Working Papers

  1. Raquel Bosch-Romeu, Julián Librero, Marina Senent-Valero, Marı́a Carmen Sanfeliu-Alonso, José Marı́a Salinas-Serrano, Jaume Forés-Martos, Beatriz Suay-Garcı́a, Joan Climent , Antonio Falcó and Marı́a Pastor-Valero A novel approach to learning through categorical variables applicable to the classification of solitary pulmonary nodule malignancy Research Square (2022)

  2. Jaume Forés-Martos, Beatriz Suay-García, Raquel Bosch-Romeu, Maria Carmen Sanfeliu-Alonso, Antonio Falcó,Joan Climent Progression Analysis of Disease with Survival (PAD-S) by SurvMap identifies different prognostic subgroups of breast cancer in a large combined set of transcriptomics and methylation studies BioArxiV (2022)

  3. P. M. Berná and A. Falcó Non-probabilistic Supervised Learning for Non-linear Convex Variational Problemss. ArxiV (2022).

  4. A. Falcó, W. Hackbusch and A. Nouy. Geometric Structures in Tensor Representations (Release 2). Preprint 56/2014 at Max Planck Institute for Mathematics in the Sciences (2014).

  5. A. Falcó, W. Hackbusch and A. Nouy. Geometric Structures in Tensor Representations. Preprint 9/2013 at Max Planck Institute for Mathematics in the Sciences (2013).

  6. E. Estellés Arolas, F. González Ladrón de Guevara and A. Falcó Montesinos. Principal Component Analysis for Automatic Tag Suggestion . Working Paper (2010).

  7. D. Santo-Orcero, C.R. Zacharias and A. Falcó. Fast matrix-vector multiplication for tight-binding hamiltonial matrices in the Lanczos method. Working Paper (2010).

  8. A. Nouy and A. Falcó. Constrained Tensor Product Approximations based on Penalized Best Approximations. Working Paper (2010).


    GSSTDA: Gene Structure Survival using Topological Data Analysis


  1. Antonio Tarín-Pelló, Beatriz Suay-García, Jaume Forés-Martos, Antonio Falcó, María-Teresa Pérez-Gracia Computer-aided drug repurposing to tackle antibiotic resistance based on topological data analysis. Computers in Biology and Medicine. Volume 166, November 2023, 107496.

  2. J. A. Conejero, A. Falcó and M. Mora-Jiménez A pre-processing procedure for the implementation of the Greedy-Rank One Algorithm to solve high–dimensional linear systems. AIMS Mathematics 2023, Volume 8, Issue 11: 25633-25653.

  3. J. A. Conejero, A. Falcó and M. Mora-Jiménez Structure and approximation properties of Laplacian-like matrices Results Math. 78, 184 (2023).
  4. A. Falcó, W. Hackbusch and A. Nouy Geometry of tree-based tensor formats in tensor Banach spaces Annali di Matematica Pura ed Applicata (1923 -) 2023.
  5. C. Blecua and A. Falcó An elasticity-based smoothing post-processing algorithm for the quality improvement of quadrilateral elements. Finite Element Analysis & Design, Volume 215, 1 March 2023, 103888.
  6. Suay-García B, Bueso-Bordils JI, Antón-Fos GM, Pérez Gracia MT, Falcó A, Alemán-López PA. Synthesis of Quinolones and Zwitterionic Quinolonate Derivatives with Broad-Spectrum Antibiotic Activity . Pharmaceuticals. 2022; 15(7),818.
  7. Suay-García B, Bueso-Bordils JI, Falcó A, Antón-Fos GM, Alemán-López PA. Virtual Combinatorial Chemistry and Pharmacological Screening: A Short Guide to Drug Design . International Journal of Molecular Sciences. 2022; 23(3):1620.
  8. Bueso-Bordils, J.I.; Antón-Fos, G.M.; Falcó, A.; Duart, M.J.; Martín-Algarra, R.; Alemán-López, P.A. New Pharmacokinetic and Microbiological Prediction Equations to Be Used as Models for the Search of Antibacterial Drugs . Pharmaceuticals 2022,15,122.
  9. Tarek Frahi, Abel Sancarlos, Matthieu Galle, Xavier Beaulieu, Anne Chambard, Antonio Falco, Elías Cueto and Francisco Chinesta Monitoring weeder robots and anticipating their functioning by using advanced topological data analysis Frontiers in Artificial Intelligence (2021).
  10. Angelo Pasquale, Amine Ammar, Antonio Falcó, Simona Perotto, Elías Cueto, Jean-Louis Duval and Francisco Chinesta A separated representation involving multiple time scales within the Proper Generalized Decomposition framework Advanced Modeling and Simulation in Engineering Sciences, volume 8, Article number: 26 (2021).
  11. Jaume Fores-Martos, Raimundo Cervera-Vidal, Julia Sierra-Roca, Carlos Lozano-Asencio, Vita Fedele, Sten Cornelissen, Hege Edvarsen, Irene Tadeo-Cervera, Pilar Eroles, Ana Lluch, Rafa Tabares-Seisdedos, Antonio Falcó, Laura J. Van’t Veer, Marjanka Schmidt, David A. Quigley, Anne-Lise Børresen-Dale, Vessela N. Kristensen, Allan Balmain and Joan Climent Circadian PERformance in Breast Cancer: A Germline and somatic genetic study of PER3VNTR polymorphisms and gene co-expression. npj Breast Cancer 7, Article number: 118 (2021).
  12. M. Billaud-Friess, A. Falcó and A. Nouy. A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds BIT Numerical Mathematics (2021).
  13. Frahi,T.;Falcó,A.;Vinh Mau, B.; Duval, J.L.; Chinesta, F. Empowering Advanced Parametric Modes Clustering from Topological Data Analysis. Appl. Sci. 2021, 11, 6554.
  14. M. Billaud-Friess, A. Falcó and A. Nouy. Principal Bundle Structure of Matrix Manifolds. Mathematics 2021, 9, 1669.
  15. Forés-Martos J, Boullosa C, Rodrigo-Domínguez D, Sánchez-Valle J, Suay-García B, Climent J, Falcó A, Valencia A, Puig-Butillé JA, Puig S, Tabarés-Seisdedos R. Transcriptomic and Genetic Associations between Alzheimer’s Disease, Parkinson’s Disease, and Cancer Cancers. 2021; 13(12): 2990.

