List of publications:
Applied mathematics, engineering, and statistics
Theoretical mathematics

A. Belton, D. Guillot, A. Khare, M. Putinar, Preservers of totally positive kernels and Pólya frequency functions, to appear in Mathematics Research Reports, 2022, arXiv: 2110.08206, 20 pages.

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.

A. Belton, D. Guillot, A. Khare, M. Putinar, Matrix compression along isogenic blocks, to appear in Acta Scientiarum Mathematicarum, 2022, arXiv: 2010.14429, 29 pages.

A. Belton, D. Guillot, A. Khare, M. Putinar, Totally positive kernels, Polya frequency functions, and their transforms, to appear in Journal d’Analyse Mathematique, 2021, arXiv: 2006.16213, 63 pages.

A. Belton, D. Guillot, A. Khare, M. Putinar, Momentsequence transforms, to appear in Journal of the European Mathematical Society, arXiv:1610.05740, 48 pages.

M. Ghandehari, D. Guillot, K. Hollingsworth, Gabortype frames for signal processing on graphs, to appear in Journal of Fourier Analysis and Applications, 2020, arXiv:2009.06058, 19 pages.

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 2125, 2018. Contemporary Mathematics. CRM Proceedings. American Mathematical Society, Providence, RI, 2020. arXiv:1812.05482.

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

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.

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

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.

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

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

A. Belton, D. Guillot, A. Khare, M. Putinar, Matrix positivity preservers in fixed dimension. I., Advances in Mathematics, 298, 325368, 2016, arXiv:1504.07674.

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

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.

D. Guillot, A. Khare, B. Rajaratnam, Critical exponents of graphs, J. Combin. Theory Ser. A, Volume 139, 2016, Pages 3058, arXiv:1504.04069.

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

P. Diao, D. Guillot, A. Khare, B. Rajaratnam, Differential calculus on graphon space, J. Combin. Theory Ser. A, Volume 133, 2015, Pages 183227, arXiv:1403.3736.

D. Guillot, B. Rajaratnam, Functions preserving positive definiteness for sparse matrices, Trans. Amer. Math. Soc. 367 (2015), 627649, arXiv:1210.3894.

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.

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 24222427, arXiv:1303.4701.

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.

D. Guillot, N. Chevrot, T. J. Ransford, De BrangesRovnyak spaces and Dirichlet spaces, J. Funct. Anal., 259 (2010), 23662383.

D. Guillot, Blaschke condition and zero sets in weighted Dirichlet spaces, Arkiv för Matematik, Volume 50, Issue 2 (2012), 269278.

D. Guillot, Fine boundary behavior and invariant subspaces of harmonically weighted Dirichlet spaces, Complex Analysis and Operator Theory, 2012, Volume 6, Issue 6, 12111230.

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

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.

D. Guillot, T.J. Ransford, Bloch’s theorem for algebroid multifunctions II, Math. Proc. R. Ir. Acad., 105A(2) (2005), 103109.
Applied mathematics, engineering, and statistics

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.

J. FlorezOspina, D. Lau, D. Guillot, K. Barner, G. Arce, Smoothness on RankOrder Path Graphs and its Use in Compressive Spectral Imaging with Side Information, to appear in Signal Processing, 2022.

I. Balogun, M. Leadingham II, D. Gulliot, and N. AttohOkine, Deep Learning Approach Towards Squat Isolation in a MultiEmbedded Track Geometry Defects, to appear in IEEE BigData workshop, 2021.

A. Vaccaro, J. EmileGeay, 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.

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

A. Lasisi, E. N. Martey, D. Guillot, N. AttohOkine, A threestep agglomerated Machine Learning: An alternative to Weibull Defect Analysis of Rail Infrastructure, IEEE International Conference on Big Data, Seattle, USA, 2018.

J. Wang, J. EmileGeay, 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.

D. Guillot, B. Rajaratnam, J. EmileGeay, Statistical paleoclimate reconstructions via Markov random fields, Ann. Appl. Stat., Volume 9, Number 1 (2015), 324352. arXiv:1309.6702.

J. Wang, J. EmileGeay, D. Guillot, J. E. Smerdon, and B. Rajaratnam, Evaluating climate field reconstruction techniques using improved emulations of realworld conditions, Clim. Past, 10, 119, 2014.

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

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.