Increasing the efficiency of combinatorial logical data analysis in recognition and classification problems

Problems of increasing the efficiency of combinatorial logical data analysis in recognition problems are examined. A technique for correct conversion of initial information for reduction of its dimensionality is proposed. Results of testing this technique for problems of real medical prognoses are given. Djukova Elena V. Born 1945. Graduated from Moscow State University in 1967. Candidate’s degree in Physics and Mathematics in 1979. Doctoral degree in Physics and Mathematics in 1997. Dorodnicyn Computing Center, Russian Academy of Sciences, leading researcher. Moscow State University, lecturer. Moscow Pedagogical University, lecturer. Scientific interests: discrete mathematics and mathematical method of pattern recognition. Author of 70 papers. Peskov Nikolai V. Born 1978. Graduated from Moscow State University in 2000. Candidate’s degree in 2004. Dorodnicyn Computing Center, Russian Academy of Sciences, junior researcher. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of ten papers. Inyakin Andrey S. Born 1978. Graduated from Moscow State University in 2000. Dorodnicyn Computing Center, Russian Academy of Sciences, junior researcher. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of ten papers. Sakharov Aleksei A. Born 1980. Graduated from Moscow State University in 2003. Moscow Pedagogical University, graduate student. Scientific interests: discrete mathematics and mathematical method of pattern recognition. Author of three papers.     

A classification algorithm based on the complete decision tree

Application of decision trees in problems of classification by precedents is considered. A new model of classifier (which is called the complete decision tree) is proposed and compared with other recognition algorithms based on constructing decision trees. Elena V. Djukova born 1945. Graduated from Moscow State University in 1967. Candidate’s degree in Physics and Mathematics in 1979. Doctoral degree in Physics and Mathematics in 1997. Dorodnicyn Computing Center, Russian Academy of Sciences, leading researcher. Moscow State University, lecturer. Moscow Pedagogical University, lecturer. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of 76 papers. Nikolai V. Peskov born 1978. Graduated from Moscow State University in 2000. Candidate’s degree in Physics and Mathematics in 2004. Dorodnicyn Computing Center, Russian Academy of Sciences, junior researcher. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of seventeen papers.     

Constructing irreducible coverings of a Boolean matrix

A polynomial delay algorithm for searching for irreducible coverings of a Boolean matrix is constructed. A similar result is obtained for the problem of constructing maximal conjunctions of a monotone Boolean function specified by its conjunctive normal form. Elena V. Djukova born 1945. Graduated from Moscow State University in 1967. Candidate’s degree in Physics and Mathematics in 1979. Doctoral degree in Physics and Mathematics in 1997. Dorodnicyn Computing Center, Russian Academy of Sciences, leading researcher. Moscow State University, lecturer. Moscow Pedagogical University, lecturer. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of 76 papers. Andrey S. Inyakin born 1978. Graduated from Moscow State University in 2000. Candidate’s degree in Physics and Mathematics in 2000. Dorodnicyn Computing Center, Russian Academy of Sciences, junior researcher. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of sixteen papers.     

Decision methods for some discrete extreme problems in recognition theory

By optimizing different models of recognition algorithms, a number of discrete extreme problems appear. The search for the maximum solvable subsystem of the system of linear inequalities is one of these tasks. The solution algorithm for this problem is described. This algorithm is effective for linear systems of small ranks. Also, an approximate method that is effective for systems of large dimensionality is proposed. The text was submitted by the author in English. Natalja N. Katerinochkina. Born 1945. Graduated from the Faculty of Mechanics and Mathematics, Moscow State University, in 1967. Received candidates degree in Physics and Mathematics in 1978. The senior scientific worker at the Dorodnicyn Computing Centre, Russian Academy of Science. Scientific interests: discrete mathematics, mathematical cybernetics, pattern recognition, discrete optimization. Author of 35 publications.     

