell surface provides detailed information on the dynamics of the molecules, which is otherwise inaccessible. To extract the quantitative information, single particle tracking (SPT) is…
A binary fluid mixture in contact with lateral particle reservoirs is considered. By imposing different particle concentrations in these reservoirs, the system can be maintained under controlled non-equilibrium conditions. Previous…
We study a discrete random walk on a one-dimensional finite lattice, where each state has different probabilities to move one step forward, backward, staying for a moment or being absorbed. We obtain expected number of arrivals and expected…