Full list of publications

  1. A. Mayora-Cebollero, J. A. Jover-Galtier, F. Drubi, S. Ibañez, Á. Lozano Rojo, C. Mayora-Cebollero and R. Barrio. Almost synchronization phenomena in the two and three coupled Brusselator systems , Physica D: Nonlinear Phenomena 472 (2025) 134457. doi 10.1016/j.physd.2024.134457
  2. S. Serrano, R. Barrio, Á. Lozano Rojo, A. Mayora-Cebollero and R. Vigara Benito. Coupling of neurons favors the bursting behavior and the predominance of the tripod gait, Chaos, Solitons & Fractals 184 (2024) 114928. doi 10.1016/j.chaos.2024.114928
  3. Á. Lozano Rojo, R. Vigara Benito, R. Barrio and C. Mayora-Cebollero. Dominant patterns in small directed bipartite networks: ubiquitous generalized tripod gait , Nonlinear Dynamics 112 (2024) 15549–15565. doi 10.1007/s11071-024-09830-2
  4. C. Mayora-Cebollero, A. Mayora-Cebollero, Á. Lozano Rojo and R. Barrio. Full Lyapunov Exponents spectrum with Deep Learning from single-variable time series , arXiv (2024).
  5. H. Kitajima, T. Yazawa and R. Barrio. Fast-slow analysis and bifurcations in the generation of the early afterdepolarization phenomenon in a realistic mathematical human ventricular myocyte model , Chaos: An Interdisciplinary Journal of Nonlinear Science 34 12 (2024).
  6. C. Mayora-Cebollero, A. Mayora-Cebollero, Á. Lozano and R. Barrio. Full Lyapunov exponents spectrum with Deep Learning from single-variable time series , Physica D: Nonlinear Phenomena (2024) 134510.
  7. R. Barrio, S. Ibáñez and L. Pérez. Exploring the geometry of the bifurcation sets in parameter space , Scientific Reports 14 1 (2024) 10900.
  8. S. Serrano, R. Barrio, Á. Martínez-Rubio, J. Belmonte-Beitia and V. M. Pérez-García. Understanding the role of B cells in CAR T-cell therapy in leukemia through a mathematical model, Chaos: An Interdisciplinary Journal of Nonlinear Science 34 8 (2024) 083142. doi 10.1063/5.0206341
  9. R. Barrio, J. A Jover-Galtier, A. Mayora-Cebollero, C. Mayora-Cebollero and S. Serrano. Synaptic dependence of dynamic regimes when coupling neural populations , Physical Review E 109 1 (2024) 6337.
  10. F. Drubi, A. Mayora-Cebollero, C. Mayora-Cebollero, S. Ibáñez, J. A. Jover-Galtier, Á. Lozano Rojo, L. Pérez and R. Barrio. Connecting chaotic regions in the Coupled Brusselator System, Chaos, Solitons & Fractals 169 (2023) 113240. doi 10.1016/j.chaos.2023.113240
  11. C. Sáenz-Royo and Á. Lozano-Rojo. Authoritarianism versus participation in innovation decisions, Technovation 124 (2023) 102741. doi 10.1016/j.technovation.2023.102741
  12. R. Barrio, S. Ibañez, J. A. Jover-Galtier, Á. Lozano Rojo, M. Á. Martínez, A. Mayora-Cebollero, C. Mayora-Cebollero, L. Pérez, S. Serrano and R. Vigara Benito. Dynamics of excitable cells: spike-adding phenomena in action, SeMA Journal (2023). doi 10.1007/s40324-023-00328-2
  13. R. Barrio, Á. Lozano Rojo, A. Mayora-Cebollero, C. Mayora-Cebollero, A. Miguel, A. Ortega, S. Serrano and R. Vigara Benito. Deep Learning for Chaos Detection, Chaos 33 7 (2023) 30310. doi 10.1063/5.0143876
  14. R. Barrio, Á. Lozano, A. Mayora-Cebollero, C. Mayora-Cebollero, A. Miguel, A. Ortega, S. Serrano and R. Vigara. Deep learning for chaos detection , Chaos: An Interdisciplinary Journal of Nonlinear Science 33 7 (2023).
  15. R. Barrio, J. A. Jover-Galtier, MA Martínez, L. Pérez and S Serrano. Mathematical birth of Early Afterdepolarizations in a cardiomyocyte model , Mathematical Biosciences 366 (2023) 109088.
  16. C. Li, R. Barrio, X. Xiao, P. Du, H. Jiang, Z. Quan and K. Li. PACF: A precision-adjustable computational framework for solving singular values , Applied Mathematics and Computation 440 (2023) 127611.
  17. F. Alcalde Cuesta, G. Guerberoff and Á. Lozano Rojo. Bernoulli and binomial proliferation on evolutionary graphs, Journal of Theoretical Biology 534 (2022) 110942. doi 10.1016/j.jtbi.2021.110942
  18. R. Barrio, M Á. Martínez, S. Serrano and E. Pueyo. Dynamical mechanism for generation of arrhythmogenic early afterdepolarizations in cardiac myocytes: Insights from in silico electrophysiological models , Physical Review E 106 2 (2022) 10498.
  19. A. R Nieto, J. M Seoane, R. Barrio and M. AF Sanjuán. A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering , Nonlinear Dynamics 109 2 (2022) 1123–1133.
