## 楊, 穎任 (Yang, Ying-Jen)

Applied Math Ph.D. student

University of Washington, Seattle.

I grew up in Taichung, Taiwan (R. O. C.).
And, I got my B.S. and M.S. in Physics at National Taiwan University in 2014 and 2016.
My master thesis is on anticipatory dynamics in adaptive neural network.
And I now pledge to understand complex systems, *e.g.* biological systems, via stochastic thermodynamics and dynamical systems.
As a Ph.D. student at UW, I am now studying the mathematical structure/foundation of statistical mecanics and thermodynamics, *i.e.* probability theory (including information theory) and large deviation principle with Professor Hong Qian.
Here is my CV.

### Research

The grand goal is to develop a theory of complex systems. I believe the keys lie in probability theory/information theory and dynamical systems. I shall explore various known schools for "the" theory of complex systems along the way....

Keywords: *Probability theory (including information theory), Large Deviation Principle, Landscape Theory, Thermodynamics of information* and * Stochastic thermodynamics*

#### 1. Stochastic Thermodynamics, Probability Theory and Large Deviation Principle

The mathematical foundation of statistical mechanics lies in Probability Theory and Large Deviation Theory. Knowing the mathematical structure allow us to generalize it to more general system, e.g. nonequilibrium system such as biological system

- Onsager's relation, Hill's cycle decomposition perspective of Entropy Production for diffusion
- Dynamical System Approach to Fluctuation Theorem and Large Deviation Theory
- Information Theory

#### 2. Energy Landscape Theory

The very definition of energy outside of Hamiltonian system is always ambiguous. From a Stochastic Dynamics point of view, a energy landscape actually emerge from the zero-noise limit!

- Emergent Energetic Description for Diffusion Process

- Gibbs potential function, gradient descent in discrete space and chemical thermodynamics!
- Fundamental Theorem of Natural Selection and Price's Equation

and Landscape that is not bounded below: theory when the system has connonstop growth

#### 3. Theory of Brain

- Helmholtz machine and "Friston's" Free Energy Principle

- Hopfield Network
- E-I Balance
- Trade off for energy efficiency, adaptability, stability, precision

### Publication

Here is my Google Scholar Page.#### Under Preparation

#### Submitted

__Ying-Jen Yang__and Hong Qian, “Unified formalism for entropy productions and fluctuation theorems” submitted to PRE

#### Published

##### 2019

__Ying-Jen Yang__and Hong Qian, “Entropy Productions and Fluctuation Theorems: A Unifying Change-of-measure Formalism.” ArXiv

##### 2016

__Ying-Jen Yang__, Sean Chen, Chun-Chung Chen and Chi-Keung Chan, “Anticipatory Dynamics in retina.”*Physics Bimonthly*. Link (Chinese General Science Article)__Ying-Jen Yang__, “The interesting and nonlinear heart and brain.”*NTU CASE Press*. Link (Chinese General Science Article)

##### 2015

__Ying-Jen Yang__, Chun-Chung Chen, Pik-Yin Lai and Chi-Keung Chan, “Adaptive Synchronization and Anticipatory Dynamical Systems.”*Phys. Rev. E***92**, 030701 (2015). Link

### Teaching

#### Instructor at University of Washington

Time period | Course Name |
---|---|

2019/06-2019/08 | AMATH 351: Introduction to Differential Equation and Applications |

#### Teaching Assistant at University of Washington

Time period | Course Name |
---|---|

2020/01-2020/04 | AMATH 402: Introduction To Dynamical Systems and Chaos |

2019/09-2019/12 | AMATH 567: Applied Complex Analysis |

2019/01-2019/03 | MATH 125: Calculus II (Integration and Differential Equations) |

2018/09-2019/01 | AMATH 351: Introduction to Differential Equation and Applications |

2018/03-2018/06 | AMATH 301: Beginning Scientific Computing |

2018/01-2018/03 | MATH 124: Calculus I (Continuity and Differentiation) |

2017/09-2018/01 | MATH 125: Calculus II (Integration and Differential Equations) |

#### Teaching Assistant at National Taiwan University

Time period | Course Name |
---|---|

2016/01-2016/06 | Applied Mathematics III: Complex Analysis and Integral Transforms |

2015/01-2015/06 | Statistical Physics I: Equilibrium Statistical Mechanics |

2014/09-2015/01 | General Physics a-1: Classical Mechanics and Special Relativity |

### Contact Info

##### Mail to

Ying-Jen Yang

University of Washington

202 Lewis Hall

UW Mailbox 353925

Seattle, WA 98195-3925