• Publications
  • Influence
Information theory and stochastics for multiscale nonlinear systems
Information theory, predictability, Jupiter's great red spot, and equilibrium statistical mechanics The fluctuation-dissipation theorem for complex nonlinear systems Mathematical strategies forExpand
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The multidimensional maximum entropy moment problem: a review of numerical methods
Recently the author developed a numerical method for the multidimensional momentconstrained maximum entropy problem, which is practically capable of solving maximum entropy problems in theExpand
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Hamiltonian structure and statistically relevant conserved quantities for the truncated Burgers‐Hopf equation
In dynamical systems with intrinsic chaos, many degrees of freedom, and many conserved quantities, a fundamental issue is the statistical relevance of suitable subsets of these conserved quantitiesExpand
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Information theory and predictability for low-frequency variability
Abstract A predictability framework, based on relative entropy, is applied here to low-frequency variability in a standard T21 barotropic model on the sphere with realistic orography. Two types ofExpand
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Statistically relevant conserved quantities for truncated quasigeostrophic flow
  • R. Abramov, A. Majda
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences…
  • 17 March 2003
Systematic applications of ideas from equilibrium statistical mechanics lead to promising strategies for assessing the unresolved scales of motion in many problems in science and engineering. AExpand
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New Approximations and Tests of Linear Fluctuation-Response for Chaotic Nonlinear Forced-Dissipative Dynamical Systems
TLDR
We develop and test two novel computational approaches for predicting the mean linear response of a chaotic dynamical system to small change in external forcing via the fluctuation–dissipation theorem, for both linear and nonlinear response functions. Expand
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Quantifying predictability through information theory: small sample estimation in a non-Gaussian framework
Many situations in complex systems require quantitative estimates of the lack of information in one probability distribution relative to another. In short term climate and weather prediction,Expand
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A New Algorithm for Low-Frequency Climate Response
Abstract The low-frequency response to changes in external forcing for the climate system is a fundamental issue. In two recent papers the authors developed a new blended response algorithm forExpand
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An improved algorithm for the multidimensional moment-constrained maximum entropy problem
  • R. Abramov
  • Mathematics, Computer Science
  • J. Comput. Phys.
  • 10 September 2007
TLDR
We introduced new computational framework for the moment-constrained maximum entropy problem in a multidimensional domain, and developed a simple numerical algorithm capable of computing maximum entropy Problem in a two-dimensional domain with moment constraints of order up to 4. Expand
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The multidimensional moment-constrained maximum entropy problem: A BFGS algorithm with constraint scaling
  • R. Abramov
  • Mathematics, Computer Science
  • J. Comput. Phys.
  • 2009
TLDR
In a recent paper we developed a new algorithm for the moment-constrained maximum entropy problem in a multidimensional setting, using a multodimensional orthogonal polynomial basis in the dual space of Lagrange multipliers to achieve numerical stability and rapid convergence of the Newton iterations. Expand
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