Preprints:
Tuyen Trung Truong, A more direct and better variant of New Q-Newton's method Backtracking for systems of equations, arXiv: 2110.07403
Tuyen Trung Truong, Generalisations and improvements of New Q-Newton's method Backtracking, arXiv:2109.11395
Tuyen Trung Truong, New Q-Newton's method meets Backtracking line search: good convergence guarantee, saddle points avoidance, quadratic rate of convergence, and easy implementation, arXiv:2108.10249. Source code is available at GitHub's link: https://github.com/tuyenttMathOslo/New-Q-Newton-s-method-Backtracking
Fei Hu and Tuyen Trung Truong, An inequality for polarized endomorphisms, arXiv:2104.12660.
Maged Helmy, Anastasiya Dykyy, Tuyen Trung Truong, Paulo Ferreira, Eric Jul, CapillaryNet: An automated system to analyze microcirculation videos from handheld vital microscopy, arXiv:2104.11574
Fei Hu and Tuyen Trung Truong, A dynamical approach to generalized Weil's Riemann hypothesis and semisimplicity, arXiv:2102.04405 (the previous version has also other results, which will be developed into another paper later).
Tuyen Trung Truong, Unconstrained optimisation on Riemannian manifolds, arXiv:2008.11091
Tuyen Trung Truong, Tat Dat To, Tuan Hang Nguyen, Thu Hang Nguyen, Hoang Phuong Nguyen and Maged Helmy, A modification of quasi-Newton's methods helping to avoid saddle points, arXiv:2006.01512. Source code is available on GitHub: (Link)
Tuyen Trung Truong, Some observations on the properness of Identity plus linear powers: part 2, arXiv:2005.02260.
Tuyen Trung Truong, Some observations on the properness of Identity plus linear powers, arXiv:2004.03309.
Tuyen Trung Truong, Coordinate-wise Armijo's condition: General case, arXiv: 2003.05252 (the preprint arXiv: 1911.07820 is incorporated as a special case).
Tuyen Trung Truong, Some convergent results for Backtracking Gradient Descent method on Banach spaces, arXiv:2001.05768.
Tuyen Trung Truong, Convergence to minima for the continuous version of Backtracking Gradient Descent, arXiv: 1911.04221.
Tuyen Trung Truong, Strong submeasures and applications to non-compact dynamical systems, arXiv:1910.06394. This is extracted and developed from the more dynamical part of arXiv: 1712.02490.
Tuyen Trung Truong and Tuan Hang Nguyen, Backtracking gradient descent method for general C^1 functions with applications to Deep Learning, 37 pages. Preprint: arXiv: 1808.05160. Accompanying source codes are available on GitHub: [Link]
Tuyen Trung Truong, Bounded birationality problem is computable, 17 pages. Preprint: arXiv: 1801.00901. (An extended version, 20 pages, with additional results compared to the arXiv version, is available in the folder PDF files.)
Tuyen Trung Truong, Relations between dynamical degrees, Weil's Riemann hypothesis and the standard conjectures, 20 pages. Preprint arXiv: 1611.01124.
Papers:
Tuyen Trung Truong and (Tuan Hang) Hang-Tuan Nguyen, Backtracking gradient descent method and some applications in Large scale optimisation. Part 1: Theory, accepted in Minimax Theory and its Applications. This is the more theoretical part of arXiv: 1808.05160, with some additional experiments. Accompanying source codes are available on GitHub: [Link]
Tuyen Trung Truong. Strong sub measures and applications to non-compact dynamical systems, (this is the more dynamical part of arXiv: 1712.02490), accepted in Ergodic Theory and Dynamical Systems. The paper is Open Access. doi.org/10.1017/etds.2020.132
Tuyen Trung Truong, When will a sequence of points in a Riemannian submanifold converge? (Mostly a survey paper, invited submission.) Special issue "Riemannian geometry of submanifolds", journal: Mathematics (MDPI), 2020, 8 (11), 1934. This is open access [Link to the paper] .
Tuyen Trung Truong and (Tuan Hang) Hang-Tuan Nguyen, Backtracking Gradient Descent method and some applications in Large scale optimisation. Part 2: algorithms and experiments. The main part of the paper is based on the more experimental part of arXiv:1808.05160, together with arXiv:2001.02005 and arXiv:2007.03618. Accompanying source codes are available on GitHub: [Link] Accepted in Applied Mathematics and Optimization. [Link to PDF]
Tuyen Trung Truong, Some new theoretical and computational results around the Jacobian conjecture, developed and revised from preprint arXiv: 1503.08733. Accepted in International Journal of Mathematics.
