GABRIEL NAVARRO

Department of Algebra
University of Granada

About me

At present, I am a professor (Catedrático de Universidad) at the Department of Algebra of the University of Granada. Prior to this, from 2007 until 2023, I was within the Department of Computer Sciences and AI.


Research Interests

Ring Theory
Representation Theory of (Co)algebras
Non-commutative Localization
Non-commutative Geometry
Fuzzy/Rough/Soft Sets Theory
Approximate Reasoning
Symbolic Computation
Coding Theory
Quantum Machine Learning
Post-Quantum Cryptography

Publications

Phd Thesis. Representation Theory of Coalgebras. Localization in coalgebras, January 2006, pdf file (revised version, 2007). Frontpage image, jpg file

  1. E. Andrés, M. P. Cuéllar, and Gabriel Navarro, Brain-inspired agents for quantum reinforcement learning, Mathematics 2024.
  2. A. Y. Darani, Y. Khedmati, H. Pakmanesh and Gabriel Navarro, Image encryption algorithm based on a new 3D chaotic system using cellular automata, Chaos, Solitons and Fractals 179 (2024), article 114396. 10.1016/j.chaos.2023.114396
  3. A. Y. Darani, Y. Khedmati, Gabriel Navarro, H. Pakmanesh and J. Sharafi, Optimal location using genetic algorithms for chaotic image steganography technique based on discrete framelet transform, Digital Signal Processing 144 (2024), article 104228. 10.1016/j.dsp.2023.104228
  4. E. Andrés, M. P. Cuéllar, and Gabriel Navarro, Efficient dimensionality reduction strategies for quantum reinforcement learning, IEEE Access 11 (2023), 104534-104553. 10.1109/ACCESS.2023.3318173
  5. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, Skew differential Goppa codes and their application to McEliece cryptosystem, Designs, codes and cryptography 91 (2023), 3995–4017. 10.1007/s10623-023-01286-6
  6. P. Jara, L. Merino, Gabriel Navarro and E. Santos, A lattice structure on hesitant fuzzy sets, IEEE Transactions on Fuzzy Systems 31(6) (2023), 2018-2028. 10.1109/TFUZZ.2022.3217400
  7. M.P. Cuéllar, J. Lobillo and Gabriel Navarro, Fast parallel computation of reduced row echelon form to find the minimum distance of linear codes, Expert Systems with Applications 224 (2023), article 119955. 10.1016/j.eswa.2023.119955
  8. E. Andrés, M. P. Cuéllar, and Gabriel Navarro, On the use of Quantum Reinforcement Learning in energy efficiency scenarios, Energies 15(16) 2022, 6034. 10.3390/en15166034
  9. L. Merino, Gabriel Navarro and E. Santos, Induced operators on bounded lattices, Information Sciences 608 (2022), 114-136. 10.1016/j.ins.2022.06.033
  10. C. Gutiérrez-Braojos, C. Rodríguez-Domínguez, F. Carranza-García and G. Navarro-Garulo, Computer supported knowledge building community: A new learning analytics tool, in: Remote Learning in Times of Pandemic. Issues, Implications and Best Practice, edited by Linda Daniela and Anna Visvizi, Routledge Research in Digital Education and Educational Technology Series, Routledge (Taylor and Francis Group), 2022, pp. 35-50.10.4324/9781003167594
  11. J. Gómez-Torrecillas, P. Kutas, F. J. Lobillo and Gabriel Navarro, Primitive idempotents in central simple algebras over F_q(t) with an application to coding theory, Finite Fields and Their Applications 77 (2022), article 101935. 10.1016/j.ffa.2021.101935
  12. J. Gómez-Torrecillas, Gabriel Navarro and J. P. Sánchez-Hernández, Decoding Reed-Solomon Skew-Differential Codes, IEEE Transactions on Information Theory 67 (12) (2021), 7891-7903.10.1109/TIT.2021.3117083
  13. J. Gómez-Torrecillas, J. Lobillo and Gabriel Navarro, Decoding linear codes over chain rings given by parity check matrices, Mathematics 9(16) 2021, article 1878. 10.3390/math9161878
  14. F.J. Lobillo, L. Merino, Gabriel Navarro and E. Santos, Induced triangular norms and negations on bounded lattices, IEEE Transactions on Fuzzy Systems 29(7) 2021, 1802-1814. 10.1109/TFUZZ.2020.2985337
  15. J. Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro and J. P. Sánchez-Hernández, Peterson-Gorenstein-Zierler algorithm for differential convolutional codes, Applicable Algebra in Engineering, Communication and Computing 32 (2021), 321-344. 10.1007/s00200-020-00464-6
