Data Analysis and Mathematical Approaches to Machine Learning

  • Bayesian Posterior Perturbation Analysis with Integral Probability Metrics with Alfredo Garbuno-Inigo, Tapio Helin, Bamdad Hosseini, arXiv
  • The Mean Field Ensemble Kalman Filter: Near-Gaussian Setting with José A. Carrillo, Andrew M. Stuart, Urbain Vaes, arXiv
  • Convergence rates for ansatz-free data-driven inference in physically constrained problems with Sergio Conti, Michael Ortiz, arXiv, doi  (ZAMM, published 28 June 2023)
  • Model-free and Prior-Free Data-Driven Inference in Mechanics with Sergio Conti, Michael Ortiz, arXiv, doi (ARMA, published 11 January 2023)
  • Consensus Based Sampling with José A. Carrillo, Andrew M. Stuart, Urbain Vaes, arXiv, doi (Studies in Applied Mathematics, published 05 January 2022)
  • Spectral analysis of weighted Laplacians arising in data clustering with Bamdad Hosseini, Assad A. Oberai, Andrew M. Stuart, arXiv, doi (ACHA, published January 2022)
  • Consistency of semi-supervised learning algorithms on graphs: Probit and one-hot methods with Bamdad Hosseini, Zhi Ren, Andrew M. Stuart, arXiv, doi (JMLR, published July 2020)
  • Interacting Langevin Diffusions: Gradient Structure And Ensemble Kalman Sampler with Alfredo Garbuno-Inigo, Wuchen Li, Andrew M. Stuart, arXiv,  doi (SIAM J. Appl. Dyn. Syst.,  published 04 February 2020)
  • Geometric structure of graph Laplacian embeddings with Nicolas Garcia Trillos, Bamdad Hosseini, arXiv , doi (JMLR, published March 2021)

Partial Differential Equations

  • Coupled Gradient Flows for Strategic Non-Local Distribution Shift with Lauren Conger, Eric Mazumdar, Lillian Ratliff, arXiv
  • Covariance-modulated optimal transport and gradient flows with Martin Burger, Matthias Erbar, Daniel Matthes, André Schlichting, arXiv
  • Nonlinear stability of chemotactic clustering with discontinuous advection with Vincent Calvez, (Annales de la Faculté des Sciences de Toulouse Mathématiques, published 2023) arXiv, doi.
  • Uniqueness of stationary states for singular Keller-Segel type models with Vincent Calvez, José A. Carrillo, (Nonlinear Analysis, published 13 December 2020) arXiv, doi
  • Reverse Hardy-Littlewood-Sobolev inequalities with José A.Carrillo, Matías G. Delgadino, Jean Dolbeault and Rupert L. Frank, (JMPA, published 10 September 2019)  arXiv,  doi
  • Ground States in the Diffusion-Dominated Regime with José A.Carrillo, Edoardo Mainini and Bruno Volzone (published 15 June 2018), arXiv,  doi
  • The geometry of diffusing and self-attracting particles in a one-dimensional fair-competition regime with José A.Carrillo and Vincent Calvez, book chapter in Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions, volume 2186 of Lecture Notes in Mathematics, Springer, (published 08 October 2017), arXiv,  doi
  • Equilibria of homogeneous functionals in the fair-competition regime with José A.Carrillo and Vincent Calvez, Nonlinear Analysis, (published August 2017), arXiv,  doi
  • Exponential decay to equilibrium for a fibre lay-down process on a moving conveyor belt with Emeric Bouin and Clément Mouhot, SIAM Journal on Mathematical Analysis (published 19 August 2017), arXivdoi
  • Non-local kinetic and macroscopic models for self-organised animal aggregations with José A.Carrillo and Raluca Eftimie, KRM (published 3 Sept 2015), arXiv,  doi

Collaborations with other Departments

Mathematics Education

  • Bringing a maths camp to Ghana with Francis Torgbor, Danny Parsons, Emily Fleming, David Stern, Jeff Goodman, Abib Duut, Chris Clarke and Santiago Borio, Proceedings of Educators International Research Conference 2015, Accra, Ghana (July 29 – August 1, 2015) ADRRI Journals
  • Exploring The Role of Extra Curricula Maths Camps and Clubs in Kenya and Beyond with Emily Fleming, Zachariah Mbasu, David Stern, Danny Parsons, Mildred Ayere, James Musyoka, Thomas Mawora, Chris Clarke, Santiago Borio, Michael Obiero, Proceedings of 7th International Conference on Education and New Learning Technonlogies (EDULEARN15 Proceedings), Barcelona, Spain (July 2015)

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