  20. R. Barrio, Á. Lozano Rojo, M. Martínez, M. Rodríguez and S. Serrano. Routes to tripod gait movement in hexapods, Neurocomputing 461 (2021) 679–695. doi 10.1016/j.neucom.2020.06.151
  21. F. Alcalde, Á. Lozano Rojo and M. Martínez. Free minimal actions of solvable Lie groups which are not affable, Proceedings of the American Mathematical Society 149 6 (2021) 2679–2691. doi 10.1090/proc/15365
  22. C. Sáenz, V. Salas-Fumás and Á. Lozano Rojo. Authority and consensus in group decision making with fallible individuals, Decision Support Systems (2021) 113670. doi 10.1016/j.dss.2021.113670
  23. C. Li, X. Xiao, P. Du, H. Jiang, R. Barrio, Z. Quan and K. Li. A high-precision dqds algorithm , In , 2021.
  24. K. He, R. Barrio, L. Chen, H. Jiang, J. Liu, T. Gu and J. Qi. A Class of Fast and Accurate Multi-layer Block Summation and Dot Product Algorithms , In , 2021.
  25. R. Barrio, S Coombes, M Desroches, F Fenton, S Luther and E Pueyo. Excitable dynamics in neural and cardiac systems, Communications in Nonlinear Science and Numerical Simulation 86 (2020) 105275.
  26. R. Barrio, S. Ibáñez and L. Pérez. Homoclinic organization in the Hindmarsh–Rose model: A three parameter study, Chaos: An Interdisciplinary Journal of Nonlinear Science 30 5 (2020) 22106.
  27. R. Barrio, M. Á. Martínez, L. Pérez and E Pueyo. Bifurcations and Slow-Fast Analysis in a Cardiac Cell Model for Investigation of Early Afterdepolarizations, Mathematics 8 6 (2020) 880.
  28. R. Barrio and D Wilczak. Distribution of stable islands within chaotic areas in the non-hyperbolic and hyperbolic regimes in the Hénon–Heiles system, Nonlinear Dynamics 102 1 (2020) 403–416.
  29. MP de Carvalho, R. Barrio, A. Rodrigues and ML Castro. Experimentally accessible orbits near a Bykov cycle, International Journal of Bifurcation and Chaos 30 10 (2020) 2030030.
  30. D. Arnas and M. Rodríguez. Range searching in multidimensional databases using navigation metadata, Applied Mathematics and Computation 386 (2020) 125510. doi 10.1016/j.amc.2020.125510
  31. R. Barrio, Á. Lozano, M. Rodríguez and S. Serrano. Numerical detection of patterns in CPGs: Gait patterns in insect movement, Communications in Nonlinear Science and Numerical Simulation 82 (2020) 105047. doi 10.1016/j.cnsns.2019.105047
  32. R. Barrio, S. Ibáñez, L. Pérez and S. Serrano. Spike-adding structure in fold/hom bursters, Communications in Nonlinear Science and Numerical Simulation 83 (2020) 105100. doi 10.1016/j.cnsns.2019.105100
  33. R. Barrio, M. Á. Martínez, L. Pérez and E Pueyo. Bifurcations and Slow-Fast Analysis in a Cardiac Cell Model for Investigation of Early Afterdepolarizations, Mathematics 8 6 (2020) 880. doi 10.3390/math8060880
  34. T Sun, R. Barrio, H Jiang and L Cheng. Convergence rates of accelerated proximal gradient algorithms under independent noise, Numerical Algorithms 81 2 (2019) 631–654.
  35. T Sun, R. Barrio, M. Rodríguez and H Jiang. Inertial nonconvex alternating minimizations for the image deblurring, IEEE Transactions on Image Processing 28 12 (2019) 6211–6224.
  36. R. Barrio. “Brainland” vs. “flatland”: How many dimensions do we need in brain dynamics?: Comment on the paper “The unreasonable effectiveness of small neural ensembles in high-dimensional brain” by Alexander N. Gorban et al, Physics of life reviews 29 (2019) 108–110.
  37. X Zhang, R. Barrio, M. Á. Martínez, H Jiang and L Cheng. Bregman proximal gradient algorithm with extrapolation for a class of nonconvex nonsmooth minimization problems, IEEE Access 7 (2019) 126515–126529.
  38. P Marziani, A del Olmo, M. Á. Martínez, GM Stirpe, CA Negrete, D Dultzin, M D’onofrio, E Bon and N Bon. Black hole mass estimates in quasars. A comparative analysis of high- and low-ionization lines, Astronomy & Astrophysics 627 (2019) A88.
  39. Á. Lozano Rojo and R. Vigara Benito. The triple point spectrum of closed orientable 3-manifolds, Mediterranean Journal of Mathematics 16 (2019) 71. doi 10.1007/s00009-019-1340-z
  40. T Sun, R. Barrio, M. Rodríguez and H Jiang. Inertial nonconvex alternating minimizations for the image deblurring, IEEE Transactions on Image Processing 28 12 (2019) 6211–6224.
  41. T. Sun, R. Barrio, L. Cheng and H. Jiang. Precompact convergence of the nonconvex Primal–Dual Hybrid Gradient algorithm, Journal of Computational and Applied Mathematics 330 (2018) 15–27.
  42. R. Barrio, P Du, H Jiang and S. Serrano. ORTHOPOLY: A library for accurate evaluation of series of classical orthogonal polynomials and their derivatives, Computer Physics Communications 231 2 (2018) 146–162.
