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Authors whose works are in public domain in at least one jurisdiction

List of works by Alexander Gorban

A Numerical Analyst’s View of the Lattice Boltzmann Method

A random six-phase switch regulates pneumococcal virulence via global epigenetic changes

scientific article

Additive generalization of the Boltzmann entropy

scientific article published on 27 June 2003

Allowed and forbidden regimes of entropy balance in lattice Boltzmann collisions

scientific article published on 24 August 2012

Approximation with random bases: Pro et Contra ⬇️

Basic, simple and extendable kinetic model of protein synthesis

scientific article published on 01 July 2019

Beyond The Concept of Manifolds: Principal Trees, Metro Maps, and Elastic Cubic Complexes

Branching Principal Components: Elastic Graphs, Topological Grammars and Metro Maps

CNN-Based Spectral Super-Resolution of Panchromatic Night-Time Light Imagery: City-Size-Associated Neighborhood Effects

scientific article published in 2021

Codon usage trajectories and 7-cluster structure of 143 complete bacterial genomic sequences

Collective dynamics: when one plus one does not make two ⬇️

scientific article published on May 5, 2011

Combustion simulation via lattice Boltzmann and reduced chemical kinetics

Computational diagnosis and risk evaluation for canine lymphoma

scientific article (publication date: October 2014)

Constructive methods of invariant manifolds for kinetic problems

Corrections and enhancements of quasi-equilibrium states

Correlations, risk and crisis: From physiology to finance

scholarly article by Alexander N. Gorban et al published August 2010 in Physica A

Coupling of the model reduction technique with the lattice Boltzmann method for combustion simulations

scientific article (publication date: October 2010)

Duality in nonextensive statistical mechanics

scientific article published on 27 February 2002

Dynamical modeling of microRNA action on the protein translation process

scientific article

Dynamical robustness of biological networks with hierarchical distribution of time scales

scientific article published in July 2007

Efficient simulations of detailed combustion fields via the lattice Boltzmann method

Ehrenfest's argument extended to a formalism of nonequilibrium thermodynamics.

scientific article published on 24 May 2001

Elastic Maps and Nets for Approximating Principal Manifolds and Their Application to Microarray Data Visualization

scholarly article published 2008

Elastic Principal Graphs and Manifolds and their Practical Applications

article published in 2005

Entropy: The Markov Ordering Approach

Evolution of adaptation mechanisms: Adaptation energy, stress, and oscillating death ⬇️

Exploring Automated Pottery Identification [Arch-I-Scan]

Family of additive entropy functions out of thermodynamic limit

scientific article

Fast construction of correcting ensembles for legacy Artificial Intelligence systems: Algorithms and a case study

scholarly article

Fluorescence-based assay as a new screening tool for toxic chemicals

scientific article

Four basic symmetry types in the universal 7-cluster structure of microbial genomic sequences

scientific article published on 30 January 2005

Fractional Norms and Quasinorms Do Not Help to Overcome the Curse of Dimensionality

scientific article published on 30 September 2020

Functional CT imaging for identification of the spatial determinants of small-airways disease in adults with asthma

scientific article published on 22 January 2019

General H-theorem and Entropies that Violate the Second Law

General stochastic separation theorems with optimal bounds

scientific article published in 2021

Geometrical Complexity of Data Approximators

Handling missing data in large healthcare dataset: A case study of unknown trauma outcomes. ⬇️

scientific article

High-Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality

scientific article published on 09 January 2020

High-Dimensional Brain: A Tool for Encoding and Rapid Learning of Memories by Single Neurons.

scientific article published on 19 March 2018

Hilbert's sixth problem: the endless road to rigour

scientific article published in April 2018

Hilbert’s 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations

How Deep Should be the Depth of Convolutional Neural Networks: a Backyard Dog Case Study

scholarly article

Independent Component Analysis for Unraveling the Complexity of Cancer Omics Datasets

scientific article published on 07 September 2019

Introduction

Invariance correction to Grad’s equations: where to go beyond approximations?

article by Alexander N. Gorban & Iliya V. Karlin published 6 July 2005 in Continuum Mechanics and Thermodynamics

Invariant Grids: Method of Complexity Reduction in Reaction Networks

article

Invariant Manifolds for Physical and Chemical Kinetics

article by Alexander N. Gorban & Ilya V. Karlin published 2005 in Lecture Notes in Physics

