119 citations · 269 across the 38 of their papers we have counts for
6 papers · 1 filter
Multiplicity structure of the arc space of a fat point
Rida Ait El Manssour, Gleb Pogudin
The equation defines a fat point on a line. The algebra of regular functions on the arc space of this scheme is the quotient of by all differe…
Differential elimination for dynamical models via projections with applications to structural identifiability
Ruiwen Dong, Christian Goodbrake, Heather A Harrington +1
Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are o…
From algebra to analysis: new proofs of theorems by Ritt and Seidenberg
Dmitrii Pavlov, Gleb Pogudin, Yury Razmyslov
Ritt's theorem of zeroes and Seidenberg's embedding theorem are classical results in differential algebra allowing to connect algebraic and model-theoretic results on nonlinear PDE…
Web-based Structural Identifiability Analyzer
Ilia Ilmer, Alexey Ovchinnikov, Gleb Pogudin
Parameter identifiability describes whether, for a given differential model, one can determine parameter values from model equations. Knowing global or local identifiability proper…
Interpretable exact linear reductions via positivity
Gleb Pogudin, Xingjian Zhang
Kinetic models of biochemical systems used in the modern literature often contain hundreds or even thousands of variables. While these models are convenient for detailed simulation…
Optimal monomial quadratization for ODE systems
Andrey Bychkov, Gleb Pogudin
Quadratization problem is, given a system of ODEs with polynomial right-hand side, transform the system to a system with quadratic right-hand side by introducing new variables. Suc…