This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the matrix exponential to evolve probability densities in time. A sampling of the approximate solutions of the chemical master equation is used to derive accele...

An analysis of regeneration by dilution of a covalently modified protein is presented. It is shown that, when protein regeneration is realized through the intermediacy of a protein-modifying agent adsorptive complex, the reaction is described by a summation of two exponential functions of reaction time plus a constant-term equation. The conditions whereby this equation reduces to a single-expon...

In computer vision, the exponential map is the natural generalisation of the ordinary exponential function to matrix elements. The technique is based on generating a manifold embedding of the geometric features of the scene on which to estimate trajectories primarily of motion or invariance. An advantage of using the exponential map is the existence of a closed form time-update equation for the...