  16. Montés, N.; Chinesta, F.; Mora, M.C.; Falcó, A.; Hilario, L.; Rosillo, N.; Nadal, E Real-Time Path Planning Based on Harmonic Functions under a Proper Generalized Decomposition-Based Framework Sensors 2021, 21, 3943.

  17. A. Falcó, W. Hackbusch and A. Nouy. Tree-based tensor formats. SeMA Journal volume 78, pages 159–173 (2021)

  18. Bueso-Bordils, J.I.; Alemán-López, P.A.; Martín-Algarra, R.; Duart, M.J.; Falcó, A.; Antón-Fos, G.M. Molecular Topology for the Search of New Anti-MRSA Compounds. Int. J. Mol. Sci. 2021, 22, 5823.

  19. Pérez-Moraga, R.; Forés-Martos, J.; Suay-García, B.; Duval, J.-L.; Falcó, A.; Climent, J A COVID-19 Drug Repurposing Strategy through Quantitative Homological Similarities Using a Topological Data Analysis-Based Framework. Pharmaceutics 2021, 13, 488.

  20. Frahi T, Chinesta F, Falcó A, Badias A, Cueto E, Choi HY, Han M, Duval J-L. Empowering Advanced Driver-Assistance Systems from Topological Data Analysis. Mathematics. 2021; 9(6):634.

  21. Falcó, Antonio; Hilario, Lucía; Montés, Nicolás; Mora, Marta C.; Nadal, Enrique. Towards a Vector Field Based Approach to the Proper Generalized Decomposition (PGD). Mathematics (2021), 9 no. 1, 34.

  22. Falcó, Antonio; Hilario, Lucía; Montés, Nicolás; Mora, Marta C.; Nadal, Enrique. A Path Planning Algorithm for a Dynamic Environment Based on Proper Generalized Decomposition. Mathematics (2020) 8, no. 12: 2245.

  23. Suay-Garcia, B.; Falcó, A.; Bueso-Bordils, J.I.; Anton-Fos, G.M.; Pérez-Gracia, M.T.; Alemán-López, P.A. Tree-Based QSAR Model for Drug Repurposing in the Discovery of New Antibacterial Compounds against Escherichia coli. Pharmaceuticals (2020), 13, 431.

  24. Jose I. Bueso-Bordils; Pedro A. Alemán-López; Beatriz Suay-García; Rafael Martín-Algarra; Maria J. Duart; Antonio Falcó; Gerardo M. Antón-Fos. Molecular Topology for the Discovery of New Broad-Spectrum Antibacterial Drugs. Biomolecules (2020).