  43. F. Alcalde Cuesta, P. González Sequeiros and Á. Lozano Rojo. Evolutionary regime transitions in structured populations, PLOS ONE 13 11 (2018) e0200670. doi 10.1371/journal.pone.0200670
  44. Á. Lozano Rojo and R. Vigara Benito. Banchoff’s sphere and branched covers over the trefoil, RACSAM 112 3 (2018) 751–765. doi 10.1007/s13398-017-0477-5
  45. D. Wilczak and R. Barrio. Systematic computer-assisted proof of branches of stable elliptic periodic orbits and surrounding invariant tori, SIAM Journal on Applied Dynamical Systems 16 3 (2017) 1618–1649.
  46. R. Barrio, S. Ibáñez and L. Pérez. Hindmarsh–Rose model: Close and far to the singular limit, Physics Letters A 381 6 (2017) 597–603.
  47. P. Du, R. Barrio, H. Jiang and L. Cheng. Accurate Quotient-Difference algorithm: error analysis, improvements and applications, Applied Mathematics and Computation 309 (2017) 245–271.
  48. F. Alcalde Cuesta, Á. Lozano Rojo and A. C. Vázquez. Insertion-tolerance and repetitiveness of random graphs, Stochastics & Dynamics 17 3 (2017) 1750023. doi 10.1142/S021949371750023X
  49. F. Alcalde Cuesta, P. González Sequeiros and Á. Lozano Rojo. Supressors of selection, Plos One 12 7 (2017) e0180549. doi 10.1371/journal.pone.018054910.1371
  50. F. Alcalde Cuesta, P. González Sequeiros and Á. Lozano Rojo. A method for validating Rent’s rule for technological and biological networks, Scientific Reports 7 (2017) 5378. doi 10.1038/s41598-017-05670-w
  51. F. Alcalde Cuesta, P. González Sequeiros, Á. Lozano Rojo and R. Vigara Benito. An accurate database of the fixation probabilities of all undirected graphs of order 10 or less, In Bioinformatics and Biomedical Engineering IWBBIO2017, Lecture Notes in Computer Science 10209, 2017. doi 10.1007/978-3-319-56154-7_20.
  52. JW Sulentic, A del Olmo, P Marziani, M. Á. Martínez, M D’onofrio, D Dultzin, J Perea, ML Martínez-Aldama, CA Negrete and GM Stirpe. What does CIVλ1549 tell us about the physical driver of the Eigenvector quasar sequence?, Astronomy & Astrophysics 608 (2017) A122.
  53. ML Martínez-Aldama, A del Olmo, P Marziani, CA Negrete, D Dultzin and M. Á. Martínez. HE0359-3959: an extremely radiating quasar, Frontiers in Astronomy and Space Sciences 4 (2017) 29.
  54. T. Sun, R. Barrio, H. Jiang and L. Cheng. Local linear convergence of a primal-dual algorithm for the augmented convex models, Journal of Scientific Computing 69 3 (2016) 1301–1315.
  55. R. Barrio. Theory and Applications of the Orthogonal Fast Lyapunov Indicator (OFLI and OFLI2) Methods, In Chaos Detection and Predictability, 2016.
  56. D. Wilczak, S. Serrano and R. Barrio. Coexistence and Dynamical Connections between Hyperchaos and Chaos in the 4D Rössler System: A Computer-Assisted Proof, SIAM Journal on Applied Dynamical Systems 15 1 (2016) 356–390. doi 10.1137/15M1039201
  57. H. Jiang, S. Graillat, R. Barrio and C. Yang. Accurate, validated and fast evaluation of elementary symmetric functions and its application, Applied Mathematics and Computation 273 (2016) 1160–1178.
  58. Á. Dena, A. Abad and R. Barrio. Efficient computational approaches to obtain periodic orbits in Hamiltonian systems: application to the motion of a lunar orbiter, Celestial Mechanics and Dynamical Astronomy 124 1 (2016) 51–71.
  59. M. Á. Marco-Buzunariz and M. Rodríguez. SIROCCO: A Library for Certified Polynomial Root Continuation, In International Congress on Mathematical Software, 2016.
  60. O. Tapia, M. Escudero, Á. Lozano Rojo, J. Anzano and E. Mantilla. New classification scheme for ozone monitoring stations based on frequency distribution of hourly data, Science of the Total Environment 544 15 (2016) 1–9. doi 10.1016/j.scitotenv.2015.11.081
  61. Á. Lozano Rojo and R. Vigara Benito. Representing knots by filling Dehn spheres, Journal of Knot Theory and its Ramifications 26 (2016) 1650018. doi 10.1142/S0218216516500188
  62. R. Vigara Benito and Á. Lozano Rojo. Representing 3-Manifolds by Filling Dehn Surfaces, Series on Knots and Everything 58. World Scientific, 2016. 978-981-4725-48-4
  63. F. Alcalde Cuesta, P. González Sequeiros and Á. Lozano Rojo. Exploring the topological sources of robustness against invasion in biological and technological networks, Scientific Reports 6 (2016) 20666. doi 10.1038/srep20666
  64. M. Escudero, Á. Lozano Rojo, J. Hierro, O. Tapia, J. del Valle, A. Alastuey, T Moreno, J. Anzano and X. Querol. Assessment of the variability of atmospheric pollution in National Parks of mainland Spain, Atmospheric Environment 132 (2016) 332–344. doi 10.1016/j.atmosenv.2016.03.006
  65. Á. Lozano Rojo, M. Rodríguez Rodríguez and R. Barrio. Control strategies of 3-cell Central Pattern Generator via global stimuli, Scientific Reports 6 (2016) 23622. doi 10.1038/srep23622
  66. V. Salas-Fumás, C. Sáenz and Á. Lozano Rojo. Organisational Structure and Performance of Consensus Decisions through Mutual Influences: A Computer Simulation Approach, Decision Support Systems 86 (2016) 61–72. doi 10.1016/j.dss.2016.03.008
  67. P Marziani, M. Á. Martínez, J W Sulentic, A del Olmo, G M Stirpe and D Dultzin. The most powerful quasar outflows as revealed by the Civλ1549 resonance line, Astrophysics and Space Science 361 (2016) 29. doi 10.1007/s10509-015-2611-1
  68. P Marziani, J W Sulentic, G M Stirpe, D Dultzin, A del Olmo and M. Á. Martínez. Blue outliers among intermediate redshift quasars, Astrophysics and Space Science 361 (2016) 3. doi 10.1007/s10509-015-2590-2
