Selected technical and scientific publications by Igor Borovikov
In English
Igor Borovikov, Michael G. Sadovsky, Sliding Window Analysis of Binary n-Grams Relative Information for Financial Time Series, Lawrence Livermore National Laboratory CASIS Workshop Proceedings 2014
Michael G. Sadovsky, Igor Borovikov, Analysis of financial time series with binary n-grams frequency dictionaries, Journal of Siberian Federal University. Mathematics and Physics 2014, 7(1), 112123
Igor Borovikov, Michael Sadovsky, A relative information approach to financial time series analysis using binary N-grams dictionaries, arXiv:1308.2732 [q-fin.ST]; 2013; 13 pages
Igor Borovikov, Guennadi Narychkine "Radiation Detection with the Camera of Consumer Mobile Devices" Poster presentation at The 17th Annual Signal and Image Sciences Workshop (CASIS at LLNL), May 22, 2013 (poster pdf)
Igor Borovikov, "Navigation Graph Generation" at, 2011
Igor Borovikov, Aleksey Kadukin, "Road Creation for Projectable Terrain Meshes" in Game Programming Gems 8, 2010
Igor Borovikov, "GPU-acceleration for Surgical Eye Imaging" SIAM MI09 San Francisco, October 2009, a presentation and an article.
E Antonov, J. Bisceglio, I. Borovikov, N. Noble, T. J. Peters Convergence of Geometric Algorithms for Graphics & Animation, Preprint, University of Connecticut, 2008, 15pages.
Igor Borovikov, Aleksey Kadukin "Building a Behavior Editor for Abstract State Machines" in Game AI Wisdom 4, Charles River Media, 2008, pp. 333-346. 
Igor Borovikov, Orwellian State Machines, in: Game AI Wisdom 3, Charles River Media, 2006, pp. 275-288
Igor Borovikov, An Orwellian approach to AI architecture, Game Developers Conference, 2005, San Francisco.
Igor Borovikov, Order Reduction of Optimal Control Systems, 2004, math.OC/0409111,, 29 pages.
Igor A.Borovikov, L-Systems with inheritance: An Object-Oriented Extension of L-Systems. ACM SIGPLAN Notices, Vol. 30, N.5, May 1995, pp. 43-60
Borovikov I.A. Invariant properties of reflexive neural networks // Advances in Modeling & Analysis, B, AMSE Press, Vol.27, N. 1, 1993, pp.18-27.
Patent Applications
Applications 20080309668, 20080279478, 20080278633, 20080240588, by Igor Borovikov with co-authors on various aspects of image processing.
In Russian
Borovikov I.A. Approximate categories and approximate decomposition //Modern group analysis. MIPT.1993,pp.21-24 (In Russian)

Introduced a notion of category with approximate morphisms. Approximate decomposition is defined as morphism in such category.

Borovikov I.A. Maximum Principle and backpropagation// Neurocomputer, Vol. 3,4; 1992, Moscow, p. 21-24 (in Russian)

Derived backpropagation equations from maximum principal. Introduced a new class of "symmetric" neural networks with learning cycle twice faster than classical.

Borovikov I.A. Groups of symmetries and decomposition of neural network models of reflexion//Proc. of International seminar "Modern group analysis", Ufa, Institute of Mathematics and Computer Center, 1991. (in Russian) p.11

Reflexion is studied in a neural networks models using methods of group analysis. Group invariants of the model are treated in terms of reflexive behavior.

Borovikov I.A. Choice of decomposition structure in optimal control, Ph.D. dissertation, MIPT, 1989, 140 p. (in Russian)

Detailed discussion with proofs and examples of results published in some of the previous papers. In addition, new numerical method of decomposition in optimal control is discussed.

Borovikov I.A. On one approach to almost controllability in nonlinear dynamic systems theory//Kibernetika i vichislit.tehnika (Cybernetics and computing technology), Kiev, 1989, Vol. 81, p. 18-23 (in Russian)

Defined almost controllability for affine systems. Criterion of almost controllability and its connections to weak controllability and controllability were obtained using non-standard analysis and differential geometry.

Borovikov I.A. On one application of nonlinear almost controllability //Modelirovanie processov upravlenia i obrabotki informatsii (Modeling of control and data processing)/Moscow, MIPT, 1989, p. 52-57 (in Russian)

Almost controllability is applied for order reduction in optimal control problem.

Borovikov I.A.,Cherniaev A.P. Regularization and numerical analysis of integral equation in the problem of ideal liquid flow...//Problemy sovremennoi matematiki v zadachah fisiki i mehaniki (Problems of modern mathematics in physics and mechanics), Moscow, MIPT, 1989, p.35-42 (in Russian)

Numerical analysis of the flow with free surface and axial symmetry based on Tikhonov regularization methods. Presented a new approach to a classical problem using integral equations.

Borovikov I.A. Approximate factorization in optimal control problems with small parameter//Problemy sovremennoi matematiki v zadachah fisiki i mehaniki (Problems of modern mathematics in physics and mechanics), Moscow, MIPT, 1989, p.30-34 (in Russian)

Artificial small parameter allows order reduction for all smooth optimal control system. This is a new behavior since order reduction is rare and unstable property of non-optimal dynamic systems.

Borovikov I.A. Approximate factorization in linear-quadratic optimal control //Matematicheskie metody obrabotk inforamtsii I upravlenia (Mathematical methods in information processing and control), Moscow, MIPT, 1988, p.88-93 (in Russian)

Linear quadratic control problem without symmetries form a set of zero measure. For each linear-quadratic problem exists arbitrary small perturbation which allows to reduce its order.

Borovikov I.A. Factorization in one class of optimal processes //Metody matematicheskogo modelirovania i obrabiotki informatsii (Methods of mathematical modeling and information processing) Moscow, MIPT, 1987, p.121-126 (in Russian)

New method of order reduction in classical Lagrange problem was found. New types of first integrals of Hamiltonian systems allow to reduce order of Hamiltonian systems in a new way. New categories of Hamiltonian and Lagrangian systems were build. Criterion of decomposition in this categories was obtained.

Cherniaev A.P.,Borovikov I.A.,Prusakov I.B. Calculation of main characteristics of ideal liquid flow with axial symmetry using von Mises method, comparison with experimental data.//Sovremennye problemy gidrodimaniki, aerofisiki i prickladnoy mekhaniki (Modern problems of hydrodynamics, aerophysics and applied mechanics), Moscow, MIPT, 1986, p. 57-62 (in Russian)

New method of transition from 2D model to 3D model of flow with axial symmetry was introduced. Computer modeling showed good correspondence to experimental data (5 percents precision).