Identification of stable description elements using an active sensor

A two-phase method for the pattern-driven recognition of objects in images is presented, implemented, and tested numerically. The method is based on the use of an active sensor. Possibilities for development are envisaged. This approach was shown to have advantages in solving the object-background separation problem and a high recognition rate was achieved with slow learning. Dmitrii I. Mednikov. Born in 1987. Fifth-year student at the Faculty of Mathematics and Mechanics of Moscow State University. Scientific interests include image recognition and image processing. Author of one paper. Alexei Milovidov. Born in 1986. Graduated from the Faculty of Mathematics and Mechanics of Moscow State University in 2008. Scientific interests include image recognition. Author of 3 papers. Semen Yu. Sergunin. Born in 1980. Graduated from the Faculty of Mathematics and Mechanics of Moscow State University in 2002. Postgraduate student at the same faculty. Scientific interests include image recognition. Author of five papers. Mikhail I. Kumskov. Born in 1956. Graduated from the Faculty of Computational Mathematics and Cybernetics of Moscow State University in 1978. Received his candidate’s degree in Physics and Mathematics in 1981 and doctoral degree in 1997. Professor at the Department of Computational Mathematics of the Faculty of Mathematics and Mechanics of Moscow State University. Scientific interests include the prediction of properties of chemical compounds, optimization of structural objects representation for classification problems, and image processing. Author of more than 50 papers.     

An algorithm for median filtering on the basis of merging of ordered columns

This paper presents algorithms for optimization of the median filtering of images. A median filtering algorithm on the basis of merging ordered columns of an image in the 3 × 3 window of a filter is developed, which allows us to perform the filtering on a personal computer in real time without use of additional hardware. This algorithm outperforms other median filtering algorithms in execution speed on a personal computer. Zalesky Boris Andreevich. Born 1953. Graduated from the Lomonosov Moscow University in 1979. Received the candidate’s degree in 1982 and doctoral degree in Physics and Mathematics in 1990. Leading researcher at the United Institute of Informatics Problems of the National Academy of Sciences of Belarus. Scientific interests: image processing, pattern recognition. Author of 81 papers. In 1987 awarded Leninskii Komsomol prize in the area of mathematics. Kravchonok Aleksandr Ivanovich. Born 1982. Graduated from the Belarussian State University in 2004. Junior researcher at the United Institute of Informatics Problems of the National Academy of Sciences of Belarus. Scientific interests: image processing, pattern recognition. Author of two papers. Lukashevich Pavel Vladimirovich. Born 1982. Graduated from the Moscow Institute of Physics and Technology in 2005. Junior researcher at the United Institute of Informatics Problems of the National Academy of Sciences of Belarus. Scientific interests: image processing, pattern recognition. Author of one paper.     

Identification of inorganic salts and determination of their concentrations in aqueous solutions based on the valence Raman band of water using artificial neural networks

The characteristic features of the valence Raman band of water in the solutions of electrolytes are revealed. These features allow the noncontact recognition of the type of salt and the determination of its concentration in aqueous solutions using artificial neural networks. Viktor V. Fadeev. Born 1935. Graduated from the Physics Faculty of Moscow State University in 1959. Received candidate’s degree in 1967 and doctoral degree in 1983. Professor of the Physics Faculty, Moscow State University. Scientific interests: optics, laser physics, spectroscopy, and inverse problems. Author of more than 300 papers and a discovery diploma. Laureate of the USSR State Prize (1983). Tat’yana A. Dolenko. Born 1961. Graduated from the Physics Faculty of Moscow State University in 1983. Received candidate’s degree in 1987. Senior Researcher of the Physics Faculty, Moscow State University. Scientific interests: laser spectroscopy, Raman spectroscopy of aqueous media, inverse problems, and artificial neural networks. Author of 57 papers and an invention certificate. Laureate of the Lenin Komsomol Prize (1985). Sergei A. Burikov. Born 1978. Graduated from the Physics Faculty of Moscow State University in 2002. Junior Researcher of the Physics Faculty, Moscow State University. Scientific interests: optics, Raman spectroscopy of aqueous media, inverse problems, and artificial neural networks. Author of 14 papers. Aleksandr V. Sugonyaev. Born 1982. Graduated from the Physics Faculty of Moscow State University in 2005. Scientific interests: Raman spectroscopy of aqueous media, inverse problems, and artificial neural networks. Author of 5 papers.     

