I am still surprised that fundamental mathematical objects, functions and properties in either of their usual appearances, analytic or determined  by some specific graphs (i.e. specific sets of the form {(a,f(a))| with a passing through a specific set of values}/ properties represented by tables-matrices in data bases) could be useful in modelling of the phenomena of the real world. Analytic versus experimental: dealing with analytic forms of these objects, with accented syntax form, or data specified form with semantic/experimental - sensor originating, perhaps should not be as distant as contemporary academic practice, divided into nicely organised fields shows. In GIS, we contributed serious quantity of work to the processing of both syntax and semantics and enjoyed in both a lot. 


When I was a 2. year student on our Math Department one of the exam problems in the course of Analysis used to be expansion of functions in Fourier series and for quite nicely tuned input functions students needed roughly one hour to calculate first four or five Fourier expansion  coefficients, where up to half members used to be zero, sometimes guessing the form of the n-th member when it was easy. That procedure was purely analytic. Now days we have numeric algorithm – fft and for nice resolution spectra, e.g. of 32k points in perceptual or sub perceptual time, i.e. within a 1/20th of a second calculation of the next, on 64 input channels, we have some 40M coefficients calculated in a second multiplied 1K, which gives some 40 billion times faster calculation of the Fourier expansions than in the example of the beginning of this paragraph. Simple function Fourier development might result in simple Fourier series and analytic method might be fine when we do not need real time. However, when dealing with just acoustic phenomena, present in neuroacoustic experimentation or in submarine echo sound analysis, we are approaching the need to resolve –explode the experimental functions with no perceived analytic form, within perceptual real time with parameters as in the above calculation. Possibility to do that in real time might mean possibility to detect some signal component of crucial importance. Recent software radio based applications in digital signal processing improve the real time demands by some orders of magnitude.

That gives example of Fourier - Hegel “transition of quantity into quality” that is really exciting.


Our Group for Intelligent Systems originates in joined inspirations with my colleague and friend Žarko Mijajlović, with whoom I had a number of pritty mental interactions, starting with application of quantifier ellimination for fields in polynomial optimisations in 1976, then developping a system supporting a cumulative  construction of Turing machines, end of 70’s, with the desire to materialize beautiful achievements of Godel, Tarski, Turing and other greats of formal thought and logic, involving syntax and semantic problems and implementations, leading to a number of provers, proof checkers, analysis of syntax chains of more complex organization. The work that we initialized alone, soon involved our graduate and undergraduate students in early 80's, E. Ljubisavljević, M. Lazić, M. Živković, T. Petrović, Z. Ognjanović, M. Živković2 and others, and that became a kind of nice and longer lasting fusion of energy that lead to the number of materialzed solutions that practicaly showed what levels of a problem were feasable within some reasonable portion of remaining future and what parts of algorithms would evolve too slow or explode in complexity so fast that, such as  they are, they are too far from any useful application. While teaching Mathematical logic in CS and Computer applications, a chance opened to atract greater number and groups of students into the syntax processing projects: Quantifier elimination in algebraicaly and real closed fields, with M. Ristić and G. Aleksić, Monadic calculus with equality that formalized Aristotelian logic, initiated with the big group of students lead by S. Milutinović and B. Blečić, provers in Intuitionistic logic, with G. Lazić and M. Radić, provers in Modal logics, provers based on interpretations, with M. Petrović and N. Lazarević, prover in Geometry, S. Kordić and P.Janičić and a variety of syntax pattern recognition algorithms involving, besides a number of students from our School of Mathematics, students from Biology Department S. Stamenkovic, M. Pjanić, T. Tošić, S. Drakulic, M. Etinski and many others. Then with T. Petrović, S. Lalević and I. Katanić we completed the first works on syntax parallelisation. Our more recent works included: correctness of formal specs, I. Mijajlović, eccology for Kinematic Turing Machines, N. Lazarević, V. Nikolin, S. Tomić, D. Predić. D. Brzaković, optimised algorithms for Quantifier elimination in Monadic logic with equality  and an intelligent interface to the relational data bases, involved a group of  almost 30 students where V. Aleksić, M. Lukić, M. Marić, F. Marić, R. Jovanović, M. Miličić, N. Dobrašinović, G. Marković, O. Jovanović, Nemanja Djurić, Vlada Perović did the major work and integrated intelligent “Cracken  prover; based on interpretation of theories and quantifier elliminatioon algorithms, provers and syntax pattern recognition, engaged A. Perović, N. Stefanović, M. Borovčanin, M. Milošević, D. Ilić, M. Filipović, M. Udovičić,  M. Jovanović, D. Doder, M. Marić and F. Marić.