  16. M. P. Cuéllar, J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, Genetic algorithms with permutation-based representation for computing the distance of linear codes, Swarm and Evolutionary Computation 60 (2021), 100797. 10.1016/j.swevo.2020.100797
  17. J. Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro and J. P. Sánchez-Hernández, Biseparable extensions are not necessarily Frobenius, Mathematische Zeitschrift 297 (2021), 517-533. 10.1007/s00209-020-02523-7
  18. J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, Cyclic Distances of Idempotent Convolutional Codes, Journal of Symbolic Computation 102 (2021), 37-62. 10.1016/j.jsc.2019.10.008
  19. J. Gómez-Torrecillas, E. Hieta-Aho, F. J. Lobillo, S. López-Permouth, Gabriel Navarro, Some remarks on non projective Frobenius algebras and linear codes, Designs, Codes and Cryptography 88 (2020), 1-15. 10.1007/s10623-019-00666-1
  20. J. Gómez-Torrecillas, F.J. Lobillo and Gabriel Navarro, Dual skew codes from annihilators: Transpose Hamming ring extensions, In: Rings, Modules and Codes, 131-148, Contemporary Mathematics 727, American Mathematical Society, Providence, RI, 2019. 10.1090/conm/727
  21. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, Computing the bound of an Ore polynomial. Applications to factorization, Journal of Symbolic Computation 92 (2019), 269-297. 10.1016/j.jsc.2018.04.018
  22. J. Gómez-Torrecillas, F.J. Lobillo and Gabriel Navarro, Minimum distance computation of linear codes via genetic algorithms with permutation encoding, ACM Communications in Computer Algebra 52(3) (2018), 71-74. 10.1145/3313880.3313886
  23. F.J. Lobillo, L. Merino, Gabriel Navarro and E. Santos, Embeddings between lattices of fuzzy sets: an application of closed-valued fuzzy sets, Fuzzy Sets and Systems 352 (2018), 56-72. 10.1016/j.fss.2018.04.014
  24. J. Gómez-Torrecillas, F.J. Lobillo and Gabriel Navarro, Computing free distances of idempotent convolutional codes, In Proceedings of the 43rd International Symposium on Symbolic and Algebraic Computation (ISSAC '18), 175-182, ACM, New York, NY, USA. 10.1145/3208976.3208985
  25. J. Gómez-Torrecillas, F.J. Lobillo, Gabriel Navarro and A. Neri, Hartmann-Tzeng bound and skew cyclic codes of designed Hamming distance, Finite Fields and Their Applications 50 (2018), 84-112. 10.1016/j.ffa.2017.11.001
  26. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, Peterson-Gorenstein-Zierler algorithm for skew RS codes, Linear and Multilinear Algebra 66 (2018), 469-487. 10.1080/03081087.2017.1301364
  27. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, A Sugiyama-like decoding algorithm for convolutional codes, IEEE Transactions on Information Theory 63 (2017) 6216-6226.10.1109/TIT.2017.2682856
  28. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, Ideal codes over separable ring extensions, IEEE Transactions on Information Theory 65 (2017), 2796-2813. 10.1109/TIT.2017.2682856
  29. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, Computing separability elements for the sentence–ambient algebra of split ideal codes, Journal of Symbolic Computation 83 (2017), 211-227. 10.1016/j.jsc.2016.11.012
  30. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, A new perspective of cyclicity in convolutional codes, IEEE Transactions on Information Theory 62 (5) (2016), 2702-2706. 10.1109/TIT.2016.2538264
  31. F.J. Lobillo, L. Merino, Gabriel Navarro and E. Santos, Rough ideals under relations associated to fuzzy ideals, Information Sciences 352-353 (2016), 121-132. 10.1016/j.ins.2016.02.058
  32. J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, An isomorphism test for modules over a non-commutative PID. Applications to similarity of Ore polynomials, Journal of Symbolic Computation 75 (2016), 149-170. 10.1016/j.jsc.2015.11.012
  33. J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, Convolutional codes with a matrix-algebra word-ambient, Advances in Mathematics of Communication 10 (2016), 29-43. 10.3934/amc.2016.10.29
