Research  

Papers

• David F. Anderson, Jingyi Ma, and Praful Gagrani, Mathematical Analysis for a Class of Stochastic Copolymerization Processes, (free link), Bulletin of Mathematical Biology, 2026.

Abstract: Life’s origins hinge on how long information-carrying polymers (RNA/DNA) grow by adding monomers—i.e., copolymerization. In this work, we study a simple copolymerization model in which a set of monomers attach to or detach from the tip of a polymer. We also assume that the attaching and detaching rates for the different monomers are different, but fixed (i.e., do not depend upon the rest of the polymer chain). By recasting the dynamics as a continuous-time Markov process on an infinite tree-like state space, we establish recurrence and transience criteria, and derive almost-sure laws for polymer growth and composition using the theory of Markov chains on trees with finitely many "cone types".

• David F. Anderson and Jingyi Ma, Low-Variance Couplings for Multivariate Parameter Sensitivity in Stochastic Chemical Reaction Networks.  In Progress, (free link), submitted to SIAM Journal on Scientific Computing.

Abstract: A central question for parameterized stochastic reaction networks is how expectations of quantities of interest change under parameter perturbations. We propose a multi-path stacked coupling (MSC) method and a corresponding simulation algorithm. This work extends the stacked-coupling framework of Anderson and Yuan to a genuinely multi-path setting. The resulting method provides a general-purpose framework for finite-difference sensitivity estimation whenever several nearby parameterized paths are used within the same estimator. We will also show how this viewpoint naturally applies in three representative settings: the simultaneous computation of many first derivatives, higher-order finite-difference estimation of a single first derivative using wider stencils, and the estimation of higher-order derivatives.

Colloquium, Seminars, and Conference Talks

• Invited talk, Stochastic Reaction Networks Workshop — June 16, 2025 — Politecnico di Torino

       Topic: Mathematical Analysis for a Class of Stochastic Copolymerization Processes

• Invited talk, SIAM Conference on Applied Algebraic Geometry (AG25) — July 11, 2025 — University of Wisconsin–Madison

       Topic: Mathematical Analysis for a Class of Stochastic Copolymerization Processes

• Invited talk, Seminar on the Mathematics of Reaction Networks — October 23, 2025 — Online

       Topic: Mathematical Analysis for a Class of Stochastic Copolymerization Processes

• Invited talk, Laboratory for Quantitative Biology, Univ. Tokyo — March 2, 2026 — Online

       Topic: Mathematical Analysis for a Class of Stochastic Copolymerization Processes

• Invited talk and poster, Chemical Reaction Networks in Hawai'i 2026— May 22, 2026 — University of Hawai'i at Mānoa

       Talk topic: Mathematical Analysis for a Class of Stochastic Copolymerization Processes

       Poster topic: Low-Variance Couplings for Multivariate Parameter Sensitivity in Stochastic CRNs

• Invited talk, 2027 Joint Mathematics Meetings — January 14, 2027— McCormick Place, Lakeside Center and South Building, Chicago, IL

       Topic: Low-Variance Couplings for Multivariate Parameter Sensitivity in Stochastic CRNs