My research interests are in mathematical modeling and uncertainty quantification, using tools such as reduced-order modeling, high-to-low fidelity model calibration, active subspaces, and Bayesian inference.  I focus primarily on biological applications—especially mathematical oncology—but also enjoy dabbling in other application areas as opportunities arise.

Scholarly publications:

  1. H. Cho, A.L. Lewis, K.M. Storey, H.M. Byrne, “Designing experimental conditions to use the Lotka-Volterra model to infer tumor cell line interaction types“, Journal of Theoretical Biology, Vol. 559, doi: 10.1016/j.jtbi.2022.111377, 2023.
  2. R.A. Everett, A.L. Lewis, A. Kuerbis, A. Peace, J. Li, J. Morgenstern, “Data driven mixed effects modeling of the dual process framework of addiction among individuals with alcohol use disorder”, PLOS One, Accepted, 2022.
  3. H. Cho, A.L. Lewis, K.M. Storey, R. Jennings, B. Shtylla, A.M. Reynolds, H.M. Byrne, “A framework for performing data-driven modeling of tumor growth with radiotherapy treatment“, Springer Special Issue: Using Mathematics to Understand Biological Complexity, Association for Women in Mathematics, Series 22, 2021.
  4. A. Henderson, E. Kose, A.L. Lewis, E.R. Swanson, “Mathematical modeling of algal blooms due to swine CAFOs in Eastern North Carolina“, Discrete and Continuous Dynamical Systems—S, doi: 10.3934/dcdss/2021151, 2021.
  5. H. Cho, A.L. Lewis, K.M. Storey, “Bayesian information-theoretic calibration of patient-specific radiotherapy sensitivity parameters to inform effective scanning protocols in cancer“, Journal of Clinical Medicine, Special Issue: Latest Developments in Mathematical Oncology and Cancer Systems Biology, Vol.9, doi: 10.3390/jcm9103208, 2020.
  6. S. Eliot, E. Kose, A.L. Lewis, A. Steinfield, E. Zollinger, “Modeling the stem cell hypothesis: investigating the effects of cancer stem cells and TGF-beta on tumor growth“, Mathematical Biosciences and Engineering, Special Issue: Practical Insights from Cancer Models, Vol. 16(6), pp. 7177-7194, 2019.
  7. K.D. Coleman, A.L. Lewis, R.C. Smith, B.J. Williams, M. Morris, B. Khuwaileh, “Gradient-free construction of active subspaces for dimension reduction in complex models with applications to neutronics“, SIAM/ASA Journal of Uncertainty Quantification, Vol. 7(1), doi: 10.1137/16M1075119, 2018.
  8. A.L. Lewis, R.C. Smith, B.J. Williams, “Bayesian model calibration on active subspaces“, Proceedings of the American Control Conference, 2017.
  9. A.L. Lewis, R.C. Smith, B.J. Williams, “Gradient-free active subspace construction using Morris screening elementary effects“, Computers and Mathematics with Applications, Vol. 72(6), pp. 1603-1615, 2016.
  10. A.L. Lewis, R.C. Smith, B.J. Williams, V. Figueroa, “An information theoretic approach to use high-fidelity codes to calibrate low-fidelity codes“, Journal of Computational Physics, Vol. 324, pp. 24-43, 2016.
  11. V. Cuff, A.L. Lewis, S.J. Miller, “The Weibull distribution and Benford’s Law“, Involve: A journal of mathematics, Vol. 8(5), pp. 859-874, doi:10.2140/involve.2015.8.859, 2015.
  12. A.L. Lewis, J.A. McMahan, R.C. Smith, “Model calibration for beam models in the presence of model discrepancy“, Proceedings of the ASME 2014 Smart Materials, Adaptive Structures, and Intelligent Systems (SMASIS), doi:10.1115/SMASIS2014-7722, pp. V001T03A041, 2014.
Pedagogical publications:
  1. A. Clifton, A.L. Lewis, “But who should have won? Simulating outcomes of judging protocols and ranking schemes“, In: E.E. Goldwyn, S. Ganzell, A. Wootton (eds.) Mathematics Research for the Beginning Student, Vol. 1, Foundations for Undergraduate Research in Mathematics, Birkhauser, Cham, doi: 10.1007/978-3-031-08560-4-6, 2022.
  2. A.L. Lewis, “6-029-S-TumorGrowth“, SIMIODE Mathematical Modeling Resources, https://www.simiode.org/resources/8496, 2021.

Other Articles:

  1. A.L. Lewis, “Bridging the gap by building lasting mentoring relationships“, Notices of the American Mathematical Society, Early Career Section, Vol. 70(4), doi: https://dx.doi.org/10.1090/noti2667, 2023.
  2. G. Gordon, A.L. Lewis, J. Zhou, “Teaching lunches at Lafayette College: don’t talk with your mouth full“, MAA Focus, Vol. 40(4), 2020.