  69. R. Barrio. Taylor Series Methods, Encyclopedia of Applied and Computational Mathematics (2015) 1465–1470.
  70. R. Barrio, M. Rodríguez, S. Serrano and A. Shilnikov. Mechanism of quasi-periodic lag jitter in bursting rhythms by a neuronal network, EPL (Europhysics Letters) 112 3 (2015) 38002. doi 10.1209/0295-5075/112/38002
  71. R. Barrio, M. Á. Martínez, S. Serrano and D. Wilczak. When chaos meets hyperchaos: 4D Rössler model, Physics Letters A 379 38 (2015) 2300–2305.
  72. A. Abad, R. Barrio, M Marco-Buzunariz and M. Rodríguez. Automatic implementation of the numerical Taylor series method: a Mathematica and Sage approach, Applied Mathematics and Computation 268 (2015) 227–245.
  73. R. Barrio, Á. Dena and W. Tucker. A database of rigorous and high-precision periodic orbits of the Lorenz model, Computer Physics Communications 194 (2015) 76–83.
  74. M. Rodríguez, F. Blesa and R. Barrio. OpenCL parallel integration of ordinary differential equations: Applications in computational dynamics, Computer Physics Communications 192 (2015) 228–236.
  75. R. Barrio, M. Lefranc, M. Á. Martínez and S. Serrano. Symbolic dynamical unfolding of spike-adding bifurcations in chaotic neuron models, EPL (Europhysics Letters) 109 2 (2015) 20002.
  76. R. Barrio, M. Rodríguez, S. Serrano and A. Shilnikov. Mechanism of quasi-periodic lag jitter in bursting rhythms by a neuronal network, EPL (Europhysics Letters) 112 3 (2015) 38002.
  77. A. Abad, R. Barrio, M. Á. Marco-Buzunariz and M. Rodríguez. Automatic implementation of the numerical Taylor series method: a Mathematica and Sage approach, Applied Mathematics and Computation 268 (2015) 227–245.
  78. M. Rodríguez, F. Blesa and R. Barrio. OpenCL parallel integration of ordinary differential equations: Applications in computational dynamics, Computer Physics Communications 192 (2015) 228–236.
  79. Á. Lozano Rojo and R. Vigara Benito. On the subadditivity of Montesinos complexity of closed orientable 3-manifolds, RACSAM 109 2 (2015) 267–279. doi 10.1007/s13398-014-0179-1
  80. F. Alcalde Cuesta, P. González Sequeiros and Á. Lozano Rojo. Fast and asymptotic computation of the fixation probability for Moran processes on graphs, BioSystems 129 (2015) 25–35. doi 10.1016/j.biosystems.2015.01.007
  81. P Marziani, J W Sulentic, C A Negrete, D Dultzin, A del Olmo, M. Á. Martínez, T. Zwitter and R. Bachev. UV spectral diagnostics for low redshift quasars: Estimating physical conditions and radius of the broad line region, Astrophysics and Space Science 356 2 (2015) 339–346. doi 10.1007/s10509-014-2136-z
  82. J W Sulentic, M. Á. Martínez, P Marziani, A del Olmo, G M Stirpe, S Zamfir and I Plauchu-Frayn. 3C 57 as an atypical radio-loud quasar: Implications for the radio-loud/radio-quiet dichotomy, Monthly Notices of the Royal Astronomical Society 450 2 (2015). doi 10.1093/mnras/stv710
  83. T. Xing, R. Barrio and A. Shilnikov. Symbolic quest into homoclinic chaos, International Journal of Bifurcation and Chaos 24 8 (2014) 1440004.
  84. R. Barrio, M. Á. Martínez, S. Serrano and A. Shilnikov. Macro-and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons, Chaos: An Interdisciplinary Journal of Nonlinear Science 24 2 (2014) 023128.
  85. R. Barrio, F. Blesa and S. Serrano. Unbounded dynamics in dissipative flows: Rössler model, Chaos: An Interdisciplinary Journal of Nonlinear Science 24 2 (2014) 024407.
  86. F. Blesa, J. M Seoane, R. Barrio and M. AF Sanjuán. Effects of periodic forcing in chaotic scattering, Physical Review E 89 4 (2014) 042909.
  87. R. Barrio and M. Rodríguez. Systematic Computer Assisted Proofs of periodic orbits of Hamiltonian systems, Communications in Nonlinear Science and Numerical Simulation 19 8 (2014) 2660–2675.
  88. T. Xing, J. Wojcik, R. Barrio and A. Shilnikov. Symbolic toolkit for chaos explorations, In International Conference on Theory and Application in Nonlinear Dynamics (ICAND 2012), 2014.
  89. R. Barrio and M. Rodríguez. Systematic Computer Assisted Proofs of periodic orbits of Hamiltonian systems, Communications in Nonlinear Science and Numerical Simulation 19 8 (2014) 2660–2675.
