List of publications:

Theoretical mathematics

Applied mathematics, engineering, and statistics

Theoretical mathematics

  1. D. Guillot, H. Gupta, P.K. Vishwakarma, Positivity preservers over finite fields, submitted, 2024, arXiv: 2404.00222, 28 pages.

  2. A. Belton, D. Guillot, A. Khare, M. Putinar, Negativity-preserving transforms of tuples of symmetric matrices, submitted, 2023, arXiv: 2310.18041, 35 pages.

  3. A. Belton, D. Guillot, A. Khare, M. Putinar, Matrix positivity preservers in fixed dimension. II:positive definiteness and strict monotonicity of Schur function ratios, submitted, 2023, arXiv: 2310.18020, 26 pages.

  4. A. Belton, D. Guillot, A. Khare, M. Putinar, Totally positive kernels, Polya frequency functions, and their transforms, Journal d’Analyse Mathématique 150 no. 1, pages 83–158, 2023, arXiv: 2006.16213, 63 pages.

  5. A. Belton, D. Guillot, A. Khare, M. Putinar, Preservers of totally positive kernels and Pólya frequency functions, Mathematics Research Reports 3, pages 35–56, 2022, arXiv: 2110.08206, 20 pages.

  6. A. Belton, D. Guillot, A. Khare, M. Putinar, Hirschman–Widder densities, to appear in Applied and Computational Harmonic Analysis, 2022, arXiv: 2101.02129, 26 pages.

  7. A. Belton, D. Guillot, A. Khare, M. Putinar, Matrix compression along isogenic blocks, Acta Scientiarum Mathematicarum (Szeged) 88 nos. 1–2, 100th anniversary special issue, pages 417–448, 2022, arXiv: 2010.14429, 29 pages.

  8. A. Belton, D. Guillot, A. Khare, M. Putinar, Moment-sequence transforms, Journal of the European Mathematical Society 24 no. 9, pages 3109–3160, 2022, arXiv:1610.05740, 48 pages.

  9. M. Ghandehari, D. Guillot, K. Hollingsworth, Gabor-type frames for signal processing on graphs, Journal of Fourier Analysis and Applications, 27, 2021, arXiv:2009.06058.

  10. A. Belton, D. Guillot, A. Khare, M. Putinar, A panorama of positivity. II: Fixed dimension, Complex Analysis and Spectral Theory. Proceedings of the CRM Workshop held at Laval University, QC, May 21-25, 2018. Contemporary Mathematics. CRM Proceedings. American Mathematical Society, Providence, RI, 2020. arXiv:1812.05482.

  11. D. Guillot and J. Wu, Total nonnegativity of GCD matrices and kernels, Linear Algebra and its Applications, 578:446–461, 2019. arXiv:1901.01947.

  12. A. Belton, D. Guillot, A. Khare, M. Putinar, A panorama of positivity. I: Dimension free, in Analysis of Operators on Function Spaces (The Serguei Shimorin Memorial Volume), A. Ale- man, H. Hedenmalm, D. Khavinson, M. Putinar, Eds., pages 117–165, Trends in Mathematics, Birkhauser, 2019, arXiv:1812.05482.

  13. M. Ghandehari, D. Guillot, K. Hollingsworth, A non-commutative viewpoint on graph signal processing, 13th International Conference on Sampling Theory and Applications (SampTA), Bordeaux, France, 2019.

  14. A. Belton, D. Guillot, A. Khare, M. Putinar, Simultaneous kernels of matrix Hadamard powers, Linear Algebra and its Applications, 576:142–157, 2019, arXiv:1709.03280.

  15. D. Guillot, A. Khare, B. Rajaratnam, The critical exponent: a novel graph invariant, 29th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC ‘17), S'eminaire Lotharingien de Combinatoire 78B, article #62, 2017, arXiv:1802.06976

  16. D. Guillot, A. Khare, B. Rajaratnam, Preserving positivity for rank-constrained matrices, Trans. Amer. Math. Soc., 369:6105–6145, 2017, arXiv:1406.0042.

  17. A. Belton, D. Guillot, A. Khare, M. Putinar, Matrix positivity preservers in fixed dimension. I., Advances in Mathematics, 298, 325-368, 2016, arXiv:1504.07674.

  18. A. Belton, D. Guillot, A. Khare, M. Putinar, Schur polynomials and matrix positivity preservers, FPSAC ‘16 Proceedings (DMTCS proc. BC), 155–166, 2016.

  19. A. Belton, D. Guillot, A. Khare, M. Putinar, Matrix positivity preservers in fixed dimension, C. R. Acad. Sci. Paris, Volume 354, Issue 2, 2016, Pages 143–148.

  20. D. Guillot, A. Khare, B. Rajaratnam, Critical exponents of graphs, J. Combin. Theory Ser. A, Volume 139, 2016, Pages 30-58, arXiv:1504.04069.

  21. D. Guillot, A. Khare, B. Rajaratnam, Preserving positivity for matrices with sparsity constraints, Trans. Amer. Math. Soc. 368:8929–8953, 2016 arXiv:1406.3408.

  22. P. Diao, D. Guillot, A. Khare, B. Rajaratnam, Differential calculus on graphon space, J. Combin. Theory Ser. A, Volume 133, 2015, Pages 183-227, arXiv:1403.3736.

