# Publications

## Preprints

### On the dimension of the solution space of linear difference equations over the ring of infinite sequences (with Abramov S.)

## Peer-reviewed articles

### Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems (with Bychkov A., Issan O., Kramer B.)

*accepted to SIAM Journal on Applied Dynamical Systems*, preprint

### Exact hierarchical reductions of dynamical models via linear transformations (with Demin A., Demitraki E.)

*Communications in Nonlinear Science and Numerical Simulation*, preprint

### Dissipative quadratizations of polynomial ODE systems (with Cai Y.)

*accepted to Tools and Algorithms for Construction and Analysis of Systems (TACAS)*, preprint

### Multiplicity structure of the arc space of a fat point (with Ait El Manssour R.)

*accepted to Algebra & Number Theory*, preprint

### Differential elimination for dynamical models via projections with applications to structural identifiability (with Dong, R. and Goodbrake C. and Harrington H.A.)

*SIAM Journal on Applied Algebra and Geometry, 2023*, preprint

### Exact linear reduction for rational dynamical systems (with Jiménez-Pastor A., Jacob J.)

*Computational Methods in Systems Biology (CMSB), 2022*, preprint

### On realizing differential-algebraic equations by rational dynamical systems (with Pavlov D.)

*International Symposium on Symbolic and Algebraic Computation (ISSAC), 2022*, preprint

### Multi-experiment parameter identifiability of ODEs and model theory (with Ovchinnikov A., Pillay A., Scanlon T.)

*SIAM Journal on Applied Algebra and Geometry, 2022*, preprint

### From algebra to analysis: new proofs of theorems by Ritt and Seidenberg (with Pavlov D. and Razmyslov Yu.)

*Proceedings of American Mathematical Society, 2022*, preprint

### Input-output equations and identifiability of linear ODE models (with Ovchinnikov A. and Thompson P.)

*IEEE Transactions on Automatic Control, 2022*, preprint

### Computing all identifiable functions of parameters for ODE models (with Ovchinnikov A., Pillay A., and Scanlon T.)

*System & Control Letters, 2021*, preprint

### Algorithms yield upper bounds in differential algebra (with Li W., Ovchinnikov A., and Scanlon T.)

*Canadian Journal of Mathematics, 2021*, preprint

### Bit-complexity of solving systems of linear evolutionary partial differential equations (with Koswara I., Selivanova S., and Ziegler M.)

*Computer Science in Russia (CSR), 2021*, preprint

### Degree bound for toric envelope of a linear algebraic group (with Amzallag E. and Minchenko A.)

*Mathematics of Computation, 2021*, preprint

### Interpretable exact linear reductions via positivity (with Zhang X.)

*Computational Methods in Systems Biology (CMSB), 2021*, preprint

### A zero test for σ-algebraic power series (with van der Hoeven J.)

*International Symposium on Symbolic and Algebraic Computation (ISSAC), 2021*, preprint

### Optimal monomial quadratization for ODE systems (with Bychkov A.)

*International Workshop on Combinatorial Algorithms (IWOCA), 2021*, preprint

### CLUE: Exact maximal reduction of kinetic models by constrained lumping of differential equations (with Ovchinnikov A., Pérez Verona I.C., and Tribastone M.)

*Bioinformatics, 2021*, preprint

### Parameter identifiability and input-output equations (with Ovchinnikov A. and Thompson P.)

*Applicable Algebra in Engineering, Communication and Computing, 2021*, preprint

### Bounds for elimination of unknowns in systems of differential-algebraic equations (with Ovchinnikov A. and Thieu Vo N.)

*International Mathematics Research Notices, 2020*, preprint

### Elimination of unknowns for systems of algebraic differential-difference equations (with Li W., Ovchinnikov A., and Scanlon T.)

