Related papers: A Reversibility Parameter for a Markovian Stepper
Negative differential mobility is the phenomenon in which the velocity of a particle decreases when the force driving it increases. We study this phenomenon in Markov jump models where a particle moves in the presence of walls that act as…
In a real life process evolving over time, the relationship between its relevant variables may change. Therefore, it is advantageous to have different inference models for each state of the process. Asymmetric hidden Markov models fulfil…
The dynamic properties of a classical tracer particle in a random, disordered medium are investigated close to the localization transition. For Lorentz models obeying Newtonian and diffusive motion at the microscale, we have performed…
Many cell functions are accomplished thanks to intracellular transport mechanisms of macromolecules along filaments. Molecular motors such as dynein or kinesin are proteins playing a primary role in these processes. The behavior of such…
The scope of this research is the identification of unknown piecewise constant parameters of linear regression equation under the finite excitation condition. Compared to the known methods, to make the computational burden lower, only one…
Fueled by the hydrolysis of ATP, the motor protein kinesin literally walks on two legs along the biopolymer microtubule. The number of accidental backsteps that kinesin takes appears to be much larger than what one would expect given the…
We define a characteristic function for probability measures on the signatures of geometric rough paths. We determine sufficient conditions under which a random variable is uniquely determined by its expected signature, thus partially…
The Steering Law has long been a fundamental model in predicting movement time for tasks involving navigating through constrained paths, such as in selecting sub-menu options, particularly for straight and circular arc trajectories.…
Dynamics of molecular motors that move along linear lattices and interact with them via reversible destruction of specific lattice bonds is investigated theoretically by analyzing exactly solvable discrete-state ``burnt-bridge'' models.…
The usual step-down and step-up multiple testing procedures most often lack an important intuitive, practical, and theoretical property called the interval property. In short, the interval property is simply that for an individual…
Motivated by discrete kinetic models for non-cooperative molecular motors on periodic tracks, we consider random walks (also not Markov) on quasi one dimensional (1d) lattices, obtained by gluing several copies of a fundamental graph in a…
The transport by molecular motors along cytoskeletal filaments is studied theoretically in the presence of static defects. The movements of single motors are described as biased random walks along the filament as well as binding to and…
Some phase space transport properties for a conservative bouncer model are studied. The dynamics of the model is described by using a two-dimensional measure preserving mapping for the variables velocity and time. The system is…
We analyze the learning properties of the stochastic gradient method when multiple passes over the data and mini-batches are allowed. We study how regularization properties are controlled by the step-size, the number of passes and the…
We propose a biochemical model providing the kinetic and energetic descriptions of the processivity dynamics of kinesin and dinein molecular motors. Our approach is a modified version of a well known model describing kinesin dynamics and…
The dynamics of motor protein molecules that have two subunits is investigated using simple discrete stochastic models. Exact steady-state analytical expressions are obtained for velocities and dispersions for any number of intermediate…
The inherent complexity of biological agents often leads to motility behavior that appears to have random components. Robust stochastic inference methods are therefore required to understand and predict the motion patterns from time…
We present a machine learning framework for modeling protein dynamics. Our approach uses L1-regularized, reversible hidden Markov models to understand large protein datasets generated via molecular dynamics simulations. Our model is…
We introduce a model for stochastic transport on a one-dimensional substrate with particles assuming different conformations during their stepping cycles. These conformations correspond to different footprints on the substrate: in order to…
We introduce the notion of order of magnitude reversibility (OM-reversibility) in Markov chains that are parametrized by a positive parameter $\ep$. OM-reversibility is a weaker condition than reversibility, and requires only the knowledge…