  23. D. Guillot, B. Rajaratnam, Functions preserving positive definiteness for sparse matrices, Trans. Amer. Math. Soc. 367 (2015), 627-649, arXiv:1210.3894.

  24. D. Guillot, A. Khare, B. Rajaratnam, Complete characterization of Hadamard powers preserving Loewner positivity, monotonicity, and convexity, Journal of Mathematical Analysis and Applications, 425 no. 1, pages 489–507, 2015, arXiv:1311.1581.

  25. D. Guillot, A. Khare, B. Rajaratnam, The critical exponent conjecture for powers of doubly nonnegative matrices, Linear Algebra and its Applications, Volume 439, Issue 8, 2013, Pages 2422-2427, arXiv:1303.4701.

  26. D. Guillot, B. Rajaratnam, Retaining positive definiteness in thresholded matrices, Linear Algebra and its Applications, Volume 436, Issue 11, 1 June 2012, Pages 4143–4160, arXiv:1108.3325.

  27. D. Guillot, N. Chevrot, T. J. Ransford, De Branges-Rovnyak spaces and Dirichlet spaces, J. Funct. Anal., 259 (2010), 2366-2383.

  28. D. Guillot, Blaschke condition and zero sets in weighted Dirichlet spaces, Arkiv för Matematik, Volume 50, Issue 2 (2012), 269-278.

  29. D. Guillot, Fine boundary behavior and invariant subspaces of harmonically weighted Dirichlet spaces, Complex Analysis and Operator Theory, 2012, Volume 6, Issue 6, 1211-1230.

  30. D. Guillot, Comportement au bord dans les espaces de Dirichlet avec poids harmoniques et espaces de de Branges-Rovnyak (Boundary behavior in Dirichlet spaces with harmonic weights and de Branges–Rovnyak spaces), Doctoral dissertation, Laval University, 2010.

  31. D. Guillot, La visibilité du spectre des algèbres de Banach et le problème de l’inversion contrôlée (Visibility of the spectrum in Banach algebras and the problem of controlled inversion), Master thesis, Laval University, 2007.

  32. D. Guillot, T.J. Ransford, Bloch’s theorem for algebroid multifunctions II, Math. Proc. R. Ir. Acad., 105A(2) (2005), 103-109.

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Applied mathematics, engineering, and statistics

  1. F. Zhu, J. Emile-Geay, G. J. Hakim, D. Guillot, D. Khider, R. Tardif, and W. A. Perkins, cfr: a Python package for climate field reconstruction, Geoscientific Model Development , Volume 17(8), 3409–3431, 2024.

  2. G. Ashley, D. Guillot, A. Lane, R. M. Humphreys, T. Mooney, Container Port Performance Assessment - A Nonnegative Matrix Factorization Approach, to appear in Maritime Economics and Logistics, 2022.

  3. J. Florez-Ospina, D. Lau, D. Guillot, K. Barner, G. Arce, Smoothness on Rank-Order Path Graphs and its Use in Compressive Spectral Imaging with Side Information, to appear in Signal Processing, 2022.

  4. I. Balogun, M. Leadingham II, D. Gulliot, and N. Attoh-Okine, Deep Learning Approach Towards Squat Isolation in a Multi-Embedded Track Geometry Defects, to appear in IEEE BigData workshop, 2021.

  5. A. Vaccaro, J. Emile-Geay, D. Guillot, R. Verna, C. Morice, J. Kennedy, B. Rajaratnam, Climate field completion via Markov random fields - Application to the HadCRUT4.6 temperature dataset, Journal of Climate, Volume 34(10), 4169–4188, 2021.

  6. D. Guillot, A. Parada, S. Cioaba, G. Arce, Optimal sampling sets in cographs, IEEE Data Science workshop, Minneapolis, USA, 2019.

  7. A. Lasisi, E. N. Martey, D. Guillot, N. Attoh-Okine, A three-step agglomerated Machine Learning: An alternative to Weibull Defect Analysis of Rail Infrastructure, IEEE International Conference on Big Data, Seattle, USA, 2018.

  8. J. Wang, J. Emile-Geay, D. Guillot, N. McKay, B. Rajaratnam, Fragility of reconstructed temperature patterns over the Common Era: Implications for model evaluation, Geophysical Research Letters, Volume 42, Issue 17, 2015, Pages 7162–7170.

  9. D. Guillot, B. Rajaratnam, J. Emile-Geay, Statistical paleoclimate reconstructions via Markov random fields, Ann. Appl. Stat., Volume 9, Number 1 (2015), 324-352. arXiv:1309.6702.

  10. J. Wang, J. Emile-Geay, D. Guillot, J. E. Smerdon, and B. Rajaratnam, Evaluating climate field reconstruction techniques using improved emulations of real-world conditions, Clim. Past, 10, 1-19, 2014.

  11. J. Wang, J. Emile-Geay, D. Guillot, and B. Rajaratnam, Spatiotemporal Patterns of low-frequency variability in a 2000-year long global temperature reconstruction, 4th International Workshop on Climate Informatics, NCAR, Boulder, CO, 2014.

  12. D. Guillot, A. Maleki, B. Rajaratnam, B. Rolfs, I. Wong, Iterative thresholding algorithms for sparse inverse covariance estimation, NIPS, Lake Tahoe, 2012, arXiv:1211.2532.

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