  90. M. Escudero, Á. Lozano Rojo, J. Hierro, J. del Valle and E. Mantilla. Urban influence on increasing ozone concentrations in a characteristic Mediterranean agglomeration, Atmospheric Environment 99 (2014) 322–332. doi 10.1016/j.atmosenv.2014.09.061
  91. R. Barrio, F. Blesa, S. Serrano and A. Shilnikov. Homoclinic Spirals: Theory and Numerics, In Progress and Challenges in Dynamical Systems, 2013.
  92. M. Á. Martínez, R. Barrio and S. Serrano. Finding periodic orbits in the Hindmarsh-Rose neuron model, In Progress and Challenges in Dynamical Systems, 2013.
  93. H. Jiang, S. Graillat and R. Barrio. Accurate and fast evaluation of elementary symmetric functions, In 21st IEEE Symposium on Computer Arithmetic (ARITH), 2013.
  94. H. Jiang, H. Li, L. Cheng, R. Barrio, C. Hu and X. Liao. Accurate, Validated and Fast Evaluation of Bézier Tensor Product Surfaces., Reliable Computing 18 (2013) 55–72.
  95. R. Barrio, H. Jiang and S. Serrano. A general condition number for polynomials, SIAM Journal on Numerical Analysis 51 2 (2013) 1280–1294. doi 10.1137/120864581
  96. H. Jiang, S. Graillat and R. Barrio. Accurate computing elementary symmetric functions, ACM Communications in Computer Algebra 46 3/4 (2013) 102–103.
  97. A. Shilnikov, L. Shilnikov and R. Barrio. Symbolic dynamics and spiral structures due to the saddle-focus bifurcations, In Chaos, CNN, Memristors and Beyond: A Festschrift for Leon Chua. Edited by Adamatzky Andrew et al., 2013.
  98. Á. Lozano Rojo and O. Lukina. Suspensions of Bernoulli shifts, Dynamical Systems: An international Journal 28 4 (2013) 551–566. doi 10.1080/14689367.2013.828680
  99. R. Barrio and A. Elipe. Dynamics and Astrometry of Natural and Artificial Celestial Bodies, In Proceedings of IAU Colloquium 165 Poznań, Poland July 1–5, 1996, 2012.
  100. S. Piasecki, R. Barrio and F. Blesa. Symmetry breaking bifurcations in a D4 symmetric Hamiltonian system, Monografías Matemáticas García de Galdeano 37 (2012) 189–196.
  101. D. H Bailey, R. Barrio and J. M Borwein. High-precision computation: Mathematical physics and dynamics, Applied Mathematics and Computation 218 20 (2012) 10106–10121.
  102. F. Blesa, J. M Seoane, R. Barrio and M. AF Sanjuan. To escape or not to escape, that is the question—perturbing the Hénon–Heiles Hamiltonian, International Journal of Bifurcation and Chaos 22 6 (2012) 1230010.
  103. R. Barrio, F. Blesa and S. Serrano. Behavior patterns in multiparametric dynamical systems: Lorenz model, International Journal of Bifurcation and Chaos 22 6 (2012) 1230019.
  104. R. Barrio, F. Blesa and S. Serrano. Topological changes in periodicity hubs of dissipative systems, Physical review letters 108 21 (2012) 214102. doi 10.1103/PhysRevLett.108.214102
  105. Á. Dena, M. Rodríguez, S. Serrano and R. Barrio. High-precision continuation of periodic orbits, Abstract and Applied Analysis 2012 (2012) 716024. doi 10.1155/2012/716024
  106. R. Barrio, A. Shilnikov and L. Shilnikov. Kneadings, symbolic dynamics and painting Lorenz chaos, International Journal of Bifurcation and Chaos 22 4 (2012) 1230016. doi 10.1142/S0218127412300169
  107. M. Rodríguez and R. Barrio. Reducing rounding errors and achieving Brouwerʼs law with Taylor Series Method, Applied Numerical Mathematics 62 8 (2012) 1014–1024. doi 10.1016/j.apnum.2012.03.008
  108. F. Blesa, S. Piasecki, Á. Dena and R. Barrio. Connecting symmetric and asymmetric families of periodic orbits in squared symmetric Hamiltonians, International Journal of Modern Physics C 23 2 (2012) 1250014.
  109. R. Barrio, M. Rodríguez and F. Blesa. Computer-assisted proof of skeletons of periodic orbits, Computer Physics Communications 183 1 (2012) 80–85.
  110. S. Serrano, R. Barrio, A Dena and M Rodríguez. Crisis curves in nonlinear business cycles, Communications in nonlinear Science and Numerical simulation 17 2 (2012) 788–794.
  111. R. Barrio, M. Rodríguez and F. Blesa. Computer-assisted proof of skeletons of periodic orbits, Computer Physics Communications 183 1 (2012) 80–85.
  112. S. Serrano, R. Barrio, Á. Dena and M. Rodríguez. Crisis curves in nonlinear business cycles, Communications in nonlinear Science and Numerical simulation 17 2 (2012) 788–794.
  113. A. Abad, R. Barrio, F. Blesa and M. Rodríguez. Algorithm 924: TIDES, a Taylor series integrator for differential equations, ACM Transactions on Mathematical Software (TOMS) 39 1 (2012) 5. doi 10.1145/2382585.2382590
  114. H. Jiang, R. Barrio, X. Liao and L. Cheng. Accurate evaluation algorithm for bivariate polynomial in Bernstein–Bézier form, Applied Numerical Mathematics 61 11 (2011) 1147–1160.
