Time-optimal neural feedback control of nilpotent systems as a binary classification problem [pdf], S. Bicego, S. Gue, D. Kalise, and N. Villamizar, 2025. arxiv:2503.17581.
Artinian Gorenstein algebras with binomial Macaulay dual generator [pdf], N. Altafi, R. Dinu, S. Faridi, S. Masuti, R. Miró-Roig, A. Seceleanu, and N. Villamizar, 2025. arxiv:2502.18149.
New families of Artinian Gorenstein algebras with the weak Lefschetz property [pdf], N. Altafi, R. Dinu, S. Masuti, R. Miró-Roig, A. Seceleanu, and N. Villamizar, 2025. arxiv:2502.16687.
An algebraic framework for geometrically continuous splines [pdf], A. Mantzaflaris, B. Mourrain, N. Villamizar, and B. Yuan, accepted for publication in Mathematics of Computation, 2025. doi:10.1090/mcom/4068.
Survey on 3D reconstruction techniques: large-scale urban city reconstruction and requirements, A. Christodoulides, G. Tam, J. Clarke, R. Smith, J. Horgan, N. Micallef, J. Morley, N. Villamizar, and S. Walton, accepted for publication in Transactions on Visualization and Computer Graphics, 2025. doi:10.1109/TVCG.2025.3540669.
A general formulation of reweighted least squares fitting [pdf], C. Giannelli, S. Imperatore, L. Kreusser, E. Loayza-Romero, F. Mohammadi, N. Villamizar, Mathematics and Computers in Simulation, 2024. doi:10.1016/j.matcom.2024.04.029.
Multivariate polynomial splines on generalized oranges [pdf], M. Sirvent, T. Sorokina, N. Villamizar, and B. Yuan, Journal of Approximation Theory, 299: 106016, 2024. doi:10.1016/j.jat.2024.106016.
A lower bound for the dimension of tetrahedral splines in large degree [pdf], M. DiPasquale and N. Villamizar, Constructive Approximation, 2023. doi:10.1007/s00365-023-09625-5.
Algebraic methods to study the dimension for supersmooth spline spaces [pdf], D. Toshniwal and N. Villamizar, Advances in Applied Mathematics, 142, 102412, 2023. doi:10.1016/j.aam.2022.102412.
Reflection groups and enumeration, A. Morales, V. Reiner, and N. Villamizar, to appear In: F. Ardila, C. Benedetti, and A. Morales (eds), Algebraic and Geometric Combinatorics, Cambridge University Press, 2021.
Completeness characterization of Type-I box splines [pdf], N. Villamizar, A. Mantzaflaris and B. Jüttler, to appear in Springer INdAM Series, 2021. arXiv:2011.01919.
A lower bound for splines on tetrahedral vertex stars [pdf], M. DiPasquale and N. Villamizar, SIAM Journal on Applied Algebraic Geometry, 5(2), pp. 250-277, 2021. doi:10.1137/20M1341118.
Dimension of polynomial splines of mixed smoothness on T-meshes [pdf], D. Toshniwal and N. Villamizar, Computer Aided Geometric Design, 80, pp. 101880, 2020. doi:10.1016/j.cagd.2020.101880.
Varieties of apolar subschemes of toric surfaces [pdf], M. Gallet, K. Ranestad and N. Villamizar, Arkiv för Matematik, 56 (1), pp. 73-99, 2018. doi:10.4310/ARKIV.2018.v56.n1.a6.
Smooth splines on quad meshes with 4-split macro-patch elements [pdf], A. Blidia, B. Mourrain and N. Villamizar, Computer Aided Geometric Design, Volume 52-53, pp. 106-125, 2017, doi:10.1016/j.cagd.2017.03.003.
Dimension and bases for geometrically continuous splines on surfaces of arbitrary topology [pdf], B. Mourrain, R. Vidunas and N. Villamizar, Computer Aided Geometric Design, 45, 108-133, 2016. doi:10.1016/j.cagd.2016.03.003.
Planar Linkages Following a Prescribed Motion [pdf], M. Gallet, C. Koutschan, Z. Li, G. Regensburger, J. Schicho and N. Villamizar, Mathematics of Computation, 2016. doi: 10.1090/mcom/3120 .
Characterization of hierarchical quartic box splines on a three directional grid [pdf], N. Villamizar, A. Mantzaflaris and B. Jüttler, Computer Aided Geometric Design, 41, 47-61, 2016. doi:10.1016/j.cagd.2015.11.004.
Degenerations of Real Irrational Toric Varieties [pdf], E. Postinghel, F. Sottile and N. Villamizar, Journal of the London Mathematical Society Second Edition, 92 (2), 223-241, 2015. doi: 10.1112/jlms/jdv024.
Bounds on the dimension of spline spaces on triangulations [pdf], N. Villamizar, Oberwolfach Reports, Multivariate Splines and Algebraic Geometry, 12 (2), 1191-1194, doi:10.4171/OWR/2015/21.
Spline spaces on triangulations [book], N. Villamizar and B.Mourrain, In: T. Dokken, G. Muntingh (eds) SAGA– Advances in ShApes, Geometry, and Algebra, Geometry and Computing 10: 177-197, Springer, Cham, 2014. doi:10.1007/978-3-319-08635-4 10.
Bounds on the dimension of spline spaces on tetrahedral partitions: a homological approach [pdf], Mathematics in Computer Science, 8 (2): 157-174, 2014. doi:10.1007/s11786-014-0187-8.
Ring structure of splines on triangulations [pdf], N. Villamizar, Proceedings Encuentro de Álgebra Computacional y Aplicaciones (EACA), Barcelona, June 2014: pp. 164-167. http://www.ub.edu/eaca2014/2014_EACA_Conference_Proceedings.pdf.
Homological techniques for the analysis of the dimension of triangular spline spaces [pdf], B. Mourrain and N. Villamizar, Journal of Symbolic Computation 50, 564-577, 2013. 564-577. doi:10.1016/j.jsc.2012.10.002.
La conjetura abc [pdf], V. Albis and N. Villamizar, Lecturas Matemáticas, 34(1), 11-75, 2013. http://scm.org.co/archivos/revista/Articulos/1100.pdf.