Effectiveness of consideration of deformations in problems of fingerprint identification

In the paper, we consider some refined methods for fingerprint recognition taking into account a distorting factor, namely, elastic deformations arising when a finger contacts with the scanner surface. We show that the consideration of elastic deformations significantly improves the quality of fingerprint recognition. Ushmaev Oleg Stanislavovich. Born 1981. Graduated from the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University in 2002. Received candidate’s degree in 2004. Scientific interests: image processing, pattern recognition, biometrics. Author of 14 publications. Novikov Sergei Olegovich, Senior Researcher at the Institute of Information Problems RAS. Born in 1963. Graduated from the Moscow Institute of Physics and Technology in 1986. In 1990 finished the postgraduate study at the Institute of Information Problems, Russian Academy of Sciences. Candidate of Technical Sciences. Scientific interests: pattern recognition, image processing, mathematical modeling in biology. Author of two patents and more than 20 publications. Member of the International Scientific Societies SPI, IEEE Computer Society, IAPR.     

Preprocessing of alphanumeric images to be recognized by autonomous computing systems

Methods and algorithms for digital image processing that increase the probability of correct recognition of alphanumeric data are considered. The computational costs of the control block of an autonomous image recognition system based on TMS320C5416 signal processor are analyzed. Natalia S. Novozhilova. Born 1955. Graduated from Moscow Institute of Electronic Engineering in 1978. Received her candidate’s degree (Mathematics and Physics) in 1984. At present, she is a senior researcher at Lukin Scientific Research Institute of Physical Problems. Scientific interests: pattern recognition and mathematical methods for processing the results of a physical experiment. Author of 22 publications. Aleksandr G. Safonov. Born 1952. Graduated from Moscow Power Engineering Institute in 1975. Received his candidate’s degree (Technical Sciences) in 1982. At present, he is a head of department at Lukin Scientific Research Institute of Physical Problems. Scientific interests: automated data processing complexes, pattern recognition, and microelectronics. Author of more than 50 publications.     

Using adaptive and intelligent methods in constructing of a model of seismic noise

In the paper, an attempt is made to develop an approach to analysis of seismic signals with the use of Data Mining techniques. A system for registering of signals of seismic noise is described. Algorithms for signal segmentation are proposed. Geppener Vladimir Vladimirovich. Born 1940. Graduated from the Leningrad Electrotechnical Institute in 1964. Received candidate’s degree (in Engineering) in 1969 and Doctoral degree (in Engineering) in 2000. Professor at the Chair of Mathematical Software and Computer Applications of the St. Petersburg Electrotechnical University. Scientific interests: systems of signal processing, methods of artificial intelligence, and pattern recognition theory. Author and coauthor of more than 150 scientific publications. Member of the Russian Association for Pattern Recognition and Image Analysis. Tristanov Aleksandr Borisovich. Born 1981. Graduated with honors from the Kamchatka State Technical University in 2003. Post-graduate student at the Kamchatka State Pedagogical University. Works as an Assistant Professor at the Kamchatka State Pedagogical University. Scientific interests: systems of digital signal processing, methods of artificial intelligence, and frequency-time analysis of signals. Author of 10 scientific publications. Firstov Pavel Pavlovich. Born 1941. Graduated with honors from Polzunov Altai State Polytechnical Institute in 1963. Candidate of Sciences in Physics and Mathematics. Since 1965 works at the Institute of Volcanology and Seismology of the Far East Division of the Russian Academy of Sciences; Head of a laboratory. Scientific interest: volcanic acoustics, nature of earthquake predecessors. Author and coauthor of more than 100 papers and one monograph. Rulenko Oleg Petrovich. Born 1946. Graduated with honors from the Department of Physics and Mathematics of the Kamchatka State Pedagogical Institute in 1968. Received candidate’s degree (in Physics and Mathematics) in 1994. Senior Researcher at the Institute of Volcanology and Seismology of the Far East Division of the Russian Academy of Sciences. Scientific interests: atmospheric electricity, interaction of lithosphere and atmosphere, physics of earthquake predecessors. Author of 29 scientific publications.     