  25. Ghnatios, Chady; Cueto, Elias; Falco, Antonio; Duyal, Jean-Louis; Chinesta, Francisco. Spurious-free interpolations for non-intrusive PGD-based parametric solutions: Application to composites forming processes. International Journal of Material Forming (2020).

  26. Beatriz Suay-García, José I. Bueso-Bordils, Antonio Falcó, María Teresa Pérez-Gracia, Gerardo M. Antón-Fos and Pedro Alemán-López. QSAR Methods in the Discovery and Development of Antibacterials. Wiley Interdisciplinary Reviews: Computational Molecular Science (2020).

  27. Frahi, Tarek; Argerich, Clara; Yun, Minyoung; Falco, Antonio; Barasinski, Anais; Chinesta, Francisco. Tape surfaces characterization with persistence images. AIMS Materials Science (2020).

  28. Beatriz Suay-García, Pedro Alemán-López, José I. Bueso-Bordils, Antonio Falcó, María Teresa Pérez-Gracia and Gerardo M. Antón-Fos. Topological Index Nclass as a factor determining the antibacterial activity of quinolones against Escherichia coli. Future Medicinal Chemistry, Volume 11, Issue 17 (2019) pp. 2255-2262.

  29. Beatriz Suay-García, Pedro Alemán-López, José I. Bueso-Bordils, Antonio Falcó, Gerardo M. Antón-Fos and María Teresa Pérez-Gracia. New solvent options for in vivo assays in the Galleria mellonella larvae model. Virulence , Volume 10 Issue 1 (2019) pp. 776-782.

  30. N. Montés; F. Chinesta; A. Falcó; M. Mora; L. Hilario; J. Duval A PGD-based Method for Robot Global Path Planning: A Primer. Proceedings of the International Conference on Informatics in Control, Automation and Robotics (2020).

  31. A. Falcó, W. Hackbusch and A. Nouy. On the Dirac-Frenkel variational principle on tensor Banach spaces. Foundations of Computational Mathematics, Volume 19 Issue 1 (2019) pp. 159–204.

  32. A. Falcó and F. Sánchez. Model order reduction for dynamical systems: A geometric approach. Comptes Rendus - Mécanique, Volume 346 (2018) pp. 515-523.

  33. A. Falcó, N. Montés, F. Chinesta, L. Hilario and M.C. Mora . On the Existence of a Progressive Variational Vademecum based in the Proper Generalized Decomposition for a Class of Elliptic Parametrised Problems Journal of Computational and Applied Mathematics. Volume 330 (2018) pp. 1093–1107.

  34. V. Candela, A. Falcó and D.P. Romero. A General Framework for a Class of Non-linear Approximations with Applications to Image Restoration Journal of Computational and Applied Mathematics. Volume 330 (2018) pp. 982–994.

  35. A. Falcó, Ll. Navarro and C. Vázquez. A Direct LU Solver for Pricing American Bond Options under Hull-White model Journal of Computational and Applied Mathematics. Volume 309, 1 (2017) pp. 442–455.

  36. L. Hilario, A. Falcó, N. Montés and M.C. Mora. A Tensor Optimization Algorithm for Bézier Shape Deformation. Journal of Computational and Applied Mathematics. Volume 291 (2016) pp. 264-280.

  37. L. Domenech, A. Falcó, V. García and F. Sánchez. Towards a 2.5D Geometric Model in Mould Filling Simulation. Journal of Computational and Applied Mathematics. Volume 291 (2016) pp. 183-196.

  38. A. Cañavate-Grimal, A. Falcó, P. Calderón, I. Payá-Zaforteza On the use of stochastic spectral methods in deep excavation inverse problems. Computer and Structures, Volume 159 (2015) pp. 41-60.

  39. F. Sánchez, L. Domenech, V. García, N. Montés, A. Falcó, E. Cueto, F. Chinesta, P. Fideu Fast and reliable gate arrangement pre-design of resin infusion processes. Composites Part A: Applied Science and Manufacturing. Volume 77 (2015), pp. 285–292.

  40. A. Falcó. Tensor formats based on subspaces are positively invariant sets for Laplacian-like Dynamical Systems. " Numerical Mathematics and Advanced Applications ‐ ENUMATH 2013 Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (Eds.)" Lecture Notes in Computational Science and Engineering, Vol. 103 Springer-Verlag pp 315-322 (2014).

  41. E. Cueto, C. Ghnatios, F. Chinesta, N. Montes, F. Sanchez and A. Falco Improving computational efficiency in LCM by using computational geometry and model reduction techniques Key Engineering Materials Vols. 611-612 (2014) pp. 339-343.

