Ryo Takei @ UCLA

Ryo Takei, PhD

E-mail me. rrtakei [a] gmail [d] com

I received my PhD in Mathematics from UCLA, June 2011.
I will be a postdoc at UC Berkeley in the EECS department, starting fall of 2011.

MY NEW WEBSITE.

The content below is slightly outdated.

CV (Updated 01/2011)

Current Research Interests:
Specific: control theory, Hamilton-Jacobi equations, level-set method, mean curvature flow.
General: numerical analysis, partial differential equations

Research Projects:

Applications of Hamilton-Jacobi equations to optimal control and pursuit-evasion problems:

Optimal path planning of simple cars, using Hamilton-Jacobi equations.
A Practical Path-planning Algorithm for a Vehicle with a Constrained Turning Radius: a Hamilton-Jacobi Approach (preprint)

Proceedings to 2010 American Control Conference, Baltimore, MD.
Joint work with R. Tsai (U Texas, Austin), Y. Landa (UCLA), H. Shen (UCLA)
dubins value function

Autonomous Source Discovery and Navigation in Complicated Environments (preprint)
Joint work with R. Tsai (U Texas, Austin), Y. Landa (UCLA), H. Shen (UCLA)
source1

Hamilton-Jacobi formulation for a general simple car.
Optimal trajectories of curvature contrained motion in the Hamilton-Jacobi formulation (preprint)

Joint work with R. Tsai (U Texas, Austin)
rs-1

Level-set visibility based pursuit-evasion (in preparation)
Joint work with R. Tsai (U Texas, Austin), Y. Landa (UCLA)
Watch the movie!
PE-sampple

Optimal path planning under budget constraints: (in preparation)
Joint work with W. Chen (Cornell), Z. Clawson (NCSU), S. Kirov, A. Vladimirsky (Cornell).

Numerical methods for mean curvature flow:

Anisotropic mean curvature with TV minimization, inverse scale space flow:
Numerical methods for anisotropic mean curvature flow based on a discrete time variational formulation (preprint)
revision submitted to Comm. Math. Sci.
Joint work with A. Oberman (Simon Fraser), S. Osher (UCLA), R. Tsai (U Texas, Austin).
aniso_mmc1

Survey of monotone finite difference schemes for mean curvature flow
Modern theory of numerical methods for Motion by Mean Curvature.
M.Sc. Thesis Simon Fraser University, July 2007

Numerical Homogenization:

Homogenization of metric Hamilton-Jacobi equations (preprint)
SIAM Multiscale Modeling and Simulation 8/1: 269-295 (2009)
Joint with A. Oberman (Simon Fraser), A. Vladimirsky (Cornell).
homog_image

Previous teaching at UCLA:
   I was a recipient of the 2011 Sorgenfrey Distinguished Teaching Award in the UCLA Math Department.
    Spring 11: Math 134 (Nonlinear Systems).
    Winter 11: Math 33B (Differential Equations).
    Winter 10: Math 135 (Differential Equations). Teaching evaluations.
    Spring 09: Math 151B (Numerical Analysis). Teaching evaluations.
    Winter 09: Math 33B (Differential Equations). Teaching evaluations.
    Fall 08: Math 151A (Numerical Analysis). Teaching evaluations.
    Spring 08: Math 33B (Differential Equations). Teaching evaluations.
    Winter 08: Math 151A (Numerical Analysis) . Teaching evaluations.