Alexander Nikolaevich Gorban | |
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Александр Николаевич Горбань | |
Born | |
Alma mater | Physics department of Novosibirsk State University and Mathematics department of Omsk State Pedagogical University |
Awards |
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Scientific career | |
Institutions | Center for Mathematical Modeling, University of Leicester, UK |
Alexander Nikolaevich Gorban (Russian : Александр Николаевич Горба́нь) is a scientist of Russian origin, working in the United Kingdom. He is a professor at the University of Leicester, and director of its Mathematical Modeling Centre. Gorban has contributed to many areas of fundamental and applied science, including statistical physics, non-equilibrium thermodynamics, machine learning and mathematical biology.
Gorban is the author of about 20 books and 300 scientific publications. [1] He has founded several scientific schools in the areas of physical and chemical kinetics, dynamical systems theory and artificial neural networks, and is ranked as one of the 1000 most cited researchers of Russian origin. [2] In 2020, Gorban presented a keynote talk at the IEEE World Congress on Computational Intelligence. [3]
Gorban has supervised 6 habilitations and more than 30 PhD theses.
Alexander N. Gorban was born in Omsk on 19 April 1952. His father Nikolai Vasilievich Gorban was a historian and writer exiled to Siberia, and his mother was a literature teacher in Omsk Pedagogical Institute. In 1965-1966 he studied at the Specialized Educational Scientific Center on Physics, Mathematics, Chemistry and Biology of Novosibirsk State University (SESC NSU). In 1967, at the age of 15, he entered Novosibirsk State University but was excluded from it in autumn 1969 because of his participation in January 1968 in political student movements against the convictions of Soviet writers Alexander Ginzburg and Yuri Galanskov.
After studying for a year in a vocational technical school and following an individual extramural program at Omsk Pedagogical Institute, he obtained a master's degree with a thesis entitled Sets of removable singularities in Banach spaces and continuous maps under the supervision of Russian mathematician Vladimir B. Melamed.
In 1973-1976 he worked in the Omsk Institute Of Transport Engineers and published his first scientific works, but his scientific career could not develop successfully because of his past political record. He had several temporary work places from 1976–1978, each time being compelled to resign, but then moved to Krasnoyarsk where he was permanently employed at the Institute of Computational Modeling. In 1980, Gorban obtained his Candidate of Sciences diploma, corresponding to PhD in the Russian scientific degree hierarchy. His thesis title was Slow relaxations and bifurcations of omega-limit sets of dynamical systems (translated later into English [a 1] ). His viva was organized by Olga Ladyzhenskaya, Mark Krasnosel'skii, and George M. Zaslavsky.
With the beginning of Perestroika he became the head of the Laboratory of Non-Equilibrium Systems in 1989 and completed his habilitation in 1990. In 1995 he became the deputy director of the Institute of Computational Modeling and head of the Computational Mathematics Department. At the same time, he taught at Krasnoyarsk State University (1981-1991) and subsequently headed the Neuroinformatics Department at the Krasnoyarsk State Technical University (1993-2006).
In the 1990s, Gorban visited several mathematical institutes in US and Europe, including the Clay Mathematics Institute, Courant Institute of Mathematical Sciences, Institut des Hautes Etudes Scientifiques, ETH (2003-2004), Isaac Newton Institute.
In 2004, Gorban became Professor of Applied Mathematics at the Leicester University, UK, and the chair of its Mathematical Modeling Centre.
Gorban is a stepbrother of Svetlana Kirdina.
Gorban's scientific contributions have been made in theoretical physics, mechanics, functional analysis, theory of natural selection, theory of adaptation, artificial neural networks, physical kinetics, bioinformatics. A top level view of scientific activity and the future of applied mathematics have been given in his book "Demon of Darwin: idea of optimality and natural selection", [b 1] articles and public lectures. [4]
In functional analysis, Gorban has investigated the properties of analytical Fredholm subsets in Banach spaces, formulated the relevant principle of maximum modulus and proved an analogue of the Remmert-Stein theorem.
