Progressive enzymes are macromolecules which hydrolyze ATP while moving unidirectionally along a linear macromolecular “track”. Examples include motor molecules such as myosin, kinesin and dynein, RNA and DNA polymerases, and chaperonins. We propose a specific mechanical model for transduction of phosphate bond energy during ATP hydrolysis into directed motion. This model falls within the class...

In articulated tracking, one is concerned with estimating the pose of a person in every frame of a film. This pose is most often represented as a kinematic skeleton where the joint angles are the degrees of freedom. Least-committed predictive models are then phrased as a Brownian motion in joint angle space. However, the metric of the joint angle space is rather unintuitive as it ignores both b...

Brownian motion refers to the mathematical models that are used to describe the random movement of particles immersed in a fluid. This random movement was discovered by botanist Robert Brown, in 1827, while studying pollen grains in water under the microscope. One of the first to describe Brownian motion was Thorvald N. Thiele, in 1880, in a paper on the method of least squares. In 1900, Louis ...

This paper begins to explore a rigorous introduction to probability theory using ideas from algebra, measure theory, and other areas. We start with a basic explanation of terms and ideas and then move onto an attempt at explaining Brownian motion.

Sheffield (2016) proposed an inventory accumulation model with two types of products which encodes the critical Fortuin-Kasteleyn model on a random planar map, and showed that a two-dimensional inventory accumulation trajectory in the discrete model scales to a correlated planar Brownian motion. In this work, we generalize the inventory model to k types of products for any integer k ≥ 2, and pr...

Brownian motion of particles affects many branches of science. We report on the Brownian motion of micrometer-sized beads of glass held in air by an optical tweezer, over a wide range of pressures, and we measured the instantaneous velocity of a Brownian particle. Our results provide direct verification of the energy equipartition theorem for a Brownian particle. For short times, the ballistic ...

Fundamental to many applications in financial engineering is the normal (Gaussian) distribution. It is the building block for simulating such basic stochastic processes as Brownian motion and geometric Brownian motion. In this section, we will go over algorithms for generating univariate normal rvs and learn how to use such algorithms for constructing sample paths of Brownian motion and geometr...