Search Results - "N. A. Gorban"

Model reduction in chemical dynamics: slow invariant manifolds, singular perturbations, thermodynamic estimates, and analysis of reaction graph by Gorban, AN

“…The paper has two goals:(1)It presents basic ideas, notions, and methods for reduction of reaction kinetics models: quasi-steady-state, quasi-equilibrium, slow…”
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Blessing of dimensionality: mathematical foundations of the statistical physics of data by Gorban, A. N., Tyukin, I. Y.

“…The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the…”
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Handling missing data in large healthcare dataset: a case study of unknown trauma outcomes by Mirkes, E.M, Coats, T.J, Levesley, J, Gorban, A.N

“…Abstract Handling of missed data is one of the main tasks in data preprocessing especially in large public service datasets. We have analysed data from the…”
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Extended detailed balance for systems with irreversible reactions by Gorban, A.N., Yablonsky, G.S.

“…The principle of detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process. For many real physico-chemical…”
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A statistical model of aggregate fragmentation by Spahn, F, Vieira Neto, E, Guimarães, A H F, Gorban, A N, Brilliantov, N V

“…A statistical model of fragmentation of aggregates is proposed, based on the stochastic propagation of cracks through the body. The propagation rules are…”
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Stochastic separation theorems by Gorban, A N, Tyukin, I Y

“…The problem of non-iterative one-shot and non-destructive correction of unavoidable mistakes arises in all Artificial Intelligence applications in the real…”
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Reciprocal relations between kinetic curves by Yablonsky, G. S, Gorban, A. N, Constales, D, Galvita, V. V, Marin, G. B

“…We study coupled irreversible processes. For linear or linearized kinetics with microreversibility, $\dot{x}=Kx $, the kinetic operator K is symmetric in the…”
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Singularities of transient processes in dynamics and beyond: Comment on “Long transients in ecology: Theory and applications” by Andrew Morozov et al by Gorban, A.N.

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Computational diagnosis and risk evaluation for canine lymphoma by Mirkes, E.M, Alexandrakis, I, Slater, K, Tuli, R, Gorban, A.N

“…Abstract The canine lymphoma blood test detects the levels of two biomarkers, the acute phase proteins (C-Reactive Protein and Haptoglobin). This test can be…”
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Beyond Navier-Stokes equations: capillarity of ideal gas by Gorban, A. N., Karlin, I. V.

“…The system of Navier-Stokes-Fourier equations is one of the most celebrated systems of equations in modern science. It describes dynamics of fluids in the…”
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Dynamic and thermodynamic models of adaptation by Gorban, A.N., Tyukina, T.A., Pokidysheva, L.I., Smirnova, E.V.

“…•The correlation graph between attributes provides a tool for studying stress and critical transitions.•We reviewed data that support or refute the hypothesis:…”
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Hilbert's sixth problem: the endless road to rigour by Gorban, A. N.

“…In this introduction, the essence of the sixth problem is discussed and the content of this issue is introduced. This article is part of the theme issue…”
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Mystery of Two Straight Lines in Bacterial Genome Statistics by Gorban, A. N, Zinovyev, A. Y

“…In special coordinates (codon position-specific nucleotide frequencies), bacterial genomes form two straight lines in 9-dimensional space: one line for…”
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Slow relaxations and bifurcations of the limit sets of dynamical systems. III. Slow relaxations of a separate semiflow by Gorban’, A. N., Cheresiz, V. M.

“…We study connections between various types of slow relaxations of a dynamical system with the peculiarities of its behavior in the general situation when the…”
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Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning by Gorban, A.N., Mirkes, E.M., Zinovyev, A.

“…Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient…”
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Reduction of dynamical biochemical reactions networks in computational biology by Radulescu, O, Gorban, A N, Zinovyev, A, Noel, V

“…Biochemical networks are used in computational biology, to model mechanistic details of systems involved in cell signaling, metabolism, and regulation of gene…”
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It is useful to analyze correlation graphs: Reply to comments on “Dynamic and thermodynamic models of adaptation” by Gorban, A.N., Tyukina, T.A., Pokidysheva, L.I., Smirnova, E.V.

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Slow relaxations and bifurcations of the limit sets of dynamical systems. II. Slow relaxations of a family of semiflows by Gorban’, A. N., Cheresiz, V. M.

“…We propose a number of approaches to the notion of the relaxation time of a dynamical system which are motivated by the problems of chemical kinetics, give…”
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Slow relaxations and bifurcations of the limit sets of dynamical systems. I. Bifurcations of limit sets by Gorban’, A. N., Cheresiz, V. M.

“…We consider one-parameter semigroups of homeomorphisms depending continuously on the parameters. We study the phenomenon of slow relaxation that consists in…”
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Asymptotology of chemical reaction networks by Gorban, A.N., Radulescu, O., Zinovyev, A.Y.

“…The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated…”
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