### Weitao Chen, Postdoctoral Scholar

I am a member of the Nie Lab at UC Irvine since 2013. I am in the job market this year looking for assistant professorship in the department of mathematics or interdisciplinary research.

### Education

- Ph.D., Mathematics, The Ohio State University, June 2013
- M.A.S., Statistics, The Ohio State University, June 2012
- M.S., Mathematics, The Ohio State University, June 2010
- B.S., Mathematics and Applied Mathematics, University of Science and Technology of China, June 2008

### Research Interests

My primary research interests are computational systems biology, numerical analysis and scientific computing.

__Computational Systems Biology__

**Modeling of Yeast Mating Reveals Robustness Strategies for Cell-Cell Interactions**. Cell polarization, in which uniformly distribution of substances becomes asymmetric due to internal or external stimuli, is a fundamental process underlying cell mobility and cell division. Yeast mating provides a good system to study cell-cell interaction, which involves coupled intracellular polarization and extracellular signaling molecules as the external stimuli, followed by cell morphological change. How cells sense the shallow gradient in spite of noises and mate successfully with multiple competitors remains mysterious. I developed a novel computational framework that allows one to capture both molecular dynamics and morphological change on multiple cells simultaneously, to identify strategies for robust cell-cell interactions.

**Pattern Formation: Positional-Turing System Governs Macropatterning of Taste Stem Cell Domains in the Mouse Tongue**. The repeated pattern of taste papillae in a developing mouse tongue along with a papillae-free midline makes it an ideal model to understand the molecular machinery underlying the formation of macropatterned tissues of different varieties. By developing a novel mechanism that combines positional information and Turing pattern, I have reproduced the macropattern formation with high precision in placing the midline. Not only does this model predict that a high level of activator signaling activity in the midline at early stage is necessary to form the particular pattern, it also reveals the strategy underlying the robust pattern formation through introducing a second inhibitor.

** Growth Control: Strategies for Precision and Robustness in Size Control during Tissue Development **. The fundamental principles underlying the robustness and precision of tissue growth remain mysterious. In particular, most cellular signaling, that growth control relies on, decays over short distances typically at micron length scale, whereas human tissues and organs are observed to reach well-controlled sizes on the scale of meters. We define the final state to capture tissue size based on continuous cell lineage model. By parallelly simulating final state systems on a growing domain within a large parameter space, I aim to investigate the capability and limitations of different control strategies, as well as develop identifications in distinguishing different strategies in experiments.

**Pattern and Growth: Scaling Dynamics of Morphogen Gradients Determine Robust Pattern in Growing Drosophila Wing Disc**. Morphogens control the formation of spatial patterns during embryonic development. It is a general feature of developmental systems that patterning scales as tissue size grows, yet little is known about its underlying molecular mechanisms. In drosophila wing disc, Dpp activation gradient is known to control patterning and proliferation of the tissue. This molecular control also exhibits strong robustness even if its receptor production varies. I constructed a spatiotemporal model to describe the dynamics of Dpp signaling pathway in a growing tissue with spatially uniform proliferation rate and investigate the scaling and robustness mechanisms. This model can be very useful for studying the interplay between spatial patterning and growth control in developmental biology.

__Numerical Methods for PDEs and Optimization__

**Fast Solver for Steady States of Complex Partial Differential Equations**. Hyperbolic conservation laws with source terms have wide range of applications in gas dynamics and shallow water systems. Steady state calculation is needed, especially for equations with self-similar solutions. It is challenging to capture singularities, which may occur in the solution, without sacrificing high order accuracy in smooth region. The classical way to achieve steady states of hyperbolic conservation laws adopts the time evolution, which is computationally expensive. I developed a more efficient iterative method by incorporating the high order numerical flux in the fast sweeping iterative scheme. This proposed scheme can solve static solutions directly with high order of accuracy and is capable of resolving shocks or rarefaction waves.

**The efficiency of this method is further improved by coupling it with multigrid framework **. The challenge in interpolating residual between different levels of meshes, especially when the singularity occurs, is handled by upwind interpolation. Overall, the new multigrid fast sweeping method saves computational cost, without sacrificing the order of accuracy and flexibility to employ high order fluxes.

**Semi-Implicit Integration Factor Methods on Sparse Grids for High-Dimensional Systems **. Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. By incorporating sparse grids, which handle high dimensionality, in the semi-implicit integration factor method that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions, I developed a novel method to solve stiff reaction-diffusion systems in high dimensions. In particular, this method is flexible and effective in solving systems involving cross-derivatives and non-constant diffusion coefficients, and has be applied to solve Fokker-Planck equations in high dimensions.

**Localizing Eigenfunctions or Optimizing Eigenvalues in Inhomogeneous Rods and Plates**. The design of photonic structures in electronic semiconductors to control the propagation of waves at different wavelength can be formulated as an optimization problem of eigenvalue problem with Laplacian or bi-Laplacian operator that represents wave propagation in an optical device or a thin plate. By applying descent gradient approach and rearrangement algorithm, I have identified the optimal density distribution in composite plates for localizing the wave propagation or controlling the frequency. To find the descent gradient, I have applied calculus of variations to obtain the linearized response in the eigenfunction and eigenvalue, as well as a new formula for descent gradient of the dielectric coefficient. This method allows one to localize waves of different wavelength at distinct locations simultaneously. I have also developed the rearrangement algorithm in which materials of different densities are re-located in a discrete fashion such that the objective function is optimized according to Raleigh quotient.

### Publications

- Weitao Chen, Qing Nie, Tau-Mu Yi, Ching-Shan Chou. Modelling of Yeast Mating Reveals Robustness Strategies for Cell-Cell Interactions, PLoS Computational Biology, 12(7):e1004988, 2016.
- Weitao Chen, Ching-Shan Chou, Chiu-Yen Kao. Minimizing Eigenvalues for Inhomogeneous Rods and Plates, Journal of Scientific Computing, 0885-7474, pp. 1-31, 2016.
- *Dongyong Wang, *Weitao Chen, Qing Nie. Semi-implicit Integration Factor Methods on Sparse Grids for High-Dimensional Systems, Journal of Computational Physics, 292, 43-55,2015 (*equal contribution).
- Weitao Chen, Ching-Shan Chou, Chiu-Yen Kao. Lax-Friedrichs Multigrid Fast Sweeping Methods for Steady State Problems for Hyperbolic Conservation Laws, Journal of Scientific Computing, 0885-7474, pp. 1-28, 2015.
- Weitao Chen, Ching-Shan Chou, Chiu-Yen Kao. Conservative Fast Sweeping Methods for Steady State Problems for Hyperbolic Conservation Laws, Journal of Computational Physics, 234, pp. 452-471, 2012.

### Book Chapter

- Weitao Chen, Kenneth Diest, Chiu Yen Kao, Daniel E. Marthaler, Luke A. Sweatlock, and Stanley Osher. Numerical Methods for Metamaterial Design, Chapter 7 on Gradient Based Optimization Methods for Metamaterial Design, Pages 175-204, Topics in Applied Physics, 127, Springer, 2013.