  34. J. Gómez-Torrecillas, F.J. Lobillo and Gabriel Navarro, Separability test and cyclic convolutuonal codes, in: XV Encuentro de Álgebra Computacional y Aplicaciones: EACA 2016, pp. 93-96. Ed: J. Heras and A. Romero, Logroño, 2014. Published by Universidad de La Rioja. ISBN 978-84-608-9024-9.Dialnet
  35. J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, Information-bit error rate and false positives in an MDS code, Advances in Mathematics of Communication 9 (2015), 149-168. 10.3934/amc.2015.9.149
  36. J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, Cyclic convolutional codes over separable extensions, in Coding Theory and Applications (eds. R. Pinto, P. R. Malonek and P. Vettori), CIM Series in Mathematical Sciences, Springer, 2015. 10.1007/978-3-319-17296-5_22
  37. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, Separable automorphisms on matrix algebras over finite field extensions: applications to ideal codes, in Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation (ISSAC '15). ACM, New York, NY, USA, 189-195. 10.1145/2755996.2756671
  38. J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, Generating idempotents in ideal codes, ACM Communications in Computer Algebra 48 (3/4) (2014), 113-115. 10.1145/2733693.2733703
  39. J. Gómez-Torrecillas, F.J. Lobillo and Gabriel Navarro, On isomorphisms of modules over non-commutative PID, in Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (ISSAC '14), Katsusuke Nabeshima (Ed.). ACM, New York, NY, USA, 210-216. 10.1145/2608628.2608665
  40. J. Gómez-Torrecillas, F.J. Lobillo and Gabriel Navarro, A similarity test for Ore polynomials, in: XIV Encuentro de Álgebra Computacional y Aplicaciones, pp. 123-126. Ed: J. Elias, J. Fernández-Sánchez, and M. Sombra, Barcelona, 2014. ISBN 978-84-697-0651-0. Dialnet
  41. Gabriel Navarro, The valued Gabriel quiver of a wedge product and semiprime coalgebras, Front. Math. China 8 (2013), 1157--1183. 10.1007/s11464-013-0310-19
  42. Gabriel Navarro, O. Cortadellas and F. J. Lobillo, Prime fuzzy ideals over noncomutative rings, Fuzzy Sets and Systems 199 (2012), 108-120. 10.1016/j.fss.2011.11.002
  43. P. Jara, J. López Peña, Gabriel Navarro and D. Stefan, On the classification of twisting maps between K^n and K^m, Algebr. Reprensent. Theory 14 (2011), 869-895. 10.1007/s10468-010-9222-x
  44. O. Cortadellas, J. López Peña and Gabriel Navarro, Factorization structures with a 2-dimensional factor, J. London Math. Soc 81 (2010), 1-23. 10.1112/jlms/jdp055
  45. P. Jara, L. Merino, Gabriel Navarro and J.F. Ruíz, Prime path coalgebras, Arab. J. Sci. Eng. 33 (2008), Number 2C, 273-283. arxiv link
  46. J. Gómez-Torrecillas and Gabriel Navarro, Serial coalgebras and their valued Gabriel quivers, J. Algebra 319 (2008), 5039-5059. 10.1016/j.jalgebra.2008.03.020
  47. J. López Peña and Gabriel Navarro, On the classification and properties of noncommutative duplicates, K-Theory 38 (2008), 223-234. 10.1007/s10977-007-9017-y
  48. Gabriel Navarro, Some remarks on localization in coalgebras, Comm. Algebra 36 (2008), 3447-3466. 10.1080/00927870802107868
  49. R. M. Ibañez Cobos, J. López Peña and Gabriel Navarro, A note on generalized path algebras, Rev. Roumaine Math. Pures Appl. 53(1) (2008), 25-36. Rrc8_1
  50. Gabriel Navarro, Simple comodules and localization in coalgebras, in: Contactforum New techniques in Hopf algebras and graded ring theory, KVAB 2007, 145-164.
  51. P. Jara, L. M. Merino and Gabriel Navarro, Localization in tame and wild coalgebras, J. Pure Appl. Algebra 211 (2007), 342-359. 10.1016/j.jpaa.2007.01.009
  52. P. Jara, L. M. Merino, Gabriel Navarro and F. Ruiz, Localization in coalgebras. Stable localizations and path coalgebras, Comm. Algebra 34 (2006), 2843-2856. 10.1080/00927870802107868
  53. P. Jara, L. M. Merino and Gabriel Navarro, On path coalgebras of quivers with relations, Colloq. Math. 102 (2005), 49-65. 10.4064/cm102-1-5