In mathematical chemistry, Gorban has investigated the thermodynamical properties of chemical systems based on the analysis of Lyapunov's function trees in the polytope of conservation laws. [b 2] [b 3] He developed a theory of thermodynamically admissible paths for complex multidimensional systems of chemical thermodynamics and kinetics. [a 2]
Together with Grigoriy Yablonsky and his team he developed methods of mathematical modeling and analysis of chemical system models for kinetics of catalytic reactions. [b 4] He investigated the relaxation properties of some chemical systems and developed the singularity theory for transient processes of dynamical systems, [a 1] developed the method of path summation for solving the chemical kinetics equations, [a 3] developed a theory of dynamic limitation and asymptotology of chemical reaction networks [a 4] which was applied to modeling of biological signalling networks and mechanisms of microRNA action on translation regulation. [a 5]
Gorban has developed a series of methods for solving equations of chemical and physical kinetics, based on constructive methods of invariant manifold approximation. [a 6] This theory has found many applications in the construction of physically consistent hydrodynamics as a part of Hilbert's sixth problem, [a 7] modeling non-equilibrium flows, in the kinetic theory of phonons, for model reduction in chemical kinetics, and modeling liquid polymers. [b 5] He developed new methods for application of the Lattice Boltzmann's Method, based on its thermodynamical properties. [a 8] Gorban has developed a mathematical model of the Gorlov helical turbine and estimated its achievable efficiency in energy capture. [a 9] He investigated general problems of geometrical interpretation of thermodynamics [a 10] and general properties of non-classical entropies. [a 11]
In the mathematical theory of natural selection, Gorban developed a theory of a special class of dynamical systems with inheritance. [a 12] [b 1] He discovered and explained theoretically the universal phenomenon of system adaptation under stress conditions, leading to simultaneous increase of correlations and variance in the multidimensional space of system parameters. The Anna Karenina principle developed by Gorban is now applied as a method of diagnostics and prognosis for economics and human physiology. [a 13] [a 14]
Gorban developed highly efficient parallel methods for artificial neural networks (ANN) learning, based on systematic use of duality of their functioning, [b 6] [b 7] and developed methods of knowledge extraction from data based on sparse ANNs. He proved the theorem of universal approximation properties of ANN. [a 15] All these approaches have found numerous applications in existing expert systems. Together with I. Tyukin, he developed a series of methods and algorithms for fast, non-iterative and non-destructive corrections of errors in legacy Artificial intelligence systems. [a 16] These methods are based on the concentration of measure phenomena, ideas of statistical mechanics and original stochastic separation theorems. [a 17]
In applied statistics, Gorban developed methods for constructing principal manifolds (Elastic maps method) and their generalizations (principal graphs, principal trees), based on the mechanical analogy with elastic membrane. The method has found numerous applications for visualization and analysis of economical, sociological and biological data. [b 8] In collaboration with E.M. Mirkes and other authors, used machine learning methods for connecting individual psychological characteristics and predisposition to consuming certain types of drugs. [b 9]
In bioinformatics Gorban was one of the first to apply the method of frequency dictionaries and Principle of maximum entropy for analysis of nucleotide and amino acid sequences. [a 18] He investigated the general properties of compact genomes and proved the existence of a 7-cluster structure in the genome sequence, which was applied for solving the de novo gene identification problem. [a 19]
Selected books:
Selected articles:
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles.
Theoretical chemistry is the branch of chemistry which develops theoretical generalizations that are part of the theoretical arsenal of modern chemistry: for example, the concepts of chemical bonding, chemical reaction, valence, the surface of potential energy, molecular orbitals, orbital interactions, and molecule activation.
In thermodynamics, dissipation is the result of an irreversible process that affects a thermodynamic system. In a dissipative process, energy transforms from an initial form to a final form, where the capacity of the final form to do thermodynamic work is less than that of the initial form. For example, transfer of energy as heat is dissipative because it is a transfer of energy other than by thermodynamic work or by transfer of matter, and spreads previously concentrated energy. Following the second law of thermodynamics, in conduction and radiation from one body to another, the entropy varies with temperature, but never decreases in an isolated system.
