Logic Separation: Discrete Modelling of Pattern Recognition

Abstract

Herein, a historical analytical survey of work of “Discrete Modelling of Pattern Recognition” (DM-Lab) research group in Armenia is presented. The group is since 1973, supervised by worldwide recognized scientist Yurii Ivanovich Zhuravlev and lead by his former student Levon Aslanyan. The general start of attention to computational mathematics and computational systems in Armenia is concerned with the times of cybernetics as a research direction, and the names of great scientists and policy makers, such as Andranik Iosifyan and Sergei Mergelyan. In early 1950’s a large number of HighTech and defense related organizations were established in area, and their theoretical, scientific cluster was formed around the Yerevan Research Institute of Mathematical Machines, and Computer Center of Academy of Sciences and Yerevan State University. This was the time for intensive stuff and student exchanges inside the larger country USSR. Rimma Podlovchenko, Rafik Tonoyan, Igor’ Zaslavski, Yuri Shoukourian started teaching at Yerevan State University in 70’s, a number of students were delegated to the recognized cybernetical centers, in Moscow, Kiev, Novosibirsk. And one of the results of these developments was appearance of DM-Lab in Armenia, composed by alumnus of Novosibirsk and Moscow State Universities, led by Levon Aslanyan, and supervised globally by RF Academician Yuri Ivanovich Zhuravlev. Further research and education activities lead to defenses of candidate and doctoral dissertations, in Armenia, and at the council of Computer Center of Academy of Sciences of Russian Federation. The initial stuff of DM-Lab group included Gevorg Tonoyan, Levon Asatryan, Vilik Karakhanyan. Local members of the group were Hasmik Sahakyan, Vladimir Sahakyan, Irina Arsenyan, Levon Kazaryan and large number of young PhD students. Research directions at the DM-Lab were and are related to the pattern recognition theory – to mathematical models of forming and analyzing learning sets, studying their properties such as the class compactness hypothesis, in terms of isoperimetry; to forming the logic of interrelations of classes, in terms of logic separation; setting up new approaches in data mining area, etc. All these studies involve intensive research over the years, addressing topics related to the geometry of n-dimensional unite cube and lattices in general, Boolean function minimization, discrete optimization problems, and algorithmic studies coming from data science and artificial intelligence. International relations and activities of the group includes: long term representation of Armenia in the ISO technical groups, representation of Armenia in ICT research programmes of European Council, membership at the ITHEA virtual research institute with its conferences and publishing house. 10’s of research projects were implemented during these years. Projects were funded by UNDP, NATO Research, INTAS, EC Esprit, IST and Horizone, RFBR, and other international and local sources. 16 candidate and 2 doctoral theses were defended by the group members.