information theory; quantum informatics; computer science; time series; financial mathematics; fractals; wavelet analysis; approximation theory; computational geometry.
Subject:
Research interests are moslty connected with analysis, approximation and compression of signals of various nature with the aid of fractal, wavelet and related methods. Have developed a method of approximation of functions of one real variable (as well as time series) by fractal functions (sequences), based on localization of the strongest Holder singularities. This technology was also applied to fractal modeling of financial time series. Have developed several compression methods for information arrays generated in computational modeling and computer graphics: approximation of the computed fields with the aid of Chebyshev, wavelet and multiwavelet expansions, compression of digital images with the aid of local palletizing and adaptive partitioning of image blocks into color clusters. Have developed a method for fast information search on nonregular planar and spatial grids. Have developed (in co- authorship) several formats for 3D models and scenes representation, to be used in the new version of multimedia format MPEG4, which is currently under development.
Biography
Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1976 (department of differential geometry). Author of more than 20 scientific publications. Since 1983 I work at the Keldysh Institute of Applied Mathematics, Russian Academy of Sciences. Since 1996 I am Senior Scientist. Was a principal investigator in several research projects on computer graphics, data processing and compression, conducted by Intel, Sandia Laboratories, Samsung Advanced Institute of Technolgy (currently in progress) and some others. Was an invited researcher to the University of Westminster (London), School of Mathematics, Tel-Aviv University. Took part in many international conferences.
Levkovich-Maslyuk L. I. Wavelet-based determination of generating matrices for fractal interpolation functions // Regular and Chaotic Dynamics, 1998, 3(2), 20–29.
Levkovich-Maslyuk L. I. Determination of the scaling parameters of affine fractal interpolation functions with the aid of wavelet analysis // SPIE Proceedings, v. 2825, paper 2825-91, 1996.
Levkovich-Maslyuk L. I. Wavelet analysis and its applications to time series // NATO Advanced Studies Institute (ASI), "Nonlinear Dynamics in Life and Social Sciences" (Moscow, Russia), 2001.
Levkovich-Maslyuk L. I., Zhirkov A., Kalyuzhny P. Texture compression with adaptive block partitions // Proceedings of 8th ACM International Conference on Multimedia "Multimedia 2000", Los Angeles, USA.
A. L. Afendikov, L. I. Levkovich-Maslyuk, A. E. Lutsky, A. V. Plenkin, “Localization of singularities in gas-dynamic fields with the aid of wavelet analyses”, Matem. Mod., 20:7 (2008), 65–84; Math. Models Comput. Simul., 1:4 (2009), 453–469
L. I. Levkovich-Maslyuk, “Detection of singularities of the gas dynamics fields with the aid of complex Gabor filters”, Keldysh Institute preprints, 2006, 087, 12 pp.
3.
R. F. Khabibulline, L. I. Levkovich-Maslyuk, “Localization of transients in sound signals with the aid of local Hölder exponent estimate”, Keldysh Institute preprints, 2006, 062, 16 pp.
2005
4.
A. L. Afendikov, V. V. Gorbunova, L. I. Levkovich-Maslyuk, A. V. Plenkin, “Localization of singularities of gas dynamics fields with the aid of complex and real wavelets”, Keldysh Institute preprints, 2005, 098, 32 pp.
A. L. Afendikov, L. I. Levkovich-Maslyuk, “Localization of singularities of gas dynamics fields with the aid of complex orthogonal wavelet transform”, Keldysh Institute preprints, 2003, 101, 15 pp.
1998
6.
L. I. Levkovich-Maslyuk, “Wavelet-based determination of generating matrices for fractal interpolation functions”, Regul. Chaotic Dyn., 3:2 (1998), 20–29
L. I. Levkovich-Maslyuk, “Determination of the Scaling Parameters of Affine Fractal Interpolation Functions with the Aid of Wavelet Analysis”, Keldysh Institute preprints, 1996, 001
1995
8.
L. I. Levkovich-Maslyuk, N. A. Naumov, E. E. Samoylova, “System for Construction of the Planar Images with the Aid of Iterated Function Systems”, Keldysh Institute preprints, 1995, 009
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