  42. F. Sanchez, L. Domenech, V. Garcia, N. Montes, A. Falco, E. Cueto and F. Chinesta A computational approach based on flow front shape dynamic behavior for the process characterization during filling in Liquid Resin Infusion. Key Engineering Materials Vols. 611-612 (2014) pp. 265-272.

  43. A. Falcó, L. Hilario, N. Montés and M.C. Mora. Numerical Strategies for the Galerkin-Proper Generalized Decomposition Method. Mathematical and Computer Modelling, Volume 57, Issues 7–8, (2013) pp. 1694–1702.

  44. A. Falcó and W. Hackbusch. On minimal subspaces in tensor representations. Foundations of Computational Mathematics, Volume 12, Issue 6 (2012), pp. 765-803.

  45. A. Falcó and A. Nouy. Proper Generalized Decomposition for Nonlinear Convex Problems in Tensor Banach Spaces. Numerische Mathematik, Volume 121, Issue 3 (2012), pp. 503-530.

  46. L.Hilario, N.Montés, M.C.Mora, A.Falcó Real-time Bézier Trajectory Deformation for Potential Fields Planning Methods . 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems September 25-30, 2011. San Francisco, CA, USA pp. 1567-1572.

  47. A. Falcó, Ll. Navarro and J. Nave. On the Calibration of a Gaussian Heath-Jarrow-Morton model using Consistent Forward Rate Curves. Quantitative Finance, Vol. 11, No. 4, April 2011, pp. 495–504.

  48. Javier Collado, Antonio Falcó, Dolores Rodrigo, Fernando Sampedro, M. Consuelo Pina and Antonio Martínez Application of Monte Carlo Simulation in Industrial Microbiological Exposure Assessment Applications of Monte Carlo Method in Science and Engineering, Shaul Mordechai (Ed.), ISBN: 978-953-307-691-1, InTech, (2011) pp. 83-94.

  49. A. Falcó and A. Nouy. A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach. Journal of Mathematical Analysis and Applications 376 (2011) pp. 469–480.

  50. A. Falcó. Algorithms and Numerical Methods for High Dimensional Financial Market Models . Revista de Economía Financiera (20) 2010, pp. 51-68.

  51. A. Ammar, F. Chinesta and A. Falcó. On the convergence of a Greedy Rank-One Update Algorithm for a class of Linear Systems . Archives of Computational Methods in Engineering, Volume 17, Number 4, (2010) pp. 473-486.

  52. A. Falcó. On the Optimization Problems for the Proper Generalized Decomposition and the n-Best Term Approximation . Proceedings of the Seventh International Conference on Engineering Computational Technology, B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru and M.L. Romero, (Editors), Civil-Comp Press, Stirlingshire, Scotland. 2010

  53. Ll. Alsedá and A. Falcó. On the structure of the kneading space of bimodal degree one circle maps . International Journal of Bifurcations and Chaos, Volume: 20, Issue: 9 (September 2010) pp. 2701–2721.

  54. L. Hilario, N. Montés, A. Falcó and F. Sánchez. An improvement of Flow Front computation through Bézier Shape Deformation guaranteeing mass conservation law. International Journal of Material Forming Volume 3, Supplement 1 / April 2010 pp. 923-926.

  55. E. Estellés, J. Pardo, F. Sánchez and A. Falcó. A Modified Agile Methodology for an ERP Academic Project Development . In "New Achievements in Technology Education and Development" Edited by Safeeullah Soomro ISBN 978-953-307-066-7, Intech (2010). pp. 89-108

  56. A. Falcó, A. Ammar and F. Chinesta A Greedy Approach to Multiscale Methods . International Journal on Material Forming , Volume 2, Suplement 1, August 2009, pp. 895-898.

  57. N. Montés, F. Sánchez and A. Falcó A Topological Approach for the Flow Behaviour Characterization in LCM Processes . International Journal on Material Forming , Volume 2, Suplement 1, August 2009, pp. 17-20.

  58. A. Falcó, Ll. Navarro and J. Nave. The Hull-White Model and Multiobjective Calibration with Consistent Curves: Empirical Evidence. RACSAM Rev. R. Acad. Cien. Serie A. Mat. Vol 103 (2) 2009, pp. 235-249.

  59. A. Falcó. Los productos financieros: de la teoría a la práctica. Mat2 Materials Matemàtics. Revista Electrònica de Divulgació Matemàtica Editada pel Departament de Matemàtiques de la Universitat Autònoma de Barcelona, Volum 2009, 2 (2009).

