Publications

Journal Papers

Dynamics and Learning

  • Martínez-Peña, R. and Ortega, J.-P. [2023] Quantum reservoir computing in finite dimensions. Physical Review E, 107(3), 035306, 0.1103/PhysRevE.107.035306. Paper
  • Gonon, L., Grigoryeva, L., and Ortega, J.-P. [2023] Approximation bounds for random neural networks and reservoir systems. The Annals of Applied Probability, 33(1), 28-69, doi.org/10.1214/22-AAP1806. Paper
  • Ortega, J.-P. and Yin, D. [2023] Expressiveness and structure preservation in learning port-Hamiltonian systems. To appear in the Proceedings of GSI’23. Paper
  • Da Costa, N., Mostajeran, C., and Ortega J.-P. [2023] The Gaussian kernel on the circle and spaces that admit isometric embeddings of the circle. To appear in the Proceedings of GSI’23. Paper
  • Cuchiero, C., Gonon, L., Grigoryeva, L., Ortega, J.-P., and Teichmann, J. [2021] Expressive power of randomized signature. NeurIPS 2021. Paper
  • Grigoryeva, L., and Ortega, J.-P. [2021] Dimension reduction in recurrent networks by canonicalization. Journal of Geometric Mechanics, 13(4): 647-677. doi:10.3934/jgm.2021028. Paper
  • Grigoryeva, L., Hart, A., and Ortega, J.-P. [2021] Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem. Physical Review E, 103, 062204. Paper
  • Cuchiero, C., Gonon, L., Grigoryeva, L., Ortega, J.-P., and Teichmann, J. [2021] Discrete-time signatures and randomness in reservoir computing. IEEE Transactions on Neural Networks and Learning Systems, 33(11):6321-6330. doi: 10.1109/TNNLS.2021.3076777 Paper
  • Gonon, L. and Ortega, J.-P. [2021] Fading memory echo state networks are universal. Neural Networks, 138, 10-13. Paper.
  • Gonon, L., Grigoryeva, L., and Ortega, J.-P. [2020] Risk bounds for reservoir computing. Journal of Machine Learning Research, 21(240), 1-61. Paper
  • Gonon, L., Grigoryeva, L., and Ortega, J.-P. [2020] Memory and forecasting capacities of nonlinear recurrent networks. Physica D, 414, 132721, 1-13. Paper
  • Gonon, L. and Ortega, J.-P. [2020] Reservoir computing universality with stochastic inputs. IEEE Transactions on Neural Networks and Learning Systems, 31(1), 100-112. Paper
  • Grigoryeva, L. and Ortega, J.-P. [2019] Differentiable reservoir computing. Journal of Machine Learning Research, 20(179), 1-62. Paper
  • Grigoryeva, L. and Ortega, J.-P. [2018] Echo state networks are universal. Neural Networks, 108, 495-508. Paper. Poster
  • Grigoryeva, L. and Ortega, J.-P. [2018] Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems. Journal of Machine Learning Research, 19(24), 1-40. Paper
  • Chrétien, S. and Ortega, J.-P. [2018] A simple formula for the Hilbert metric with respect to a sub-Gaussian cone. Mathematics, 6, 35; doi:10.3390/math6030035. Paper
  • Grigoryeva, L., Henriques, J., Larger, L., and Ortega, J.-P. [2016] Nonlinear memory capacity of parallel time-delay reservoir computers in the processing of multidimensional signals. Neural Computation, 28, 1411-1451; doi:10.1162/NECO_a_00845. Paper
  • Grigoryeva, L., Henriques, J., and Ortega, J.-P. [2016] Reservoir computing: information processing of stationary signals. Proceedings of the IEEE International Conference on Computational Science and Engineering.  doi 10.1109/CSE-EUC-DCABES.2016.231. Paper presented with the Best Paper Award. Paper. Award.
  • Grigoryeva, L., Henriques, J., Larger, L., and Ortega, J.-P. [2016] Time-delay reservoir computers and high-speed information processing capacity. Proceedings of the IEEE International Conference on Computational Science and Engineering. doi 10.1109/CSE-EUC-DCABES.2016.230. Paper
  • Grigoryeva, L., Henriques, J., Larger, L., and Ortega, J.-P. [2015] Optimal nonlinear information processing capacity in delay-based reservoir computers. Scientific Reports, 5(12858), 1-11; doi: 10.1038/srep12858. Nature Publishing Group. Paper. Supplementary material (24 pp). Poster.

