Prof. Juan Carlos Jimenez

[ Academic Degree | Current Position | Research Interests | Publications | Awards | Technical Reports | Full CV ]  

ACADEMIC DEGREE

- M.S. in Nuclear Physics, Havana University, Cuba

- Ph.D. in Mathematics, Havana University, Cuba

CURRENT POSITION

Senior Professor,

Departamento de Matemática Interdisciplinaria,

Instituto de Cibernética, Matemática y Física

Calle 15 No. 551 e/ C y D, Vedado,

La Habana 4, C.P. 10400,

Cuba.

e-mail: juan_carlos_js@yahoo.com,   jcarlos@icimaf.cu

ORCID ID: http://orcid.org/0000-0001-6014-0505

Long Term Positions:

Oct 1983/ Oct 1986, Assistant Professor, Dept. of Neuro Physics, Cuban Neurosciences Center, Havana, Cuba

Oct 1986/ Sept 1999, Associate Professor, Dept. of Neuro Analysis, Cuban Neurosciences Center, Havana, Cuba

Nov 1999/ Sept 2015, Professor, Dept. of Interdisciplinary Mathematics, Institute of Cybernetics, Mathematics and Physics, Havana, Cuba

Oct 2015/ ....., Senior Professor, Dept. of Interdisciplinary Mathematics, Institute of Cybernetics, Mathematics and Physics, Havana, Cuba

Short Term Positions:

Sept 1995/ Dec 1995, Visiting Associate Professor, Dept. of Prediction and Control, The Institute of Statistical Mathematics, Tokyo, Japan

Sept 1997/ Dec 1997, Visiting Associate Professor, Dept. of Prediction and Control, The Institute of Statistical Mathematics, Tokyo, Japan

May 2000/ Mar 2001, Visiting Professor, Dept. of Prediction and Control, The Institute of Statistical Mathematics, Tokyo, Japan

Apr 2005/ Jun 2005, Visiting Professor, New Industry Creation Hatchery Center, Sendai, Japan

Sept 2005/ Dec 2005, Visiting Professor, Dept. Statistical Modeling, The Institute of Statistical Mathematics, Tokyo, Japan

Jan 2008/ Mar 2008, Visiting Professor, Dept. Statistical Modeling, The Institute of Statistical Mathematics, Tokyo, Japan

Jan 2010/Mar 2010:  Visiting Professor, Dept. of Mathematical Analysis & Statistical Inference, The Institute of Statistical Mathematics, Tokyo, Japan

Nov 2011/Feb 2012:  Visiting Professor, Risk Analysis Research Center, The Institute of Statistical Mathematics, Tokyo, Japan

Jun 2013/Jul 2013:   Visiting Professor, Centro de Investigación y Modelamiento de Fenómenos Aleatorios, Universidad de Valparaiso, Chile

Oct 2013/Dec 2013:  Visiting Professor, Risk Analysis Research Center, The Institute of Statistical Mathematics, Tokyo, Japan

Oct 2014:   Visiting Professor, School of Applied Mathematics, FGV, Rio de Janeiro, Brazil

Nov 2014:  Visiting Professor, Dept. of Mathematical Engineering, University of Concepcion, Chile

May 2015/Jun 2015:  Visiting Professor, Dept. of Probability and Statistics, CIMAT, Guanajuato, Mexico

Nov 2015:  Visiting Professor, Dept. of Mathematical Engineering, University of Concepcion, Chile

Apr 2016/May 2016:  Visiting Professor, Dept. of Probability and Statistics, CIMAT, Guanajuato, Mexico

Oct 2016/Dec 2016:  Visiting Professor, School of Applied Mathematics, FGV, Rio de Janeiro, Brazil

Apr & Nov 2017:  Visiting Professor, Dept. of Mathematical Engineering, University of Concepcion, Chile

Nov. 18: Visiting Professor, Dept. of Mathematical Engineering, University of Concepcion, Chile

Feb. 19/May. 19: Visiting Professor, School of Applied Mathematics, Fundação Getulio Vargas (FGV), Rio de Janeiro, Brasil