Application of probability filter to signal processing problems

A method of signal filtering based on the maximum likelihood principle is presented. This method provides elimination of random distortions caused by noises, conserving local specific features of the signal. The concept of probability filtering ensures processing of both discrete and piecewise-continuous signals. Dmitrii P. Vetrov. Born 1981. Post-graduate student at Moscow State University, to graduate in 2006. Works at the Dorodnicyn Computing Center, Russian Academy of Sciences. Scientific interests: pattern recognition, machine learning, mathematical statistics, expert systems. Nine publications. Dmitrii A. Kropotov. Born 1981. Post-graduate student at Moscow State University, to graduate in 2006. Works at the Dorodnicyn Computing Center, Russian Academy of Sciences. Scientific interests: pattern recognition, machine learning, mathematical statistics, expert systems. Eight publications.     

Optimal signal interpolation using the values of signal and its derivative

The effect of the bias in a sequence of signal samples and sequence of signal derivative samples on the signal reconstruction accuracy is considered for a bandwidth-limited signal. Vitalii M. Efimov. Born 1933. Graduated from the Moscow Institute of Aviation. Received candidate’s degree in 1964. Leading researcher at the Institute of Automatics and Electrometry, Siberian Division, Russian Academy of Sciences. Scientific interests: signal sampling and quantization and processing and squeezing of digital data. Author of 85 papers. Aleksandr L. Reznik. Born 1948. Graduated from Novosibirsk State University in 1969. Received candidate’s degree in 1981. Head of the laboratory of the Institute of Automatics and Electrometry, Siberian Division, Russian Academy of Sciences. Scientific interests: analytical and numerical methods for solving complex probability problems with computer calculations. Author of 64 papers. Andrei V. Torgov. Born 1959. Graduated from Novosibirsk State University in 1983. Leading software engineer at the Institute of Automatics and Electrometry, Siberian Division, Russian Academy of Sciences. Scientific interests: image processing and digital filtering. Author of 17 papers.     

Methods of recognition based on the function of rival similarity

A unified approach to the development of pattern recognition methods is proposed. The approach is based on the employment of the function of rival similarity (FRiS-function), which adequately represents human methods of evaluation of similarity and difference. Methods of recognition based on this approach are briefly described. Examples of solution of actual and benchmark problems using FRiS-function are given. Nikolai Grigor’evich Zagoruiko finished a secondary school in Novosibirsk oblast. Graduated from the Electroengineering Department of the Leningrad Institute of Motion-picture Engineers in 1953. Since 1960 has been working at the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. Received candidate’s degree in 1962 and doctoral degree in Pattern Recognition in 1969. Since 1973 to 1982 had been working as a vice-rector of the Novosibirsk State University. In 1988–1990 had been heading a project in the International Laboratory of Artificial Intelligence in Bratislava (Slovakia). Scientific interests: pattern recognition and prediction. Author of 219 publications, including 13 monographs. Vladimir Vladimirovich Dyubanov. Born 1981. Graduated from the Krasnoyarsk State University in 2002. Currently is a postgraduate at the Novosibirsk State University. Scientific interests: data mining and pattern recognition and prognosis. Author of eight papers. Ol’ga Andreevna Kutnenko. Born 1958. Graduated from the Novosibirsk State University in 1980. Received candidate’s degree in 2000. Scientific interests: data analysis, determination of empirical principles, pattern recognition. Author of 13 papers. Irina Artemovna Borisova. Born 1978. Graduated from the Novosibirsk State University in 2002. Currently is a chief programmer at the Institute of Mathematics, Siberian Division, Russian Academy of Sciences. Scientific interests: pattern recognition. Author of nine papers.     

