I study parameter identifiability, which concerns finding which unknown parameters of a model can be quantified from given input-output data. Many biological models are unidentifiable, which means that the parameters can take on an infinite number of values, yet yield the same input-output data. The goal is then to find identifiable parameter combinations to reparameterize the model. My work has been focused on the differential algebra approach to identifiability and on an algorithm I wrote for finding identifiable parameter combinations using Groebner Bases.
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Papers in Preparation
Finding identifiable functions using numerical algebraic geometry methods (with D. Bates and J. Hauenstein).
Model rejection using differential algebra (with H. Harrington and K. Ho).
Identifiability of chemical reaction networks (with A. Shiu).
N. Meshkat, S. Sullivant, and M. Eisenberg, Identifiability results for several classes of linear compartment models, Submitted to Bulletin of Mathematical Biology.
N. Meshkat, C. E. Kuo, and J. J. DiStefano III, On Finding and Using Identifiable Parameter Combinations in Nonlinear Dynamics Systems Biology Models and COMBOS: a Novel Web Implementation, PLoS ONE 9(10) (2014): e110261. PLoS ONE
N. Meshkat, C. Anderson, and J. J. DiStefano III, Alternative to Ritt’s Pseudodivision for finding the input-output equations of multi-output models, Math. Biosci. 239 (2012) 117-123. ScienceDirect arXiv
N. Meshkat, C. Anderson, and J. J. DiStefano III, Finding identifiable parameter combinations in nonlinear ODE models and the rational reparameterization of their input-output equations, Math. Biosci. 233 (2011) 19-31. ScienceDirect
N. Meshkat, M. Eisenberg, and J. J. DiStefano III, An algorithm for finding globally identifiable parameter combinations of nonlinear ODE models using Groebner Bases, Math. Biosci. 222 (2009) 61-72. PubMed