Manuscripts under consideration

  1. P. Jara, L. Merino, Gabriel Navarro and E. Santos, On gradual sets, set-valued fuzzy sets and representation theorems, 2023.

Others

  1. J. López Peña and G. Navarro, Quantum duplicates of algebras, 8 pages, 2007.
  2. J. Gómez-Torrecillas, F.J. Lobillo, and G. Navarro, Factoring Ore polynomials over $\mathbb{F}_q(t)$ is difficult, arxiv link

Posters

  1. J. Gómez-Torrecillas, F. J. Lobillo and G. Navarro, Minimum distance computation of linear codes via genetic algorithms with permutation encoding, in the 43rd International Symposium on Symbolic and Algebraic Computation (ISSAC '18), July 2018, New York (USA). pdf
  2. J. Gómez-Torrecillas, F. J. Lobillo and G. Navarro, Skew Reed-Solomon Codes: Construction and Decoding, in the 5th IEEE Spanish Workshop on Signal Processing, Information Theory and Communications. Barcelona (Spain), January 24th, 2017. pdf
  3. J. Gómez-Torrecillas, F. J. Lobillo and G. Navarro, Constructing and decoding a class of convolutional codes, in the 3rd AICA Industrial Workshop 2106, June 2016, Logroño (Spain). pdf
  4. J. Gómez-Torrecillas, F. J. Lobillo and G. Navarro, Separable algebras and Convolutional Codes, in the 39th International Symposium on Symbolic and Algebraic Computation (ISSAC '14), July 2014, Kobe (Japan). Distinguished Poster Award. pdf
  5. G. Navarro, On path coalgebras of quivers with relations of tame comodule type, in the International Congress of Mathematicians (ICM2006), August 2006, Madrid (Spain). pdf
  6. G. Navarro, Semicentral and split idempotents, in the III Seminario de CategorÌas y Aplicaciones (SECA III), September 2005, Santiago de Compostela (Spain).pdf