Jan. 20/Mar. 20: Visiting Professor, Research Center for Medical and Health Data Science, The Institute of Statistical Mathematics, Tokyo, Japan

Oct. 22/Nov. 22: Visiting Professor, Dept. Statistical Modeling, The Institute of Statistical Mathematics, Tokyo, Japan

Oct. 23/Nov. 23: Visiting Professor, Dept. Statistical Modeling, The Institute of Statistical Mathematics, Tokyo, Japan

Other visiting appointments:

Oct 1988: Super Conductors Lab., Kruchatov Institute of Nuclear Energy, Moscow, Russia

Mar 2002: Dept. of Prediction and Control, The Institute of Statistical Mathematics, Tokyo, Japan

Mar 2003: Dept. of Prediction and Control, The Institute of Statistical Mathematics, Tokyo, Japan

Mar 2005: Dept. of Statistical Modeling, The Institute of Statistical Mathematics, Tokyo, Japan

Jun 2006: School of Finance and Economics, University of Technology, Sydney, Australia

Oct 2007/Dec 2007: Division of Developmental Cognitive Neuroscience, Tohoku University, Sendai, Japan

Apr 2009/Jun 2009: Dept. of Mathematics, International Center for Theoretical Physics, Trieste, Italy

Sep 2010/Nov 2010: Dept. of Mathematics, International Center for Theoretical Physics, Trieste, Italy

May 2012/Jul 2012: Dept. of Mathematics, International Center for Theoretical Physics, Trieste, Italy

RESEARCH INTERESTS

Nonlinear Dynamical Systems and their Applications

• Integration and inference of deterministic and random dynamical systems, with emphasis in systems modelled by: Ordinary Differential Equations, Stochastic Differential Equations, Random Differential Equations, Delay Differential Equation and Stochastic Delay Differential Equations.

• Qualitative study of deterministic and random dynamical systems

• Stochastic processes

• Numerical methods 

• Identification, prediction and control of dynamical systems from actual data

• Time series analysis of actual data with emphasis in bio-physiological, financial and forest data

• Evolutionary Computation with Probabilistic Models

PUBLICATIONS

Papers in Journals:

• “Jacobian-free Locally Linearized Runge-Kutta method of Dormand and Prince for large systems of differential equations”, J. Comput. Appl. Math., 449 (2024) 115974. PDF

• “Matrix-free computation of linear combinations of phi-functions times vectors in exponential integrators”, Ciencias Matemáticas Vol. 36 (2024) 13-19. PDF

• “Modeling the interaction between donor-derived regulatory T cells and effector T cells early after allogeneic hematopoietic stem cell transplantation”, BioSystems, 227-228 (2023) 104889. PDF

• "Weak variable step-size schemes for stochastic differential equations based on controlling conditional moments", Appl. Numer. Math., 187 (2023) 235–261. PDF

• "Jacobian-free High Order Local Linearization methods for large systems of initial value problems", Appl. Numer. Math., 187 (2023) 158–175. PDF

• “Computing high dimensional multiple integrals involving matrix exponentials”, J. Comput. Appl. Math., 421 (2023) 114844.  PDF

• "State and parameter estimation of stochastic physical systems from uncertain and indirect measurements", Eur. Phys. J. Plus, 136 (2021) 869. PDF

• "Estimation of distribution algorithms for the computation of innovation estimators of diffusion processes”, Math. & Comput. in Simulations, 187 (2021) 449–467. PDF

• "Locally Linearized Runge-Kutta method of Dormand and Prince for large systems of initial value problems", J. Comput. Physics, 426 (2021) 109946. PDF

• "Bias reduction in the estimation of diffusion processes from discrete observations", IMA J. Math. Control Inform., 37 (2020) 1468–1505. PDF

• "Efficient computation of phi-functions in exponential integrators”, J. Comput. Appl. Math., 374 (2020) 112758. PDF