Financial Econometrics and Forecasting

  • Audrino, F., Chassot, J., Huang, C., Knaus, M., Lechner, M., and Ortega, J.-P. [2022]  How does post-earnings announcement sentiment affect firms’ dynamics? New evidence from causal machine learning. Journal of Financial Econometrics, nbac018, doi.org/10.1093/jjfinec/nbac018. Paper
  • Audrino, F., Kostrov, A., and Ortega, J.-P. [2019] Extending the logit model with Midas aggregation: the case of US bank failures.  Journal of Financial and Quantitative Analysis, 54(6), 2575-2603.  Paper
  • Badescu, A., Cui, Z., and Ortega, J.-P. [2019] Closed-form variance swap prices under general affine GARCH models and their continuous-time limits. Annals of Operations Research, 282, 27-57. Paper
  • Grigoryeva, L., Ortega, J.-P., and Peresetsky, A. [2018] Volatility forecasting using global stochastic financial trends extracted from non-synchronous data. Econometrics and Statistics, 5, 67-82. Paper
  • Badescu, A., Cui, Z., and Ortega, J.-P. [2017] Non-affine GARCH option pricing models, variance dependent kernels, and diffusion limits. Journal of Financial Econometrics, 15(4), 602-648.  Paper
  • Bauwens, L., Grigoryeva, L., and Ortega, J.-P. [2016] Estimation and empirical performance of non-scalar dynamic conditional correlation models. Computational Statistics and Data Analysis, 100, 17-36. doi:10.1016/j.csda.2015.02.013. Paper. Poster. Matlab Code.
  • Badescu, A., Cui, Z., and Ortega, J.-P. [2016] A note on the Wang transform for stochastic volatility pricing models. Finance Research Letters, 19, 189-196. Paper.
  • Badescu, A., Del Castillo, J., and Ortega, J.-P. [2016] Hedging of time discrete auto-regressive stochastic volatility options. Annals of Economics and Statistics, 123/124, 271-306. Paper.
  • Badescu, A., Elliott, R. J., and Ortega, J.-P. [2015] Non-Gaussian GARCH option pricing models and their diffusion limits. European Journal of Operational Research, 247, 820-830. Paper.
  • Grigoryeva, L. and Ortega, J.-P. [2015] Asymptotic forecasting error evaluation for estimated temporally aggregated linear processes. International Journal of Computational Economics and Econometrics, 5(3), 289-318. Paper. Matlab code.
  • Grigoryeva, L. and Ortega, J.-P. [2014] Hybrid forecasting with estimated temporally aggregated linear processes. Journal of Forecasting, 33, 577-595. Paper.
  • Badescu, A., Elliott, R. J., and Ortega, J.-P. [2014] Quadratic hedging schemes for non-Gaussian GARCH models. Journal of Economic Dynamics and Control, 42, 13-32.  Paper.
  • Ferrara, L., Marsilli, C., and Ortega, J.-P. [2014] Forecasting growth during the Great Recession: is financial volatility the missing ingredient? Economic Modelling, 36, 44-50. Paper.
  • Henriques, J. and Ortega, J.-P. [2014] Construction, management, and performance of sparse Markowitz portfolios. Studies in Nonlinear Dynamics and Econometrics, 18(4), 383-402. Paper. Matlab code and data.
  • Chrétien, S. and Ortega, J.-P. [2014] Multivariate GARCH estimation via a Bregman-proximal trust-region method. Computational Statistics and Data Analysis, 76, 210-236. Paper.
  • Chevassu, F. and Ortega, J.-P. [2013] Maximum likelihood estimation of state-space models. InterStat, paper 1, January 2013.  Paper.
  • Ortega, J.-P. [2012] GARCH options via local risk minimization. Quantitative Finance, 12(7), 1095-1110. Paper.  Matlab code.