Computational model for recognition of scene objects with an active sensor

In the paper, a computational model for recognition of objects in a scene image is presented. The model is based on the use of an active sensor. The structure of the object model (OM) is described. This structure is a component that stores different representations of the object and puts at user’s disposal an interface whose operations are used in the scene recognition process. Semen Yu. Sergunin. Born 1980. Graduated from the Faculty of Mathematics and Mechanics of Moscow State University in 2002. Finished postgraduate course of the Department of Computational Mathematics of the same faculty. Scientific interests include image recognition. Author of about 20 papers. Mikhail I. Kumskov. Graduated from the Faculty of Computational Mathematics and Cybernetics of Moscow State University in 1978. Received his candidate’s degree (in Physics and Mathematics) in 1981 and doctoral degree in 1997. In 1981–1997 taught at the Faculty of Computational Mathematics and Cybernetics in the special seminar on Computer Graphics and Image Processing of the Department of Automation of Systems of Computational Complexes. Since 1992 works at the laboratory of Mathematical Chemistry of the Zelinsky Institute of Organic Chemistry of the Russian Academy of Sciences. Since 1997 teaches at the Department of Computational Mathematics of the Faculty of Mathematics and Mechanics of Moscow State University. Author of more than 50 papers. Scientific interests include prediction of properties of chemical compounds, optimization of structural object representation for classification problems, and image understanding.     

Fast algorithms for a multidimensional hypercomplex discrete Fourier transform with radix-3 decomposition

Combined algorithms for the multidimensional hypercomplex discrete Fourier transform (HDFT) of a real signal with data representation in the Hamilton-Eisenstein generalized codes are synthesized. The complexity of arithmetic operations in a commutative-associative hypercomplex algebra and its representation in generalized codes are obtained. It is shown that there exist only two essentially different commutative-associative hypercomplex algebras: the direct sums of real or complex algebras. The computational complexity of the algorithm synthesized is estimated. Marat Vyacheslavovich Aliev. Born 1978. Graduated from Adygeya State University in 2000. Received candidate’s degree in physics and mathematics in 2004. Presently he is a senior lecturer at the Department of Applied Mathematics and Information Technologies, Adygeya State University. Scientific interests: image processing, fractals, fast algorithms of discrete transforms, and finite-dimensional algebras. Author of 14 publications, including 7 papers. Member of the Russian Association of Pattern Recognition and Image Analysis. Marina Aleksandrovna Chicheva. Born 1964. Graduated from the Kuibyshev Aviation Institute (now Samara State Aerospace University) in 1987. Received candidate’s degree in Engineering in 1998. Presently, she is a senior researcher at the Image Processing Systems Institute, Russian Academy of Sciences. Scientific interests: image processing, compression, and fast algorithms of discrete transforms. Author of more than 50 publications, including 18 papers and 1 monograph. Member of the Russian Association of Pattern Recognition and Image Analysis.     

The use of pattern recognition methods in tasks of biomedical diagnostics and forecasting

Questions of use of pattern recognition methods in medical tasks are discussed. The Recognition program system is presented, which contains a variety of pattern recognition and cluster analysis methods. Some methods based on voting by a system of regularities are discussed in more detail. An example of solved tasks of hysteromyoma relapse forecasting is given. The text was submitted by the authors in English. Yuri Ivanovich Zhuravlev. Born in Voronezh on January 14, 1935. In 1957, graduated from Moscow State University. Doctor of physics and mathematics since 1965, professor since 1967, and an academician of the RAS since 1992. Deputy director of the Dorodnicyn Computing Center of the RAS, chair of the Mathematics Department of the RAS, head of the Chair of Moscow State University, and editor in chief of Pattern Recognition and Image Analysis. Foreign member of the Spanish Royal Academy of Sciences, the National Academy of Sciences of Ukraine, and the European Academy of Sciences. Winner of the Lenin and Lomonosov prizes. Main fields of scientific interest: mathematical logic; control systems theory; the mathematical theory of pattern recognition, image analysis, and forecasting; operation research; and artificial intelligence. Developed such new lines of research as the theory of local optimization algorithms, algorithms of estimate calculation, and the algebraic theory of recognition algorithms. Oleg Valentinovich Senko. Born in Salavat, Bashkortostan, in 1957. In 1981, graduated from the Moscow Institute of Physical Technology; in 1985–1989, took graduate courses, receiving a PhD in 1990. Senior researcher, Dorodnicyn Computing Center, RAS. Doctor of physics and mathematics since 2007. Scientific interests: data mining, mathematical models of pattern recognition, classification and forecasting, and practical applications in medicine and other fields. Vladimir Vasilievich Ryazanov. Graduated from the Moscow Institute of Physical Technology in 1973 and completed graduate courses at the Computing Center of the USSR Academy of Sciences in 1976. Received a PhD in 1977 in computer science and the degree of professor in 1994 (“Applications of Mathematical Methods, Mathematical Modeling, and Computers in Scientific Research”). At the Dorodnicyn Computing Center of the RAS since 1976. Head of the Situations Recognition Sector in the Department of Recognition Problems and Combinatorial Analysis. Author of approximately 150 papers. Scientific interests: data mining; mathematical models of pattern recognition; classification and forecasting; optimization of recognition and classification models; learning; synthesis of optimal collective solutions in the problem of classification; creation of intelligent program systems for data analysis and recognition; and practical applications in technology, medicine, and industry. Anna Victorovna Kuznetsova. Born in Samara (Kuibyshev) in 1961. In 1986 graduated from the Second Moscow Medical Institute. In 1991–1994, took graduate courses, receiving a PhD in biology in 1995. Senior researcher, Emanuel Institute of Biochemical Physics. Scientific interests: pattern recognition, intellectual methods of data analysis, and development of diagnostic and forecasting algorithms in medicine and biological and medical applications in medicine and other fields. Mikhail Afanasievich Botwin. Born in the village of Rashevka of Poltava oblast in Ukraine in 1941. Doctor of medical sciences and Professor of the Sechenov Moscow Medical Academy. Scientific interests: hysteromyoma: pathogenesis, diagnostics, influence on pregnancy, aperiodicities of birth activity, methods of treatment.     