Parallely, we have been involved in the work on  image and signal processing, starting with NMR deconvolutions, end of 70’s through mid 80’s that lead to the integration of NMR tomography, with S. Macura and Z. Zsolt, fast imaging algorithms, spectral analysis and pattern recognition in astronomy, Transputer parallelized multiple fft, T. Petrović,. S. Lalević and I. Katanić, computerized EEG and other biomedical signal analysis and CCD imaging in microscopy, with with S. Kordić, Z. Obradović, G. Popović, S. Malkov, G. Lazić, I. Jovanović. That work continued with V. Todorović, N. Andonovski, D. Perišić, G. Marković, R. Todorović, M. Bulat, V. Ivandski, A. Uzelac, M. Oklobdzija, M. Jovanović, M. Marić, M. Borovčanin, A. Perović and A. Jovanović, jr.  This portion of engagement of our Group is presented in this volume.


All and all, more than 200 students more or less seriously participated in these activities.

Four groups of students received awards from University of Belgrade for the research work of young scientists, works of two teams were awarded by Engineering congress ETRAN for the works in Artificial Intelligence. Great number of our coleagues continued their careers in computer industries, a fraction continued their careers in research-science, many all over the world. Besides software implementations, a number of papers was generated and presentations on conferences.


I owe highest thanks to the above mentioned coleagues and many others who contributed seriously to the developements undertook in GIS over the mentioned longer period of time with joy and enthusiasm and would be happy if my catalising initiatives and efforts were useful in their later destinations.


I owe acknowledgements as well to Dr. Dick Treffers from UCB, who introduced me in ccd imaging of quasars in his first robotic astronomic observatory and Dr. Istvan Vince from Belgrade Astronomic Observatory, that armed me with courage to make our first CCD microscope for dot counting- which is how our applied developments evolved further, here in 93. It was in the labs of Dr. Selma Kanazir, molecular biology, Dr. Mladen Vujošević, genetics, Dr. Rosica Veskov, rat EEG, all from the Institute for Biology Research “Siniša Stanković” in Belgrade, Dr. Vlada Radivojević, human EEG, Institute for mental care, Belgrade, prof. Nina Japundžić-Žigon, Institute for farmacology and toxicology, School of Medicine, Un. of Belgrade, Dr. Milka Ćulić with collaborators, lab for neurobiology, Center for multidisciplinary study, Un. of Belgrade,

prof. Dragan Marinković and prof. Vlada Kekić, School of Biology, Un. of Belgrade, Dr. Angelina Novak, lab for human genetics, Institute for Haematology, Clinic center of Serbia, prof. Milan Oprić, Institute of pathology, School of Medicine, Un. Of Belgrade,  Dimitar Jakimov, MS. of the Institute for Oncology, Sremska kamenica and researchers from the Institute for molecular biology and genetic engineering, Belgrade, where we discussed their problems, defined strategies, developed and implemented solutions. Without them there would be no applications to show on this CD and I am very grateful to all of them. All microscopic preparation images in the included presentations were taken by the author in the above mentioned labs. The same with the biomedical signals, except the signals of  rat arterial pressure, courtesy of  Nina Japundžić-Žigon and rat neurology signals, courtesy of Milka Ćulić. The other signals and images in the libraries are of more broad origins and I am grateful to our partners in the above mentioned institutions for their submission and inclusion here. One little anegdote: our recent partner prof. Stanka Romac and her  collaborators from her Center for application and development of PCR at the School of Biology, Un. of Belgrade opened recently a new issue, the existing algorithms for comparison and similarity definition of genetic sequences work with unpredictable satisfaction, giving often meaningless measures, and maybe more often non perceptible wrong results. We are facing the problem of similarity of complex discrete information bearing structures, i.e. (complex) syntax pattern matching and it will be non easily solvable, maybe on the longer run. More than ten years ago we were introducing mathematical representation of chromosomes and used these to define precisely the similarity of these big packs of discrete genetic material, and topology and algebraic features of these small objects were of the utmost relevance in that work that will have a lot of future, since many syndromes are characterised or accompanied by certain defects on chromosomes. The Mathematics working here is the Mathematics of continuum. However, going deeper into these structures and approaching the level of information atoms, investigating just the same objects smaller portions, it is now the syntax structure of these sequences that dominates the issue of similarity. The Mathematics working here is the Mathematics of information bearing discrete structures, the best viewed so far from Mathematical logic and Formal languages. To me it is amazing that the same phenomena at different levels of magnification have so different good Mathematical clothes. Working on both since a long ago and percepting these areas (of Mathematics) as mostly distant, I am happy that there are objects in the surrounding nature that play with us in such unexpected way that looks like a signature of the superior intelligence.


Portion of these works was supported by 3.5 projects of Ministery of Science and technology of Serbia, in the period from 1994. till 1999. which helped it reach a kind of polishing that made them look professional and useful to the intended application targets - our partners in those projects.