Geometric Mechanics

  • Grigoryeva, L., Ortega, J.-P., and Zub, S. [2014] Stability of Hamiltonian relative equilibria in symmetric magnetically confined rigid bodies. Journal of Geometric Mechanics, 6(3), 373-415. Paper
  • Lázaro-Camí, J.-A. and Ortega, J.-P [2009] Superposition rules and stochastic Lie-Scheffers systems. Annales de l’Institut Henri Poincaré, Probabilité, 45(4), 910-931. Paper
  • Lázaro-Camí, J.-A. and Ortega, J.-P [2009] The stochastic Hamilton-Jacobi equation. Journal of Geometric Mechanics, 1(3), 295-315. Paper
  • Lázaro-Camí, J.-A. and Ortega, J.-P [2009] Reduction, reconstruction, and skew-product decomposition of symmetric stochastic differential equations. Stochastics and Dynamics, 9(1), 1-46. Paper
  • Montaldi, J. and Ortega, J.-P [2009] Symplectic Group Actions and Covering Spaces. Differential Geometry and its Applications, 27, 598-604. Paper
  • Loja Fernandes, R., Ortega, J.-P., and Ratiu, T. S. [2009] The momentum map in Poisson geometry. American Journal of Mathematics, 131(5), 1261-1310. Paper
  • Birtea, P., Ortega, J.-P., and Ratiu, T. S. [2009] Openness and convexity for momentum maps. Transactions of the American Mathematical Society, 361(2), 603–630. Paper
  • Lázaro-Camí, J.-A. and Ortega, J.-P [2008] Variational principles for stochastic Hamiltonian systems. Oberwolfach Reports, 5(3), 1896-1899.
  • Lázaro-Camí, J.-A., and Ortega, J.-P [2008] Stochastic Hamiltonian dynamical systems. Reports on Mathematical Physics, 61(1), 65-122. Paper
  • Birtea, P., Ortega, J.-P., and Ratiu, T. S. [2008] Metric convexity in the symplectic category. Journal of Lie Theory, 18(2), 445-469. Paper
  • Ortega, J.-P. and Ratiu, T. S. [2006] The reduced spaces of a symplectic Lie group action. Annals of Global Analysis and Geometry, 30(4), 335-381. Paper
  • Ortega, J.-P. and Ratiu, T. S. [2006] The stratified spaces of a symplectic Lie group action. Reports on Mathematical Physics, volume 58, 51-75. Paper
  • Ortega, J.-P. and Ratiu, T. S. [2006] Cotangent bundle reduction. In the Encyclopedia of Mathematical Physics, volume 1, 658-667. J.-P. Françoise, G.L. Naber and Tsou S.T. (editors) Oxford: Elsevier. Paper
  • Ortega, J.-P. and Ratiu, T. S. [2006] Poisson reduction. In the Encyclopedia of Mathematical Physics, volume 4, 79-83. J.-P. Françoise, G.L. Naber and Tsou S.T. (editors) Oxford: Elsevier. Paper
  • Ortega, J.-P. and Ratiu, T. S. [2006] Symmetry and symplectic reduction. In the Encyclopedia of Mathematical Physics, volume 5, 190-197. J.-P. Françoise, G.L. Naber and Tsou S.T. (editors) Oxford: Elsevier. Paper
  • Ortega, J.-P., Planas-Bielsa, V., and Ratiu, T. S. [2005] Asymptotic and Lyapunov stability of constrained and Poisson equilibria. Journal of Differential Equations, 214, 92-127. Paper
  • Ortega, J.-P. and Ratiu, T. S. [2004] Symmetry reduction in symplectic and Poisson geometry. Letters in Mathematical Physics, 69, 11-60. Paper
  • Ortega, J.-P. and Ratiu, T. S. [2004] The universal covering and covered spaces of a symplectic Lie algebra action. In The Breadth of Symplectic and Poisson Geometry: Festschrift in Honor of Alan Weinstein (J.E. Marsden and T.S. Ratiu, eds.), Progress in Mathematics, 232, 571-581. Birkhauser-Verlag, Boston. Paper 