  115. R. Barrio, M. Rodríguez, A. Abad and S. Serrano. Uncertainty propagation or box propagation, Mathematical and Computer Modelling 54 11 (2011) 2602–2615. doi 10.1016/j.mcm.2011.06.036
  116. H. Li, H. Jiang, R. Barrio, X. Liao, L. Cheng and F. Su. Incremental manifold learning by spectral embedding methods, Pattern Recognition Letters 32 10 (2011) 1447–1455.
  117. R. Barrio, F. Blesa, A. Dena and S. Serrano. Qualitative and numerical analysis of the Rössler model: Bifurcations of equilibria, Computers & Mathematics with Applications 62 11 (2011) 4140–4150.
  118. A. Abad, R. Barrio and A. Dena. Computing periodic orbits with arbitrary precision, Physical review E 84 1 (2011) 016701. doi 10.1103/PhysRevE.84.016701
  119. R. Barrio, F. Blesa, S. Serrano and A. Shilnikov. Global organization of spiral structures in biparameter space of dissipative systems with Shilnikov saddle-foci, Physical Review E 84 3 (2011) 035201.
  120. H. Jiang, R. Barrio, H. Li, X. Liao, L. Cheng and F. Su. Accurate evaluation of a polynomial in Chebyshev form, Applied Mathematics and Computation 217 23 (2011) 9702–9716.
  121. R. Barrio and A. Shilnikov. Parameter-sweeping techniques for temporal dynamics of neuronal systems: case study of Hindmarsh-Rose model, The Journal of Mathematical Neuroscience 1 (2011) 6. doi 10.1186/2190-8567-1-6
  122. R. Barrio, M. Rodríguez, A. Abad and F. Blesa. Breaking the limits: the Taylor series method, Applied mathematics and computation 217 20 (2011) 7940–7954. doi 10.1016/j.amc.2011.02.080
  123. F. Alcalde Cuesta, Á. Lozano Rojo and M. Macho-Stadler. Transversely Cantor laminations as inverse limits, Proceedings of the AMS 139 7 (2011) 2615–2630. doi 10.1090/S0002-9939-2010-10665-2
  124. Á. Lozano Rojo. An example of non-uniquely ergodic lamination, Ergod. Th. & Dynam. Sys. 31 2 (2011) 449–457. doi 10.1017/S0143385710000064
  125. M. Á. Martínez, A del Olmo, J Perea, R Coziol and P Focardi. The influence of local environment on the emergence of AGN activity in galaxies, In Highlights of Spanish Astrophysics VI, 2011.
  126. O González-Martín, I Papadakis, V Braito, J Masegosa, I Márquez, S Mateos, J A Acosta-Pulido, M. Á. Martínez, J Ebrero, P Esquej, P O’Brien, J Tueller, R S Warwick and M G Watson. Suzaku observation of the LINER NGC 4102, Astronomy and Astrophysics 527 (2011) A142. doi 10.1051/0004-6361/201016097
  127. R. Barrio, F. Blesa and S. Serrano. Bifurcations and chaos in Hamiltonian systems, International Journal of Bifurcation and Chaos 20 5 (2010) 1293–1319. doi 10.1142/S0218127410026496
  128. R. Barrio, J. M. Peña and T. Sauer. Three term recurrence for the evaluation of multivariate orthogonal polynomials, Journal of Approximation Theory 162 2 (2010) 407–420.
  129. M. Á. Martínez, A del Olmo, R Coziol, J Perea and P Focardi. Relationship between AGNs and Environment. Deficiency of BLAGNs in Compact Groups, In Galaxies in Isolation: Exploring Nature Versus Nurture, proceedings of a conference held 12 to 15 May 2009 in Granada, Spain. Edited by Lourdes Verdes-Montenegro, Ascencíon del Olmo, and Jack Sulentic, ASP Conference Series 421, 2010.
  130. A del Olmo, M. Á. Martínez, J Perea, R Coziol and P Focardi. AGNs and Environment: AGN Population and Deficiency of BLAGNs in Compact Groups of Galaxies, In Accretion and Ejection in AGN: a Global View. Proceedings of a conference held June 22-26, 2009 in Como, Italy. Edited by Laura Maraschi, Gabriele Ghisellini, Roberto Della Ceca, and Fabrizio Tavecchio, ASP Conference Series 427, 2010.
  131. M. Á. Martínez, A del Olmo, R Coziol and J Perea. AGN population in hickson compact groups. I. Data and nuclear activity classification, Astronomical Journal 139 (2010) 1199–1211. doi 10.1088/0004-6256/139/3/1199
  132. R. Barrio and S. Serrano. Sobre el método de Variación de los Parámetros, Boletín ROA 1 (2009) 25–31.
  133. R. Barrio, F. Blesa and S. Serrano. Periodic, escape and chaotic orbits in the Copenhagen and the (n+1)-body ring problems, Communications in Nonlinear Science and Numerical Simulation 14 5 (2009) 2229–2238.
  134. R. Barrio and S. Serrano. Bounds for the chaotic region in the Lorenz model, Physica D: Nonlinear Phenomena 238 16 (2009) 1615–1624.
  135. R. Barrio, F. Blesa and S. Serrano. Bifurcations and safe regions in open Hamiltonians, New Journal of Physics 11 5 (2009) 053004.
  136. R. Barrio, F. Blesa and S. Serrano. Qualitative analysis of the Rössler equations: Bifurcations of limit cycles and chaotic attractors, Physica D: Nonlinear Phenomena 238 13 (2009) 1087–1100. doi j.physd.2009.03.010
  137. R. Barrio, W. Borczyk and S Breiter. Spurious structures in chaos indicators maps, Chaos, Solitons & Fractals 40 4 (2009) 1697–1714.