Nonlinear dimensionality reduction, also known as manifold learning, refers to various related techniques that aim to project high-dimensional data onto lower-dimensional latent manifolds, with the goal of either visualizing the data in the low-dimensional space, or learning the mapping itself. The techniques described below can be understood as generalizations of linear decomposition methods used for dimensionality reduction, such as singular value decomposition and principal component analysis.
In chemistry, the law of mass action is the proposition that the rate of the chemical reaction is directly proportional to the product of the activities or concentrations of the reactants. It explains and predicts behaviors of solutions in dynamic equilibrium. Specifically, it implies that for a chemical reaction mixture that is in equilibrium, the ratio between the concentration of reactants and products is constant.
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is different from chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction.
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics, astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions.
Hilbert's sixth problem is to axiomatize those branches of physics in which mathematics is prevalent. It occurs on the widely cited list of Hilbert's problems in mathematics that he presented in the year 1900. In its common English translation, the explicit statement reads:
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side. Theoretical biology focuses more on the development of theoretical principles for biology while mathematical biology focuses on the use of mathematical tools to study biological systems, even though the two terms are sometimes interchanged.
The principle of detailed balance can be used in kinetic systems which are decomposed into elementary processes. It states that at equilibrium, each elementary process is in equilibrium with its reverse process.
Nikolay Nikolayevich Bogolyubov, also transliterated as Bogoliubov and Bogolubov, was a Soviet and Russian mathematician and theoretical physicist known for a significant contribution to quantum field theory, classical and quantum statistical mechanics, and the theory of dynamical systems; he was the recipient of the 1992 Dirac Medal.
The mathematical expressions for thermodynamic entropy in the statistical thermodynamics formulation established by Ludwig Boltzmann and J. Willard Gibbs in the 1870s are similar to the information entropy by Claude Shannon and Ralph Hartley, developed in the 1940s.
The principle of microscopic reversibility in physics and chemistry is twofold:
Physics is a scientific discipline that seeks to construct and experimentally test theories of the physical universe. These theories vary in their scope and can be organized into several distinct branches, which are outlined in this article.
A cellular model is a mathematical model of aspects of a biological cell, for the purposes of in silico research.
Elastic maps provide a tool for nonlinear dimensionality reduction. By their construction, they are a system of elastic springs embedded in the data space. This system approximates a low-dimensional manifold. The elastic coefficients of this system allow the switch from completely unstructured k-means clustering to the estimators located closely to linear PCA manifolds. With some intermediate values of the elasticity coefficients, this system effectively approximates non-linear principal manifolds. This approach is based on a mechanical analogy between principal manifolds, that are passing through "the middle" of the data distribution, and elastic membranes and plates. The method was developed by A.N. Gorban, A.Y. Zinovyev and A.A. Pitenko in 1996–1998.
Chemical reaction network theory is an area of applied mathematics that attempts to model the behaviour of real-world chemical systems. Since its foundation in the 1960s, it has attracted a growing research community, mainly due to its applications in biochemistry and theoretical chemistry. It has also attracted interest from pure mathematicians due to the interesting problems that arise from the mathematical structures involved.
Grigoriy Yablonsky is an expert in the area of chemical kinetics and chemical engineering, particularly in catalytic technology of complete and selective oxidation, which is one of the main driving forces of sustainable development.
Eitan Tadmor is a distinguished university professor at the University of Maryland, College Park, known for his contributions to the theory and computation of PDEs with diverse applications to shock wave, kinetic transport, incompressible flows, image processing, and self-organized collective dynamics.
The manifold hypothesis posits that many high-dimensional data sets that occur in the real world actually lie along low-dimensional latent manifolds inside that high-dimensional space. As a consequence of the manifold hypothesis, many data sets that appear to initially require many variables to describe, can actually be described by a comparatively small number of variables, likened to the local coordinate system of the underlying manifold. It is suggested that this principle underpins the effectiveness of machine learning algorithms in describing high-dimensional data sets by considering a few common features.