Dr. Ankit Gupta

Looking at life through a mathematical lens

About me:

I am an Applied Mathematician, specializing in Probability Theory, Stochastic Processes, and allied areas. I focus on developing computational, analytical, and statistical tools for stochastic models in Biology. Many of these tools can also be applied in other domains, such as Quantitative Finance and Statistical Physics.

Research Interests: Over the years, I have worked on many different topics. Below I list them in no specific order. Click here to see my papers sorted by research area.

  • Biomolecular Control Theory (Cybergenetics): Design and characterization of intracellular circuits that exhibit the property of robust perfect adaptation (RPA) at the cell-population level.

  • Stability Analysis for stochastic reaction networks: Finding sufficient computationally verifiable conditions for establishing ergodicity of Markov chain models of reaction networks.

  • Sensitivity Analysis: Design of efficient Monte Carlo approaches for estimating the partial derivatives of some expected observable w.r.t. model parameters.

  • Frequency Domain Analysis: Efficient simulation-based estimation of the frequency spectrum of stochastic single-cell trajectories.

  • Master Equation Solvers: Developing solvers for the Chemical Master Equation (CME) associated with a stochastic reaction network model. These include direct project-based approaches, approximate simulation-based approaches, as well as deep-learning-based approaches for high-dimensional CMEs.

  • Stochastic Filtering Theory: Design of efficient particle filters and projection methods for estimating the conditional distributions of hidden state variables given the time-trajectory of an observed variable.

  • Role of Noise in Systems Biology: Understanding how randomness in intracellular dynamics affects the population-level behavior, such as entrainment by or amplification of external signals.

  • Phylodynamics/Phylogenetics: Bayesian Inference of transmission tree along with epidemiological parameters from the observed phylogeny of pathogen molecular sequencing data.

  • Adaptive Dynamics: Proving limit theorems for evolutionary models based on the adaptive dynamics framework where there is feedback between the environment and the trait substitution process.

  • Measure-Valued Processes: Investigating how Fleming-Viot processes arise in the study of spatial models related to the phenomenon of cell polarity.

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