  138. R. Barrio and F. Blesa. Systematic search of symmetric periodic orbits in 2DOF Hamiltonian systems, Chaos, Solitons & Fractals 41 2 (2009) 560–582.
  139. F. Alcalde Cuesta, P. Gonzalez Sequeiros and Á. Lozano Rojo. Affability of Euclidean tilings, C. R. Acad. Sci. Paris, Ser. I 347 (2009) 947–952.
  140. F. Alcalde Cuesta, Á. Lozano Rojo and M. Macho-Stadler. Dynamique transverse de la lamination de Ghys-Kenyon, Astérisque 323 (2009) 1–16. arXiv 0809.0772
  141. R. Barrio and S. Serrano. Performance of perturbation methods on orbit prediction, Mathematical and Computer Modelling 48 3 (2008) 594–600.
  142. R. Barrio, F. Blesa and S. Serrano. Fractal structures in the Henon-Heiles hamiltonian, EPL (Europhysics Letters) 82 1 (2008) 10003.
  143. R. Barrio, F. Blesa and S. Serrano. Qualitative analysis of the (N+1)-body ring problem, Chaos, Solitons & Fractals 36 4 (2008) 1067–1088.
  144. Á. Lozano Rojo. Dinámica transversa de laminaciones definidas por grafos repetitivos, Publicaciones del Departamento de Geometría y Topología 112. USC, 2008. 978-84-89390-29-4
  145. M. Á. Martínez, A del Olmo, R Coziol and J Perea. Agn population in compact groups galaxies, Revista Mexicana de Astronomia y Astrofisica: Serie de Conferencias 32 (2008) 164–166.
  146. M. Á. Martínez, A del Olmo, R Coziol and P Focardi. Deficiency of broad-line AGNs in compact groups of galaxies, Astrophysical Journal 678 1 PART 2 (2008) L9–L12. doi 10.1086/588498
  147. A del Olmo, M. Á. Martínez, P Focardi and J Perea. Spectral classification and analysis of nuclear activity in the UZC-compact group sample, Revista Mexicana de Astronomia y Astrofisica: Serie de Conferencias 32 (2008) 174.
  148. R. Barrio, F. Blesa and S. Serrano. Is there chaos in Copenhagen problem?, Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza 30 (2007) 51–65.
  149. R. Barrio Gil, S. Serrano Pastor and F. Blesa Moreno. Evolución paramétrica del sistema de Lorenz, In XX Congreso de Ecuaciones Diferenciales y Aplicaciones. Sevilla, 24-28 de septiembre de 2007, 2007.
  150. R. Barrio and S. Serrano. A three-parametric study of the Lorenz model, Physica D: Nonlinear Phenomena 229 1 (2007) 43–51.
  151. Á. Lozano Rojo. Espacios foliados definidos por grafos, Revista del Seminario Iberoamericano de Matemáticas 3 IV (2007) 21–38.
  152. M. Á. Martínez, A del Olmo, J Perea and R Coziol. Low luminosity activity in Hickson Compact Groups, ESO Astrophysics Symposia 2007 (2007) 163–167. doi 10.1007/978-3-540-71173-5_27
  153. R. Barrio. Painting chaos: OFLI2TT, Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza 28 (2006) 85–94.
  154. R. Barrio, F. Blesa and A Elipe. On the use of chaos indicators in rigid-body motion, The Journal of the Astronautical Sciences 54 3 (2006) 359–368.
  155. R. Barrio and S. Serrano. Modifications of the method of variation of parameters, Computers & Mathematics with Applications 51 3-4 (2006) 451–466.
  156. R. Barrio. Painting chaos: a gallery of sensitivity plots of classical problems, International Journal of Bifurcation and Chaos 16 10 (2006) 2777–2798.
  157. R. Barrio. Sensitivity analysis of ODEs/DAEs using the Taylor series method, SIAM Journal on Scientific Computing 27 6 (2006) 1929–1947. doi 10.1137/030601892
  158. Á. Lozano Rojo. The Cayley foliated space of a graphed pseudogroup, In Proceedings of the XIV Fall Workshop on Geometry and Physics (Bilbao, 2005), Publ. de la RSME 10, 2006.
  159. J Gorosabel, V Larionov, A J Castro-Tirado, S Guziy, L Larionova, A del Olmo, M. Á. Martínez, J Cepa, B Cedré, A De Ugarte Postigo, M Jelínek, O Bogdanov and A LLorente. Detection of optical linear polarization in the SN 2006aj/XRF 060218 non-spherical expansion, Astronomy and Astrophysics 459 3 (2006) L33–L36. doi 10.1051/0004-6361:20066391
  160. M. Á. Martínez, A del Olmo, P Focardi and J Perea. Nuclear activity in UZC compact groups, Proceedings of the International Astronomical Union 2 (2006) 222. doi 10.1017/S1743921306006284
  161. R. Barrio and S. Serrano. Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces II: numerical stability, Journal of computational and applied mathematics 181 2 (2005) 299–320.
  162. R. Barrio and J. M. Peña. Evaluation of the derivative of a polynomial in Bernstein form, Applied mathematics and computation 167 1 (2005) 125–142.
  163. R. Barrio, B Melendo and S. Serrano. Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces I: algorithms, Journal of computational and applied mathematics 181 2 (2005) 280–298.