• "Exact pathwise simulation of multi-dimensional Ornstein-Uhlenbeck processes", Appl. Math. Comput., 366 (2020) 124734. PDF

• "On the oscillatory behavior of coupled stochastic harmonic oscillators driven by random forces", Statist. Prob. Letters, 146 (2019) 85–89. PDF

• "Approximate linear minimum variance filters for continuous-discrete state space models: convergence and practical adaptive algorithms",  IMA J. Math. Control Inform. 36 (2019) 341–378.  PDF

• "A stable numerical scheme for stochastic differential equations with multiplicative noise", SIAM J. Numer. Analysis, 55 (2017) 1614-1649. PDF

• "Locally Linearized methods for the simulation of stochastic oscillators driven by random forces", BIT Numer. Math., 57 (2017) 123-151. PDF

• "A weak Local Linearization scheme for stochastic differential equations with multiplicative noise", J. Comput. Appl. Math., 313 (2017) 202-217. PDF

• "Convergence rate refinement of the Local Linearization schemes for deterministic, random and stochastic differential equations", Anal. Acad. Ciencias Cuba, 7 (2017).  PDF

• "Multiple Shooting-Local Linearization method for the identification of dynamical systems", Commun. Nonlinear Sci. Numer. Simul., 37 (2016) 292–304. PDF

• "Simplified formulas for the mean and variance of linear stochastic differential equations", Appl. Math. Letters, 49 (2015) 12-19. PDF

• "Convergence rate of weak Local Linearization schemes for stochastic differential equations with additive noise", J. Comput. Appl. Math., 279 (2015) 106-122. PDF

• "Locally Linearized Runge Kutta method of Dormand and Prince", Appl. Math. Comput., 247 (2014) 589-606. PDF

• “Construction and study of Local Linearization adaptive codes for ordinary differential equations”, Rev. Mat. Teor. Apl., 21 (2014) 21–53.  PDF

• “Local Linearization - Runge Kutta Methods: a class of A-stable explicit integrators for dynamical systems”, Math. Comput. Modelling, 57 (2013) 720-740. PDF

• “Convergence rate of strong Local Linearization schemes for stochastic differential equations with additive noise”, BIT Numer. Math., 52 (2012) 357-382. PDF

• “QR-based methods for computing Lyapunov exponents of stochastic differential equations”, Int. J. Numer. Anal. Model., Ser. B, 1 (2010) 147-171. PDF

• “High Order Local Linearization methods: an approach for constructing A-stable high order explicit schemes for stochastic differential equations with additive noise”, BIT Numer. Math., 50 (2010) 509–539. PDF

• “Rate of convergence of Local Linearization schemes for random differential equations”, BIT Numer. Math., 49 (2009) 357–373. PDF

• “Identification and comparison of stochastic metabolic/hemodynamic models (sMHM) for the generation of the BOLD signal“, J. Comput. Neuroscience, 26 (2009) 251-269. PDF

• “Weak Local Linear discretizations for stochastic differential equations with jumps”, J. Appl. Prob., 45 (2008) 201-210. PDF

• “Computing multiple integrals involving matrix exponentials”, J. Comput. Appl. Math., 213 (2008) 300-305. PDF

• “Numerical simulation of nonlinear dynamical systems driven by commutative noise”, J. Comput. Physics, 226 (2007) 1219-1233. PDF

• “A higher order Local Linearization method for solving ordinary differential equations”, Appl. Math. Comput., 185 (2007) 197-212. PDF

• “Realistically coupled neural mass models can generate EEG rhythms”, Neural Computation, 19 (2007) 478-512. PDF

• “Nonlinear local electro-vascular coupling. Part II: From data to neural masses”, Human Brain Mapping, 28 (2007) 335-354. PDF

• “Nonlinear local electro-vascular coupling. Part I: A theoretical model”, Human Brain Mapping, 27 (2006) 896-914. PDF

• “Local Linearization method for numerical integration of delay differential equations”, SIAM J. Numer. Analysis, 44 (2006) 2584-2609. PDF

