157 citations · 2.9k across the 96 of their papers we have counts for
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PCA Beyond The Concept of Manifolds: Principal Trees, Metro Maps, and Elastic Cubic Complexes
A. N. Gorban, N. R. Sumner, A. Y. Zinovyev
Multidimensional data distributions can have complex topologies and variable local dimensions. To approximate complex data, we propose a new type of low-dimensional ``principal obj…
Elastic Maps and Nets for Approximating Principal Manifolds and Their Application to Microarray Data Visualization
A. N. Gorban, A. Y. Zinovyev
Principal manifolds are defined as lines or surfaces passing through ``the middle'' of data distribution. Linear principal manifolds (Principal Components Analysis) are routinely u…
Stable simulation of fluid flow with high-Reynolds number using Ehrenfests' steps
R. A. Brownlee, A. N. Gorban, J. Levesley
The Navier--Stokes equations arise naturally as a result of Ehrenfests' coarse-graining in phase space after a period of free-flight dynamics. This point of view allows for a very…
Nonequilibrium entropy limiters in lattice Boltzmann methods
R. A. Brownlee, A. N. Gorban, J. Levesley
We construct a system of nonequilibrium entropy limiters for the lattice Boltzmann methods (LBM). These limiters erase spurious oscillations without blurring of shocks, and do not…
Dynamical robustness of biological networks with hierarchical distribution of time scales
A. N. Gorban, O. Radulescu
We propose the concepts of distributed robustness and r-robustness, well adapted to functional genetics. Then we discuss the robustness of the relaxation time using a chemical reac…