Rafail Abramov

Department of Mathematics, Statistics and Computer Science
University of Illinois at Chicago
851 S. Morgan St.
Chicago, IL 60607
E-mail: abramov@math.uic.edu
Phone: (312) 413 7945

Teaching

MATH 220 — Differential Equations
MATH 585 — Ordinary Differential Equations

Publications

  1. R. Abramov, Linear response of the Lyapunov exponent to a small constant perturbation, submitted to Physical Review E, 2014.
    [arXiv.org]

  2. R. Abramov, A simple stochastic parameterization for reduced models of multiscale dynamics, submitted to Journal of Computational Dynamics, 2013.
    [arXiv.org]

  3. R. Abramov and M. Kjerland, The response of reduced models of multiscale dynamics to small external perturbations, submitted to Communications in Mathematical Sciences, 2013.
    [arXiv.org]

  4. R. Abramov, A simple closure approximation for slow dynamics of a multiscale system: Nonlinear and multiplicative coupling, Multiscale Modeling and Simulation, 2013, vol. 11, no. 1, 134—151.
    [PDF] [PDF preprint] [arXiv.org]

  5. R. Abramov, A simple linear response closure approximation for slow dynamics of a multiscale system with linear coupling, Multiscale Modeling and Simulation, 2012, vol. 10, no. 1, 28—47.
    [PDF] [PDF preprint] [arXiv.org]

  6. R. Abramov, Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling, Communications in Mathematical Sciences, 2012, vol. 10, no. 2, 595—624.
    [PDF] [PDF preprint] [arXiv.org]

  7. R. Abramov & A. Majda, Low Frequency Climate Response of Quasigeostrophic Wind-Driven Ocean Circulation, Journal of Physical Oceanography, 2012, vol. 42, no. 2, 243—260.
    [PDF] [PDF preprint]

  8. R. Abramov, Improved linear response for stochastically driven systems, Frontiers of Mathematics in China, 2012, vol. 7, no. 2, 199—216.
    [PDF] [arXiv.org]

  9. R. Abramov, Approximate linear response for slow variables of dynamics with explicit time scale separation, Journal of Computational Physics, 2010, vol. 229, no. 20, 7739—7746.
    [DOI link]

  10. A. Majda, R. Abramov & B. Gershgorin, High skill in low frequency climate response through fluctuation dissipation theorems despite structural instability, Proceedings of the National Academy of Sciences, 2010, vol. 107, no. 2, 581—586.
    [PDF]

  11. R. Abramov, The multidimensional maximum entropy moment problem: A review on numerical methods, Communications in Mathematical Sciences, 2010, vol. 8, no. 2, 377—392.
    [PDF]

  12. R. Abramov, Short-time linear response with reduced-rank tangent map, Chinese Annals of Mathematics series B, 2009, vol. 30B, no. 5, 447—462.
    [PDF]

  13. R. Abramov, The multidimensional moment-constrained maximum entropy problem: A BFGS algorithm with constraint scaling, Journal of Computational Physics, 2009, vol. 228, 96—108.
    [DOI link]

  14. R. Abramov & A. Majda, A new algorithm for low frequency climate response, Journal of the Atmospheric Sciences, 2009, vol. 66, 286—309.
    [DOI link]

  15. R. Abramov & A. Majda, New approximations and tests of linear fluctuation-response for chaotic nonlinear forced-dissipative dynamical systems, Journal of Nonlinear Science, 2008, vol. 18, 303—341.
    [PDF]

  16. R. Abramov & A. Majda, Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems, Nonlinearity, 2007, vol. 20, 2793—2821.
    [PDF]

  17. R. Abramov, An improved algorithm for the multidimensional moment-constrained maximum entropy problem, Journal of Computational Physics, 2007, vol. 226, 621—644.
    [DOI link]

  18. R. Abramov, A practical computational framework for the multidimensional moment-constrained maximum entropy principle, Journal of Computational Physics, 2006, vol. 211, 198—209.
    [DOI link]

  19. A. Majda, R. Abramov & M. Grote, Information theory and stochastics for multiscale nonlinear systems, vol. 25 of CRM Monograph Series, Centre de Recherches Mathématiques, Université de Montréal. Published by American Mathematical Society, 2005. ISBN 0-8218-3843-1. 141 pp.
    [Amazon] [Barnes & Noble]

  20. K. Haven, A. Majda & R. Abramov, Quantifying predictability through information theory: Small sample estimation in a non-Gaussian framework, Journal of Computational Physics, 2005, vol. 206, 334—362.
    [DOI link]

  21. R. Abramov, A. Majda & R. Kleeman, Information Theory and Predictability for Low Frequency Variability, Journal of Atmospheric Sciences, 2005, vol. 62, no. 1, 65—87.
    [PDF]

  22. R. Abramov & A. Majda, Quantifying uncertainty for non-Gaussian ensembles in complex systems, SIAM Journal on Scientific Computing, 2003, vol. 26, no. 2, 411—447.
    [PDF]

  23. R. Abramov & A. Majda, Discrete approximations with additional conserved quantities: Deterministic and statistical behavior, Methods and Applications of Analysis, 2003, vol. 10, no. 2, 151—190.
    [PDF]

  24. R. Abramov & A. Majda, Statistically relevant conserved quantities for truncated quasi-geostrophic flow, Proceedings of the National Academy of Sciences, 2003, vol. 100, no. 7, 3841—3846.
    [PDF]

  25. R. Abramov, G. Kovačič & A. Majda, Hamiltonian structure and statistically relevant conserved quantities for the truncated Burgers-Hopf equation, Communications in Pure and Applied Mathematics, 2003, vol. 56, 1—46.
    [PDF]

Ph.D. Rensselaer Polytechnic Institute, Department of Mathematics, 2002.
Thesis title: Statistically relevant and irrelevant conserved quantities for the equilibrium statistical description of the truncated Burgers-Hopf equation and the equations for barotropic flow.
[PDF]

Software

The multidimensional moment-constrained maximum entropy algorithm
The library for the PC and some other platforms is there with few examples in C, C++ and FORTRAN (see file maxent_dist.tar.gz). A short manual is included.
A new, better version of the maxent algorithm
I am working on a better version of what I wrote years ago. The new code is aimed at use in various applications with different moment problems. Currently, the code is in its initial stage, and the manual is not yet available.

Last modified: Tue Sep 2 09:53:28 CDT 2014