Alexei Tsygvintsev

Maître de conférences Hors Classe · UMPA, École Normale Supérieure de Lyon

Dynamical systems · mathematical biology · integrability

alexei.tsygvintsev@ens-lyon.fr· Google Scholar· ORCID

Expert consulting

Mathematical modelling of tumour–immune dynamics, cancer immunotherapy and antiviral immune response; delay differential equation models; neural network methods for biological sequence analysis. Also dynamical systems, celestial mechanics and integrability.

Available for expert consultations, independent model review and short advisory engagements. Enquiries: alexei.tsygvintsev@ens-lyon.fr

Mathematical biology

Tumour–immune dynamics, immunotherapy, antiviral immunity — 6 papers

  1. [19] On the global attractors in one mathematical model of antiviral immunity
    Comptes Rendus. Mathématique, 358 (11–12), 1199–1205, 2020. PDF
  2. [21] Evolutionary paradigm in cancer immunology
    ESAIM: Proceedings and Surveys, 45, 285–289, 2014.
  3. [22] A mathematical model of gene therapy for the treatment of cancer
    with D. Kirschner and S. Marino. In Mathematical Models and Methods in Biomedicine, Springer-Verlag, Berlin, 2012.
  4. [23] On the global dynamics of a model for tumor immunotherapy
    with D. Kirschner. Mathematical Biosciences and Engineering, 6(3), 573–583, 2009.
  5. [24] Bounded immune response in immunotherapy described by the deterministic delay Kirschner–Panetta model
    with S. Banerjee. Applied Mathematics Letters, 35, 90–94, 2014.
  6. [25] Stability and bifurcations of equilibria in a delayed Kirschner–Panetta model
    with S. Banerjee. Applied Mathematics Letters, 40, 65–71, 2015.

Artificial neural networks and deep learning

2 papers

  1. [30] On the overfly algorithm in deep learning of neural networks
    Applied Mathematics and Computation, 349, 348–358, 2019. arXiv
  2. [31] Natural vs. random protein sequences — a novel neural network approach based on time series analysis
    Journal of Proteins and Proteomics, 11, 11–16, 2020. Read-only version

Differential equations, integrability and the three-body problem

15 papers

  1. [1] Velocity syzygies and bounding syzygy moments in the planar three-body problem
    Comptes Rendus. Mathématique, 362, 1785–1791, 2024. Article
  2. [2] On some collinear configurations in the planar three-body problem
    Nonlinearity, 36, 6827, 2023. arXiv
  3. [3] On the existence of generalised syzygies in the planar three-body problem
    C. R. Acad. Sci. Paris, 361, 331–335, 2023. PDF
  4. [4] On the analytic non-integrability of the rattleback problem
    with H. Dullin. Annales de la Faculté des Sciences de Toulouse, XVII(3), 495–517, 2008.
  5. [5] On some exceptional cases in the integrability of the three-body problem
    Celestial Mechanics and Dynamical Astronomy, 99(1), 237–247, 2007.
  6. [6] Non-existence of new meromorphic first integrals in the planar three-body problem
    Celestial Mechanics and Dynamical Astronomy, 86(3), 237–247, 2003.
  7. [7] The meromorphic non-integrability of the three-body problem
    Journal für die reine und angewandte Mathematik (Crelle), 537, 127–149, 2001.
  8. [8] Sur l'absence d'une intégrale première supplémentaire méromorphe dans le problème plan des trois corps
    C. R. Acad. Sci. Paris, 333, Série I, 125–128, 2001.
  9. [9] On the existence of polynomial first integrals of quadratic homogeneous systems of ordinary differential equations
    J. Phys. A: Math. Gen., 34, 2185–2193, 2001.
  10. [10] Algebraic invariant curves of plane polynomial differential systems
    J. Phys. A: Math. Gen., 34, 663–672, 2001.
  11. [11] La non-intégrabilité méromorphe du problème plan des trois corps
    C. R. Acad. Sci. Paris, 331, Série I, 241–244, 2000.
  12. [12] Kovalevskaya exponents of systems with exponential interaction
    with K. Emelyanov. Russian Acad. Sci. Sbornik Math., 191(10), 39–50, 2000.
  13. [13] Sur l'intégrabilité algébrique d'un système d'équations différentielles dérivé des équations d'Euler sur l'algèbre so(4)
    Bulletin des Sciences Mathématiques, 123(8), 665–670, 1999.
  14. [14] Kovalevskaya's method in the dynamics of a rigid body
    with A. Borisov. J. Appl. Math. Mech., 61(1), 27–32, 1997.
  15. [15] Kovalevskaya exponents and integrable systems of classical dynamics, I & II
    with A. Borisov. Regular and Chaotic Dynamics, 1(1), 15–28 and 29–37, 1996.

Analytic theory of continued fractions

3 papers

  1. [16] Bounded analytic maps, Wall fractions and ABC flow
    Journal of Approximation Theory, 174, 206–219, 2013.
  2. [17] Continued g-fractions and geometry of bounded analytic maps
    Journal of Dynamical and Control Systems, 19(14), 2013.
  3. [18] On the convergence of continued fractions at Runckel's points
    The Ramanujan Journal, 15(3), 407–413, 2008.

Renormalization theory and holomorphic dynamics

4 papers

  1. [26] On the Julia set of permutable transcendental entire functions
    with A. Singh. Journal of the Calcutta Mathematical Society, 6(2), 2010.
  2. [27] Bounds on the unstable eigenvalue for the asymmetric renormalization operator for period doubling
    with B. D. Mestel and A. Osbaldestin. Communications in Mathematical Physics, 250(2), 241–257, 2004.
  3. [28] On the connection between g-fractions and solutions of the Feigenbaum–Cvitanović equation
    Communications in the Analytic Theory of Continued Fractions, XI, 103–112, 2003.
  4. [29] Continued fractions and solutions of the Feigenbaum–Cvitanović equation
    with B. D. Mestel and A. Osbaldestin. C. R. Acad. Sci. Paris, 334, Série I, 683–688, 2002.

History of mathematics

1 entry

  1. [32] Poincaré theorems
    with J.-M. Strelcyn. In Encyclopedia of Nonlinear Science, ed. A. Scott, Routledge, New York and London, 2004.

Popularization of mathematics

3 entries

  1. [20] L'immunité antivirale : la guerre invisible à la loupe des mathématiciens
    Images des Mathématiques, CNRS, 2020. Article
  2. [33] L'anagyre. Un objet curieux…
    with L. Lazrag. Images des Mathématiques, CNRS. Article
  3. [34] Magique ou scientifique ?
    Television programme, France 5. Video