• “Weak Local Linear discretizations for stochastic differential equations: convergence and numerical schemes”, J. Comput. Appl. Math., 197 (2006) 578-596. PDF

• “Local Linear approximations for jump diffusion processes”, J. Appl. Prob., 43 (2006) 185-194. PDF

• “An approximate innovation method for the estimation of diffusion processes from discrete data”, J. Time Series Analysis, 27 (2006) 77-97. PDF

• “Inference methods for discretely observed continuous-time stochastic volatility models: A commented overview”, Asia-Pacific Financial Markets, 12 (2006) 109-141. PDF

• “Rate of convergence of Local Linearization schemes for initial-value problems”, Appl. Math. Comput., 171 (2005) 1282-1295. PDF

• “The Local Linearization method for numerical integration of random differential equations”, BIT Numer. Math., 45 (2005) 1-14. PDF

• “A class of automatic orthogonal integrators for stochastic differential equations”, J. Comput. Appl. Math., 182 (2005) 350-361. PDF

• “Local Linearization filters for nonlinear continuous-discrete state space models with multiplicative noise“, Int. J. Control, 76 (2003) 1159-1170. PDF 

• “Linear estimation of continuous-discrete linear state space models with multiplicative noise”, System & Control Letters, 47 (2002) 91-101. PDF

• “A simple algebraic expression to evaluate the Local Linearization schemes for stochastic differential equations”, Appl. Math. Letters, 15 (2002) 775-780. PDF

• “A numerical method for the computation of the Lyapunov exponents for nonlinear ordinary differential equations”, Appl. Math. Comput., 31 (2002) 21-37. PDF

• “Approximation of continuous time stochastic processes by the Local Linearization method revisited", Stochast. Anal. & Appl., 20 (2002), 105-121. PDF 

• “Dynamic properties of the Local Linearization method for initial-value problems”, Appl. Math. Comput., 126 (2002) 63-80. PDF

• "Role of the likelihood function in the estimation of chaos models", J. Time Series Analysis, 21 (2000) 363-387. PDF

• "Simulation of stochastic differential equations through the local linearization method. A comparative study". J. Statist. Physics, 94 (1999) 587-602. PDF

• "Testing non-linearity and directedness of interactions between neural groups in the macaque inferotemporal cortex". J. Neurosci. Methods, 94 (1999) 105-119.  PDF

• “Nonlinear EEG analysis based on a neural mass model”. Biological Cybernetics, 81 (1999) 415-424. PDF 

• “Geometric selection of centers for radial basis function approximations involved in intensive computer simulations”. Math. & Comput. in Simulations, 48 (1999) 295-306. PDF

• "Computing the noise covariance matrix of the Local Linearization scheme for the numerical solution of stochastic differential equations". Appl. Math. Letters, 11 (1998) 19-23. PDF

• "Numerical integration of ODEs modelling the evolution of biological systems: the adaptive Local Linearization scheme with approximate Jacobian". Ciencias Biológicas., 29 (1998) 41-43. PDF (in Spanish)

• "Reparameterization of auto-regressive models with coefficients depending on covariables: Application to EEG spectrum. Statistic in Medicine, 16 (1997) 1745-1752. PDF

• "Local Linearization method for the numerical solution of stochastic differential equations". Annals of Inst. Statist. Math., 48 (1996) 631-644. PDF

• "Parametric representation of anatomical structures of the human body by means of trigonometric interpolating sums". J. Comput. Physics, 126 (1996) 243-250.  PDF

• "EGG predictability. Properness of nonlinear forecasting methods". Int. J. Biomedical Computing, 38 (1995) 197-206. PDF

• "Measuring the dissimilarity between EEG recording through a nonlinear dynamical system approach". Int. J. Biomedical Computing, 38 (1995) 121-129. PDF 

• "Modelling the electroencephalogram by means of spatial spline smoothing and temporal autoregression". Biological Cybernetics, 72 (1995) 249-259. PDF

• "High resolution quantitative EEG analysis". Brain Topography, 6 (1994) 211-219. PDF