  • Montaldi, J., Ortega, J.-P., Ratiu, T. S. [2004] The relation between local and global dual pairs. Mathematical Research Letters, 11, no. 2-3, 355-363. Paper
  • Grabsi, F., Montaldi, J., Ortega, J.-P. [2004] Bifurcation and forced symmetry breaking in Hamiltonian systems. Comptes Rendus Mathématique Académie des Sciences. Paris,338, no. 7, 565-570. Paper
  • Ortega, J.-P. and Planas-Bielsa, V. [2004] Dynamics on Leibniz manifolds. Journal of Geometry and Physics, 52, 1-27. Paper 
  • Ortega, J.-P. and Ratiu, T. S. [2004] Relative equilibria near stable and unstable Hamiltonian relative equilibria. Proceedings of the Royal Society London Ser. A Math. Phys. Eng. Sci., 460, no. 2045, 1407-1431. Paper
  • Ortega, J.-P. [2003] Relative normal modes for nonlinear Hamiltonian systems. Proceedings of the Royal Society of Edinburgh, Sect. A, 133, 665-704. Paper
  • Ortega, J.-P. [2003] Singular dual pairs. Differential Geometry and its Applications, 19, 61-95. Paper
  • Chossat, P., Lewis, D., Ortega, J.-P., and Ratiu, T.S. [2003] Bifurcation of relative equilibria in mechanical systems with symmetry. Advances in Applied Mathematics, 31, 10-45. Paper
  • Ortega, J.-P. [2002] Some remarks about the geometry of Hamiltonian conservation laws. In Symmetry and Perturbation Theory, pages 162-170. S. Abenda, G. Gaeta, and S. Walcher, World Scientific. Paper
  • Ortega, J.-P. and Ratiu, T. S. [2002] The optimal momentum map. In Geometry, Dynamics, and Mechanics: 60th Birthday Volume for J.E. Marsden, pages 329-362. P. Holmes, P. Newton, and A. Weinstein, eds., Springer-Verlag. Paper
  • Ortega, J.-P. [2002] The symplectic reduced spaces of a Poisson action. Comptes Rendus Mathématique Académie des Sciences. Paris. 334, 999-1004. Paper
  • Ortega, J.-P. and Ratiu, T. S. [2002] A symplectic slice theorem. Letters in Mathematical Physics, 59, 81-93. Paper
  • Chossat, P., Ortega, J.-P., and Ratiu, T. S. [2002] Hamiltonian Hopf bifurcation with symmetry. Archive for Rational Mechanics and Analysis, 163, 1-33. Paper Correction in Archive for Rational Mechanics and Analysis, 167 (2003), no. 1, 83-84. Paper
  • Ortega, J.-P. and Ratiu, T. S. [2001] Critical point theory and Hamiltonian dynamics around critical elements. In Symmetry and Perturbation Theory, pages 151-158. D. Bambusi, G. Gaeta, M. Cadoni, eds., World Scientific. Paper
  • Ortega, J.-P. and Ratiu, T.S. [1999] Non-linear  stability of  singular relative periodic orbits in Hamiltonian systems with symmetry. Journal of Geometry and Physics, 32, 160-188. Paper
  • Ortega, J.-P. and Ratiu, T.S. [1999] A Dirichlet criterion for the stability of periodic and relative periodic orbits in Hamiltonian systems. Journal of Geometry and Physics, 32, 131-159. Paper
  • Ortega, J.-P. and Ratiu, T.S. [1999] Stability of Hamiltonian relative equilibria. Nonlinearity, 12(3), 693-720. Paper
  • Ortega, J.-P. and Ratiu, T.S. [1998] Singular reduction of Poisson manifolds. Letters in Mathematical Physics, 46, 359-372. Paper
  • Ortega, J.-P. and Ratiu, T.S. [1997] Persistence and smoothness of critical relative elements in Hamiltonian systems with symmetry. Comptes Rendus Mathématique Académie des Sciences. Paris. 325, 1107-1111. Paper

