119 citations · 269 across the 38 of their papers we have counts for
51 papers
Observable functions of rational ODE models and how to find them
Alexander Demin, Gleb Pogudin, Christopher Rackauckas
Consider a parametric ODE control model. A function of the states and parameters is called observable if its value can in principle be reconstructed from input-output data. The obs…
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…
Quadratization of Autonomous Partial Differential Equations: Algorithmic Solutions
Albani Olivieri, Gleb Pogudin, Boris Kramer
Quadratization for partial differential equations (PDEs) is a process that formally transforms a PDE with a nonquadratic right-hand side into a quadratic form by introducing auxili…
Simple generators of rational function fields
Alexander Demin, Gleb Pogudin
Consider a subfield of the field of rational functions in several indeterminates. We present an algorithm that, given a set of generators of such a subfield, finds a simple generat…
Support bound for differential elimination in polynomial dynamical systems
Yulia Mukhina, Gleb Pogudin
We study an important special case of the differential elimination problem: given a polynomial parametric dynamical system and…
Discovering Polynomial and Quadratic Structure in Nonlinear Ordinary Differential Equations
Boris Kramer, Gleb Pogudin
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, an…
Projecting dynamical systems via a support bound
Yulia Mukhina, Gleb Pogudin
For a polynomial dynamical system, we study the problem of computing the minimal differential equation satisfied by a chosen coordinate (in other words, projecting the system on th…
Wronskians form the inverse system of the arcs of a double point
Rida Ait El Manssour, Gleb Pogudin
The ideal of the arc scheme of a double point or, equivalently, the differential ideal generated by the ideal of a double point is a primary ideal in an infinite-dimensional polyno…
Time-efficient filtering of polarimetric data by checking physical realizability of experimental Mueller matrices
Tatiana Novikova, Alexey Ovchinnikov, Gleb Pogudin +1
Imaging Mueller polarimetry has already proved its potential for metrology, remote sensing and biomedicine. The real-time applications of this modality require both video rate imag…
Algebraic identifiability of partial differential equation models
Helen Byrne, Heather Harrington, Alexey Ovchinnikov +3
Differential equation models are crucial to scientific processes. The values of model parameters are important for analyzing the behaviour of solutions. A parameter is called globa…
Persistent components in Canny's Generalized Characteristic Polynomial
Gleb Pogudin
When using resultants for elimination, one standard issue is that the resultant vanishes if the variety contains components of dimension larger than the expected dimension. J. Cann…
Linear difference operators with sequence coefficients having infinite-dimentional solution spaces
Sergei Abramov, Gleb Pogudin
The notion of lacunary infinite numerical sequence is introduced. It is shown that for an arbitrary linear difference operator L with coefficients belonging to the set R of infinit…
Dissipative quadratizations of polynomial ODE systems
Yubo Cai, Gleb Pogudin
Quadratization refers to a transformation of an arbitrary system of polynomial ordinary differential equations to a system with at most quadratic right-hand side. Such a transforma…
On the dimension of the solution space of linear difference equations over the ring of infinite sequences
Sergei Abramov, Gleb Pogudin
For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the soluti…
Identifiable specializations for ODE models
Alexey Ovchinnikov, Anand Pillay, Gleb Pogudin +1
The parameter identifiability problem for a dynamical system is to determine whether the parameters of the system can be found from data for the outputs of the system. Verifying wh…
Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems
Andrey Bychkov, Opal Issan, Gleb Pogudin +1
Quadratization of polynomial and nonpolynomial systems of ordinary differential equations is advantageous in a variety of disciplines, such as systems theory, fluid mechanics, chem…
Exact hierarchical reductions of dynamical models via linear transformations
Alexander Demin, Elizaveta Demitraki, Gleb Pogudin
Dynamical models described by ordinary differential equations (ODEs) are a fundamental tool in the sciences and engineering. Exact reduction aims at producing a lower-dimensional m…
More Efficient Identifiability Verification in ODE Models by Reducing Non-Identifiability
Ilia Ilmer, Alexey Ovchinnikov, Gleb Pogudin +1
Structural global parameter identifiability indicates whether one can determine a parameter's value from given inputs and outputs in the absence of noise. If a given model has para…
On realizing differential-algebraic equations by rational dynamical systems
Dmitrii Pavlov, Gleb Pogudin
Real-world phenomena can often be conveniently described by dynamical systems (that is, ODE systems in the state-space form). However, if one observes the state of the system only…
Faster Gröbner bases for Lie derivatives of ODE systems via monomial orderings
Mariya Bessonov, Ilia Ilmer, Tatiana Konstantinova +3
Symbolic computation for systems of differential equations is often computationally expensive. Many practical differential models have a form of polynomial or rational ODE system w…
Exact linear reduction for rational dynamical systems
Antonio Jiménez-Pastor, Joshua Paul Jacob, Gleb Pogudin
Detailed dynamical systems models used in life sciences may include dozens or even hundreds of state variables. Models of large dimension are not only harder from the numerical per…
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…