Talks

  1. P. Jara, L. Merino, Gabriel Navarro and E. Santos, On lattice orders on hesitant fuzzy sets, XXI Congreso de Tecnologías y Lógica Fuzzy (ESTYLF’22), Toledo, Universidad de Castilla-La Mancha,2022.
  2. M. P. Cuéllar, J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Heuristic methods for computing the distance of linear codes, in the Congreso Bienal de la Real Sociedad Matemática Española, Ciudad Real (Spain), 17-21 January 2022. slides
  3. J. Gómez-Torrecillas, P. Kutas, J. Lobillo and G. Navarro, Decoding constacyclic codes by means of non commutative polynomials, in the Congreso Bienal de la Real Sociedad Matemática Española, Santander (Spain), 4-8 February 2019. slides
  4. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Computing free distances of idempotent convolutional codes, in the 43th International Symposium on Symbolic and Algebraic Computation (ISSAC 2018), July 2018, New York (USA). slides
  5. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Skew cyclic codes, in Some Trends in Algebra 2017, September 2017, Prague (Czech Republic). slides
  6. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Decoding skew RS codes, in IV Encuentro conjunto RSME-SMM 2017, June 2017, Valladolid (Spain). slides
  7. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Códigos convolucionales cíclicos torcidos, in JNIC2016 (Jornadas Nacionales de Investigación en Ciberseguridad), June 2016, Granada (Spain).
  8. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Constructing and decoding a class of convolutional codes, in XIII Non-Commutative Algebra days, June 2016, Cádiz (Spain). slides
  9. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Separable automorphisms on matrix algebras over finite field extensions: applications to ideal codes., in the 40th International Symposium on Symbolic and Algebraic Computation (ISSAC 2015), July 2015, Bath (England). slides
  10. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Cyclic convolutional codes over separable extensions, in the IV Castle Meeting on Coding Theory and Applications, September 2014, Palmela Castle (Portugal). slides
  11. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, On isomorphisms of modules over non-commutative PDI, in the 39th International Symposium on Symbolic and Algebraic Computation (ISSAC 2014), July 2014, Kobe (Japan). slides
  12. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, A similarity test for Ore polynomials, in the XIV Encuentro de Álgebra Computacional y Aplicaciones (EACA 2014), June 2014, Barcelona (Spain). slides
  13. O. Cortadellas, J. López Peña and G. Navarro, Prime fuzzy ideals over noncommutative rings, in the XIII Encuentro de Álgebra Computacional y Aplicaciones (EACA 2012), June 2012, Alcalá de Henares (Spain). slides
  14. O. Cortadellas, F. J. Lobillo and G. Navarro, Prime fuzzy ideals over noncommutative rings, in XI Jornadas de Teoría de Anillos, May 2012, Granada (Spain). slides
  15. O. Cortadellas, J. López Peña and G. Navarro, Factorization structures with a 2-dimensional factor, in The First International Conference on Mathematics and Statistics, March 2010, Sharjah (United Arab Emirates). slides
  16. O. Cortadellas, J. López Peña and G. Navarro, Quantum duplicates of algebras, in the Journèe d'Algèbre, March 2008, Tetouan (Morocco). slides
  17. J. Gómez-Torrecillas and G. Navarro, Serial coalgebras and their valued Gabriel quivers, in the International Conference on Noncommutative Rings and Geometry, September 2007, Almería (Spain). slides
  18. G. Navarro, Localization in coalgebras and applications to their representation theory, in the XII International Conference on Representation of Algebras (ICRA12), August 2007, Torun (Poland). slides
  19. J. López-Peña and G. Navarro, On the classification and properties of noncommutative duplicates, in the XVI International Colloquium on Integrable Systems and Quantum Symmetries (ISQS-16), June 2007, Prague (Czech Republic). slides
  20. G. Navarro, Simple and injective comodules and localization in coalgebras, in the New techniques in Hopf algebras and graded ring theory international conference, September 2006, Brussels (Belgium). slides
  21. P. Jara, L. Merino and G. Navarro, Localization and comodule types of coalgebras, in the Algebras and Coalgebras Conferences: Tools for Geometry, Physics and Computer Science, March 2006, Cairo (Egypt). slides
  22. P. Jara, L. Merino, G. Navarro and J. F. Ruíz, On stable localizations of coalgebras, in the Congreso Internacional Mediterraneo de Matemáticas (CIMMA '05), June 2005, Almería (Spain). slides
  23. P. Jara, L. Merino and G. Navarro, Localización y teoría de representación de coálgebras, in the Seminario de Álgebra No Conmutativa, May 2005, Almuñecar (Spain). slides
  24. P. Jara, L. Merino and G. Navarro, Representación de coálgebras, in the VIII Jornadas de Teoría de Anillos, February 2004, Oviedo (Spain). slides

Teaching (23-24)

Modelos de Computación

5º semestre, Grado en Ingeniería Informática
  • Prácticas DGIM A2: Miércoles 15:30--17:30, 1.1
  • Prácticas DGIM A1: Viernes 15:30--17:30, 1.4
  • Prácticas GII A2: Miércoles 17:30--19:30, 1.2
  • Prácticas GII A3: Viernes 17:30--19:30, 1.3
  • Contenidos: Web de PRADO

Lógica y Método Discretos

2º semestre, Grado en Ingeniería Informática
  • Teoría B: Martes (10:30--11:30, 0.6) y Viernes (11:30--13:30, 0.6)
  • Prácticas B2: Martes (11:30--12:30, 2.3)
  • Prácticas B3: Lunes (11:30--12:30, 0.6)
  • Teoría E: Martes (17:30--18:30, 0.3) y Miércoles (17:30--19:30, 0.3)
  • Contenidos: Web de PRADO

Tratamiento Inteligente de Datos

1º semestre, Master Universitario en Ingeniería Informática
  • Prácticas TID2: Martes 19:00--20:30, 3.3
  • Contenidos: Web de PRADO

Others

  1. Curso de Linux. Introducción al SO Linux

Contact Details

Address: Escuela Técnica Superior de Ingenierías Informática y de Telecomunicaciones.
                    C/ Periodista Daniel Saucedo Aranda, s/n
                    18071, Granada, España.
Phone: --
Fax: --
E-Mail: gnavarro@ugr.es
E-Mail: gnavarro@decsai.ugr.es