I am interested in following research projects which are significant for leading to Ph.D. dissertations in mathematical biology.

(1) **Energy-Balanced Biochemical Systems.** Lambda
Phage, Cell Cycle, and Phototransduction.

(2) **Mathematical Theory of Nonlinear DNA Elasticity.** Both
deterministic and stochastic approaches will be employed.

(3) **Mathematical Theory of Ionic Distribution around Cylindrical
Molecules and Its Applications to DNA.** ODE and its asymptotic
analysis, numerical investigation, and Painleve equation.

(4) **Mathematical Foundation of Fluorescence Correlation Spectroscopy
and Its Related Methods.** Including high-order time correlation function and
generalization of Green-Kubo formulae.

(5) **Protein Folding and Its Related Mathematical Problems.**
Kinetics in energy landscape, dimension reduction and simplex
search, and relation to mutual information.

(6) **Fluctuating Nonlinear Biochemical Reactions and Stochastic
Resonance.** Birth-death processes and Brownian motion, nonlinear
oscillation, and phase space analysis: developing a stochastic version
of the Wymann-DiCera kinetic network (hypercycle) and show its nonlinear
stochastic behavior as well as SR.

(7) **Stochastic Macromolecular Mechanics, Nonequilibrium Thermodynamics,
and Their Applications.** Brownian motion, large deviation theory, and
nonlinear diffusion equation.

(8) **An Algebreic-Topological Approach to Irreversible Markov
Processes.** Graph and network theory, asymmetric linear operator
and its eigenvalues, non-normal matrix, and Markov processes.