Invariant grids for reaction kinetics

Irreversibility in the short memory approximation

Kinetic signatures of microRNA modes of action

scientific article

Knowledge Transfer Between Artificial Intelligence Systems

scholarly article by Ivan Y Tyukin et al published 2018 in Frontiers in neurorobotics

Law of the Minimum paradoxes

scientific article published on 19 November 2010

Legendre integrators, post-processing and quasiequilibrium

Local equivalence of reversible and general Markov kinetics

Macroscopic dynamics through coarse-graining: a solvable example

scientific article published on 18 January 2002

Mathematical modeling of microRNA-mediated mechanisms of translation repression

scientific article published on January 2013

Maximum Entropy Principle for Lattice Kinetic Equations

scientific article published in Physical Review Letters

Method of invariant manifold for chemical kinetics

article by Alexander N. Gorban & Iliya V. Karlin published November 2003 in Chemical Engineering Science

Modeling Progression of Single Cell Populations Through the Cell Cycle as a Sequence of Switches

scientific article published on 01 February 2022

Multivariate Gaussian and Student-t process regression for multi-output prediction ⬇️

scholarly article

Order–disorder separation: Geometric revision

PCA and K-Means Decipher Genome

Personality Traits and Drug Consumption

Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning. ⬇️

scientific article

Principal Graphs and Manifolds

Principal manifolds and graphs in practice: from molecular biology to dynamical systems

scientific article published in June 2010

Pseudo-outcrop Visualization of Borehole Images and Core Scans

scholarly article by Evgeny Mirkes et al published 11 September 2017 in Mathematical Geosciences

Quasi-equilibrium closure hierarchies for the Boltzmann equation ⬇️

Reduction of dynamical biochemical reactions networks in computational biology

scientific article

Robust and Scalable Learning of Complex Intrinsic Dataset Geometry via ElPiGraph

scientific article published on 04 March 2020

Robust simplifications of multiscale biochemical networks

scientific article

SOM: Stochastic initialization versus principal components

STREAM: Single-cell Trajectories Reconstruction, Exploration And Mapping of omics data

Scikit-Dimension: A Python Package for Intrinsic Dimension Estimation

scientific article published on 20 October 2021

Self-Organizing Approach for Automated Gene Identification

article

Seven clusters in genomic triplet distributions.

scientific article published in January 2003

Simple model of complex dynamics of activity patterns in developing networks of neuronal cultures

scientific article published on 27 June 2019

Single-cell trajectories reconstruction, exploration and mapping of omics data with STREAM

scientific article published on 23 April 2019

Singularities of transient processes in dynamics and beyond: Comment on "Long transients in ecology: Theory and applications" by Andrew Morozov et al

scientific article published on 10 December 2019

Stability and stabilization of the lattice Boltzmann method.

scientific article published on 29 March 2007

Stabilization of the lattice Boltzmann method using the Ehrenfests' coarse-graining idea.

scientific article published on 25 September 2006

Stochastic Separation Theorems: How Geometry May Help to Correct AI Errors

scientific article published in 2023

Stochastic separation theorems.

scientific article published on 31 July 2017

Symphony of high-dimensional brain: Reply to comments on "The unreasonable effectiveness of small neural ensembles in high-dimensional brain"

scientific article published on 25 June 2019

The Michaelis-Menten-Stueckelberg Theorem

The Role of Thermodynamics in Model Reduction when Using Invariant Grids

article

The unreasonable effectiveness of small neural ensembles in high-dimensional brain

Theoretical aspects of peptide imprinting: screening of MIP (virtual) binding sites for their interactions with amino acids, di- and tripeptides

scholarly article published on 10 May 2018

Thermodynamic Tree: The Space of Admissible Paths

Trajectories, bifurcations, and pseudo-time in large clinical datasets: applications to myocardial infarction and diabetes data

scientific article published on 01 November 2020

Uniqueness of thermodynamic projector and kinetic basis of molecular individualism

Universal Lyapunov functions for non-linear reaction networks

scholarly article

Universal Seven-Cluster Structure of Genome Fragment Distribution: Basic Symmetry in Triplet Frequencies

What can the randomness of missing values tell you about clinical practice in large data sets of children's vital signs?

scientific article published on 15 April 2020

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