119 citations · 269 across the 38 of their papers we have counts for
10 papers · 1 filter
The Lie algebra of polynomial vector fields on the affine space with constant divergence is -generated
Ivan Beldiev, Gleb Pogudin
A Lie algebra is said to be -generated if every nonzero element can be completed to a two-element generating set. We prove that the Lie algebra of polynomial vector fields wit…
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…
Multi-experiment parameter identifiability of ODEs and model theory
Alexey Ovchinnikov, Anand Pillay, Gleb Pogudin +1
Structural identifiability is a property of an ODE model with parameters that allows for the parameters to be determined from continuous noise-free data. This is a natural prerequi…
Parameter identifiability and input-output equations
Alexey Ovchinnikov, Gleb Pogudin, Peter Thompson
Structural parameter identifiability is a property of a differential model with parameters that allows for the parameters to be determined from the model equations in the absence o…
Solving difference equations in sequences: Universality and Undecidability
Gleb Pogudin, Thomas Scanlon, Michael Wibmer
We study solutions of difference equations in the rings of sequences and, more generally, solutions of equations with a monoid action in the ring of sequences indexed by the mon…
Degree bound for toric envelope of a linear algebraic group
Eli Amzallag, Andrei Minchenko, Gleb Pogudin
Algorithms working with linear algebraic groups often represent them via defining polynomial equations. One can always choose defining equations for an algebraic group to be of the…
Irredundant Triangular Decomposition
Gleb Pogudin, Agnes Szanto
Triangular decomposition is a classic, widely used and well-developed way to represent algebraic varieties with many applications. In particular, there exist sharp degree bounds fo…
Effective difference elimination and Nullstellensatz
Alexey Ovchinnikov, Gleb Pogudin, Thomas Scanlon
We prove effective Nullstellensatz and elimination theorems for difference equations in sequence rings. More precisely, we compute an explicit function of geometric quantities asso…
Complexity of Triangular Representations of Algebraic Sets
Eli Amzallag, Gleb Pogudin, Mengxiao Sun +1
Triangular decomposition is one of the standard ways to represent the radical of a polynomial ideal. A general algorithm for computing such a decomposition was proposed by A. Szant…