*Transactions of American Mathematical Society, 2020*, preprint

### Separating variables in bivariate polynomial ideals (with Buchacher M. and Kauers M.)

*International Symposium on Symbolic and Algebraic Computation (ISSAC), pp. 54-61, 2020*, preprint

### Solving difference equations in sequences: Universality and Undecidability (with Scanlon T. and Wibmer M.)

*Forum of Mathematics, Sigma, vol. 8, e33, 2020*, preprint

### Global identifiability of differential models (with Hong H., Ovchinnikov A., and Yap C.)

*Communications in Pure and Applied Mathematics, vol. 73(9), pp. 1831-1879, 2020*, preprint

### Effective difference elimination and Nullstellensatz (with Ovchinnikov A. and Scanlon T.)

*Journal of the European Mathematical Society, 2020*, preprint

### The dynamics of canalizing Boolean networks (with Paul E., Qin W., and Laubenbacher R.)

*Complexity, volume 2020, ID 3687961, 2020*, preprint

### Primitive element theorem for fields with commuting derivations and automorphisms

*Selecta Mathematica, 25:57, 2019*, preprint

### SIAN: software for structural identifiability analysis of ODE models (with Hong H., Ovchinnikov A., and Yap C.)

*Bioinformatics, vol. 35(16), pp. 2873–2874, 2019*, preprint

### Complexity of Triangular Representations of Algebraic Sets (with Amzallag E., Sun M., and Thieu Vo N.)

*Journal of Algebra, vol. 523, pp. 342-364, 2019*, preprint

### Irrendundant Triangular Decomposition (with Szanto A.)

*International Symposium on Symbolic and Algebraic Computation (ISSAC), pp. 311-318, 2018*, preprint

### A differential analog of the Noether normalization lemma

*International Mathematics Research Notices, vol. 2018(4), pp. 1177-1199, 2018*, preprint

### Products of ideals and jet schemes

*Journal of Algebra, vol.502, pp. 61-78, 2018*, preprint

### New order bounds in differential elimination algorithms (with Gustavson R. and Ovchinnikov A.)

*Journal of Symbolic Computation, vol. 85, pp. 128-146, 2018*, preprint

### Power series expansions for the planar monomer-dimer problem

*Physical Review E, vol. 96, 2017*, preprint

### Bounds for substituting algebraic functions into D-finite functions (with Kauers M.)

*International Symposium on Symbolic and Algebraic Computation (ISSAC), pp. 245-252, 2017*, preprint

### Rolling Simplexes and Their Commensurability. III (Capelli Identities and Their Application to Differential Algebras) (with Gerasimova O. and Razmyslov Yu.P.)

*Journal of Mathematical Sciences, vol. 221(3), pp. 315-325, 2017*

### Prime Lie algebras satisfying the standard Lie identity of degree 5 (with Razmyslov Yu.P.)

*Journal of Algebra, vol. 468, pp. 182--192, 2016*, preprint

### Bounds for orders of derivatives in differential elimination algorithms (with Gustavson R. and Ovchinnikov A.)

*International Symposium on Symbolic and Algebraic Computation (ISSAC), pp. 239-246, 2016*

### Modules of zero Gorenstein dimension over graph algebras (with Golod E.S.)

*Sbornik:Mathematics, vol. 207, issue 7, pp. 81-100, 2016*

### The primitive element theorem for differential fields with zero derivation on the base field

*Journal of Pure and Applied Algebra, vol 219(9), pp. 4035-4041, 2015*, preprint

### Primary differential nil-algebras do exist

*Moscow University Mathematics Bulletin, vol 69(1), pp 33-36, 2014*, preprint

### The Heisenberg envelope for the Hochschild algebra of a finite-dimensional Lie algebra (with Razmyslov Yu.P.)

*Journal of Mathematical Sciences, vol. 193(4), pp 580-585, 2013*

### Paradigm of Max-Factor and finite-dimensional representation of Lie algebras (with Razmyslov Yu.P.)

*Moscow University Mathematics Bulletin, vol. 67(4), pp 170-172, 2012*

### Wronskian of derivations

*Moscow University Mathematics Bulletin, Volume 66(1), pp 47-49, 2011*

## Other publications

### Linear Difference Operators with Sequence Coefficients Having Infinite-Dimentional Solution Spaces (with Abramov S.)

*ACM Communications in Computer Algebra*, preprint

### Problem 11997 (with Drmota M. and Krattenthaler C.)

*The American Mathematical Monthly, vol. 124, number 7, p.660, 2017*

## Notes

### Lecture notes on linear recurrences with nonconstant coefficients

*AESC MSU, 2016 (in Russian)*

### Lecture notes on differential Galois theory

*MSU, 2013 (in Russian)*