Denis Volk (Денис Волк)

Here is my    Curriculum Vitae (Sep 2019)

My current interests are

• • Solving real-world problems using my skills in math, data analysis, machine learning

  • Educating other people in these skills

           I am an expert in

• • Bayesian Machine Learning: Bayesian inference, probabilistic graphical models, MCMC & VI methods

  • Machine Learning: time series prediction, classic ML

• Mathematics (dynamical systems, ergodic theory, stochastic processes): 

  • • partial and non-uniform hyperbolicity, fast-slow dynamics, attractors, chaos, physical measures, Lyapunov exponents

    • nonlinear random walks, Markov chains

• • piecewise isometries, tilings, discrete geometry and applications to machine learning and other algorithms

• Neuroscience: brain rhythms and their cross-frequency interactions

• • 3D computer vision, 3D image processing

  • Applications of math in medicine, biology, neuroscience

My industry projects and experience are best reflected on my Toptal page.

My scientific achievements include:

Publications in Neuroscience

• • Generalized Cross-Frequency Decomposition: A Method for the Extraction of Neuronal Components Coupled at Different Frequencies (with I. Dubinin, A. Myasnikova, B. Gutkin, V. Nikulin)     [Frontiers in Neuroinformatics, 18 October 2018 | https://doi.org/10.3389/fninf.2018.00072]    [see also source code for GCFD Tool (in MATLAB)]

Publications in Math

• Attractors of Piecewise Translation Maps // Preprint [arXiv:1708.03780] 

  • Fast-slow partially hyperbolic systems versus Freidlin-Wentzell random systems (with J. De Simoi, C. Liverani, C. Poquet) // Journal of Statistical Physics, 166:650--679, 2017    [see also arXiv:1607.04319]

• Nonwandering sets of interval skew products (with V. Kleptsyn) // Nonlinearity, 27:1595--1601, 2014    [see also arXiv:1302.6929]

• Physical measures for nonlinear random walks on interval (with V. Kleptsyn) // Moscow Mathematical Journal, 14(2):339--365, 2014   [see also arXiv:1110.2117]

  • Translation numbers define generators of F+k → Homeo+(S1) (with T. Golenishcheva--Kutuzova, A. Gorodetski, V. Kleptsyn) // Moscow Mathematical Journal, 14(2):291--308, 2014  [see also arXiv:1306.5522]

  • Almost every Interval Translation Map of three intervals is finite type // Discrete and Continuous Dynamical Systems - Series A, 34(5):2307--2314, 2014 [see also arXiv:1203.3405]

  • Persistent massive attractors of smooth maps // Ergodic Theory and Dynamical Systems, 34(2):693--704, 2014 [see also arXiv:1108.5330]

  • Cascades of ε-invisibility (with Yu. Ilyashenko) // Journal of Fixed Point Theory and Applications, 7(1):161--188, 2010    [see also arXiv:0906.3567]

  • Theorem on the density of separatrix connections for polynomial foliations in CP2 // Journal of Mathematical Sciences, 150(5):2326--2334, 2008  [Translated from Fundamentalnaya i Prikladnaya Matematika, 12(4):53--64, 2006 (Russian)]

  • The density of separatrix connections in the space of polynomial foliations in CP2 // Proceedings of the Steklov Institute of Mathematics, 254(1):169--179, 2006  [Translated from Trudy Matematicheskogo Instituta imeni V. A. Steklova, 254:181--191, 2006 (Russian)]

Publications in Math Medicine/Biology

• • Mapping placental topology from 3D scans, the graphic display of variation in arborisation across gestation (C. Salafia, M. Yampolsky, D. Volk, C.J. Stodgell, P.J. Katzman, J. Culhane, P. Landrigan, S. Szabo, N. Thieux, J. Swanson, N. Dole, M.W. Varner, J. Moye, R. Miller) // Placenta, 34(9):A73--A74, 2013 (see also Erratum)

Conference publications

• • Fast-slow partially hyperbolic systems and pathological foliations (with De Simoi, C. Liverani, C. Poquet) // International Conference "Anosov systems and modern dynamics", 2016, pp. 25–27, ISBN 978-5-98419-073-2

  • Dynamics of Piecewise Translations // Proceedings of International Conference "Dynamics, Bifurcations and Strange Attractors", 2013, pp. 112–113

  • Interval Translation Maps of Three Intervals // Proceedings of International Conference on Differential Equations and Dynamical Systems, 2012, ISBN 978-5-98419-046-6

  • Persistent massive attractors of smooth maps // Proceedings of International Mathematical Conference “50 Years of IITP”, 2011, ISBN 978-5-901158-15-9

  • Skew products with interval fiber // Conference on Geometry and Topology of Foliations, 2010, p. 23

  • Thin attractors (with V. Kleptsyn) // Topology, Geometry and Dynamics: Rokhlin Memorial, 2010, pp. 70–72

  • The density of separatrix connections in C2 // International conference “Differential equations and related topics” dedicated to I. G. Petrovskii, 2004. Book of Abstracts, p. 241 (Russian).

My past grants

• RSCF 17-11-01273 grant "Изучение роли нейрональных осцилляций в реализации функций рабочей памяти с применением математического моделирования и неинвазивной стимуляции переменным током"

• Young Russian Mathematics award

• Russian Ministry of Education (Contract no. 14.6008.21.0001, unique ID project RFMEFI60815X0001)

• RFBR 13-01-00969-a [Russia]

  • ERC Advanced Investigator Grant MALADY 246953 [European Union]

  • President's of Russia MK-7567.2013.1 (Co-PI with I. Schurov) [Russia]

  • RFBR 12-01-31241-mol_a (Co-PI with I. Schurov) [Russia]

  • President's of Russia MK-2790.2011.1 (Co-PI with V. Timorin and I. Schurov) [Russia]

  • “Young SISSA Scientists” (Principal Investigator) [Italy]

  • RFBR 10-01-00739-a [Russia]

  • RFBR/CNRS 10-01-93115 [Russia-France]

  • PRIN [Italy]

  • RFBR 07-01-00017-a [Russia]

• RFBR/CNRS 05-01-02801-CNRS_a [Russia-France]

  • CRDF RM1-2358 [USA]

  • RFBR 02-01-22002 [Russia]