  164. R. Barrio. Sensitivity tools vs. Poincaré sections, Chaos, Solitons & Fractals 25 3 (2005) 711–726.
  165. R. Barrio. Performance of the Taylor series method for ODEs/DAEs, Applied Mathematics and Computation 163 2 (2005) 525–545. doi 10.1016/j.amc.2004.02.015
  166. R. Barrio, F. Blesa and M Lara. VSVO formulation of the Taylor method for the numerical solution of ODEs, Computers & mathematics with Applications 50 1 (2005) 93–111. doi 10.1016/j.camwa.2005.02.010
  167. J. Delgado and R. Barrio. Trajectories of zeros of Sobolev-Gegengauer orthogonal polynomials, Revista de la Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza 59 (2004) 101–108.
  168. R. Barrio and S. Serrano. High-order recurrences satisfied by classical orthogonal polynomials, Applied mathematics letters 17 6 (2004) 667–670.
  169. R. Barrio. Algorithms for the integration and derivation of Chebyshev series, Applied mathematics and computation 150 3 (2004) 707–717.
  170. R. Barrio and J. M. Peña. Basis conversions among univariate polynomial representations, Comptes Rendus Mathematique 339 4 (2004) 293–298.
  171. R. Barrio, B. Melendo and S. Serrano. Some remarks on the evaluation of linear recurrences, In VII Jornadas Zaragoza-Pau de Matemática Aplicada y estadística: Jaca (Huesca), 17-18 de septiembre de 2001, 2003.
  172. R. Barrio, F. Blesa and M. Lara Coira. High-precision numerical solution of ODE with high-order Taylor methods in parallel, Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza 22 (2003) 67–74.
  173. R. Barrio and P Yalamov. Stability of parallel algorithms for polynomial evaluation, Computers & Mathematics with Applications 46 5-6 (2003) 769–781.
  174. R. Barrio. Compression of almost-periodic data, Applied mathematics and computation 134 2 (2003) 431–444.
  175. R. Barrio and J. Palacián. High-order averaging of eccentric artificial satellites perturbed by the Earth’ potential and air-drag terms, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 459 (2003) 1517–1534.
  176. R. Barrio. A unified rounding error bound for polynomial evaluation, Advances in Computational Mathematics 19 4 (2003) 385–399.
  177. R. Barrio, B Melendo and S. Serrano. On the numerical evaluation of linear recurrences, Journal of computational and applied mathematics 150 1 (2003) 71–86.
  178. R. Barrio and A. Elipe. Compression of Satellite Data, Revista Matemática Complutense 15 1 (2002) 85–100.
  179. R. Barrio. Rounding error bounds for the Clenshaw and Forsythe algorithms for the evaluation of orthogonal polynomial series, Journal of computational and applied mathematics 138 2 (2002) 185–204.
  180. R. Barrio and JM Peña. Numerical evaluation of the p-th derivative of Jacobi series, Applied numerical mathematics 43 4 (2002) 335–357.
  181. R. Barrio. Stability of parallel algorithms to evaluate Chebyshev series, Computers & Mathematics with Applications 41 10-11 (2001) 1365–1377.
  182. R. Barrio and P. Yalamov. Stability analysis of parallel evaluation of finite series of orthogonal polynomials, In International Conference on Numerical Analysis and Its Applications, 2000.
  183. R. Barrio. Construction of seminumerical schemes: Application to the artificial satellite problem, In International Conference on Numerical Analysis and Its Applications, 2000.
  184. R. Barrio. Parallel algorithms to evaluate orthogonal polynomial series, SIAM Journal on Scientific Computing 21 6 (2000) 2225–2239.
  185. R. Barrio. Characterization of low degree A-stable symmetric RK collocation methods, Journal of computational and applied mathematics 111 1 (1999) 1–11.
  186. R. Barrio and J Sabadell. Parallel evaluation of Chebyshev and trigonometric series, Computers & Mathematics with Applications 38 11-12 (1999) 99–106.
  187. R. Barrio. On the A-Stability of Runge–Kutta Collocation Methods Based on Orthogonal Polynomials, SIAM journal on numerical analysis 36 4 (1999) 1291–1303.
  188. R. Barrio, M. Palacios and A. Elipe. Chebyshev collocation methods for fast orbit determination, Applied Mathematics and Computation 99 2-3 (1999) 195–207.
  189. R. Barrio. A matrix analysis of the stability of the Clenshaw algorithm, Extracta mathematicae 13 1 (1998) 21–26.
  190. R. Barrio, A Elipe and M Vallejo. Compression Ephemerides in Attitude Dynamics (AAS 98-207), Advances in the Astronautical Sciences 99 (1998) 1519–1532.
  191. R. Barrio and J. Berges. Perturbation simulations of rounding errors in the evaluation of Chebyshev series, Journal of Universal Computer Science 4 6 (1998) 561–573.
  192. R. Barrio and J. Sabadell. A parallel algorithm to evaluate chebyshev series on a message passing environment, SIAM Journal on Scientific Computing 20 3 (1998) 964–969.
  193. R. Barrio and A. Elipe. Integration of orbital motions with Chebyshev Polynomials, In International Astronomical Union Colloquium, 1997.
  194. R. Barrio and J. Palacian. Semianalytical methods for high eccentric orbits- Zonal harmonics and air drag terms, Spaceflight mechanics 1997 (1997) 331–339.
  195. R. Barrio and J. Palacian. Lie transforms for ordinary differential equations: taking advantage of the Hamiltonian form of terms of the perturbation, International journal for numerical methods in engineering 40 12 (1997) 2289–2300.