Compensation for local defects in an image created using a triple-color photo technique

Problems connected with the creation of elements of technology for automated detection and the correction of image local defects obtained in the triple-color photo technique are considered. Automated procedures of detection and correction are developed. Procedures are implemented in software-tool and used in works on the reconstruction of S. M. Prokudin-Gorskii’s collection of photos taken in the early 20th century. Viktor Vasil’evich Minakhin. Born in 1948. Candidate of Sciences in physics and mathematics. Graduated from Faculty of Mechanics and Mathematics of Moscow State University in 1971 with a specialty in common control problems. Deputy Director at Restavrator-M Research and Restoration Center. Scientific interests include representations of noncommutatively algebraic structure, processing and analysis of images, image recognition, and architecture of databases. Author of 28 papers. Dmitrii Mikhailovich Murashov. Candidate of Sciences in engineering, associate professor. Born in 1958. Graduated from Moscow Aviation Institute in 1981 with a specialty in automatic control systems. He works at Dorodnitsyn Computing Center of the Russian Academy of Sciences, Moscow. Scientific interests include automatic control, processing and analysis of the images, and image recognition. Author of 50 papers. Yurii Pavlovich Davidov. Born in 1964. Graduated from Moscow Aviation Institute in 1987 with a specialty in radio engineering. 1989–1999 worked for the Scientific Council on the Complex Problem of Cybernetics at the Russian Academy of Sciences. Since 1996, he has worked at Restavrator-M Ltd. Scientific interests include the development of Image databases; development of software for 3D reconstruction and processing data of geodesic measurements; and software for color registration, color correction, and the removal of image defects. Dmitrii Abramovich Dimentman. Born in 1962. Graduated from Moscow State Historical-Archive Institute in 1990 with a specialty in historical archiving. Since 1979, he has worked at the State Historical Museum, Moscow, currently as the curator of author negatives in the arts department and leading researcher. Scientific interests include photo history and the study of photo document collections. Author of 20 papers.     

