Publications

Referred Journal Articles

  • Jérôme Darbon and Gabriel P. Langlois. “On Bayesian posterior mean estimators in imaging sciences and Hamilton–Jacobi partial differential equations.” Journal of Mathematical Imaging and Vision 33 (2021): 1-34. (doi: 10.1007/s10851-021-01036-0)
  • Jérôme Darbon, Gabriel P. Langlois, and Tingwei Meng. “Overcoming the curse of dimensionality for some Hamilton–Jacobi partial differential equations via neural network architectures.” Research in the Mathematical Sciences 7, no. 3 (2020): 1-50. (doi: 10.1007/s40687-020-00215-6)
  • Tiemo Pedergnana, David Oettinger, Gabriel P. Langlois, and George Haller. “Explicit unsteady Navier–Stokes solutions and their analysis via local vortex criteria.” Physics of Fluids 32, no. 4 (2020): 046603. (doi: 10.1063/5.0003245)
  • Gabriel P. Langlois, Donald M. Arnold, Jayson Potts, Brian Leber, David C. Dale, and Michael C. Mackey. “Cyclic thrombocytopenia with statistically significant neutrophil oscillations.” Clinical Case Reports 6 (2018): 1347-1352. (doi: 10.1002/ccr3.1611)
  • Gabriel P. Langlois, Morgan Craig, Antony Humphries, Michael C. Mackey, Joseph M. Mahaffy, Jacques Bélair, Thibault Moulin, Sean R. Sinclair, and Liangliang Wang. “Normal and pathological dynamics of platelets in humans.” Journal of Mathematical Biology 75 (2017): 1-52. (doi: 10.1007/s00285-017-1125-6)
  • Gabriel P. Langlois, Mohammad Farazmand, and George Haller. “Asymptotic dynamics of inertial particles with memory.” Journal of Nonlinear Science 25, no. 6 (2015): 1225-1255. (doi: 10.1007/s00332-015-9250-0)
  • Grace Brooks, Gabriel P. Langlois, Jinzhi Lee, and Michael C. Mackey. “Neutrophil dynamics after chemotherapy and G-CSF: The role of pharmacokinetics in shaping the response.” Journal of Theoretical Biology 315 (2012): 97-109. (doi: 10.1016/j.jtbi.2012.08.028)

Book Chapters

  • Jérôme Darbon, Gabriel P. Langlois, and Tingwei Meng. “Connecting Hamilton-Jacobi Partial Differential Equations with Maximum a Posteriori and Posterior Mean Estimators for Some Non-convex Priors.” Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision (2021): 1-25. (doi: 10.1007/978-3-030-03009-4_56-1)

Manuscripts in preparation

  • Jérôme Darbon and Gabriel P. Langlois. “Accelerated nonlinear primal-dual hybrid gradient algorithms with applications to machine learning”. Under revision. A preprint is available on arXiv (arxiv.org/abs/2109.12222).
  • Gabriel P. Langlois and Jatan Buch and Jérôme Darbon. “Efficient and robust large-scale maximum entropy estimation via nonlinear primal-dual hybrid gradient algorithms.”

Theses

  • Variational and Bayesian methods for solving Hamilton–Jacobi equations in machine learning and imaging science. Ph.D. thesis, Brown University, 2022. Advisor: Prof. Jérôme Darbon.
  • Nonlinear dynamics of finite-size particles in unsteady fluid flows, and spatially linear solutions to the Navier–Stokes equations. M.Sc. thesis, ETH Zürich, 2015. Advisor: Prof. George Haller. (PDF link)