I work on dynamical systems arising from network interactions, typically deterministic models for biochemical kinetics. A realistic model of the chemistry within cells is complex: with many chemical species, uncertain kinetic rate functions and unknown parameters. Understandably, analytical solutions of the dynamics is difficult to obtain. Instead of purely relying on numerical methods, I am interested in inferring dynamical properties from the network structure.

My work so far can roughly be seen in the light of several (non-orthogonal) directions: 

1. There are some very strong results for mass-action systems. Which of these results are inherited under other chemically reasonable kinetic assumptions?

2. Network motifs for interesting dynamics, including multistability, oscillations, global stability, (or lack thereof). Can network structures provide biological insights?

3. The relation between network geometry and topology, and polynomial dynamics on the positive orthant. In this view, an interaction network is a formal object that encodes information about the polynomial system.

I am also exploring different ways that mathematics can be used to understand biological systems, especially in the context of signalling pathways.

18. Polly Y. Yu.  Global stability of perturbed complex-balanced systems.  arXiv:2210.13633.
[ arXiv | pdf ] 

17. Diego Rojas La Luz, Gheorghe Craciun, Polly Y. Yu. Generalized Lotka-Volterra Systems and Complex Balanced Polyexponential Systems. arXiv:2412.13367.
[ arXiv | pdf ]

16. Oskar Henriksson, Carlos Améndola, Jose Israel Rodriguez, Polly Y. Yu.  Maximum likelihood estimation of log-affine models using detailed-balanced reaction networks.  arXiv:2411.07986.
[ arXiv | pdf | GitHub ]

15. Xingchi Yan, Polly Y. Yu, Arvind Srinivasan, Sohaib Abdul Rehman, Maxim B. Prigozhin.  Identifying Intermolecular Interactions in Single-Molecule Localization Microscopy.  bioRxiv doi: 10.1101/2024.05.10.593617.
[ bioRxiv | pdf | Supplemental Info ]

14. Polly Y. Yu, Eduardo D. Sontag.  A necessary condition for nonmonotonic dose response, with an application to a kinetic proofreading model.  In 2024 63rd IEEE Conference on Decision and Control (CDC). Accepted 2024.  Appendix in arXiv:2403.13862.
[ arXiv | doi | pdf with appendix ]

13. Gheorghe Craciun, Jiaxin Jin, Polly Y. Yu.  An algorithm for finding weakly reversible deficiency zero realizations of polynomial dynamical systems.  SIAM Journal on Applied Mathematics, 83(4),  pp. 1717-1737, 2023.
[ arXiv | doi | pdf ]  

12. Sabina J. Haque, Matthew Satriano, Miruna-Ștefana Sorea, Polly Y. Yu.  The disguised toric locus and affine equivalence of reaction networks.  SIAM Journal on Applied Dynamical Systems, 22(2), pp. 1423-1444, 2023
[ arXiv | doi | pdf ]

11. Benjamin Nordick, Polly Y. Yu, Guangyuan Liao, Tian Hong.  Nonmodular oscillator and switch based on RNA decay drive regeneration of multimodal gene expression.  Nucleic Acid Research, 50(7), pp. 3693-3708, 2022.  
[ bioRxiv | doi | pdf | Supplemental Info ]

10.  Polly Y. Yu, Gheorghe Craciun, Maya Mincheva, Casian Pantea.  A graph-theoretic condition for delay stability of reaction systems.  SIAM Journal on Applied Dynamical Systems, 21(2), pp. 1092-1118, 2022.
[ arXiv* | doi | pdf ]    

9.  Gheorghe Craciun, Abhishek Deshpande, Badal Joshi, Polly Y. Yu.  Autocatalytic recombination systems: A reaction network perspective.  Mathematical Biosciences, 345, 108784, 2022.
[ arXiv | doi | pdf ]

8.  Gheorghe Craciun, Jiaxin Jin, Polly Y. Yu.  Single-target networks.  Discrete & Continuous Dynamical Systems - B,  27(2), pp. 799-819, 2022.
[ arXiv | doi | pdf ]

7.  Gheorghe Craciun, Jiaxin Jin, Polly Y. Yu.  Uniqueness of weakly reversible and deficiency zero realizations of dynamical systems.  Mathematical Biosciences, 342, 108720, 2021.
[ arXiv | doi | pdf ]

6.  Balázs Boros, Gheorghe Craciun, Polly Y. Yu.  Weakly reversible mass-action systems with infinitely many positive steady states.  SIAM Journal on Applied Mathematics, 80(4), pp. 1936-1946, 2020.
[ arXiv | doi | pdf ]

5.  Gheorghe Craciun, Maya Mincheva, Casian Pantea, Polly Y. Yu.  Delay stability of reaction systems.  Mathematical Biosciences, 326, 108387, 2020.
[ arXiv | doi | pdf ]

4.  Gheorghe Craciun, Jiaxin Jin, Polly Y. Yu.  An efficient characterization of complex-balanced, detailed-balanced, and weakly reversible systems.  SIAM Journal on Applied Mathematics, 80(1), pp. 183-205, 2020.
[ arXiv | doi | pdf ]

3.  Gheorghe Craciun, Matthew D. Johnston, Gábor Szederkényi, Elisa Tonello, János Tóth, Polly Y. Yu.  Realizations of kinetic differential equations.  Mathematical Biosciences and Engineering, 17(1), pp. 862-892, 2020.
[ arXiv* | doi | pdf ] 

2.  Gheorghe Craciun, Stefan Müller, Casian Pantea, Polly Y. Yu.  A generalization of Birch's theorem and vertex-balanced steady states for generalized mass-action systems.  Mathematical Biosciences and Engineering, 16(6), pp. 8243-8267, 2019.
[ arXiv | doi | pdf ]

1.  Polly Y. Yu, Gheorghe Craciun.  Mathematical analysis of chemical reaction systems.  Israel Journal of Chemistry, 58(6-7), pp. 733-741, 2018.
[ arXiv | doi | pdf ]