• "High resolution analysis of the coherences and energy spectrum in patients with localized symptomatic epilepsy". Revista de Neurofisiología Clínica, 7 (1994) 15-22. (in Spanish) link

• "Comparison of EEG abnormal activities in learning disabled, behavioural disordered and normal children". Archivos del Instituto Nacional de Neurología y Neurocirugía, 8 (1993) 67-72.  link

• "Multivariate Box-Cox transformations with applications to neurometric data". Computer in Biology and Medicine, 19 (1989) 263-267. PDF

• "Numeric solution of integral equations using parametric approximation for the surfaces". Ciencias Biológicas, 19 (1988) 197-199. (in Spanish).

• "EEG sub-band codification". Ciencias Biológicas, 19 (1988) 119-121. (in Spanish).

• "Comparison between different quantitative measures of normality for evoked potentials". Ciencias Biológicas, 19 (1988) 139-141. (in Spanish).

• "Topography image evaluator for microcomputers. Design and implementation". Ciencias Biológicas, 17 (1986) 141-144. (in Spanish).

Papers in Books:

• "Time variant distribution of Sugi log prices based on reverting mean model for risk valuation", In: Forest Resources Management and Mathematical Modeling (FORMATH), Vol.18, 1-13, Japanese Society of Forest Planning Press, 2019. PDF

•  "A higher order and stable method for the numerical integration of random differential equations", In: Anais do Congresso Nacional de Matemática Aplicada à Indústria, Vol. 1, 103-110, Blucher, São Paul, 2015. PDF

• "Reverted mean and asymptotic stationary distribution for timber price using a mean-reverting stochastic model”, In: Forest Resources Management and Mathematical Modeling (FORMATH), Vol.11, 167-180, Japanese Society of Forest Planning Press, 2012. PDF

• “Local Linearization-Runge Kutta (LLRK) methods for solving ordinary differential equations”, In: Lecture Note in Computer Sciences 3991, Springer-Verlag, 2006, 132-139. PDF

• “The innovation approach to the identification of nonlinear causal models in time series analysis”, In: Time series analysis and applications to geophysical systems, Brillinger D.R., Robinson E.A., and Schoenberg F.P. (Eds),. IMA Volumes in Mathematics and its Applications, Vol. 139, Springer- Verlag, 2004, 195-226. PDF

• “The statistical identification of nonlinear brain dynamics”. In: Nonlinear Dynamics and Brain Functioning, Pradhan N., Rapp P.E., Sreenivasan R. (Eds.), Nova Science Publishers, 1999, 243-264. link

• “Nonlinear time series models and neural dynamical systems”. In: Nonlinear Dynamics and Brain Functioning, Pradhan N., Rapp P.E., Sreenivasan R. (Eds.), Nova Science Publishers, 1999, 155-200. link

• "Smooth approximation of nonnegative definite kernels". In: Approximation and Optimization in the Caribbean, Florenzano M. et al. (Eds.), Peter Lang, 1995, 114-128. link

• "Projective methods for the magnetic direct problem. In: Advances in Biomagnetism. S. Williamson and L. Kaufman (Eds.), Plenum Press, 1990, 615-618. PDF

• "Functionally based statistical methods for the analysis of the EEG and event related potential". In: Progress in Computer-Assisted Function Analysis, J.L. Willems, J.H. van Bemmel and J. Michel (Eds.), North-Holland, 1988, 91-96. link

• "Current source density estimation: a new method’. In: Estudios Avanzados en Neurociencias", M. Valdes and A. Alvarez (Eds.), Editorial CENIC, 125-133, 1987.

• "Selecting Box-Cox transformations for neurometric data". In: Estudios Avanzados en Neurociencias, M. Valdes and A. Alvarez (Eds.), Editorial CENIC, 134-141, 1987.

• "A parametric model for the analysis of evoked responses to multiple events". In: Estudios Avanzados en Neurociencias, M. Valdes and A. Alvarez (Eds.), Editorial CENIC, 98-109, 1987. (in Spanish).