Physiological Signal Treatment and Analysis

  • Ramanathan, V., Ariffin, M.Z., Goh, G.D., Goh, G.L., Rikat, M.A., Tan, X.X., Yeong, W.Y., Ortega, J.-P., Leong, V., and Campolo, D. [2022] Design and development of instrumented toys for social interactive assessment of infant cognitive flexibility. Sensors, 23, 2709. DOI: 10.3390/s23052709. Paper
  • Joucla, C., Gabriel, D., Ortega, J.-P., and Haffen, E. [2022] Journal of Neurophysiology. 128(6), 1375-1382. DOI: 10.1152/jn.00221.2022
  • Gabriel, D., Muzard, E., Henriques, J., Mignot, C., Pazart, L., André-Obadia, N., Ortega, J.-P., and Moulin, T. [2016] Replicability and impact of statistics in the detection of neural responses of conciousness. Brain. DOI: 10.1093/brain/aww065. Paper.
  • Gabriel, D., Muzard, E., Henriques, J., Mignot, C., Pazart, L., André-Obadia, N., Ortega, J.-P., and Moulin, T. [2016] L’emploi de méthodes mathématiques pour détecter la présence de potentiels évoqués dans le coma : un aide ou un fardeau ? Neurophysiologie Clinique/Clinical Neurophysiology, 46(2), 84-85.
  • Henriques, J., Pazart, L., Grigoryeva, L., Muzart, E., Beaussant, Y., Haffen, E.,  Moulin, T., Aubry, R., Ortega, J.-P., and Gabriel, D. [2016] Bedside evaluation of the functional organization of the auditory cortex in patients with disorders of conciousness. PLOS ONE. DOI: 10.1371/journal.pone.0146788. Paper.
  • Henriques, J., Gabriel, D., Grigoryeva, L., Haffen, E.,  Moulin, T., Aubry, R., Pazart, L., and Ortega, J.-P. [2016] Protocol design challenges in the detection of awareness in aware subjects using EEG signals. Clinical EEG and Neuroscience, 33(4), 266-275. Paper.
  • Gabriel, D., Henriques, J., Comte, A., Grigoryeva, L., Ortega, J.-P., Cretin, E.,  Haffen, E.,  Moulin, T., Pazart, L., and Aubry, R. [2015] Substitute or complement? Defining the relative place of EEG and fMRI in the detection of voluntary brain reactions. Neuroscience, 290, 435-444. Paper.
  • Gabriel, D., Comte, A., Henriques, J., Magnin, E., Grigoryeva, L., Ortega, J.-P., Haffen, E., Moulin, T., Pazart, L., and Aubry, R. [2013] EEG- and fMRI-based communication tools in disorders of consciousness: which is the most reliable method? Clinical EEG and Neuroscience, 44(4), E111. DOI: 10.1177/1550059413507209. Poster.

Other Publications

  • Tanaka, G., Gallicchio, C., Michelli, A., Ortega, J.-P., and Hirose, A. [2022] Guest editorial special issue on new frontiers in extremely efficient reservoir computing. IEEE Transactions on Neural Networks and Learning Systems, 33, 2571-2574. doi.org/10.1109/TNNLS.2022.3172586. Paper
  • García-Naranjo, L. C., de León, M., and Ortega, J.-P. [2020] Preface. Special issue dedicated to James Montaldi. Journal of Geometric Mechanics, 12(3), i-iv. Preface
  • de León, M., Lewis, A., and Ortega, J.-P. [2020] In memory of Geneviève Raugel. Journal of Geometric Mechanics, 12(1), i-ii. Document
  • Grigoryeva, Ortega, J.-P., and Silvestrini, A. [2016] Preface. Recent Developments in Forecasting and Macroeconometrics. Special Issue of the International Journal of Computational Economics and Econometrics, 7(1/2), 1-4. Preface. Contents.
  • Ortega, J.-P. [2012] Book review: Change of Time and Change of Measure by O. E. Barndorff-Nielsen and A. Shiryaev. European Mathematical Society Newsletter, 86, 57-59. Paper
  • Ortega, J.-P. [2011] Preface. Special issue dedicated to Tudor S. Ratiu on the occasion of his 60th birthday. Journal of Geometric Mechanics, 3(4), i-iv. Document