Publications (60)
Uniqueness of thermodynamic projector and kinetic basis of molecular individualism
A. N. Gorban, I. V. Karlin
Possibility and Impossibility of the Entropy Balance in Lattice Boltzmann Collisions
A. N. Gorban, D. Packwood
Neural network modeling of data with gaps: method of principal curves, Carleman's formula, and other
A. N. Gorban, A. A. Rossiev, D. C. Wunsch
Reciprocal Relations Between Kinetic Curves
G. S. Yablonsky, A. N. Gorban, D. Constales +2
Selection theorem for systems with inheritance
A. N. Gorban
Mathematical modeling of microRNA-mediated mechanisms of translation repression
A. Zinovyev, N. Morozova, A. N. Gorban +1
Extremal property of a simple cycle
A. N. Gorban
Principal manifolds and graphs in practice: from molecular biology to dynamical systems
A. N. Gorban, A. Zinovyev
Order--disorder separation: Geometric revision
A. N. Gorban
Computational diagnosis and risk evaluation for canine lymphoma
E. M. Mirkes, I. Alexandrakis, K. Slater +2
The Michaelis-Menten-Stueckelberg Theorem
A. N. Gorban, M. Shahzad
Dynamical robustness of biological networks with hierarchical distribution of time scales
A. N. Gorban, O. Radulescu
Local Equivalence of Reversible and General Markov Kinetics
A. N. Gorban
Legendre Integrators, Post-Processing and Quasiequilibrium
A. N. Gorban, P. A. Gorban, I. V. Karlin
Entropy: The Markov Ordering Approach
A. N. Gorban, P. A. Gorban, G. Judge
Neuroinformatics: What are us, where are we going, how to measure our way?
A. N. Gorban
Seven clusters in genomic triplet distributions
A. N. Gorban, A. Yu. Zinovyev, T. G. Popova
Stable simulation of fluid flow with high-Reynolds number using Ehrenfests' steps
R. A. Brownlee, A. N. Gorban, J. Levesley
Maxallent: Maximizers of all Entropies and Uncertainty of Uncertainty
A. N. Gorban
Add-ons for Lattice Boltzmann Methods: Regularization, Filtering and Limiters
R. A. Brownlee, J. Levesley, D. Packwood +1
Methods of nonlinear kinetics
A. N. Gorban, I. V. Karlin
Thermodynamics in the Limit of Irreversible Reactions
A. N. Gorban, E. M. Mirkes, G. S. Yablonsky
Four basic symmetry types in the universal 7-cluster structure of 143 complete bacterial genomic sequences
A. N. Gorban, T. G. Popova, A. Yu. Zinovyev
Dynamic and static limitation in multiscale reaction networks, revisited
A. N. Gorban, O. Radulescu
Multiscale principal component analysis
A. A. Akinduko, A. N. Gorban
PCA Beyond The Concept of Manifolds: Principal Trees, Metro Maps, and Elastic Cubic Complexes
A. N. Gorban, N. R. Sumner, A. Y. Zinovyev
Thermodynamic theory of kinetic overshoots
A. N. Gorban, G. S. Yablonsky
Stable multispeed lattice Boltzmann methods
R. A. Brownlee, A. N. Gorban, J. Levesley
A Statistical Model of Aggregates Fragmentation
F. Spahn, E. V. Neto, A. H. F. Guimaraes +2
Simultaneously Dissipative Operators And The Infinitesimal Moore Effect In Interval Spaces
A. N. Gorban, Yu. I. Shokin, V. I. Verbitskii
Elastic principal manifolds and their practical applications
A. N. Gorban, A. Yu. Zinovyev
Invariance correction to Grad's equations: Where to go beyond approximations?
A. N. Gorban, I. V. Karlin
Extended Detailed Balance for Systems with Irreversible Reactions
A. N. Gorban, G. S. Yablonsky
Hilbert's 6th Problem: Exact and Approximate Hydrodynamic Manifolds for Kinetic Equations
A. N. Gorban, I. Karlin
Stabilisation of the lattice-Boltzmann method using the Ehrenfests' coarse-graining
R. A. Brownlee, A. N. Gorban, J. Levesley
Principal Graphs and Manifolds
A. N. Gorban, A. Y. Zinovyev
Asymptotology of Chemical Reaction Networks
A. N. Gorban, O. Radulescu, A. Y. Zinovyev
PCA and K-Means decipher genome
A. N. Gorban, A. Y. Zinovyev
The Mystery of Two Straight Lines in Bacterial Genome Statistics. Release 2007
A. N. Gorban, A. Yu. Zinovyev
Generation of Explicit Knowledge from Empirical Data through Pruning of Trainable Neural Networks
A. N. Gorban, Eu. M. Mirkes, V. G. Tsaregorodtsev
Geometry of irreversibility: The film of nonequilibrium states
A. N. Gorban, I. V. Karlin
Correlations, Risk and Crisis: From Physiology to Finance
A. N. Gorban, E. V. Smirnova, T. A. Tyukina
Thermodynamic Tree: The Space of Admissible Paths
A. N. Gorban
Quasichemical Models of Multicomponent Nonlinear Diffusion
A. N. Gorban, H. P. Sargsyan, H. A. Wahab
Detailed balance in micro- and macrokinetics and micro-distinguishability of macro-processes
A. N. Gorban
Constructive Methods of Invariant Manifolds for Kinetic Problems
A. N. Gorban, I. V. Karlin, A. Yu. Zinovyev
Informational Way to Protein Alphabet: Entropic Classification of Amino Acids
A. N. Gorban, M. Kudryashev, T. Popova
Topological Grammars for Data Approximation
A. N. Gorban, N. R. Sumner, A. Y. Zinovyev
Quasi-Equilibrium Lattice Boltzmann Method
S. Ansumali, S. Arcidiacono, S. Chikatamarla +3
Basic Types of Coarse-Graining
A. N. Gorban
Nonlinear Quality of Life Index
A. Zinovyev, A. N. Gorban
Kinetic Path Summation, Multi--Sheeted Extension of Master Equation, and Evaluation of Ergodicity Coefficient
A. N. Gorban
Singularities of Transition Processes in Dynamical Systems: Qualitative Theory of Critical Delays
A. N. Gorban
Grasping Complexity
A. N. Gorban, G. S. Yablonsky
Nonequilibrium entropy limiters in lattice Boltzmann methods
R. A. Brownlee, A. N. Gorban, J. Levesley
Explicit Reduced-Order Integral Formulations of State and Parameter Estimation Problems for a Class of Nonlinear Systems
I. Yu. Tyukin, A. N. Gorban
Stability and stabilisation of the lattice Boltzmann method: Magic steps and salvation operations
R. A. Brownlee, A. N. Gorban, J. Levesley
Elastic Maps and Nets for Approximating Principal Manifolds and Their Application to Microarray Data Visualization
A. N. Gorban, A. Y. Zinovyev
Is it possible to predict long-term success with k-NN? Case Study of four market indices (FTSE100, DAX, HANGSENG, NASDAQ)
Y. Shi, A. N. Gorban, T. Y. Yang
MultiNeuron - Neural Networks Simulator For Medical, Physiological, and Psychological Applications
A. N. Gorban, D. A. Rossiyev, M. G. Dorrer