  60. M. González, A. I. Mateos and A. Falcó. Where the dirty surplus accounting flows are?. Review of Accounting and Finance , Volume 7, Issue: 3, (2008) pp. 308 - 328.

  61. N. Montés, F. Sánchez, L. Hilario and A. Falcó. Flow numerical computation through Bezier shape deformation for LCM process simulation methods. International Journal on Material Forming , Volume 1, Supplement 1 January 2008 pp. 919–922.

  62. J. Amigó, A. Falcó, J. Gálvez and V. Villar. Topología molecular. Boletín de la Sociedad Española de Matemática Aplicada, 39 (2007) pp. 135–149,

  63. F. Chinesta, A. Ammar, A. Falcó and M. Laso. On the reduction of Stochastic Kinetic Theory Models of Complex Fluids. Modelling and Simulation in Materials Science and Engineering, 15 (2007) pp. 639–652.

  64. N. Montés, F. Sanchez, J. A. García, A. Falcó, J. Tornero, and F. Chinesta Application of Artificial Vision in flow redirection during filling of Liquid Composite Molding processes. AIP Conference Proceedings, Volume 907 10TH ESAFORM CONFERENCE ON MATERIAL FORMING Zaragoza (Spain), 18-20 April 2007 pp. 902–907.

  65. Ll. Alsedà and A. Falcó. On the topological dynamics and phase–locking renormalization of Lorenz–like maps. Ann. Inst. Fourier (Grenoble), 53 no. 3 (2003) pp. 859–883.

  66. A. Falcó and M. González. Valoración de empresas. aplicación de la teoría del precio libre de arbitraje a sociedades españolas. Economía Industrial, 351 no. III (2003) pp. 173–186.

  67. F. Acedo, F. Benito, A. Falcó, A. Rubia and J. Torres. A computational approach to the fundamental theorem of asset pricing in a single-period market. Computational Economics, 18 no. 4 (2001) pp. 233–249.

  68. J. S. Cánovas and A. Falcó. The set of periods for a class of skew-products. Discrete Contin. Dynam. Systems, 6 (2000) no. 4 pp. 893–900.

  69. F. Balibrea and A. Falcó. Kneading theory and bifurcations for a class of degree one circle maps: the Arnol'd tongues revisited. Grazer Mathematische Berichte ITERATION THEORY (ECIT `96), Proceedings of the European Conference on Iteration Theory, Urbino, Italy, September 8 - 14, 1996 (Karl-Franzens-Univ. Graz), Graz, (1999) pp. 29–50.,

  70. Ll. Alsedà and A. Falcó. On the structure of the kneading space of bimodal degree one circle maps. In XV CEDYA/V Congress on Applied Mathematics (Vigo, 1997), . Univ. Vigo, Vigo, 1998 pp. 145–149.

  71. A. Falcó. The set of periods for a class of crazy maps. J. Math. Anal. Appl., 217 no. 2 (1998) pp. 546–554.

  72. Ll. Alsedà and A. Falcó. A characterization of the kneading pair for bimodal degree one circle maps. Ann. Inst. Fourier (Grenoble), 47 no. 1 (1997) pp. 273–304.

  73. Ll. Alsedà and A. Falcó. Devil's staircase route to chaos in a forced relaxation oscillator. Ann. Inst. Fourier (Grenoble), 44 no. 1 (1994) pp. 109–128.

  74. Ll. Alsedà and A. Falcó. An entropy formula for a class of circle maps. C. R. Acad. Sci. Paris Sér. I Math., 314 no. 9 (1992) pp. 677–682. (Proofs of the results)

  75. Ll. Alsedà and A. Falcó. The bifurcations of a piecewise monotone family of circle maps related to the van der Pol equation. In European Conference on Iteration Theory (Caldes de Malavella, 1987), World Sci. Publishing, Teaneck NJ, 1989. pp. 113–120.

Habilitation à diriger des Recherches

  1. A. Falcó. Contributions sur les systèmes dynamiques en petite dimension et sur les problèmes variationnelles dans les espaces avec structure tensorielle . Département de Mathématiques, Université de Nantes, June 2016.

PhD Thesis

  1. A. Falcó. Bifurcations and Symbolic Dynamics for bimodal degree one circle maps: The Arnol'd Tongues and the Devil's Staircase. Departament de Matemàtiques, Universitat Autònoma de Barcelona, March 1995.