Seminar on Applied Mathematics
Miodrag Mihaljevic, Matematicki institut SANU, Beograd
ON CERTAIN CODING TECHNIQUES FOR CRYPTO APPLICATIONS
Abstract: This talk points out to a number of research problems which are based on involvement of coding techniques in crypto applications. It is shown that techniques based on coding theory can be employed as the key elements for solving certain problems of design and security evaluation of cryptographic primitives. These techniques provides opportunities for effective treatment of pseudo-randomness and randomness which jointly exist in a number of crypto problems. Accordingly, this talk considers employment of homophonic (wire-tap channel) coding and decoding techniques for solving certain LPN problems. We summarize some of our recent achievements as well as open research problems which could be topics of interest for students within areas of cryptology and information security.
Milica Bulajic, Fakultet organizacionih nauka, Beograd
APLICATION OF QUANTYTATIVE METHODS IN RANKING OF BANKS IN SERBIA
Abstract: It is often very difficult to rank entities characterized by more than one indicator. In the case of banking sector, especially in transition countries, it would be important to determine the relationship among the banks, regarding their efficiency and relevant characteristics. The results obtained in two different ranking processes will be presented, discussed and compared here. The first procedure is based on Data Envelopment Analysis (DEA), mathematical programming technique that can be applied to assessing the efficiency of a variety of entities, using variety of data. The second procedure is based on I-distance, a multivariate statistical method for ranking entities. Both methods allow the use of several criteria, and they both give one single index which can be considered as a rank. In the set of DMUs (decision-making units), DEA gives measure of DMU's efficiency by comparing performances of DMU with efficient entity. On the other hand, in I-distance ranking process, rank is determined as the distance from referent DMU, defined at the beginning of the analysis, usually virtual one with average, minimal or maximal values for all the variables. The complementary use of the two methods provides more realistic picture of the tendencies in the banking sector and the combination of the results obtained in two processes provides a useful background for more comprehensive evaluation of the banks efficiency.
Keywords: Data Envelopment Analysis, I-distance, ranking, banks.
Boban Marinkovic, Rudarsko-geoloski fakultet, Beograd
USLOVI EKSTREMUMA U DISKRETNIM PROBLEMIMA OPTIMALNOG UPRAVLJANJA
Sadrzaj: Razmatracemo diskretne probleme optimalnog upravljanja sa ogranicenjima tipa jednakosti i nejednakosti na krajevima i na upravljajucim promenljivim. Bice prikazani neophodni uslovi optimalnosti prvog i drugog reda koji vaze bez a-priori pretpostavki o normalnosti.
Zoran Radojicic, Fakultet organizacionih nauka, Beograd
APPLICATION OF VECTOR CORRELATION COEFFICIENT IN THE EVALUATION OF EDUCATION SYSTEMS
Abstract: Knowledge is essential for human kind, and knowing how successful scholar system in one country is very important. To evaluate a scholar systems start at elementary school and finish at faculty. Through educational process, we have three breaking points: one - finishing elementary school, second - finishing high school, and third - finishing college/faculty. Elementary school is obligation for all children at most all countries in the world. In that meaning the first breaking point is most important for evaluation. As a evaluation results, we can obtain rank of elementary school attained comparison between advancement at last three classes and test for enrollment for a high school (sublimation knowledge from elementary school at mathematics and native language).
In this paper, we used Vector Correlation Coefficient (VCC) as an evaluation measure. The value of VCC was used as a ponder coefficient for ranking school in one scholar systems as aim to achieve objective evaluation.