Finnur Larusson and Tuyen Trung Truong, Approximation and interpolation of regular maps from affine varieties to algebraic manifolds, 9 pages. Preprint: arXiv: 1706.00519. Accepted in Mathematica Scandinavia.
Tuyen Trung Truong, Etale dynamical systems and topological entropy, 13 pages. Preprint arXiv: 1607.07412. Accepted in Proceedings of the American Mathematical Society.
Shulim Kaliman, Frank Kutzschebauch and Tuyen Trung Truong, On subelliptic manifolds, 19 pages. Preprint: 1611:01311v3. Accepted in Israel Journal of Mathematics.
Tuyen Trung Truong, Relative dynamical degrees of correspondences over a field of arbitrary characteristic, 41 pages. Preprint arXiv: 1605.05049. Accepted in Journal fur die Reine und Agnewandte Mathematik (Crelle's journal). DOI: 10.1515/crelle-2017-0052.
Tien-Cuong Dinh, Viet-Anh Nguyen and Tuyen Trung Truong, Growth of the number of periodic points of meromorphic maps, 18 pages. Preprint arXiv: 1601.03910. Accepted in Bulletin of the London Mathematical Society.
Finnur Larusson and Tuyen Trung Truong, Algebraic subellipticity and dominability of blowups of affine spaces, 10 pages. Preprint: arXiv: 1606.08115. Accepted in Documenta Mathematica.
Tuyen Trung Truong, Comments on Sampson's approach toward Hodge conjecture on Abelian varieties, accepted in Annali di Matematica Pura ed Applicata. Preprint arXiv: 1409.0495.
Tuyen Trung Truong, Automorphisms of blowups of threefolds being Fano or having Picard number 1, accepted in Ergodic Theory and Dynamical Systems. Preprint arXiv: 1501.01515.
Tuyen Trung Truong, Some dynamical properties of pseudo-automorphisms in dimension 3. Transactions of the American Mathematical Society 368 (2016), no 1, 727--753.
Keiji Oguiso and Tuyen Trung Truong, Explicit examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy. Kodaira Centennial Volume, J. Math. Sci. Univ. Tokyo 22 (2015), no 1, 361--385.
Tien-Cuong Dinh, Viet-Anh Nguyen and Tuyen Trung Truong, Equidistribution for meromorphic maps with dominant topological degree. Indiana University Journal of Mathematics 64, No 6 (2015), 1805--1828.
Dan Coman and Tuyen Trung Truong, Geometric properties of upper level sets of Lelong numbers on projective spaces. Mathematische Annalen 361 (2015), no 3--4, 981--994.
Fabrizio Catanese, Keiji Oguiso and Tuyen Trung Truong, Unirationality of the Ueno-Campana's threefold. Manuscripta Mathematica 145 (2014), no 3--4, 399--406.
Kenji Oguiso and Tuyen Trung Truong, Salem numbers in dynamics of Kahler 3-folds and complex tori. Mathematische Zeitschrift 278 (2014), no 1--2, 93--117.
Tuyen Trung Truong, The simplicity of the first spectral radius of a meromorphic map. Michigan Mathematics Journal 63 (2014), no 3, 623--633.
Dang Duc Trong, Cao Xuan Phuong, Dinh Ngoc Thanh and Tuyen Trung Truong, Tikhonov's regularization to deconvolution problem, Communications in Statistics: Theory and Methods, vol 43, issue 20, 2014, pp. 4384-4400.
Tuyen Trung Truong, Pullback of currents by meromorphic maps, Bulletin de la Societe Mathematique de France 141 (2013), no 4, 517--555.
Tien-Cuong Dinh, Viet-Anh Nguyen and Tuyen Trung Truong, On the dynamical degrees of meromorphic maps preserving a fibration, Communications in Contemporary Mathematics 14, 1250042, 2012.
Tuyen Trung Truong, Degree complexities of birational maps related to matrix inversions: Symmetric case, Mathematische Zeitschrift 270 (2012), no 3--4, 725--738.
Eric Bedford and Tuyen Trung Truong, Degree complexities of birational maps related to matrix inversion, Communications in Mathematical Physics 298 (2010), no. 2, 357--368.
Tuyen Trung Truong, Sets non-thin at infinity in C ^m, Journal of Mathematical Analysis and Applications 356 (2009), no 2, 517--524.
Dang Duc Trong, Alain Pham Ngoc Dinh, Phan Thanh Nam and Tuyen Trung Truong, Determination of the body force of a two dimensional isotropic elastic body, Journal of Computational and Applied Mathematics 229 (2009), 192--207.