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

Publications

R. Abramov, The multidimensional moment-constrained maximum entropy problem: A BFGS algorithm with constraint scaling, accepted to Journal of Computational Physics, 2008.
[PDF] (preprint)

R. Abramov & A. Majda, New algorithms for low frequency climate response, accepted to Journal of the Atmospheric Sciences, 2008.
[PDF] (preprint)

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]

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

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

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

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]

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.
[PDF]

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]

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]

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.
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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.
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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.
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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
This page is currently under heavy construction, however the full algorithm library for the i586 platform is there with few examples in C, C++ and FORTRAN (see file maxent_dist.tar.gz). The proper manual is currently lacking.

Teaching

MCS 507 — Mathematical, Statistical and Scientific Software