• "Neuronica: A data acquisition and analysis system for bioelectric signals". In: Estudios Avanzados en Neurociencias, M. Valdes and A. Alvarez (Eds.), Editorial CENIC, 71-80, 1987. (in Spanish)

Papers in Proceedings:

•  “Application of a continuous univariate marginal distribution algorithm to the computation of innovation estimators for diffusion processes”, In: Boletín de la Sociedad Cubana de Matemática y Computación. Vol. 3, No. 1, 2005 (Proceeding of the IX National Congress of Mathematics and Computation, La Habana, 2005).

• “Modeling and control for foreign exchange based on a continuous time stochastic microstructure model”, In:  Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada USA, Dec. 2002, (2002) 4440-4445. PDF

• “Use of stochastic differential equation models in financial time series analysis: monitoring and control of currencies in exchange market”. In: Proceedings of 3er Japan-US joint seminar on statistical time series analysis, Kyoto, Japan, June 2001, (2001) 17-24. PDF

• “Estimating continuous-discrete state space models and applications” In: Proceedings of ISM Symposium: Statistical Research in Complex Systems, Tokyo, Japan, March 2001, (2001) 39-45. link

• "Local linearization method for the numerical solution of stochastic differential equations and nonlinear Kalman filters". In: Proceeding of the Symposium: Studies on data analysis by statistical software, Fuji Kenshu-Jyo, Japan, Nov. 1995, (1996) 291-292.

Patents:

·         Patent No. US5282474 A: Methods and system for the evaluation and visual display of abnormal electromagnetic physiological activity of the brain and the heart. USA. 1994. link

·         Patent No. 4/91: Method and system for the anatomic deconvolution of brain and heart electromagnetic activity. Cuba. 1991.

·         Patent No. 169/90: Methods and system for evaluation and visual display of abnormal electromagnetic physiological activity of the brain and the heart. Cuba. 1990.

AWARDS

·   Annual Award of the Cuban Academy of Sciences (2022): “Reduction of bias in the estimation of stochastic differential equations”.

· Annual Award of the Cuban Academy of Sciences (2016): “Convergence rate refinement of the Local Linearization schemes for deterministic, random and stochastic differential equations”.

·   Annual Award of the Cuban Academy of Sciences (2006): “Estimation of continuous-discrete space state models with multiplicative noise: Local Linearization filters and Innovation method”.

·  Annual Award of the Cuban Academy of Sciences (2003): “Local Linearization methods for the approximation of ordinary and stochastic differential equations”.

·  Annual Award of the Cuban Academy of Sciences (1999): “Statistical identification of the nonlinear dynamic of the normal and epileptic brain”.

·   Annual Award of the Cuban Academy of Sciences (1997): “3-D statistical mapping for the spectrum of EEG generators”.

·  Annual Award for the Scientific Research Applied to the Development of the Cuban Society (1991), Ministry of Higher Education: “Early Detection of Hearing Defects”. 

·   National Award Carlos J. Finlay (1990), for developing the bio-medical equipments MEDICID II and NEURONICA.

NOPUBLISHED TECHNICAL REPORTS

• Strong Local Linearization methods for the numerical integration of stochastic differential equations with additive noise: An overview. Preprint 2010093, International Center for Theoretical Physics, Trieste, 2010. PDF

• Local Linearization methods for the numerical integration of ordinary differential equations: An overview. Preprint 2009035, International Center for Theoretical Physics, Trieste, 2009. PDF

• Parameter estimation of a dynamical model for EEG/MEG generators on the brain cortex. Technical Report ICIMAF 208-467, Instituto de Cibernética, Matemática y Física, La Habana, Cuba.

• An innovation approach for the estimation, selection and prediction of discretely observed continuous-time stochastic volatility models. Research Memo 855, The Institute of Statistical Mathematics, Tokyo, 2002. Abstract PDF

• Identification of continuous-discrete state space models with delays. Research Memo 658, The Institute of Statistical Mathematics, Tokyo, 1997. PDF