Software environment for simulating algorithms for image analysis and processing

We consider the purpose, functionality, configuration, and structure of a software environment designed for simulation and investigation of methods, algorithms, and information technology for digital images analysis and processing. Mikhail V. Gashnikov. Born 1975. Graduated from the Samara State Airspace University (SSAU) in 1998. Received candidate’s degree in Technology in 2004. He is now an assistant professor at the chair of earth information of the SSAU. Scientific interests: image processing, compression, statistical coding. Author of more than 30 publications, including 12 papers and one monograph (in coauthorship). Member of the Russian Association for Pattern Recognition and Image Analysis. Evgenii V. Myasnikov. Born 1981. Graduated from the Samara State Airspace University in 2004. He is now a post-graduate student at the Chair of Earth Information of the Samara State Airspace University. Scientific interests: development of software systems, image processing, image retrieval in databases. Author of 6 publications, including one paper. Member of the Russian Association for Pattern Recognition and Image Analysis. Andrei V. Chernov. Born 1975. Graduated from the Samara State Airspace University (SSAU) in 1998. Received candidate’s degree in Technology in 2004. He is now an assistant professor at the Chair of Earth Information of the SSAU and a research fellow at the Institute of Image Processing Systems, Russian Academy of Sciences. Scientific interests: image processing, pattern recognition, geoinformation systems. Author of more than 50 publications, including 11 papers and one monograph (in coauthorship). Member of the Russian Association for Pattern Recognition and Image Analysis. Nikolai I. Glumov. Born 1962. Graduated from the Kuibyshev Airspace Institute (at present, the Samara State Airspace University) in 1985. Received candidate’s degree in Technology in 1994. He is now a senior researcher at the Institute of Image Processing Systems, Russian Academy of Sciences. Scientific interests: image processing and pattern recognition, compression of images, simulation of systems of digital image formation. Author of more than 50 publications, including 21 papers and one monographs (in coauthorsip). Member of the Russian Association for Pattern Recognition and Image Analysis. Vladislav V. Sergeev. Born 1951. Graduated from the Kuibyshev Airspace Institute (at present, the Samara State Airspace University) in 1974. Received doctoral degree in Technology in 1993. Head of the Laboratory of Mathematical Methods for Image Processing at the Institute of Image Processing Systems, Russian Academy of Sciences. Scientific interests: digital signal processing, image analysis, pattern recognition, earth information. Author of more than 150 publications, including approximately 40 papers and two monographs (in coauthorship). President of the Povolzh’e Branch of the Russian Association for Pattern Recognition and Image Analysis. Corresponding member of the Russian Ecological Academy and of the Russian Academy of Engineering Sciences. Member of the International Society for Optical Engineering. A laureate of the Samara Provincial Government prize in science and engineering. Marina A. Chicheva. Born 1964. Graduated from the Kuibyshev Airspace Institute (at present, the Samara State Airspace University) in 1987. Received candidate’s degree in Technology in 1998. She is now a senior researcher at the Institute of Image Processing Systems, Russian Academy of Sciences. Scientific interests: image recognition, compression, fast algorithms for discrete transformations. Author of more than 40 publications, including 15 papers and one monograph (in coauthorship). Member of the Russian Association for Pattern Recognition and Image Analysis.     

Bounds for the number of modes of the simplest Gaussian mixture

Several theorems on sufficient unimodality conditions are formulated for a sum of k normal distributions with the same variance and with different mean values μ _i , i = 1, ..., k, 2 ≤ k < ∞, taken with their a priori probabilities π_i. On the basis of these theorems, estimates for the lower and upper bounds for the mode numbers m are obtained for k ≥ 3 in the case when the mixture contains k* components, 2 ≤ k* < k, satisfying the unimodality conditions. Aprausheva Nina Nikolaevna (b. 1940). Graduated from the Moscow State University (Department of Mechanics and Mathematics) in 1966. In 1982, defended the Cand. Sci. thesis “On the Application of Mixtures of Normal Distributions in Pattern Recognition.” Senior scientist at Dorodnicyn Computing Center, Russian Academy of Sciences. Scientific interests: mathematical statistics, computational mathematics, mathematical methods in pattern recognition, and decision theory (about 70 publications). Member of Association of Pattern Recognition. Mollaverdi Naser (b. 1967). Graduated from the Isfahan University of Technology (Iran) in 1990. In 1995, graduated from the Educational University (Teheran, Iran). Third-year scholar at Moscow State University (Department of Computational Mathematics and Cybernetics). Scientific interests: computational mathematics, pattern recognition, programming, and statistics (12 publications). Sorokin Stanislav Viktorovich (b. 1947). Graduated from Moscow State University (Department of Computational Mathematics and Cybernetics) in 1971. Programmer at Dorodnicyn Computing Center, Russian Academy of Sciences. Scientific interests: computational mathematics, system programming, and pattern recognition (15 publications).